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Spatiotemporal dynamics in the early stages of the 2009 A/H1N1 influenza pandemic. )] TJ ET BT 26.250 639.438 Td /F1 9.8 Tf [(PLOS Currents Influenza. 2009 Aug 31 . Edition 1. doi: 10.1371/currents.RRN1026.)] TJ ET q 15.000 72.206 577.500 564.851 re W n 0.271 0.267 0.267 rg BT 26.250 610.335 Td /F4 12.0 Tf [(Abstract)] TJ ET BT 26.250 590.381 Td /F1 9.8 Tf [(Epidemiology and public health planning will increasingly rely on the analysis of genetic sequence data. The ongoing influenza )] TJ ET BT 26.250 578.476 Td /F1 9.8 Tf [(A/H1N1 pandemic may represent a tipping point in this trend, with A/H1N1 being the first human pathogen routinely genotyped )] TJ ET BT 26.250 566.571 Td /F1 9.8 Tf [(from the beginning of its spread. To take full advantage of this genetic information, we introduce a novel method to reconstruct )] TJ ET BT 26.250 554.667 Td /F1 9.8 Tf [(the spatiotemporal dynamics of outbreaks from sequence data. The approach is based on a new paradigm were ancestries are )] TJ ET BT 26.250 542.762 Td /F1 9.8 Tf [(inferred directly rather than through the reconstruction of most recent common ancestors \(MRCAs\) as in phylogenetics. Using )] TJ ET BT 26.250 530.857 Td /F1 9.8 Tf [(279 A/H1N1 hemagglutinin \(HA\) sequences, we confirm the emergence of the 2009 flu pandemic in Mexico. The virus initially )] TJ ET BT 26.250 518.952 Td /F1 9.8 Tf [(spread to the US, and then to the rest of the world with both Mexico and the US acting as the main sources. While compatible )] TJ ET BT 26.250 507.048 Td /F1 9.8 Tf [(with current epidemiological understanding of the 2009 H1N1 pandemic, our results provide a much finer picture of the )] TJ ET BT 26.250 495.143 Td /F1 9.8 Tf [(spatiotemporal dynamics. The results also highlight how much additional epidemiological information can be gathered from )] TJ ET BT 26.250 483.238 Td /F1 9.8 Tf [(genetic monitoring of a disease outbreak.)] TJ ET BT 26.250 446.636 Td /F4 12.0 Tf [(Introduction)] TJ ET BT 26.250 426.681 Td /F1 9.8 Tf [(As the first pandemic of the 21 )] TJ ET BT 160.654 430.570 Td /F1 8.7 Tf [(st)] TJ ET BT 167.396 426.681 Td /F1 9.8 Tf [( century, the 2009 influenza A/H1N1 outbreak acts as a timely reminder of the looming threat )] TJ ET BT 26.250 414.777 Td /F1 9.8 Tf [(posed by emerging infectious diseases. Indeed, the worldwide spread of a new deadly pathogen with sustained human-to-)] TJ ET BT 26.250 402.872 Td /F1 9.8 Tf [(human transmission is one of the most worrying public health scenarios. Early containment based on robust scientific evidence )] TJ ET BT 26.250 390.967 Td /F1 9.8 Tf [(is recognised as our best hope to avert a catastrophic situation if faced with the global spread of a deadly pathogen )] TJ ET 0.267 0.267 0.267 rg BT 524.855 390.967 Td /F1 9.8 Tf [([1])] TJ ET BT 535.697 390.967 Td /F1 9.8 Tf [([2])] TJ ET BT 546.539 390.967 Td /F1 9.8 Tf [([3])] TJ ET 0.271 0.267 0.267 rg BT 557.381 390.967 Td /F1 9.8 Tf [( . To )] TJ ET BT 26.250 379.062 Td /F1 9.8 Tf [(be most effective, prophylactic interventions must be implemented early on and will be based on only very preliminary scientific )] TJ ET BT 26.250 367.158 Td /F1 9.8 Tf [(evidence. Thus, it is crucial that all sources of useful information be considered. Genetic sequence data can now be generated )] TJ ET BT 26.250 355.253 Td /F1 9.8 Tf [(essentially in real time and the analysis of sequence data has already been added to the toolbox of epidemiology and pandemic )] TJ ET BT 26.250 343.348 Td /F1 9.8 Tf [(planning )] TJ ET 0.267 0.267 0.267 rg BT 65.816 343.348 Td /F1 9.8 Tf [([4])] TJ ET BT 76.657 343.348 Td /F1 9.8 Tf [([5])] TJ ET BT 87.499 343.348 Td /F1 9.8 Tf [([6])] TJ ET 0.271 0.267 0.267 rg BT 98.341 343.348 Td /F1 9.8 Tf [( . However, the statistical methodologies are currently lacking to harness the full potential of genetic sequence )] TJ ET BT 26.250 331.443 Td /F1 9.8 Tf [(information. In particular there is to date no available method for reconstructing the spatiotemporal dynamics of a set of strains )] TJ ET BT 26.250 319.539 Td /F1 9.8 Tf [(collected during an outbreak.)] TJ ET BT 26.250 300.134 Td /F1 9.8 Tf [(Current state of the art genetic methods for the reconstruction of pathogen genealogies rely on the phylogenetic paradigm )] TJ ET 0.267 0.267 0.267 rg BT 553.569 300.134 Td /F1 9.8 Tf [([7])] TJ ET BT 564.411 300.134 Td /F1 9.8 Tf [([8])] TJ ET BT 26.250 288.229 Td /F1 9.8 Tf [([9])] TJ ET BT 37.092 288.229 Td /F1 9.8 Tf [([10])] TJ ET 0.271 0.267 0.267 rg BT 53.355 288.229 Td /F1 9.8 Tf [( based on the inference of putative most recent common ancestors \(MRCAs\) between pairs of sequences. The analysis )] TJ ET BT 26.250 276.324 Td /F1 9.8 Tf [(of sequence data collected during disease outbreaks poses considerable challenges. Phylogenetic reconstruction is hampered )] TJ ET BT 26.250 264.420 Td /F1 9.8 Tf [(by the limited genetic diversity inherent to the early stages of an outbreak as obtaining statistical support behind MRCAs )] TJ ET BT 26.250 252.515 Td /F1 9.8 Tf [(requires extensive genetic polymorphism. More fundamentally, the reconstruction of MRCAs becomes inappropriate when )] TJ ET BT 26.250 240.610 Td /F1 9.8 Tf [(ancestors and their descendents are both present in the sample analyzed, as is bound to happen during the early stages of an )] TJ ET BT 26.250 228.705 Td /F1 9.8 Tf [(outbreak. To circumvent these problems, we introduce a new methodological paradigm for the analysis of genetic data )] TJ ET BT 26.250 216.801 Td /F1 9.8 Tf [(structured in space and time \(Fig. 1\). Rather than reconstructing hypothetical MRCAs, we developed an algorithm called )] TJ ET BT 26.250 204.896 Td /F5 9.8 Tf [(SeqTrack)] TJ ET BT 67.970 204.896 Td /F1 9.8 Tf [( , which directly reconstructs the most likely ancestries in space and time.)] TJ ET BT 26.250 185.491 Td /F1 9.8 Tf [(We applied the novel methodology to 297 hemagglutinin \(HA\) sequences of the 2009 H1N1 pandemic influenza virus )] TJ ET 0.267 0.267 0.267 rg BT 533.494 185.491 Td /F1 9.8 Tf [([11])] TJ ET BT 549.757 185.491 Td /F1 9.8 Tf [([12])] TJ ET 0.271 0.267 0.267 rg BT 566.020 185.491 Td /F1 9.8 Tf [( . )] TJ ET BT 26.250 173.586 Td /F1 9.8 Tf [(This allowed us to reconstruct the spread of this newly emerged pathogen in considerable detail.)] TJ ET 0.965 0.965 0.965 rg 26.250 72.206 555.000 91.500 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 163.706 m 581.250 163.706 l 581.250 162.956 l 26.250 162.956 l f q 225.000 0 0 75.750 35.250 78.206 cm /I4 Do Q q 35.250 72.206 537.000 0.000 re W n Q Q q 15.000 684.354 577.500 53.646 re W n 0.267 0.267 0.267 rg BT 15.000 718.042 Td /F2 21.0 Tf [(Spatiotemporal dynamics in the early stages of the 2009 )] TJ ET BT 15.000 693.094 Td /F2 21.0 Tf [(A/H1N1 influenza pandemic)] TJ ET Q 0.271 0.267 0.267 rg BT 15.000 675.088 Td /F3 9.8 Tf [(August 31, 2009)] TJ ET 0.267 0.267 0.267 rg BT 26.250 663.247 Td /F1 9.8 Tf [(Thibaut Jombart)] TJ ET 0.271 0.267 0.267 rg BT 96.694 663.247 Td /F1 9.8 Tf [(, )] TJ ET 0.267 0.267 0.267 rg BT 102.115 663.247 Td /F1 9.8 Tf [(Rosalind M Eggo)] TJ ET 0.271 0.267 0.267 rg BT 176.351 663.247 Td /F1 9.8 Tf [(, )] TJ ET 0.267 0.267 0.267 rg BT 181.772 663.247 Td /F1 9.8 Tf [(Pete Dodd)] TJ ET 0.271 0.267 0.267 rg BT 227.841 663.247 Td /F1 9.8 Tf [(, )] TJ ET 0.267 0.267 0.267 rg BT 233.262 663.247 Td /F1 9.8 Tf [(Francois Balloux)] TJ ET 0.271 0.267 0.267 rg BT 26.250 651.342 Td /F1 9.8 Tf [(Jombart T, Eggo RM, Dodd P, Balloux F. Spatiotemporal dynamics in the early stages of the 2009 A/H1N1 influenza pandemic. )] TJ ET BT 26.250 639.438 Td /F1 9.8 Tf [(PLOS Currents Influenza. 2009 Aug 31 . Edition 1. doi: 10.1371/currents.RRN1026.)] TJ ET q 15.000 72.206 577.500 564.851 re W n 0.271 0.267 0.267 rg BT 26.250 610.335 Td /F4 12.0 Tf [(Abstract)] TJ ET BT 26.250 590.381 Td /F1 9.8 Tf [(Epidemiology and public health planning will increasingly rely on the analysis of genetic sequence data. The ongoing influenza )] TJ ET BT 26.250 578.476 Td /F1 9.8 Tf [(A/H1N1 pandemic may represent a tipping point in this trend, with A/H1N1 being the first human pathogen routinely genotyped )] TJ ET BT 26.250 566.571 Td /F1 9.8 Tf [(from the beginning of its spread. To take full advantage of this genetic information, we introduce a novel method to reconstruct )] TJ ET BT 26.250 554.667 Td /F1 9.8 Tf [(the spatiotemporal dynamics of outbreaks from sequence data. The approach is based on a new paradigm were ancestries are )] TJ ET BT 26.250 542.762 Td /F1 9.8 Tf [(inferred directly rather than through the reconstruction of most recent common ancestors \(MRCAs\) as in phylogenetics. Using )] TJ ET BT 26.250 530.857 Td /F1 9.8 Tf [(279 A/H1N1 hemagglutinin \(HA\) sequences, we confirm the emergence of the 2009 flu pandemic in Mexico. The virus initially )] TJ ET BT 26.250 518.952 Td /F1 9.8 Tf [(spread to the US, and then to the rest of the world with both Mexico and the US acting as the main sources. While compatible )] TJ ET BT 26.250 507.048 Td /F1 9.8 Tf [(with current epidemiological understanding of the 2009 H1N1 pandemic, our results provide a much finer picture of the )] TJ ET BT 26.250 495.143 Td /F1 9.8 Tf [(spatiotemporal dynamics. The results also highlight how much additional epidemiological information can be gathered from )] TJ ET BT 26.250 483.238 Td /F1 9.8 Tf [(genetic monitoring of a disease outbreak.)] TJ ET BT 26.250 446.636 Td /F4 12.0 Tf [(Introduction)] TJ ET BT 26.250 426.681 Td /F1 9.8 Tf [(As the first pandemic of the 21 )] TJ ET BT 160.654 430.570 Td /F1 8.7 Tf [(st)] TJ ET BT 167.396 426.681 Td /F1 9.8 Tf [( century, the 2009 influenza A/H1N1 outbreak acts as a timely reminder of the looming threat )] TJ ET BT 26.250 414.777 Td /F1 9.8 Tf [(posed by emerging infectious diseases. Indeed, the worldwide spread of a new deadly pathogen with sustained human-to-)] TJ ET BT 26.250 402.872 Td /F1 9.8 Tf [(human transmission is one of the most worrying public health scenarios. Early containment based on robust scientific evidence )] TJ ET BT 26.250 390.967 Td /F1 9.8 Tf [(is recognised as our best hope to avert a catastrophic situation if faced with the global spread of a deadly pathogen )] TJ ET 0.267 0.267 0.267 rg BT 524.855 390.967 Td /F1 9.8 Tf [([1])] TJ ET BT 535.697 390.967 Td /F1 9.8 Tf [([2])] TJ ET BT 546.539 390.967 Td /F1 9.8 Tf [([3])] TJ ET 0.271 0.267 0.267 rg BT 557.381 390.967 Td /F1 9.8 Tf [( . To )] TJ ET BT 26.250 379.062 Td /F1 9.8 Tf [(be most effective, prophylactic interventions must be implemented early on and will be based on only very preliminary scientific )] TJ ET BT 26.250 367.158 Td /F1 9.8 Tf [(evidence. Thus, it is crucial that all sources of useful information be considered. Genetic sequence data can now be generated )] TJ ET BT 26.250 355.253 Td /F1 9.8 Tf [(essentially in real time and the analysis of sequence data has already been added to the toolbox of epidemiology and pandemic )] TJ ET BT 26.250 343.348 Td /F1 9.8 Tf [(planning )] TJ ET 0.267 0.267 0.267 rg BT 65.816 343.348 Td /F1 9.8 Tf [([4])] TJ ET BT 76.657 343.348 Td /F1 9.8 Tf [([5])] TJ ET BT 87.499 343.348 Td /F1 9.8 Tf [([6])] TJ ET 0.271 0.267 0.267 rg BT 98.341 343.348 Td /F1 9.8 Tf [( . However, the statistical methodologies are currently lacking to harness the full potential of genetic sequence )] TJ ET BT 26.250 331.443 Td /F1 9.8 Tf [(information. In particular there is to date no available method for reconstructing the spatiotemporal dynamics of a set of strains )] TJ ET BT 26.250 319.539 Td /F1 9.8 Tf [(collected during an outbreak.)] TJ ET BT 26.250 300.134 Td /F1 9.8 Tf [(Current state of the art genetic methods for the reconstruction of pathogen genealogies rely on the phylogenetic paradigm )] TJ ET 0.267 0.267 0.267 rg BT 553.569 300.134 Td /F1 9.8 Tf [([7])] TJ ET BT 564.411 300.134 Td /F1 9.8 Tf [([8])] TJ ET BT 26.250 288.229 Td /F1 9.8 Tf [([9])] TJ ET BT 37.092 288.229 Td /F1 9.8 Tf [([10])] TJ ET 0.271 0.267 0.267 rg BT 53.355 288.229 Td /F1 9.8 Tf [( based on the inference of putative most recent common ancestors \(MRCAs\) between pairs of sequences. The analysis )] TJ ET BT 26.250 276.324 Td /F1 9.8 Tf [(of sequence data collected during disease outbreaks poses considerable challenges. Phylogenetic reconstruction is hampered )] TJ ET BT 26.250 264.420 Td /F1 9.8 Tf [(by the limited genetic diversity inherent to the early stages of an outbreak as obtaining statistical support behind MRCAs )] TJ ET BT 26.250 252.515 Td /F1 9.8 Tf [(requires extensive genetic polymorphism. More fundamentally, the reconstruction of MRCAs becomes inappropriate when )] TJ ET BT 26.250 240.610 Td /F1 9.8 Tf [(ancestors and their descendents are both present in the sample analyzed, as is bound to happen during the early stages of an )] TJ ET BT 26.250 228.705 Td /F1 9.8 Tf [(outbreak. To circumvent these problems, we introduce a new methodological paradigm for the analysis of genetic data )] TJ ET BT 26.250 216.801 Td /F1 9.8 Tf [(structured in space and time \(Fig. 1\). Rather than reconstructing hypothetical MRCAs, we developed an algorithm called )] TJ ET BT 26.250 204.896 Td /F5 9.8 Tf [(SeqTrack)] TJ ET BT 67.970 204.896 Td /F1 9.8 Tf [( , which directly reconstructs the most likely ancestries in space and time.)] TJ ET BT 26.250 185.491 Td /F1 9.8 Tf [(We applied the novel methodology to 297 hemagglutinin \(HA\) sequences of the 2009 H1N1 pandemic influenza virus )] TJ ET 0.267 0.267 0.267 rg BT 533.494 185.491 Td /F1 9.8 Tf [([11])] TJ ET BT 549.757 185.491 Td /F1 9.8 Tf [([12])] TJ ET 0.271 0.267 0.267 rg BT 566.020 185.491 Td /F1 9.8 Tf [( . )] TJ ET BT 26.250 173.586 Td /F1 9.8 Tf [(This allowed us to reconstruct the spread of this newly emerged pathogen in considerable detail.)] TJ ET 0.965 0.965 0.965 rg 26.250 72.206 555.000 91.500 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 163.706 m 581.250 163.706 l 581.250 162.956 l 26.250 162.956 l f q 225.000 0 0 75.750 35.250 78.206 cm /I6 Do Q q 35.250 72.206 537.000 0.000 re W n Q Q q 15.000 684.354 577.500 53.646 re W n 0.267 0.267 0.267 rg BT 15.000 718.042 Td /F2 21.0 Tf [(Spatiotemporal dynamics in the early stages of the 2009 )] TJ ET BT 15.000 693.094 Td /F2 21.0 Tf [(A/H1N1 influenza pandemic)] TJ ET Q 0.271 0.267 0.267 rg BT 15.000 675.088 Td /F3 9.8 Tf [(August 31, 2009)] TJ ET 0.267 0.267 0.267 rg BT 26.250 663.247 Td /F1 9.8 Tf [(Thibaut Jombart)] TJ ET 0.271 0.267 0.267 rg BT 96.694 663.247 Td /F1 9.8 Tf [(, )] TJ ET 0.267 0.267 0.267 rg BT 102.115 663.247 Td /F1 9.8 Tf [(Rosalind M Eggo)] TJ ET 0.271 0.267 0.267 rg BT 176.351 663.247 Td /F1 9.8 Tf [(, )] TJ ET 0.267 0.267 0.267 rg BT 181.772 663.247 Td /F1 9.8 Tf [(Pete Dodd)] TJ ET 0.271 0.267 0.267 rg BT 227.841 663.247 Td /F1 9.8 Tf [(, )] TJ ET 0.267 0.267 0.267 rg BT 233.262 663.247 Td /F1 9.8 Tf [(Francois Balloux)] TJ ET 0.271 0.267 0.267 rg BT 26.250 651.342 Td /F1 9.8 Tf [(Jombart T, Eggo RM, Dodd P, Balloux F. Spatiotemporal dynamics in the early stages of the 2009 A/H1N1 influenza pandemic. )] TJ ET BT 26.250 639.438 Td /F1 9.8 Tf [(PLOS Currents Influenza. 2009 Aug 31 . Edition 1. doi: 10.1371/currents.RRN1026.)] TJ ET q 15.000 72.206 577.500 564.851 re W n 0.271 0.267 0.267 rg BT 26.250 610.335 Td /F4 12.0 Tf [(Abstract)] TJ ET BT 26.250 590.381 Td /F1 9.8 Tf [(Epidemiology and public health planning will increasingly rely on the analysis of genetic sequence data. The ongoing influenza )] TJ ET BT 26.250 578.476 Td /F1 9.8 Tf [(A/H1N1 pandemic may represent a tipping point in this trend, with A/H1N1 being the first human pathogen routinely genotyped )] TJ ET BT 26.250 566.571 Td /F1 9.8 Tf [(from the beginning of its spread. To take full advantage of this genetic information, we introduce a novel method to reconstruct )] TJ ET BT 26.250 554.667 Td /F1 9.8 Tf [(the spatiotemporal dynamics of outbreaks from sequence data. The approach is based on a new paradigm were ancestries are )] TJ ET BT 26.250 542.762 Td /F1 9.8 Tf [(inferred directly rather than through the reconstruction of most recent common ancestors \(MRCAs\) as in phylogenetics. Using )] TJ ET BT 26.250 530.857 Td /F1 9.8 Tf [(279 A/H1N1 hemagglutinin \(HA\) sequences, we confirm the emergence of the 2009 flu pandemic in Mexico. The virus initially )] TJ ET BT 26.250 518.952 Td /F1 9.8 Tf [(spread to the US, and then to the rest of the world with both Mexico and the US acting as the main sources. While compatible )] TJ ET BT 26.250 507.048 Td /F1 9.8 Tf [(with current epidemiological understanding of the 2009 H1N1 pandemic, our results provide a much finer picture of the )] TJ ET BT 26.250 495.143 Td /F1 9.8 Tf [(spatiotemporal dynamics. The results also highlight how much additional epidemiological information can be gathered from )] TJ ET BT 26.250 483.238 Td /F1 9.8 Tf [(genetic monitoring of a disease outbreak.)] TJ ET BT 26.250 446.636 Td /F4 12.0 Tf [(Introduction)] TJ ET BT 26.250 426.681 Td /F1 9.8 Tf [(As the first pandemic of the 21 )] TJ ET BT 160.654 430.570 Td /F1 8.7 Tf [(st)] TJ ET BT 167.396 426.681 Td /F1 9.8 Tf [( century, the 2009 influenza A/H1N1 outbreak acts as a timely reminder of the looming threat )] TJ ET BT 26.250 414.777 Td /F1 9.8 Tf [(posed by emerging infectious diseases. Indeed, the worldwide spread of a new deadly pathogen with sustained human-to-)] TJ ET BT 26.250 402.872 Td /F1 9.8 Tf [(human transmission is one of the most worrying public health scenarios. Early containment based on robust scientific evidence )] TJ ET BT 26.250 390.967 Td /F1 9.8 Tf [(is recognised as our best hope to avert a catastrophic situation if faced with the global spread of a deadly pathogen )] TJ ET 0.267 0.267 0.267 rg BT 524.855 390.967 Td /F1 9.8 Tf [([1])] TJ ET BT 535.697 390.967 Td /F1 9.8 Tf [([2])] TJ ET BT 546.539 390.967 Td /F1 9.8 Tf [([3])] TJ ET 0.271 0.267 0.267 rg BT 557.381 390.967 Td /F1 9.8 Tf [( . To )] TJ ET BT 26.250 379.062 Td /F1 9.8 Tf [(be most effective, prophylactic interventions must be implemented early on and will be based on only very preliminary scientific )] TJ ET BT 26.250 367.158 Td /F1 9.8 Tf [(evidence. Thus, it is crucial that all sources of useful information be considered. Genetic sequence data can now be generated )] TJ ET BT 26.250 355.253 Td /F1 9.8 Tf [(essentially in real time and the analysis of sequence data has already been added to the toolbox of epidemiology and pandemic )] TJ ET BT 26.250 343.348 Td /F1 9.8 Tf [(planning )] TJ ET 0.267 0.267 0.267 rg BT 65.816 343.348 Td /F1 9.8 Tf [([4])] TJ ET BT 76.657 343.348 Td /F1 9.8 Tf [([5])] TJ ET BT 87.499 343.348 Td /F1 9.8 Tf [([6])] TJ ET 0.271 0.267 0.267 rg BT 98.341 343.348 Td /F1 9.8 Tf [( . However, the statistical methodologies are currently lacking to harness the full potential of genetic sequence )] TJ ET BT 26.250 331.443 Td /F1 9.8 Tf [(information. In particular there is to date no available method for reconstructing the spatiotemporal dynamics of a set of strains )] TJ ET BT 26.250 319.539 Td /F1 9.8 Tf [(collected during an outbreak.)] TJ ET BT 26.250 300.134 Td /F1 9.8 Tf [(Current state of the art genetic methods for the reconstruction of pathogen genealogies rely on the phylogenetic paradigm )] TJ ET 0.267 0.267 0.267 rg BT 553.569 300.134 Td /F1 9.8 Tf [([7])] TJ ET BT 564.411 300.134 Td /F1 9.8 Tf [([8])] TJ ET BT 26.250 288.229 Td /F1 9.8 Tf [([9])] TJ ET BT 37.092 288.229 Td /F1 9.8 Tf [([10])] TJ ET 0.271 0.267 0.267 rg BT 53.355 288.229 Td /F1 9.8 Tf [( based on the inference of putative most recent common ancestors \(MRCAs\) between pairs of sequences. The analysis )] TJ ET BT 26.250 276.324 Td /F1 9.8 Tf [(of sequence data collected during disease outbreaks poses considerable challenges. Phylogenetic reconstruction is hampered )] TJ ET BT 26.250 264.420 Td /F1 9.8 Tf [(by the limited genetic diversity inherent to the early stages of an outbreak as obtaining statistical support behind MRCAs )] TJ ET BT 26.250 252.515 Td /F1 9.8 Tf [(requires extensive genetic polymorphism. More fundamentally, the reconstruction of MRCAs becomes inappropriate when )] TJ ET BT 26.250 240.610 Td /F1 9.8 Tf [(ancestors and their descendents are both present in the sample analyzed, as is bound to happen during the early stages of an )] TJ ET BT 26.250 228.705 Td /F1 9.8 Tf [(outbreak. To circumvent these problems, we introduce a new methodological paradigm for the analysis of genetic data )] TJ ET BT 26.250 216.801 Td /F1 9.8 Tf [(structured in space and time \(Fig. 1\). Rather than reconstructing hypothetical MRCAs, we developed an algorithm called )] TJ ET BT 26.250 204.896 Td /F5 9.8 Tf [(SeqTrack)] TJ ET BT 67.970 204.896 Td /F1 9.8 Tf [( , which directly reconstructs the most likely ancestries in space and time.)] TJ ET BT 26.250 185.491 Td /F1 9.8 Tf [(We applied the novel methodology to 297 hemagglutinin \(HA\) sequences of the 2009 H1N1 pandemic influenza virus )] TJ ET 0.267 0.267 0.267 rg BT 533.494 185.491 Td /F1 9.8 Tf [([11])] TJ ET BT 549.757 185.491 Td /F1 9.8 Tf [([12])] TJ ET 0.271 0.267 0.267 rg BT 566.020 185.491 Td /F1 9.8 Tf [( . )] TJ ET BT 26.250 173.586 Td /F1 9.8 Tf [(This allowed us to reconstruct the spread of this newly emerged pathogen in considerable detail.)] TJ ET 0.965 0.965 0.965 rg 26.250 72.206 555.000 91.500 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 163.706 m 581.250 163.706 l 581.250 162.956 l 26.250 162.956 l f q 225.000 0 0 75.750 35.250 78.206 cm /I8 Do Q q 35.250 72.206 537.000 0.000 re W n Q Q q 225.000 0 0 75.750 35.250 78.206 cm /I10 Do Q q 0.000 0.000 0.000 rg BT 291.710 19.825 Td /F1 11.0 Tf [(1)] TJ ET BT 25.000 19.825 Td /F1 11.0 Tf [(PLOS Currents Influenza)] TJ ET Q endstream endobj 8 0 obj << /Type /Font /Subtype /Type1 /Name /F1 /BaseFont /Helvetica /Encoding /WinAnsiEncoding >> endobj 9 0 obj << /Type /Font /Subtype /Type1 /Name /F2 /BaseFont /Times-Bold /Encoding /WinAnsiEncoding >> endobj 10 0 obj << /Type /Font /Subtype /Type1 /Name /F3 /BaseFont /Times-Italic /Encoding /WinAnsiEncoding >> endobj 11 0 obj << /Type /Font /Subtype /Type1 /Name /F4 /BaseFont /Helvetica-Bold /Encoding /WinAnsiEncoding >> endobj 12 0 obj << /Type /Font /Subtype /Type1 /Name /F5 /BaseFont /Helvetica-Oblique /Encoding /WinAnsiEncoding >> endobj 13 0 obj << /Type /XObject /Subtype /Image /Width 500 /Height 52 /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 1 /Columns 500 /BitsPerComponent 8>> /ColorSpace /DeviceGray /BitsPerComponent 8 /Length 144>> stream x1 0 'ݲ؎"e{dzAdzAdzAdzAdzAdzAdzAdzAdzAdzAdzAdzAtlM0\ endstream endobj 14 0 obj << /Type /XObject /Subtype /Image /Width 500 /Height 52 /SMask 13 0 R /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 3 /Columns 500 /BitsPerComponent 8>> /ColorSpace /DeviceRGB /BitsPerComponent 8 /Length 3574>> stream x}ƕK*8+0T ֮ S L*0߇d" sl2FBiFwY0 00 0ŝa0 aqgR܋x||lu2 03UL۶BxI 0:UU0x;֝($z%șHڶ ÐVz ]IS> â(.* TQUuL5 $>BvpH0U:xkkGJT{OɗRNyGOΙyn)q7`(~_Ji2vgk]qVꔷ3N'ȴy4Ikm6!q:FJ)-0n܋v!^}_Z l61va_~Bxw8mv;EJY8}zzQ3]Pȹ,2_jfY4MQ[ '.uO O͋kշ9b6.#ߦUUzhf09+nKɿ4 f7Bu7ĨMfrF0`s8429j1}ZWDW;A4ҫ'TQ{7Cb[$ -"ΨMQgzN/2R7Tco*W:N݋6TUu8`RSi O>r;z^m(0w`:m=]գCE&t |ZYQ%{X[nR+zbEFΧ5pzq`ުం Ih{9G 4wMx' nmvEZ sg7?ZQ}&ҎKGuPu.j8UgNKꓙQC)s#$1䧈x[Z(|Xzc;t<~50Hh_T3Ur>a$]B8Fz[?K>Y/rQ=E4?EaLqzpX!(nNut]}e(/S\fz,<ZOEa]0 sCS_}I Y}n۶r(fg7#)h6ա}$ üvq]Aא$c0ddBDQ)ueypU-z~9Hk<$I©y'Tk`yY d}e{䨙ǐu>&w񚓶('GI\rm[G4 Sk7$B pEkYYC/ 9&Ʋ[V9MQ':X|C֨ʉ jt"ޡ+rttBռGdiM FuTEi(łv]fk"8Ldp' ^הMup2`M?dE!|KJ-\.MzکC=&¾HfR7$ev,La0+$OFuEQ"i,ːN?~E*t4qΚF:t`,{RkR]ޜ(Ԕѣ$IbN}5لS1(Ȱ$I$(eWp8Lٱ3߯ky۶&. 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a„dIaUUU]]?z?ަA |kTTT Y%Kc)W*!5558pUTLbY] PD,=r IJJ'PUP d-3`۶m3gC h4www~e@www~~0{hb( Rat:KKKPb"yWȇ;Cmݺ5''gƌPyjc^PM{ܧΰoEP *Ν;y~B)Sfɑ\ jx5jϞ=,K^^x01BF' 0tMo3%  ~QzI}'eC3Fx hL($Cb6G,V0L( CᾯaFQ`0 <7\$nJ$gϞeYa!D {HBqw9;=>aXCAH{wEA[ vU(IDR4-Y)>p1w\nND'-t敚{kkknn8ƞq r. 4M;]]NOBj)uMV!tjEVBBέȢx5[i@ivm_7aٗiTj7t XI&)k+&-f(PRl'8Ne,6441`0(vPj|zPғɓȟhLSiyi,x~sQiI.b6Z-fsH"rPՇۛ4s摗)?FJySTkׯiwDUs_͍sIXA%L$~rdh$$bJ5r5(*bz/=zpk@E1a s%>ięΞ.ᦶ+`o4!}WN(4[QAvzZNV GMIApbïb@}ٻAC!/=|Maumnϗ!e@vަ}uGZN=mc*~}ʔ)'NbeiӦΝ;2v؋JAh:C@fXnqـ_Qxa@‚yC ron7hlKaz b}-/~'*q75#^}1s@Y߭t9%~6rI`2eIEuO"r4C !f"9]hF :@P'[:,iE@u yuGZ(prSq2SN-mh/|N7(ԼWQ16F*!PNu:+M~昒tY%U^c\B å1Wm'B +b4 7`V 3,&|V@NBt 8͊-PJ-kW]!p_3ZOZhBH hcg)QssJ;衡~Mq7 Exi~jSG]n3Va7Qf5LFDbWPJ V!Ӳg ziasX_Y 1*u2.>9 tanecjFˇe2!@2#r_Nv3- @ Gκ]=MtBI2 #N.% Ld 7mt3]|j9hT6,#7 >|l ,-)f(r$+-3MP{WAsAK]f3jjjꪫ c`'ԫXI}Kp72_^$Z L#Y,.r ͖J9lFHT1;98p8ޱc8eiáP( ĖDFF m-b@-PZG=XwVPt= dT1 I8&@Q(!+ Tw59TYE %ք^sh}8n="Y臒7nyB$I&'%(nz}@0L3 $ YVf[lA4 `(fX E&h4[۴&gAupoU?$喇1vE}~aI@qyV+JJ'tN(1rB$q7Ivp$Ikܹ'N9s5kiNwO7`84RlLI%'fvbK`lP Pߢ~̙3n; _}*nj'033ٳ ,ww(R:>!HŎ UL;q`婙ze^.Op񥎚;_5˰9=~j5ɡeGAUȤ$ǎ3LԩS %%%UUU:cc5pP RmVA:ӓ֬Y3mڴƃ(ՠ;*!2s)F8. z_aM7M !T^\kgMI6+#tb(=V *_xѦ&{~)F)$Ar{nuTm5ӫGg-+IEڭ|^yE-YDJ}G gJ(֗%.DžB@(L3\éUeZ͝X;r0sO(([$Pm\ɐҀ 0''gӦMͻ)8ps ZLU]+Pbb8G!BaP!~!Uh ˲j%!d&bqfAmzgdaԱUlvӧ͔9 @p4k'?iD(m5Bz$\还8fDq9hbZ%Cx8N|NC'H"“>~qxY,^ԍQ$7Gǻϭ@£^\"aIH`Yam]Gd%cRnH:=Ve2d`&%%EcUO2P}/=ҩfpuMIl/y霌g%;* "qQI,8bf4-fӓaش.ؗv7v4J$p)2S+e jjjBP(20 9FԊj:U1<xa`r@аL}TxX e5 =>P|E½--Y6} 3 )vҬm׷q OIO:"0L[,};PP(4{2 CDvvveeU䀊V"9AomGM> endobj 138 0 obj << /Length 33278 >> stream q 15.000 26.728 577.500 750.272 re W n 0.965 0.965 0.965 rg 26.250 675.832 555.000 101.168 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 675.832 m 581.250 675.832 l 581.250 676.582 l 26.250 676.582 l f q 35.250 687.082 537.000 89.918 re W n 0.271 0.267 0.267 rg BT 35.250 766.011 Td /F4 9.8 Tf [(Figure 1. Illustration of possible reconstructions of genealogical relations.)] TJ ET BT 378.762 766.011 Td /F1 9.8 Tf [( Panel a represents a hypothetical )] TJ ET BT 35.250 752.275 Td /F1 9.8 Tf [(genealogy of five strains from which three were sampled \(highlighted by a blue glow\). Panel b and c illustrate phylogenetic )] TJ ET BT 35.250 738.538 Td /F1 9.8 Tf [(reconstructions where the red dots represent inferred nodes; panel b corresponds to a classical phylogenetic reconstruction )] TJ ET BT 35.250 724.802 Td /F1 9.8 Tf [(and c to a tree that accounts for heterochronous sampling \(e.g. Beast software )] TJ ET 0.267 0.267 0.267 rg BT 376.675 724.802 Td /F1 9.8 Tf [([8])] TJ ET 0.271 0.267 0.267 rg BT 387.517 724.802 Td /F1 9.8 Tf [( \). Panel d illustrates the direct ancestry )] TJ ET BT 35.250 711.066 Td /F1 9.8 Tf [(reconstruction method implemented in )] TJ ET BT 203.233 711.066 Td /F5 9.8 Tf [(SeqTrack)] TJ ET BT 244.953 711.066 Td /F1 9.8 Tf [( . While none of the methods recovers the correct genealogy \(panels b-d\), )] TJ ET BT 35.250 697.330 Td /F1 9.8 Tf [(the best reconstruction is provided by )] TJ ET BT 199.450 697.330 Td /F5 9.8 Tf [(SeqTrack)] TJ ET BT 241.170 697.330 Td /F1 9.8 Tf [( in this example \(panel d\).)] TJ ET Q BT 26.250 641.611 Td /F4 12.0 Tf [(Methods)] TJ ET BT 26.250 621.657 Td /F4 9.8 Tf [(SeqTrack algorithm)] TJ ET BT 26.250 609.752 Td /F1 9.8 Tf [(Our method aims at uncovering ancestries between strains of an outbreak using their genotype and collection date. The )] TJ ET BT 26.250 597.847 Td /F1 9.8 Tf [(fundamental innovation of our approach is to seek ancestors directly from the sampled strains, rather than attempting to )] TJ ET BT 26.250 585.942 Td /F1 9.8 Tf [(reconstruct unobserved and hypothetical ancestral genotypes. Because ancestries are in essence temporally-oriented )] TJ ET BT 26.250 574.038 Td /F1 9.8 Tf [(connections between strains, it seemed natural to tackle the problem of inferring genealogies within graph theory.)] TJ ET BT 26.250 554.633 Td /F5 9.8 Tf [(SeqTrack)] TJ ET BT 67.970 554.633 Td /F1 9.8 Tf [( relies on three fundamental, yet simple observations. First, each observed strain has one, and only one ancestor. )] TJ ET BT 26.250 542.728 Td /F1 9.8 Tf [(Second, ancestors always precede their descendents in time. And third, among all possible ancestries of a given strain, some )] TJ ET BT 26.250 530.823 Td /F1 9.8 Tf [(are more likely than others, and this likelihood can be inferred from the amount of genetic differentiation between the strains )] TJ ET BT 26.250 518.919 Td /F1 9.8 Tf [(considered. The purpose of )] TJ ET BT 147.647 518.919 Td /F5 9.8 Tf [(SeqTrack)] TJ ET BT 189.368 518.919 Td /F1 9.8 Tf [( is to identify the most likely genealogy. Technically, this problem translates into finding )] TJ ET BT 26.250 507.014 Td /F1 9.8 Tf [(the optimum branching in a directed graph, where each node is a strain, and where a given strain is connected to all strains )] TJ ET BT 26.250 495.109 Td /F1 9.8 Tf [(occurring strictly later.)] TJ ET BT 26.250 473.228 Td /F1 9.8 Tf [(Let )] TJ ET q 66.750 0 0 14.250 42.513 470.978 cm /I12 Do Q BT 109.263 473.228 Td /F1 9.8 Tf [( be a directed, weighted graph where )] TJ ET q 78.750 0 0 15.000 272.390 470.228 cm /I14 Do Q BT 351.140 473.228 Td /F1 9.8 Tf [( is the set of vertices corresponding to the )] TJ ET q 8.250 0 0 7.500 534.313 477.728 cm /I16 Do Q BT 26.250 458.228 Td /F1 9.8 Tf [(sampled strains, with associated collection dates )] TJ ET q 80.250 0 0 15.000 239.209 455.228 cm /I18 Do Q BT 319.459 458.228 Td /F1 9.8 Tf [(. )] TJ ET q 10.500 0 0 10.500 324.880 459.728 cm /I20 Do Q BT 335.380 458.228 Td /F1 9.8 Tf [( is the set of directed edges of )] TJ ET q 9.000 0 0 12.750 468.166 457.478 cm /I22 Do Q BT 477.166 458.228 Td /F1 9.8 Tf [( modelling all possible )] TJ ET BT 26.250 441.428 Td /F1 9.8 Tf [(ancestries in )] TJ ET q 9.000 0 0 11.250 83.687 443.978 cm /I24 Do Q BT 92.687 441.428 Td /F1 9.8 Tf [(, such that )] TJ ET q 58.500 0 0 17.250 140.384 437.978 cm /I26 Do Q BT 198.884 441.428 Td /F1 9.8 Tf [( if and only if )] TJ ET q 30.000 0 0 12.750 256.331 442.478 cm /I28 Do Q BT 286.331 441.428 Td /F1 9.8 Tf [(. The weight function )] TJ ET q 48.000 0 0 10.500 379.005 444.728 cm /I30 Do Q BT 427.005 441.428 Td /F1 9.8 Tf [( assigns a weight to each possible )] TJ ET BT 26.250 428.454 Td /F1 9.8 Tf [(ancestry, which can reflect the genetic similarity or dissimilarity between the considered pairs of strains. For instance, )] TJ ET q 9.750 0 0 7.500 533.426 430.478 cm /I32 Do Q BT 543.176 428.454 Td /F1 9.8 Tf [( could )] TJ ET BT 26.250 416.550 Td /F1 9.8 Tf [(be defined as a genetic distance or similarity, or as the log-likelihood resulting from a probabilistic model of evolution. The )] TJ ET BT 26.250 400.369 Td /F1 9.8 Tf [(weight of a subset )] TJ ET q 10.500 0 0 11.250 107.546 402.919 cm /I34 Do Q BT 118.046 400.369 Td /F1 9.8 Tf [( of )] TJ ET q 10.500 0 0 10.500 131.598 403.669 cm /I36 Do Q BT 142.098 400.369 Td /F1 9.8 Tf [( is computed as )] TJ ET q 96.000 0 0 17.250 213.088 396.919 cm /I38 Do Q BT 309.088 400.369 Td /F1 9.8 Tf [(. The best genealogy of the sampled strains is the directed )] TJ ET BT 26.250 385.519 Td /F1 9.8 Tf [(spanning tree \()] TJ ET BT 91.282 385.519 Td /F5 9.8 Tf [(i.e.)] TJ ET BT 104.289 385.519 Td /F1 9.8 Tf [(, branching reaching all the nodes\) )] TJ ET q 69.750 0 0 14.250 260.903 382.669 cm /I40 Do Q BT 330.653 385.519 Td /F1 9.8 Tf [( with )] TJ ET q 34.500 0 0 12.750 353.410 384.169 cm /I42 Do Q BT 387.910 385.519 Td /F1 9.8 Tf [( optimizing \()] TJ ET BT 440.462 385.519 Td /F5 9.8 Tf [(i.e.)] TJ ET BT 453.469 385.519 Td /F1 9.8 Tf [(, minimizing or maximizing\) )] TJ ET q 18.000 0 0 10.500 26.250 372.169 cm /I44 Do Q BT 44.250 373.145 Td /F1 9.8 Tf [(.)] TJ ET BT 26.250 353.664 Td /F1 9.8 Tf [(This problem has been solved by Edmonds/Chu-Liu )] TJ ET 0.267 0.267 0.267 rg BT 252.762 353.664 Td /F1 9.8 Tf [([13])] TJ ET BT 269.025 353.664 Td /F1 9.8 Tf [([14])] TJ ET 0.271 0.267 0.267 rg BT 285.288 353.664 Td /F1 9.8 Tf [(, who developed an algorithm to find )] TJ ET q 11.250 0 0 12.000 444.623 351.264 cm /I46 Do Q BT 455.873 353.664 Td /F1 9.8 Tf [( so that )] TJ ET q 18.000 0 0 10.500 490.563 352.764 cm /I48 Do Q BT 508.563 353.664 Td /F1 9.8 Tf [(is maximum or )] TJ ET BT 26.250 341.740 Td /F1 9.8 Tf [(minimum. The algorithm proceeds by identifying optimum ancestors for each node at the exception of the root \(the oldest )] TJ ET BT 26.250 329.835 Td /F1 9.8 Tf [(strain\), and then recursively removes potential cycles. However, in our case, cycles are impossible as ancestries cannot go )] TJ ET BT 26.250 317.931 Td /F1 9.8 Tf [(back in time, which greatly simplifies computations.)] TJ ET BT 26.250 298.526 Td /F1 9.8 Tf [(The entire )] TJ ET BT 72.855 298.526 Td /F5 9.8 Tf [(SeqTrack)] TJ ET BT 114.575 298.526 Td /F1 9.8 Tf [( procedure has been implemented in the )] TJ ET BT 291.791 298.526 Td /F5 9.8 Tf [(adegenet)] TJ ET BT 332.449 298.526 Td /F1 9.8 Tf [( package )] TJ ET 0.267 0.267 0.267 rg BT 374.725 298.526 Td /F1 9.8 Tf [([15])] TJ ET 0.271 0.267 0.267 rg BT 390.988 298.526 Td /F1 9.8 Tf [( for the R software )] TJ ET 0.267 0.267 0.267 rg BT 473.356 298.526 Td /F1 9.8 Tf [([16])] TJ ET 0.271 0.267 0.267 rg BT 489.619 298.526 Td /F1 9.8 Tf [( . This )] TJ ET BT 26.250 286.621 Td /F1 9.8 Tf [(implementation allows specifying any weight and choosing the type of optimization \(minimization or maximization of total weight\) )] TJ ET BT 26.250 274.716 Td /F1 9.8 Tf [(to take advantage of the methods versatility. In this study, we considered that ancestries involving the fewest mutational steps )] TJ ET BT 26.250 262.812 Td /F1 9.8 Tf [(were the most likely. The chosen weights were therefore simply the number of mutations separating two strains. In the case of )] TJ ET BT 26.250 250.907 Td /F1 9.8 Tf [(an influenza outbreak, this parsimony approach is justified by the low amount of genetic differentiation between emerging flu )] TJ ET BT 26.250 239.002 Td /F1 9.8 Tf [(strains, and the absence of recombination and reverse mutations. The resulting ancestry path connects all the sampled strains )] TJ ET BT 26.250 227.097 Td /F1 9.8 Tf [(while minimizing the required number of mutational steps, and respecting their temporal ordering. Mapping these results allows )] TJ ET BT 26.250 215.193 Td /F1 9.8 Tf [(visualization of the inferred spatiotemporal spread of the new influenza virus.)] TJ ET BT 26.250 195.788 Td /F1 9.8 Tf [(For biological interpretation, it can be desirable to measure the reliability of some specific segments of the obtained optimum )] TJ ET BT 26.250 183.883 Td /F1 9.8 Tf [(genealogy. The support of inferred ancestries can be assessed by computing the likelihood of the number of mutations \()] TJ ET q 14.250 0 0 11.250 543.254 182.157 cm /I50 Do Q BT 557.504 183.883 Td /F1 9.8 Tf [(, )] TJ ET BT 26.250 170.702 Td /F1 9.8 Tf [(with )] TJ ET q 59.250 0 0 13.500 46.296 168.002 cm /I52 Do Q BT 105.546 170.702 Td /F1 9.8 Tf [(\) observed between the two strains of the edge )] TJ ET q 12.750 0 0 13.500 310.949 168.002 cm /I54 Do Q BT 323.699 170.702 Td /F1 9.8 Tf [(. This probability depends on the length \()] TJ ET q 9.000 0 0 10.500 499.833 171.002 cm /I56 Do Q BT 508.833 170.702 Td /F1 9.8 Tf [(, in number of )] TJ ET BT 26.250 158.478 Td /F1 9.8 Tf [(nucleotides\) and mutation rate \()] TJ ET q 8.250 0 0 10.500 163.355 157.502 cm /I58 Do Q BT 171.605 158.478 Td /F1 9.8 Tf [(, in number of mutations per nucleotides and per day\) of the considered DNA sequences, and )] TJ ET BT 26.250 145.297 Td /F1 9.8 Tf [(on the period of time elapsed \()] TJ ET q 15.750 0 0 13.500 157.943 142.597 cm /I60 Do Q BT 173.693 145.297 Td /F1 9.8 Tf [(, in days\) between the two strains collection dates. It is then simply derived from the )] TJ ET BT 26.250 131.797 Td /F1 9.8 Tf [(probability mass function of a Binomial distribution with probability )] TJ ET q 8.250 0 0 10.500 312.354 132.097 cm /I62 Do Q BT 320.604 131.797 Td /F1 9.8 Tf [( and )] TJ ET q 24.750 0 0 13.500 342.288 129.097 cm /I64 Do Q BT 367.038 131.797 Td /F1 9.8 Tf [( trials:)] TJ ET q 258.000 0 0 32.250 26.250 89.347 cm /I66 Do Q BT 26.250 72.324 Td /F1 9.8 Tf [(This likelihood can be represented on all edges using a color coding to allow a better assessment of the results \(Fig. 2\).)] TJ ET BT 26.250 52.919 Td /F4 9.8 Tf [(Sequence data)] TJ ET BT 26.250 41.014 Td /F1 9.8 Tf [(Genetic data were used to infer the spatiotemporal spread of the swine-derived influenza A/H1N1 pandemic. We analyzed all )] TJ ET Q q 15.000 26.728 577.500 750.272 re W n 0.965 0.965 0.965 rg 26.250 675.832 555.000 101.168 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 675.832 m 581.250 675.832 l 581.250 676.582 l 26.250 676.582 l f q 35.250 687.082 537.000 89.918 re W n 0.271 0.267 0.267 rg BT 35.250 766.011 Td /F4 9.8 Tf [(Figure 1. Illustration of possible reconstructions of genealogical relations.)] TJ ET BT 378.762 766.011 Td /F1 9.8 Tf [( Panel a represents a hypothetical )] TJ ET BT 35.250 752.275 Td /F1 9.8 Tf [(genealogy of five strains from which three were sampled \(highlighted by a blue glow\). Panel b and c illustrate phylogenetic )] TJ ET BT 35.250 738.538 Td /F1 9.8 Tf [(reconstructions where the red dots represent inferred nodes; panel b corresponds to a classical phylogenetic reconstruction )] TJ ET BT 35.250 724.802 Td /F1 9.8 Tf [(and c to a tree that accounts for heterochronous sampling \(e.g. Beast software )] TJ ET 0.267 0.267 0.267 rg BT 376.675 724.802 Td /F1 9.8 Tf [([8])] TJ ET 0.271 0.267 0.267 rg BT 387.517 724.802 Td /F1 9.8 Tf [( \). Panel d illustrates the direct ancestry )] TJ ET BT 35.250 711.066 Td /F1 9.8 Tf [(reconstruction method implemented in )] TJ ET BT 203.233 711.066 Td /F5 9.8 Tf [(SeqTrack)] TJ ET BT 244.953 711.066 Td /F1 9.8 Tf [( . While none of the methods recovers the correct genealogy \(panels b-d\), )] TJ ET BT 35.250 697.330 Td /F1 9.8 Tf [(the best reconstruction is provided by )] TJ ET BT 199.450 697.330 Td /F5 9.8 Tf [(SeqTrack)] TJ ET BT 241.170 697.330 Td /F1 9.8 Tf [( in this example \(panel d\).)] TJ ET Q BT 26.250 641.611 Td /F4 12.0 Tf [(Methods)] TJ ET BT 26.250 621.657 Td /F4 9.8 Tf [(SeqTrack algorithm)] TJ ET BT 26.250 609.752 Td /F1 9.8 Tf [(Our method aims at uncovering ancestries between strains of an outbreak using their genotype and collection date. The )] TJ ET BT 26.250 597.847 Td /F1 9.8 Tf [(fundamental innovation of our approach is to seek ancestors directly from the sampled strains, rather than attempting to )] TJ ET BT 26.250 585.942 Td /F1 9.8 Tf [(reconstruct unobserved and hypothetical ancestral genotypes. Because ancestries are in essence temporally-oriented )] TJ ET BT 26.250 574.038 Td /F1 9.8 Tf [(connections between strains, it seemed natural to tackle the problem of inferring genealogies within graph theory.)] TJ ET BT 26.250 554.633 Td /F5 9.8 Tf [(SeqTrack)] TJ ET BT 67.970 554.633 Td /F1 9.8 Tf [( relies on three fundamental, yet simple observations. First, each observed strain has one, and only one ancestor. )] TJ ET BT 26.250 542.728 Td /F1 9.8 Tf [(Second, ancestors always precede their descendents in time. And third, among all possible ancestries of a given strain, some )] TJ ET BT 26.250 530.823 Td /F1 9.8 Tf [(are more likely than others, and this likelihood can be inferred from the amount of genetic differentiation between the strains )] TJ ET BT 26.250 518.919 Td /F1 9.8 Tf [(considered. The purpose of )] TJ ET BT 147.647 518.919 Td /F5 9.8 Tf [(SeqTrack)] TJ ET BT 189.368 518.919 Td /F1 9.8 Tf [( is to identify the most likely genealogy. Technically, this problem translates into finding )] TJ ET BT 26.250 507.014 Td /F1 9.8 Tf [(the optimum branching in a directed graph, where each node is a strain, and where a given strain is connected to all strains )] TJ ET BT 26.250 495.109 Td /F1 9.8 Tf [(occurring strictly later.)] TJ ET BT 26.250 473.228 Td /F1 9.8 Tf [(Let )] TJ ET q 66.750 0 0 14.250 42.513 470.978 cm /I68 Do Q BT 109.263 473.228 Td /F1 9.8 Tf [( be a directed, weighted graph where )] TJ ET q 78.750 0 0 15.000 272.390 470.228 cm /I70 Do Q BT 351.140 473.228 Td /F1 9.8 Tf [( is the set of vertices corresponding to the )] TJ ET q 8.250 0 0 7.500 534.313 477.728 cm /I72 Do Q BT 26.250 458.228 Td /F1 9.8 Tf [(sampled strains, with associated collection dates )] TJ ET q 80.250 0 0 15.000 239.209 455.228 cm /I74 Do Q BT 319.459 458.228 Td /F1 9.8 Tf [(. )] TJ ET q 10.500 0 0 10.500 324.880 459.728 cm /I76 Do Q BT 335.380 458.228 Td /F1 9.8 Tf [( is the set of directed edges of )] TJ ET q 9.000 0 0 12.750 468.166 457.478 cm /I78 Do Q BT 477.166 458.228 Td /F1 9.8 Tf [( modelling all possible )] TJ ET BT 26.250 441.428 Td /F1 9.8 Tf [(ancestries in )] TJ ET q 9.000 0 0 11.250 83.687 443.978 cm /I80 Do Q BT 92.687 441.428 Td /F1 9.8 Tf [(, such that )] TJ ET q 58.500 0 0 17.250 140.384 437.978 cm /I82 Do Q BT 198.884 441.428 Td /F1 9.8 Tf [( if and only if )] TJ ET q 30.000 0 0 12.750 256.331 442.478 cm /I84 Do Q BT 286.331 441.428 Td /F1 9.8 Tf [(. The weight function )] TJ ET q 48.000 0 0 10.500 379.005 444.728 cm /I86 Do Q BT 427.005 441.428 Td /F1 9.8 Tf [( assigns a weight to each possible )] TJ ET BT 26.250 428.454 Td /F1 9.8 Tf [(ancestry, which can reflect the genetic similarity or dissimilarity between the considered pairs of strains. For instance, )] TJ ET q 9.750 0 0 7.500 533.426 430.478 cm /I88 Do Q BT 543.176 428.454 Td /F1 9.8 Tf [( could )] TJ ET BT 26.250 416.550 Td /F1 9.8 Tf [(be defined as a genetic distance or similarity, or as the log-likelihood resulting from a probabilistic model of evolution. The )] TJ ET BT 26.250 400.369 Td /F1 9.8 Tf [(weight of a subset )] TJ ET q 10.500 0 0 11.250 107.546 402.919 cm /I90 Do Q BT 118.046 400.369 Td /F1 9.8 Tf [( of )] TJ ET q 10.500 0 0 10.500 131.598 403.669 cm /I92 Do Q BT 142.098 400.369 Td /F1 9.8 Tf [( is computed as )] TJ ET q 96.000 0 0 17.250 213.088 396.919 cm /I94 Do Q BT 309.088 400.369 Td /F1 9.8 Tf [(. The best genealogy of the sampled strains is the directed )] TJ ET BT 26.250 385.519 Td /F1 9.8 Tf [(spanning tree \()] TJ ET BT 91.282 385.519 Td /F5 9.8 Tf [(i.e.)] TJ ET BT 104.289 385.519 Td /F1 9.8 Tf [(, branching reaching all the nodes\) )] TJ ET q 69.750 0 0 14.250 260.903 382.669 cm /I96 Do Q BT 330.653 385.519 Td /F1 9.8 Tf [( with )] TJ ET q 34.500 0 0 12.750 353.410 384.169 cm /I98 Do Q BT 387.910 385.519 Td /F1 9.8 Tf [( optimizing \()] TJ ET BT 440.462 385.519 Td /F5 9.8 Tf [(i.e.)] TJ ET BT 453.469 385.519 Td /F1 9.8 Tf [(, minimizing or maximizing\) )] TJ ET q 18.000 0 0 10.500 26.250 372.169 cm /I100 Do Q BT 44.250 373.145 Td /F1 9.8 Tf [(.)] TJ ET BT 26.250 353.664 Td /F1 9.8 Tf [(This problem has been solved by Edmonds/Chu-Liu )] TJ ET 0.267 0.267 0.267 rg BT 252.762 353.664 Td /F1 9.8 Tf [([13])] TJ ET BT 269.025 353.664 Td /F1 9.8 Tf [([14])] TJ ET 0.271 0.267 0.267 rg BT 285.288 353.664 Td /F1 9.8 Tf [(, who developed an algorithm to find )] TJ ET q 11.250 0 0 12.000 444.623 351.264 cm /I102 Do Q BT 455.873 353.664 Td /F1 9.8 Tf [( so that )] TJ ET q 18.000 0 0 10.500 490.563 352.764 cm /I104 Do Q BT 508.563 353.664 Td /F1 9.8 Tf [(is maximum or )] TJ ET BT 26.250 341.740 Td /F1 9.8 Tf [(minimum. The algorithm proceeds by identifying optimum ancestors for each node at the exception of the root \(the oldest )] TJ ET BT 26.250 329.835 Td /F1 9.8 Tf [(strain\), and then recursively removes potential cycles. However, in our case, cycles are impossible as ancestries cannot go )] TJ ET BT 26.250 317.931 Td /F1 9.8 Tf [(back in time, which greatly simplifies computations.)] TJ ET BT 26.250 298.526 Td /F1 9.8 Tf [(The entire )] TJ ET BT 72.855 298.526 Td /F5 9.8 Tf [(SeqTrack)] TJ ET BT 114.575 298.526 Td /F1 9.8 Tf [( procedure has been implemented in the )] TJ ET BT 291.791 298.526 Td /F5 9.8 Tf [(adegenet)] TJ ET BT 332.449 298.526 Td /F1 9.8 Tf [( package )] TJ ET 0.267 0.267 0.267 rg BT 374.725 298.526 Td /F1 9.8 Tf [([15])] TJ ET 0.271 0.267 0.267 rg BT 390.988 298.526 Td /F1 9.8 Tf [( for the R software )] TJ ET 0.267 0.267 0.267 rg BT 473.356 298.526 Td /F1 9.8 Tf [([16])] TJ ET 0.271 0.267 0.267 rg BT 489.619 298.526 Td /F1 9.8 Tf [( . This )] TJ ET BT 26.250 286.621 Td /F1 9.8 Tf [(implementation allows specifying any weight and choosing the type of optimization \(minimization or maximization of total weight\) )] TJ ET BT 26.250 274.716 Td /F1 9.8 Tf [(to take advantage of the methods versatility. In this study, we considered that ancestries involving the fewest mutational steps )] TJ ET BT 26.250 262.812 Td /F1 9.8 Tf [(were the most likely. The chosen weights were therefore simply the number of mutations separating two strains. In the case of )] TJ ET BT 26.250 250.907 Td /F1 9.8 Tf [(an influenza outbreak, this parsimony approach is justified by the low amount of genetic differentiation between emerging flu )] TJ ET BT 26.250 239.002 Td /F1 9.8 Tf [(strains, and the absence of recombination and reverse mutations. The resulting ancestry path connects all the sampled strains )] TJ ET BT 26.250 227.097 Td /F1 9.8 Tf [(while minimizing the required number of mutational steps, and respecting their temporal ordering. Mapping these results allows )] TJ ET BT 26.250 215.193 Td /F1 9.8 Tf [(visualization of the inferred spatiotemporal spread of the new influenza virus.)] TJ ET BT 26.250 195.788 Td /F1 9.8 Tf [(For biological interpretation, it can be desirable to measure the reliability of some specific segments of the obtained optimum )] TJ ET BT 26.250 183.883 Td /F1 9.8 Tf [(genealogy. The support of inferred ancestries can be assessed by computing the likelihood of the number of mutations \()] TJ ET q 14.250 0 0 11.250 543.254 182.157 cm /I106 Do Q BT 557.504 183.883 Td /F1 9.8 Tf [(, )] TJ ET BT 26.250 170.702 Td /F1 9.8 Tf [(with )] TJ ET q 59.250 0 0 13.500 46.296 168.002 cm /I108 Do Q BT 105.546 170.702 Td /F1 9.8 Tf [(\) observed between the two strains of the edge )] TJ ET q 12.750 0 0 13.500 310.949 168.002 cm /I110 Do Q BT 323.699 170.702 Td /F1 9.8 Tf [(. This probability depends on the length \()] TJ ET q 9.000 0 0 10.500 499.833 171.002 cm /I112 Do Q BT 508.833 170.702 Td /F1 9.8 Tf [(, in number of )] TJ ET BT 26.250 158.478 Td /F1 9.8 Tf [(nucleotides\) and mutation rate \()] TJ ET q 8.250 0 0 10.500 163.355 157.502 cm /I114 Do Q BT 171.605 158.478 Td /F1 9.8 Tf [(, in number of mutations per nucleotides and per day\) of the considered DNA sequences, and )] TJ ET BT 26.250 145.297 Td /F1 9.8 Tf [(on the period of time elapsed \()] TJ ET q 15.750 0 0 13.500 157.943 142.597 cm /I116 Do Q BT 173.693 145.297 Td /F1 9.8 Tf [(, in days\) between the two strains collection dates. It is then simply derived from the )] TJ ET BT 26.250 131.797 Td /F1 9.8 Tf [(probability mass function of a Binomial distribution with probability )] TJ ET q 8.250 0 0 10.500 312.354 132.097 cm /I118 Do Q BT 320.604 131.797 Td /F1 9.8 Tf [( and )] TJ ET q 24.750 0 0 13.500 342.288 129.097 cm /I120 Do Q BT 367.038 131.797 Td /F1 9.8 Tf [( trials:)] TJ ET q 258.000 0 0 32.250 26.250 89.347 cm /I122 Do Q BT 26.250 72.324 Td /F1 9.8 Tf [(This likelihood can be represented on all edges using a color coding to allow a better assessment of the results \(Fig. 2\).)] TJ ET BT 26.250 52.919 Td /F4 9.8 Tf [(Sequence data)] TJ ET BT 26.250 41.014 Td /F1 9.8 Tf [(Genetic data were used to infer the spatiotemporal spread of the swine-derived influenza A/H1N1 pandemic. We analyzed all )] TJ ET Q q 15.000 26.728 577.500 750.272 re W n 0.965 0.965 0.965 rg 26.250 675.832 555.000 101.168 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 675.832 m 581.250 675.832 l 581.250 676.582 l 26.250 676.582 l f q 35.250 687.082 537.000 89.918 re W n 0.271 0.267 0.267 rg BT 35.250 766.011 Td /F4 9.8 Tf [(Figure 1. Illustration of possible reconstructions of genealogical relations.)] TJ ET BT 378.762 766.011 Td /F1 9.8 Tf [( Panel a represents a hypothetical )] TJ ET BT 35.250 752.275 Td /F1 9.8 Tf [(genealogy of five strains from which three were sampled \(highlighted by a blue glow\). Panel b and c illustrate phylogenetic )] TJ ET BT 35.250 738.538 Td /F1 9.8 Tf [(reconstructions where the red dots represent inferred nodes; panel b corresponds to a classical phylogenetic reconstruction )] TJ ET BT 35.250 724.802 Td /F1 9.8 Tf [(and c to a tree that accounts for heterochronous sampling \(e.g. Beast software )] TJ ET 0.267 0.267 0.267 rg BT 376.675 724.802 Td /F1 9.8 Tf [([8])] TJ ET 0.271 0.267 0.267 rg BT 387.517 724.802 Td /F1 9.8 Tf [( \). Panel d illustrates the direct ancestry )] TJ ET BT 35.250 711.066 Td /F1 9.8 Tf [(reconstruction method implemented in )] TJ ET BT 203.233 711.066 Td /F5 9.8 Tf [(SeqTrack)] TJ ET BT 244.953 711.066 Td /F1 9.8 Tf [( . While none of the methods recovers the correct genealogy \(panels b-d\), )] TJ ET BT 35.250 697.330 Td /F1 9.8 Tf [(the best reconstruction is provided by )] TJ ET BT 199.450 697.330 Td /F5 9.8 Tf [(SeqTrack)] TJ ET BT 241.170 697.330 Td /F1 9.8 Tf [( in this example \(panel d\).)] TJ ET Q BT 26.250 641.611 Td /F4 12.0 Tf [(Methods)] TJ ET BT 26.250 621.657 Td /F4 9.8 Tf [(SeqTrack algorithm)] TJ ET BT 26.250 609.752 Td /F1 9.8 Tf [(Our method aims at uncovering ancestries between strains of an outbreak using their genotype and collection date. The )] TJ ET BT 26.250 597.847 Td /F1 9.8 Tf [(fundamental innovation of our approach is to seek ancestors directly from the sampled strains, rather than attempting to )] TJ ET BT 26.250 585.942 Td /F1 9.8 Tf [(reconstruct unobserved and hypothetical ancestral genotypes. Because ancestries are in essence temporally-oriented )] TJ ET BT 26.250 574.038 Td /F1 9.8 Tf [(connections between strains, it seemed natural to tackle the problem of inferring genealogies within graph theory.)] TJ ET BT 26.250 554.633 Td /F5 9.8 Tf [(SeqTrack)] TJ ET BT 67.970 554.633 Td /F1 9.8 Tf [( relies on three fundamental, yet simple observations. First, each observed strain has one, and only one ancestor. )] TJ ET BT 26.250 542.728 Td /F1 9.8 Tf [(Second, ancestors always precede their descendents in time. And third, among all possible ancestries of a given strain, some )] TJ ET BT 26.250 530.823 Td /F1 9.8 Tf [(are more likely than others, and this likelihood can be inferred from the amount of genetic differentiation between the strains )] TJ ET BT 26.250 518.919 Td /F1 9.8 Tf [(considered. The purpose of )] TJ ET BT 147.647 518.919 Td /F5 9.8 Tf [(SeqTrack)] TJ ET BT 189.368 518.919 Td /F1 9.8 Tf [( is to identify the most likely genealogy. Technically, this problem translates into finding )] TJ ET BT 26.250 507.014 Td /F1 9.8 Tf [(the optimum branching in a directed graph, where each node is a strain, and where a given strain is connected to all strains )] TJ ET BT 26.250 495.109 Td /F1 9.8 Tf [(occurring strictly later.)] TJ ET BT 26.250 473.228 Td /F1 9.8 Tf [(Let )] TJ ET q 66.750 0 0 14.250 42.513 470.978 cm /I124 Do Q BT 109.263 473.228 Td /F1 9.8 Tf [( be a directed, weighted graph where )] TJ ET q 78.750 0 0 15.000 272.390 470.228 cm /I126 Do Q BT 351.140 473.228 Td /F1 9.8 Tf [( is the set of vertices corresponding to the )] TJ ET q 8.250 0 0 7.500 534.313 477.728 cm /I128 Do Q BT 26.250 458.228 Td /F1 9.8 Tf [(sampled strains, with associated collection dates )] TJ ET q 80.250 0 0 15.000 239.209 455.228 cm /I130 Do Q BT 319.459 458.228 Td /F1 9.8 Tf [(. )] TJ ET q 10.500 0 0 10.500 324.880 459.728 cm /I132 Do Q BT 335.380 458.228 Td /F1 9.8 Tf [( is the set of directed edges of )] TJ ET q 9.000 0 0 12.750 468.166 457.478 cm /I134 Do Q BT 477.166 458.228 Td /F1 9.8 Tf [( modelling all possible )] TJ ET BT 26.250 441.428 Td /F1 9.8 Tf [(ancestries in )] TJ ET q 9.000 0 0 11.250 83.687 443.978 cm /I136 Do Q BT 92.687 441.428 Td /F1 9.8 Tf [(, such that )] TJ ET q 58.500 0 0 17.250 140.384 437.978 cm /I138 Do Q BT 198.884 441.428 Td /F1 9.8 Tf [( if and only if )] TJ ET q 30.000 0 0 12.750 256.331 442.478 cm /I140 Do Q BT 286.331 441.428 Td /F1 9.8 Tf [(. The weight function )] TJ ET q 48.000 0 0 10.500 379.005 444.728 cm /I142 Do Q BT 427.005 441.428 Td /F1 9.8 Tf [( assigns a weight to each possible )] TJ ET BT 26.250 428.454 Td /F1 9.8 Tf [(ancestry, which can reflect the genetic similarity or dissimilarity between the considered pairs of strains. For instance, )] TJ ET q 9.750 0 0 7.500 533.426 430.478 cm /I144 Do Q BT 543.176 428.454 Td /F1 9.8 Tf [( could )] TJ ET BT 26.250 416.550 Td /F1 9.8 Tf [(be defined as a genetic distance or similarity, or as the log-likelihood resulting from a probabilistic model of evolution. The )] TJ ET BT 26.250 400.369 Td /F1 9.8 Tf [(weight of a subset )] TJ ET q 10.500 0 0 11.250 107.546 402.919 cm /I146 Do Q BT 118.046 400.369 Td /F1 9.8 Tf [( of )] TJ ET q 10.500 0 0 10.500 131.598 403.669 cm /I148 Do Q BT 142.098 400.369 Td /F1 9.8 Tf [( is computed as )] TJ ET q 96.000 0 0 17.250 213.088 396.919 cm /I150 Do Q BT 309.088 400.369 Td /F1 9.8 Tf [(. The best genealogy of the sampled strains is the directed )] TJ ET BT 26.250 385.519 Td /F1 9.8 Tf [(spanning tree \()] TJ ET BT 91.282 385.519 Td /F5 9.8 Tf [(i.e.)] TJ ET BT 104.289 385.519 Td /F1 9.8 Tf [(, branching reaching all the nodes\) )] TJ ET q 69.750 0 0 14.250 260.903 382.669 cm /I152 Do Q BT 330.653 385.519 Td /F1 9.8 Tf [( with )] TJ ET q 34.500 0 0 12.750 353.410 384.169 cm /I154 Do Q BT 387.910 385.519 Td /F1 9.8 Tf [( optimizing \()] TJ ET BT 440.462 385.519 Td /F5 9.8 Tf [(i.e.)] TJ ET BT 453.469 385.519 Td /F1 9.8 Tf [(, minimizing or maximizing\) )] TJ ET q 18.000 0 0 10.500 26.250 372.169 cm /I156 Do Q BT 44.250 373.145 Td /F1 9.8 Tf [(.)] TJ ET BT 26.250 353.664 Td /F1 9.8 Tf [(This problem has been solved by Edmonds/Chu-Liu )] TJ ET 0.267 0.267 0.267 rg BT 252.762 353.664 Td /F1 9.8 Tf [([13])] TJ ET BT 269.025 353.664 Td /F1 9.8 Tf [([14])] TJ ET 0.271 0.267 0.267 rg BT 285.288 353.664 Td /F1 9.8 Tf [(, who developed an algorithm to find )] TJ ET q 11.250 0 0 12.000 444.623 351.264 cm /I158 Do Q BT 455.873 353.664 Td /F1 9.8 Tf [( so that )] TJ ET q 18.000 0 0 10.500 490.563 352.764 cm /I160 Do Q BT 508.563 353.664 Td /F1 9.8 Tf [(is maximum or )] TJ ET BT 26.250 341.740 Td /F1 9.8 Tf [(minimum. The algorithm proceeds by identifying optimum ancestors for each node at the exception of the root \(the oldest )] TJ ET BT 26.250 329.835 Td /F1 9.8 Tf [(strain\), and then recursively removes potential cycles. However, in our case, cycles are impossible as ancestries cannot go )] TJ ET BT 26.250 317.931 Td /F1 9.8 Tf [(back in time, which greatly simplifies computations.)] TJ ET BT 26.250 298.526 Td /F1 9.8 Tf [(The entire )] TJ ET BT 72.855 298.526 Td /F5 9.8 Tf [(SeqTrack)] TJ ET BT 114.575 298.526 Td /F1 9.8 Tf [( procedure has been implemented in the )] TJ ET BT 291.791 298.526 Td /F5 9.8 Tf [(adegenet)] TJ ET BT 332.449 298.526 Td /F1 9.8 Tf [( package )] TJ ET 0.267 0.267 0.267 rg BT 374.725 298.526 Td /F1 9.8 Tf [([15])] TJ ET 0.271 0.267 0.267 rg BT 390.988 298.526 Td /F1 9.8 Tf [( for the R software )] TJ ET 0.267 0.267 0.267 rg BT 473.356 298.526 Td /F1 9.8 Tf [([16])] TJ ET 0.271 0.267 0.267 rg BT 489.619 298.526 Td /F1 9.8 Tf [( . This )] TJ ET BT 26.250 286.621 Td /F1 9.8 Tf [(implementation allows specifying any weight and choosing the type of optimization \(minimization or maximization of total weight\) )] TJ ET BT 26.250 274.716 Td /F1 9.8 Tf [(to take advantage of the methods versatility. In this study, we considered that ancestries involving the fewest mutational steps )] TJ ET BT 26.250 262.812 Td /F1 9.8 Tf [(were the most likely. The chosen weights were therefore simply the number of mutations separating two strains. In the case of )] TJ ET BT 26.250 250.907 Td /F1 9.8 Tf [(an influenza outbreak, this parsimony approach is justified by the low amount of genetic differentiation between emerging flu )] TJ ET BT 26.250 239.002 Td /F1 9.8 Tf [(strains, and the absence of recombination and reverse mutations. The resulting ancestry path connects all the sampled strains )] TJ ET BT 26.250 227.097 Td /F1 9.8 Tf [(while minimizing the required number of mutational steps, and respecting their temporal ordering. Mapping these results allows )] TJ ET BT 26.250 215.193 Td /F1 9.8 Tf [(visualization of the inferred spatiotemporal spread of the new influenza virus.)] TJ ET BT 26.250 195.788 Td /F1 9.8 Tf [(For biological interpretation, it can be desirable to measure the reliability of some specific segments of the obtained optimum )] TJ ET BT 26.250 183.883 Td /F1 9.8 Tf [(genealogy. The support of inferred ancestries can be assessed by computing the likelihood of the number of mutations \()] TJ ET q 14.250 0 0 11.250 543.254 182.157 cm /I162 Do Q BT 557.504 183.883 Td /F1 9.8 Tf [(, )] TJ ET BT 26.250 170.702 Td /F1 9.8 Tf [(with )] TJ ET q 59.250 0 0 13.500 46.296 168.002 cm /I164 Do Q BT 105.546 170.702 Td /F1 9.8 Tf [(\) observed between the two strains of the edge )] TJ ET q 12.750 0 0 13.500 310.949 168.002 cm /I166 Do Q BT 323.699 170.702 Td /F1 9.8 Tf [(. This probability depends on the length \()] TJ ET q 9.000 0 0 10.500 499.833 171.002 cm /I168 Do Q BT 508.833 170.702 Td /F1 9.8 Tf [(, in number of )] TJ ET BT 26.250 158.478 Td /F1 9.8 Tf [(nucleotides\) and mutation rate \()] TJ ET q 8.250 0 0 10.500 163.355 157.502 cm /I170 Do Q BT 171.605 158.478 Td /F1 9.8 Tf [(, in number of mutations per nucleotides and per day\) of the considered DNA sequences, and )] TJ ET BT 26.250 145.297 Td /F1 9.8 Tf [(on the period of time elapsed \()] TJ ET q 15.750 0 0 13.500 157.943 142.597 cm /I172 Do Q BT 173.693 145.297 Td /F1 9.8 Tf [(, in days\) between the two strains collection dates. It is then simply derived from the )] TJ ET BT 26.250 131.797 Td /F1 9.8 Tf [(probability mass function of a Binomial distribution with probability )] TJ ET q 8.250 0 0 10.500 312.354 132.097 cm /I174 Do Q BT 320.604 131.797 Td /F1 9.8 Tf [( and )] TJ ET q 24.750 0 0 13.500 342.288 129.097 cm /I176 Do Q BT 367.038 131.797 Td /F1 9.8 Tf [( trials:)] TJ ET q 258.000 0 0 32.250 26.250 89.347 cm /I178 Do Q BT 26.250 72.324 Td /F1 9.8 Tf [(This likelihood can be represented on all edges using a color coding to allow a better assessment of the results \(Fig. 2\).)] TJ ET BT 26.250 52.919 Td /F4 9.8 Tf [(Sequence data)] TJ ET BT 26.250 41.014 Td /F1 9.8 Tf [(Genetic data were used to infer the spatiotemporal spread of the swine-derived influenza A/H1N1 pandemic. 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W>s_ y1Ma6cg8%,H8$r |H;Fvaja0 MehaDh͓&Kʀ2-Uyׇ/}8U槡&m0 `)m졷Gq|kswƘ؅yvyXkK>qYA8O<>L|U`ز^A;MvZVo*?VI5)xUdfZX&.Pg5Cw#k`W(N oERDX;3Le!{b"r*M3( bƎA)H7[:( 4`<[>= e"5Ua =Ezw/*9)-N e91!~MG `яFdm[쩐{-wLv1љKLy8~`j+FNDSlzK KɼH04BLYB7ϐh?| ##d 7Hi &a dGʣ)6O+qiaa5xS59ۤ!sb/Eq!45xx˨f%W"Vp/Q u$)IӮF:qs7=P]7(]$rNPLmjs8EZ`c_ s LB+~^_ql4p,baEa z vhVOґ5OTLsՆ3.XxwcرolҨ Igm :qv*~hM@c#)CR:H?+:0s{+$b+̽h7|S h˰ֱC1ƺި!/Z)O?#x$BGh\fFW ~ ˛ x+4ߜ{(~c3wU?Q+7>Ԭ>paF{sE\tBeU9s~}m~K4#[Wڼ(mwJ>|AuhD,II:c'u4 f9nk@a̗~ +VWE \K67(q;Jңubr=A<>G,&/0_X 9M$Mo5Np3]YhE`nG_Byv‹tDmn߭[Nlۅ-goNo>*_r\pr9z9XDZw;\?у3Y*)%h0Z<.,Y)iq\&qsZw6vәQw\QCxZ[f7t{G+0)k1V]x Ok\ endstream endobj 336 0 obj << /Type /XObject /Subtype /Image /Width 344 /Height 43 /SMask 335 0 R /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 3 /Columns 344 /BitsPerComponent 8>> /ColorSpace /DeviceRGB /BitsPerComponent 8 /Length 66>> stream xàS_U endstream endobj 337 0 obj << /Type /Page /Parent 3 0 R /Annots [ 339 0 R 341 0 R 343 0 R 345 0 R 347 0 R 349 0 R 351 0 R 353 0 R 355 0 R 359 0 R 361 0 R 363 0 R 365 0 R 367 0 R 369 0 R 371 0 R 373 0 R 375 0 R 379 0 R 381 0 R 383 0 R 385 0 R 387 0 R 389 0 R 391 0 R 393 0 R 395 0 R ] /Contents 338 0 R >> endobj 338 0 obj << /Length 26188 >> stream 0.271 0.267 0.267 rg q 15.000 -68.401 577.500 845.401 re W n 0.271 0.267 0.267 rg BT 26.250 767.476 Td /F1 9.8 Tf [(full-length HA segments available from Genbank \( )] TJ ET 0.267 0.267 0.267 rg BT 244.084 767.476 Td /F1 9.8 Tf [([17])] TJ ET 0.271 0.267 0.267 rg BT 260.347 767.476 Td /F1 9.8 Tf [( , http://www.ncbi.nlm.nih.gov/Genbank/index.html\) as of the 26/06/2009. )] TJ ET BT 26.250 755.571 Td /F1 9.8 Tf [(DNA sequences and their annotations \(including sampling dates and locations\) were retrieved and processed using )] TJ ET BT 526.435 755.571 Td /F5 9.8 Tf [(ad hoc)] TJ ET BT 26.250 743.667 Td /F1 9.8 Tf [(scripts in the R language )] TJ ET 0.267 0.267 0.267 rg BT 136.259 743.667 Td /F1 9.8 Tf [([16])] TJ ET 0.271 0.267 0.267 rg BT 152.522 743.667 Td /F1 9.8 Tf [( . Only strains for which collection date and location were available were retained. Duplicates )] TJ ET BT 26.250 731.762 Td /F1 9.8 Tf [(existed for some strains due to different passages, sometimes resulting in slightly different sequences for the same strain. In )] TJ ET BT 26.250 719.857 Td /F1 9.8 Tf [(these cases, significantly shorter sequences were discarded, as well as sequences obtained from amplification in eggs since )] TJ ET BT 26.250 707.952 Td /F1 9.8 Tf [(this method is known to induce additional artificial mutations )] TJ ET 0.267 0.267 0.267 rg BT 291.772 707.952 Td /F1 9.8 Tf [([18])] TJ ET 0.271 0.267 0.267 rg BT 308.035 707.952 Td /F1 9.8 Tf [( .)] TJ ET BT 26.250 688.548 Td /F1 9.8 Tf [(The alignment of all retained sequences was realised using Clustalw )] TJ ET 0.267 0.267 0.267 rg BT 324.288 688.548 Td /F1 9.8 Tf [([19])] TJ ET 0.271 0.267 0.267 rg BT 340.551 688.548 Td /F1 9.8 Tf [( and refined by hand using Jalview )] TJ ET 0.267 0.267 0.267 rg BT 492.836 688.548 Td /F1 9.8 Tf [([20])] TJ ET 0.271 0.267 0.267 rg BT 509.099 688.548 Td /F1 9.8 Tf [( . The final )] TJ ET BT 26.250 676.643 Td /F1 9.8 Tf [(alignment contained 279 sequences of 1668 nucleotides, with collection dates ranging from 30/03/2009 to 18/06/2009. Raw )] TJ ET BT 26.250 664.738 Td /F1 9.8 Tf [(pairwise genetic distances \(in number of differing nucleotides\) were computed using the )] TJ ET BT 407.202 664.738 Td /F5 9.8 Tf [(ape)] TJ ET BT 423.465 664.738 Td /F1 9.8 Tf [( package )] TJ ET 0.267 0.267 0.267 rg BT 465.741 664.738 Td /F1 9.8 Tf [([21])] TJ ET 0.271 0.267 0.267 rg BT 482.004 664.738 Td /F1 9.8 Tf [( for the R software.)] TJ ET BT 26.250 645.333 Td /F1 9.8 Tf [(Flight data was used to assess the role played by air traffic in the dispersal of the pathogen. Passenger flows between countries )] TJ ET BT 26.250 633.429 Td /F1 9.8 Tf [(were compiled from a list of all commercial flights that occurred between 5th May 2008 and 4th April 2009, purchased from OAG )] TJ ET BT 26.250 621.524 Td /F1 9.8 Tf [(\( )] TJ ET 0.267 0.267 0.267 rg BT 32.207 621.524 Td /F1 9.8 Tf [(http://www.oag.com/)] TJ ET 0.271 0.267 0.267 rg BT 120.532 621.524 Td /F1 9.8 Tf [( \). Numbers of passengers between countries were then correlated to the number of inferred )] TJ ET BT 26.250 609.619 Td /F1 9.8 Tf [(transmissions, and tested using the usual Student )] TJ ET BT 244.114 609.619 Td /F5 9.8 Tf [(t)] TJ ET BT 246.824 609.619 Td /F1 9.8 Tf [( -test.)] TJ ET BT 26.250 590.214 Td /F4 9.8 Tf [(Simulated data)] TJ ET BT 26.250 578.310 Td /F1 9.8 Tf [(Individual-based simulations were used to further assess the power of our method to uncover ancestries from outbreak genetic )] TJ ET BT 26.250 566.405 Td /F1 9.8 Tf [(data. All simulations were performed in the R software, using procedures newly implemented in the )] TJ ET BT 455.416 566.405 Td /F5 9.8 Tf [(adegenet)] TJ ET BT 496.073 566.405 Td /F1 9.8 Tf [( package. )] TJ ET BT 26.250 554.500 Td /F1 9.8 Tf [(Datasets were obtained by simulating genealogies of haplotypes evolving stochastically in time and space.)] TJ ET BT 26.250 535.095 Td /F1 9.8 Tf [(Two types of simulations, differing in the process governing the spatial spread of the strains, were performed. The first scheme )] TJ ET BT 26.250 523.191 Td /F1 9.8 Tf [(allowed strains to disperse on a 5-by-5 regular grid according to a random Poisson process, with identical probabilities to move )] TJ ET BT 26.250 511.286 Td /F1 9.8 Tf [(in all directions. This scheme is later referred to as random diffusion. The second type of simulation used a stochastic dispersal )] TJ ET BT 26.250 499.381 Td /F1 9.8 Tf [(based on pre-defined probabilities of new strains to migrate from one location to another. This allowed us to recreate the effect )] TJ ET BT 26.250 487.476 Td /F1 9.8 Tf [(of sources and sinks, )] TJ ET BT 129.200 487.476 Td /F5 9.8 Tf [(i.e.)] TJ ET BT 142.207 487.476 Td /F1 9.8 Tf [( some locations seeding many other locations, including very distant ones, and other locations )] TJ ET BT 26.250 475.572 Td /F1 9.8 Tf [(attracting migration but not seeding other places, respectively. This type of simulation is later referred to as structured dispersal.)] TJ ET BT 26.250 456.167 Td /F1 9.8 Tf [(Because the number of strains grows exponentially in outbreak simulations, the number of haplotypes that need to be handled )] TJ ET BT 26.250 444.262 Td /F1 9.8 Tf [(rapidly becomes intractable. This issue can be solved by randomly discarding a sufficient number of strains at each generation, )] TJ ET BT 26.250 432.357 Td /F1 9.8 Tf [(so that the number of strains never exceeds a given threshold. The advantage of this approach is that the average pairwise )] TJ ET BT 26.250 420.453 Td /F1 9.8 Tf [(genetic differentiation between strains should not differ statistically between the sample and the population.)] TJ ET BT 26.250 401.048 Td /F1 9.8 Tf [(Another limiting factor for simulating outbreaks relates to the number of simulated generations. For instance, swine-derived )] TJ ET BT 26.250 389.143 Td /F1 9.8 Tf [(influenza A/H1N1 virus typically has a short generation time \(1.91 days, IC )] TJ ET BT 349.755 387.079 Td /F1 8.7 Tf [(95%)] TJ ET BT 367.097 389.143 Td /F1 9.8 Tf [( =[1.30-2.71]; )] TJ ET 0.267 0.267 0.267 rg BT 427.537 389.143 Td /F1 9.8 Tf [([22])] TJ ET 0.271 0.267 0.267 rg BT 443.800 389.143 Td /F1 9.8 Tf [( \), which would make realistic )] TJ ET BT 26.250 377.238 Td /F1 9.8 Tf [(simulation time-consuming. As an alternative, we simulated haplotypes on fewer generations \(10 on average\), using a larger )] TJ ET BT 26.250 365.334 Td /F1 9.8 Tf [(mutation rate. The average level of genetic differentiation among simulated strains was of the same order of magnitude as that )] TJ ET BT 26.250 353.429 Td /F1 9.8 Tf [(of the analyzed influenza sequences.)] TJ ET BT 26.250 334.024 Td /F1 9.8 Tf [(For each simulation scheme \(random diffusion and structured dispersal\), ten datasets were simulated, each of which gave rise )] TJ ET BT 26.250 322.119 Td /F1 9.8 Tf [(to ten samples of 300 haplotypes.)] TJ ET BT 26.250 285.517 Td /F4 12.0 Tf [(Results)] TJ ET BT 26.250 265.563 Td /F1 9.8 Tf [(To evaluate the performance of the )] TJ ET BT 180.709 265.563 Td /F5 9.8 Tf [(SeqTrack)] TJ ET BT 222.430 265.563 Td /F1 9.8 Tf [( algorithm we analyzed simulated data. Outbreak data were generated using two )] TJ ET BT 26.250 253.658 Td /F1 9.8 Tf [(different spatial models. In the first set of simulations, we assumed a random uniform diffusion of strains in space. These )] TJ ET BT 26.250 241.753 Td /F1 9.8 Tf [(simulations were complemented by a second set of simulations run under structured dispersal, where strains had variable )] TJ ET BT 26.250 229.848 Td /F1 9.8 Tf [(probabilities of seeding different locations. This allowed for a source and sink dynamics more representative of actual )] TJ ET BT 26.250 217.944 Td /F1 9.8 Tf [(outbreaks. Analysis of the simulations indicated that the true ancestral haplotype \(100% identity\) was successfully retrieved in )] TJ ET BT 26.250 206.039 Td /F1 9.8 Tf [(77% of cases on average throughout all simulations \(CI )] TJ ET BT 267.943 203.975 Td /F1 8.7 Tf [(95%)] TJ ET BT 285.285 206.039 Td /F1 9.8 Tf [( =[77%-78%]; Fig. 2\). The correct location was inferred more )] TJ ET BT 26.250 194.134 Td /F1 9.8 Tf [(frequently under source and sink dynamics than under homogeneous dispersal \(79% and 56%, respectively; t=-22.11, df=237, )] TJ ET BT 26.250 182.229 Td /F1 9.8 Tf [(p<2e-16; Fig. 2\).)] TJ ET 0.965 0.965 0.965 rg 26.250 -68.401 555.000 240.750 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 172.349 m 581.250 172.349 l 581.250 171.599 l 26.250 171.599 l f q 225.000 0 0 225.000 35.250 -62.401 cm /I180 Do Q q 35.250 -68.401 537.000 0.000 re W n Q Q q 15.000 -68.401 577.500 845.401 re W n 0.271 0.267 0.267 rg BT 26.250 767.476 Td /F1 9.8 Tf [(full-length HA segments available from Genbank \( )] TJ ET 0.267 0.267 0.267 rg BT 244.084 767.476 Td /F1 9.8 Tf [([17])] TJ ET 0.271 0.267 0.267 rg BT 260.347 767.476 Td /F1 9.8 Tf [( , http://www.ncbi.nlm.nih.gov/Genbank/index.html\) as of the 26/06/2009. )] TJ ET BT 26.250 755.571 Td /F1 9.8 Tf [(DNA sequences and their annotations \(including sampling dates and locations\) were retrieved and processed using )] TJ ET BT 526.435 755.571 Td /F5 9.8 Tf [(ad hoc)] TJ ET BT 26.250 743.667 Td /F1 9.8 Tf [(scripts in the R language )] TJ ET 0.267 0.267 0.267 rg BT 136.259 743.667 Td /F1 9.8 Tf [([16])] TJ ET 0.271 0.267 0.267 rg BT 152.522 743.667 Td /F1 9.8 Tf [( . Only strains for which collection date and location were available were retained. Duplicates )] TJ ET BT 26.250 731.762 Td /F1 9.8 Tf [(existed for some strains due to different passages, sometimes resulting in slightly different sequences for the same strain. In )] TJ ET BT 26.250 719.857 Td /F1 9.8 Tf [(these cases, significantly shorter sequences were discarded, as well as sequences obtained from amplification in eggs since )] TJ ET BT 26.250 707.952 Td /F1 9.8 Tf [(this method is known to induce additional artificial mutations )] TJ ET 0.267 0.267 0.267 rg BT 291.772 707.952 Td /F1 9.8 Tf [([18])] TJ ET 0.271 0.267 0.267 rg BT 308.035 707.952 Td /F1 9.8 Tf [( .)] TJ ET BT 26.250 688.548 Td /F1 9.8 Tf [(The alignment of all retained sequences was realised using Clustalw )] TJ ET 0.267 0.267 0.267 rg BT 324.288 688.548 Td /F1 9.8 Tf [([19])] TJ ET 0.271 0.267 0.267 rg BT 340.551 688.548 Td /F1 9.8 Tf [( and refined by hand using Jalview )] TJ ET 0.267 0.267 0.267 rg BT 492.836 688.548 Td /F1 9.8 Tf [([20])] TJ ET 0.271 0.267 0.267 rg BT 509.099 688.548 Td /F1 9.8 Tf [( . The final )] TJ ET BT 26.250 676.643 Td /F1 9.8 Tf [(alignment contained 279 sequences of 1668 nucleotides, with collection dates ranging from 30/03/2009 to 18/06/2009. Raw )] TJ ET BT 26.250 664.738 Td /F1 9.8 Tf [(pairwise genetic distances \(in number of differing nucleotides\) were computed using the )] TJ ET BT 407.202 664.738 Td /F5 9.8 Tf [(ape)] TJ ET BT 423.465 664.738 Td /F1 9.8 Tf [( package )] TJ ET 0.267 0.267 0.267 rg BT 465.741 664.738 Td /F1 9.8 Tf [([21])] TJ ET 0.271 0.267 0.267 rg BT 482.004 664.738 Td /F1 9.8 Tf [( for the R software.)] TJ ET BT 26.250 645.333 Td /F1 9.8 Tf [(Flight data was used to assess the role played by air traffic in the dispersal of the pathogen. Passenger flows between countries )] TJ ET BT 26.250 633.429 Td /F1 9.8 Tf [(were compiled from a list of all commercial flights that occurred between 5th May 2008 and 4th April 2009, purchased from OAG )] TJ ET BT 26.250 621.524 Td /F1 9.8 Tf [(\( )] TJ ET 0.267 0.267 0.267 rg BT 32.207 621.524 Td /F1 9.8 Tf [(http://www.oag.com/)] TJ ET 0.271 0.267 0.267 rg BT 120.532 621.524 Td /F1 9.8 Tf [( \). Numbers of passengers between countries were then correlated to the number of inferred )] TJ ET BT 26.250 609.619 Td /F1 9.8 Tf [(transmissions, and tested using the usual Student )] TJ ET BT 244.114 609.619 Td /F5 9.8 Tf [(t)] TJ ET BT 246.824 609.619 Td /F1 9.8 Tf [( -test.)] TJ ET BT 26.250 590.214 Td /F4 9.8 Tf [(Simulated data)] TJ ET BT 26.250 578.310 Td /F1 9.8 Tf [(Individual-based simulations were used to further assess the power of our method to uncover ancestries from outbreak genetic )] TJ ET BT 26.250 566.405 Td /F1 9.8 Tf [(data. All simulations were performed in the R software, using procedures newly implemented in the )] TJ ET BT 455.416 566.405 Td /F5 9.8 Tf [(adegenet)] TJ ET BT 496.073 566.405 Td /F1 9.8 Tf [( package. )] TJ ET BT 26.250 554.500 Td /F1 9.8 Tf [(Datasets were obtained by simulating genealogies of haplotypes evolving stochastically in time and space.)] TJ ET BT 26.250 535.095 Td /F1 9.8 Tf [(Two types of simulations, differing in the process governing the spatial spread of the strains, were performed. The first scheme )] TJ ET BT 26.250 523.191 Td /F1 9.8 Tf [(allowed strains to disperse on a 5-by-5 regular grid according to a random Poisson process, with identical probabilities to move )] TJ ET BT 26.250 511.286 Td /F1 9.8 Tf [(in all directions. This scheme is later referred to as random diffusion. The second type of simulation used a stochastic dispersal )] TJ ET BT 26.250 499.381 Td /F1 9.8 Tf [(based on pre-defined probabilities of new strains to migrate from one location to another. This allowed us to recreate the effect )] TJ ET BT 26.250 487.476 Td /F1 9.8 Tf [(of sources and sinks, )] TJ ET BT 129.200 487.476 Td /F5 9.8 Tf [(i.e.)] TJ ET BT 142.207 487.476 Td /F1 9.8 Tf [( some locations seeding many other locations, including very distant ones, and other locations )] TJ ET BT 26.250 475.572 Td /F1 9.8 Tf [(attracting migration but not seeding other places, respectively. This type of simulation is later referred to as structured dispersal.)] TJ ET BT 26.250 456.167 Td /F1 9.8 Tf [(Because the number of strains grows exponentially in outbreak simulations, the number of haplotypes that need to be handled )] TJ ET BT 26.250 444.262 Td /F1 9.8 Tf [(rapidly becomes intractable. This issue can be solved by randomly discarding a sufficient number of strains at each generation, )] TJ ET BT 26.250 432.357 Td /F1 9.8 Tf [(so that the number of strains never exceeds a given threshold. The advantage of this approach is that the average pairwise )] TJ ET BT 26.250 420.453 Td /F1 9.8 Tf [(genetic differentiation between strains should not differ statistically between the sample and the population.)] TJ ET BT 26.250 401.048 Td /F1 9.8 Tf [(Another limiting factor for simulating outbreaks relates to the number of simulated generations. For instance, swine-derived )] TJ ET BT 26.250 389.143 Td /F1 9.8 Tf [(influenza A/H1N1 virus typically has a short generation time \(1.91 days, IC )] TJ ET BT 349.755 387.079 Td /F1 8.7 Tf [(95%)] TJ ET BT 367.097 389.143 Td /F1 9.8 Tf [( =[1.30-2.71]; )] TJ ET 0.267 0.267 0.267 rg BT 427.537 389.143 Td /F1 9.8 Tf [([22])] TJ ET 0.271 0.267 0.267 rg BT 443.800 389.143 Td /F1 9.8 Tf [( \), which would make realistic )] TJ ET BT 26.250 377.238 Td /F1 9.8 Tf [(simulation time-consuming. As an alternative, we simulated haplotypes on fewer generations \(10 on average\), using a larger )] TJ ET BT 26.250 365.334 Td /F1 9.8 Tf [(mutation rate. The average level of genetic differentiation among simulated strains was of the same order of magnitude as that )] TJ ET BT 26.250 353.429 Td /F1 9.8 Tf [(of the analyzed influenza sequences.)] TJ ET BT 26.250 334.024 Td /F1 9.8 Tf [(For each simulation scheme \(random diffusion and structured dispersal\), ten datasets were simulated, each of which gave rise )] TJ ET BT 26.250 322.119 Td /F1 9.8 Tf [(to ten samples of 300 haplotypes.)] TJ ET BT 26.250 285.517 Td /F4 12.0 Tf [(Results)] TJ ET BT 26.250 265.563 Td /F1 9.8 Tf [(To evaluate the performance of the )] TJ ET BT 180.709 265.563 Td /F5 9.8 Tf [(SeqTrack)] TJ ET BT 222.430 265.563 Td /F1 9.8 Tf [( algorithm we analyzed simulated data. Outbreak data were generated using two )] TJ ET BT 26.250 253.658 Td /F1 9.8 Tf [(different spatial models. In the first set of simulations, we assumed a random uniform diffusion of strains in space. These )] TJ ET BT 26.250 241.753 Td /F1 9.8 Tf [(simulations were complemented by a second set of simulations run under structured dispersal, where strains had variable )] TJ ET BT 26.250 229.848 Td /F1 9.8 Tf [(probabilities of seeding different locations. This allowed for a source and sink dynamics more representative of actual )] TJ ET BT 26.250 217.944 Td /F1 9.8 Tf [(outbreaks. Analysis of the simulations indicated that the true ancestral haplotype \(100% identity\) was successfully retrieved in )] TJ ET BT 26.250 206.039 Td /F1 9.8 Tf [(77% of cases on average throughout all simulations \(CI )] TJ ET BT 267.943 203.975 Td /F1 8.7 Tf [(95%)] TJ ET BT 285.285 206.039 Td /F1 9.8 Tf [( =[77%-78%]; Fig. 2\). The correct location was inferred more )] TJ ET BT 26.250 194.134 Td /F1 9.8 Tf [(frequently under source and sink dynamics than under homogeneous dispersal \(79% and 56%, respectively; t=-22.11, df=237, )] TJ ET BT 26.250 182.229 Td /F1 9.8 Tf [(p<2e-16; Fig. 2\).)] TJ ET 0.965 0.965 0.965 rg 26.250 -68.401 555.000 240.750 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 172.349 m 581.250 172.349 l 581.250 171.599 l 26.250 171.599 l f q 225.000 0 0 225.000 35.250 -62.401 cm /I182 Do Q q 35.250 -68.401 537.000 0.000 re W n Q Q q 15.000 -68.401 577.500 845.401 re W n 0.271 0.267 0.267 rg BT 26.250 767.476 Td /F1 9.8 Tf [(full-length HA segments available from Genbank \( )] TJ ET 0.267 0.267 0.267 rg BT 244.084 767.476 Td /F1 9.8 Tf [([17])] TJ ET 0.271 0.267 0.267 rg BT 260.347 767.476 Td /F1 9.8 Tf [( , http://www.ncbi.nlm.nih.gov/Genbank/index.html\) as of the 26/06/2009. )] TJ ET BT 26.250 755.571 Td /F1 9.8 Tf [(DNA sequences and their annotations \(including sampling dates and locations\) were retrieved and processed using )] TJ ET BT 526.435 755.571 Td /F5 9.8 Tf [(ad hoc)] TJ ET BT 26.250 743.667 Td /F1 9.8 Tf [(scripts in the R language )] TJ ET 0.267 0.267 0.267 rg BT 136.259 743.667 Td /F1 9.8 Tf [([16])] TJ ET 0.271 0.267 0.267 rg BT 152.522 743.667 Td /F1 9.8 Tf [( . Only strains for which collection date and location were available were retained. Duplicates )] TJ ET BT 26.250 731.762 Td /F1 9.8 Tf [(existed for some strains due to different passages, sometimes resulting in slightly different sequences for the same strain. In )] TJ ET BT 26.250 719.857 Td /F1 9.8 Tf [(these cases, significantly shorter sequences were discarded, as well as sequences obtained from amplification in eggs since )] TJ ET BT 26.250 707.952 Td /F1 9.8 Tf [(this method is known to induce additional artificial mutations )] TJ ET 0.267 0.267 0.267 rg BT 291.772 707.952 Td /F1 9.8 Tf [([18])] TJ ET 0.271 0.267 0.267 rg BT 308.035 707.952 Td /F1 9.8 Tf [( .)] TJ ET BT 26.250 688.548 Td /F1 9.8 Tf [(The alignment of all retained sequences was realised using Clustalw )] TJ ET 0.267 0.267 0.267 rg BT 324.288 688.548 Td /F1 9.8 Tf [([19])] TJ ET 0.271 0.267 0.267 rg BT 340.551 688.548 Td /F1 9.8 Tf [( and refined by hand using Jalview )] TJ ET 0.267 0.267 0.267 rg BT 492.836 688.548 Td /F1 9.8 Tf [([20])] TJ ET 0.271 0.267 0.267 rg BT 509.099 688.548 Td /F1 9.8 Tf [( . The final )] TJ ET BT 26.250 676.643 Td /F1 9.8 Tf [(alignment contained 279 sequences of 1668 nucleotides, with collection dates ranging from 30/03/2009 to 18/06/2009. Raw )] TJ ET BT 26.250 664.738 Td /F1 9.8 Tf [(pairwise genetic distances \(in number of differing nucleotides\) were computed using the )] TJ ET BT 407.202 664.738 Td /F5 9.8 Tf [(ape)] TJ ET BT 423.465 664.738 Td /F1 9.8 Tf [( package )] TJ ET 0.267 0.267 0.267 rg BT 465.741 664.738 Td /F1 9.8 Tf [([21])] TJ ET 0.271 0.267 0.267 rg BT 482.004 664.738 Td /F1 9.8 Tf [( for the R software.)] TJ ET BT 26.250 645.333 Td /F1 9.8 Tf [(Flight data was used to assess the role played by air traffic in the dispersal of the pathogen. Passenger flows between countries )] TJ ET BT 26.250 633.429 Td /F1 9.8 Tf [(were compiled from a list of all commercial flights that occurred between 5th May 2008 and 4th April 2009, purchased from OAG )] TJ ET BT 26.250 621.524 Td /F1 9.8 Tf [(\( )] TJ ET 0.267 0.267 0.267 rg BT 32.207 621.524 Td /F1 9.8 Tf [(http://www.oag.com/)] TJ ET 0.271 0.267 0.267 rg BT 120.532 621.524 Td /F1 9.8 Tf [( \). Numbers of passengers between countries were then correlated to the number of inferred )] TJ ET BT 26.250 609.619 Td /F1 9.8 Tf [(transmissions, and tested using the usual Student )] TJ ET BT 244.114 609.619 Td /F5 9.8 Tf [(t)] TJ ET BT 246.824 609.619 Td /F1 9.8 Tf [( -test.)] TJ ET BT 26.250 590.214 Td /F4 9.8 Tf [(Simulated data)] TJ ET BT 26.250 578.310 Td /F1 9.8 Tf [(Individual-based simulations were used to further assess the power of our method to uncover ancestries from outbreak genetic )] TJ ET BT 26.250 566.405 Td /F1 9.8 Tf [(data. All simulations were performed in the R software, using procedures newly implemented in the )] TJ ET BT 455.416 566.405 Td /F5 9.8 Tf [(adegenet)] TJ ET BT 496.073 566.405 Td /F1 9.8 Tf [( package. )] TJ ET BT 26.250 554.500 Td /F1 9.8 Tf [(Datasets were obtained by simulating genealogies of haplotypes evolving stochastically in time and space.)] TJ ET BT 26.250 535.095 Td /F1 9.8 Tf [(Two types of simulations, differing in the process governing the spatial spread of the strains, were performed. The first scheme )] TJ ET BT 26.250 523.191 Td /F1 9.8 Tf [(allowed strains to disperse on a 5-by-5 regular grid according to a random Poisson process, with identical probabilities to move )] TJ ET BT 26.250 511.286 Td /F1 9.8 Tf [(in all directions. This scheme is later referred to as random diffusion. The second type of simulation used a stochastic dispersal )] TJ ET BT 26.250 499.381 Td /F1 9.8 Tf [(based on pre-defined probabilities of new strains to migrate from one location to another. This allowed us to recreate the effect )] TJ ET BT 26.250 487.476 Td /F1 9.8 Tf [(of sources and sinks, )] TJ ET BT 129.200 487.476 Td /F5 9.8 Tf [(i.e.)] TJ ET BT 142.207 487.476 Td /F1 9.8 Tf [( some locations seeding many other locations, including very distant ones, and other locations )] TJ ET BT 26.250 475.572 Td /F1 9.8 Tf [(attracting migration but not seeding other places, respectively. This type of simulation is later referred to as structured dispersal.)] TJ ET BT 26.250 456.167 Td /F1 9.8 Tf [(Because the number of strains grows exponentially in outbreak simulations, the number of haplotypes that need to be handled )] TJ ET BT 26.250 444.262 Td /F1 9.8 Tf [(rapidly becomes intractable. This issue can be solved by randomly discarding a sufficient number of strains at each generation, )] TJ ET BT 26.250 432.357 Td /F1 9.8 Tf [(so that the number of strains never exceeds a given threshold. The advantage of this approach is that the average pairwise )] TJ ET BT 26.250 420.453 Td /F1 9.8 Tf [(genetic differentiation between strains should not differ statistically between the sample and the population.)] TJ ET BT 26.250 401.048 Td /F1 9.8 Tf [(Another limiting factor for simulating outbreaks relates to the number of simulated generations. For instance, swine-derived )] TJ ET BT 26.250 389.143 Td /F1 9.8 Tf [(influenza A/H1N1 virus typically has a short generation time \(1.91 days, IC )] TJ ET BT 349.755 387.079 Td /F1 8.7 Tf [(95%)] TJ ET BT 367.097 389.143 Td /F1 9.8 Tf [( =[1.30-2.71]; )] TJ ET 0.267 0.267 0.267 rg BT 427.537 389.143 Td /F1 9.8 Tf [([22])] TJ ET 0.271 0.267 0.267 rg BT 443.800 389.143 Td /F1 9.8 Tf [( \), which would make realistic )] TJ ET BT 26.250 377.238 Td /F1 9.8 Tf [(simulation time-consuming. As an alternative, we simulated haplotypes on fewer generations \(10 on average\), using a larger )] TJ ET BT 26.250 365.334 Td /F1 9.8 Tf [(mutation rate. The average level of genetic differentiation among simulated strains was of the same order of magnitude as that )] TJ ET BT 26.250 353.429 Td /F1 9.8 Tf [(of the analyzed influenza sequences.)] TJ ET BT 26.250 334.024 Td /F1 9.8 Tf [(For each simulation scheme \(random diffusion and structured dispersal\), ten datasets were simulated, each of which gave rise )] TJ ET BT 26.250 322.119 Td /F1 9.8 Tf [(to ten samples of 300 haplotypes.)] TJ ET BT 26.250 285.517 Td /F4 12.0 Tf [(Results)] TJ ET BT 26.250 265.563 Td /F1 9.8 Tf [(To evaluate the performance of the )] TJ ET BT 180.709 265.563 Td /F5 9.8 Tf [(SeqTrack)] TJ ET BT 222.430 265.563 Td /F1 9.8 Tf [( algorithm we analyzed simulated data. Outbreak data were generated using two )] TJ ET BT 26.250 253.658 Td /F1 9.8 Tf [(different spatial models. In the first set of simulations, we assumed a random uniform diffusion of strains in space. These )] TJ ET BT 26.250 241.753 Td /F1 9.8 Tf [(simulations were complemented by a second set of simulations run under structured dispersal, where strains had variable )] TJ ET BT 26.250 229.848 Td /F1 9.8 Tf [(probabilities of seeding different locations. This allowed for a source and sink dynamics more representative of actual )] TJ ET BT 26.250 217.944 Td /F1 9.8 Tf [(outbreaks. Analysis of the simulations indicated that the true ancestral haplotype \(100% identity\) was successfully retrieved in )] TJ ET BT 26.250 206.039 Td /F1 9.8 Tf [(77% of cases on average throughout all simulations \(CI )] TJ ET BT 267.943 203.975 Td /F1 8.7 Tf [(95%)] TJ ET BT 285.285 206.039 Td /F1 9.8 Tf [( =[77%-78%]; Fig. 2\). The correct location was inferred more )] TJ ET BT 26.250 194.134 Td /F1 9.8 Tf [(frequently under source and sink dynamics than under homogeneous dispersal \(79% and 56%, respectively; t=-22.11, df=237, )] TJ ET BT 26.250 182.229 Td /F1 9.8 Tf [(p<2e-16; Fig. 2\).)] TJ ET 0.965 0.965 0.965 rg 26.250 -68.401 555.000 240.750 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 172.349 m 581.250 172.349 l 581.250 171.599 l 26.250 171.599 l f q 225.000 0 0 225.000 35.250 -62.401 cm /I184 Do Q q 35.250 -68.401 537.000 0.000 re W n Q Q q 225.000 0 0 225.000 35.250 -62.401 cm /I186 Do Q q 0.000 0.000 0.000 rg BT 291.710 19.825 Td /F1 11.0 Tf [(3)] TJ ET BT 25.000 19.825 Td /F1 11.0 Tf [(PLOS Currents Influenza)] TJ ET Q endstream endobj 339 0 obj << /Type /Annot /Subtype /Link /A 340 0 R /Border [0 0 0] /H /I /Rect [ 244.0845 766.5743 260.3475 776.4950 ] >> endobj 340 0 obj << /Type /Action >> endobj 341 0 obj << /Type /Annot /Subtype /Link /A 342 0 R /Border [0 0 0] /H /I /Rect [ 136.2593 742.7648 152.5223 752.6854 ] >> endobj 342 0 obj << /Type /Action >> endobj 343 0 obj << /Type /Annot /Subtype /Link /A 344 0 R /Border [0 0 0] /H /I /Rect [ 291.7717 707.0506 308.0347 716.9712 ] >> endobj 344 0 obj << /Type /Action >> endobj 345 0 obj << /Type /Annot /Subtype /Link /A 346 0 R /Border [0 0 0] /H /I /Rect [ 324.2880 687.6458 340.5510 697.5665 ] >> endobj 346 0 obj << /Type /Action >> endobj 347 0 obj << /Type /Annot /Subtype /Link /A 348 0 R /Border [0 0 0] /H /I /Rect [ 492.8362 687.6458 509.0992 697.5665 ] >> endobj 348 0 obj << /Type /Action >> endobj 349 0 obj << /Type /Annot /Subtype /Link /A 350 0 R /Border [0 0 0] /H /I /Rect [ 465.7410 663.8363 482.0040 673.7569 ] >> endobj 350 0 obj << /Type /Action >> endobj 351 0 obj << /Type /Annot /Subtype /Link /A 352 0 R /Border [0 0 0] /H /I /Rect [ 32.2073 620.6221 120.5325 630.5427 ] >> endobj 352 0 obj << /Type /Action /S /URI /URI (http://www.oag.com/) >> endobj 353 0 obj << /Type /Annot /Subtype /Link /A 354 0 R /Border [0 0 0] /H /I /Rect [ 427.5373 388.2413 443.8003 398.1620 ] >> endobj 354 0 obj << /Type /Action >> endobj 355 0 obj << /Type /Annot /Subtype /Link /A 356 0 R /Border [0 0 0] /H /I /Rect [ 35.2500 -62.4015 260.2500 162.5985 ] >> endobj 356 0 obj << /Type /Action /S /URI /URI (http://currents.plos.org/influenza/files/2009/08/figure3.png) >> endobj 357 0 obj << /Type /XObject /Subtype /Image /Width 300 /Height 300 /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 1 /Columns 300 /BitsPerComponent 8>> /ColorSpace /DeviceGray /BitsPerComponent 8 /Length 629>> stream xA 0 =fy9뀟\E endstream endobj 358 0 obj << /Type /XObject /Subtype /Image /Width 300 /Height 300 /SMask 357 0 R /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 3 /Columns 300 /BitsPerComponent 8>> /ColorSpace /DeviceRGB /BitsPerComponent 8 /Length 15269>> stream xyXWτ5l FPV KݵjU]W\^XժZK_׶źałE E@d@ ,!!b0L&p뗙}fnd&a Jw2A 0jO@:+o>H/jm@@ (2սPPPt,hc JaP FX :((jG%hsфQ5m d4hGt,hGt,hGi9&((lG t1йMAK(((:hGt,hGt,hG!@1@; cA; cA; Q(( Q(( Qt ЎBAXЎBAXjw$В"ИVA0%$@; cA; cA;Jd4hGt,(at%gddn1{7@1~L Yثܱcdž{+p\:ݶ1 8pYl4NݣƘ`k.&˂҉(LrVG1 {Ǐ+++;̄B@a݌B @y="d4vT,ϟ?޾>So!- qHHpvٳgaaa}qƍMMMVVV*B2xQWGu  OOOKKK?D dB,V&*pvom*= m4ꨍ `ƍ .^H$vJdPa QJܧOaÆi2&9aqqĥuLΝK![aVL@T\.ꫯVZHMM3gGE"MXXX ɫ<]YA`?(MHp&Ld Nݎ/={X[[wPLˋB)Lrꫣ(Mm{-mצ tQX,rjAq'D|===vZk0U 5(:t9@HpQ(aFFFO9 %2d=tƥ<05'..N糂 0( 04L֟ЎB0 e\hGu| 95(^pA糂 VwZ8DёR7\(Zb9sNU7DW0 N0,]]Ɂ u\sjiJi2Su޹>@cn 7ZQЎ P\.~dd$B;Kuʍ׏S muT1#zAqR gwU dY]V&R+ Q:J*++a lӒ]]Auh9phGeD]shG(k)d=qq mwuwQhnnwf͚&2by 4MG-CSuѣGvT_| . 6b177W7 Qdhߎʱ%װQm9֮Άhcǎ%HjkkGFF_OѰtRoؠynv֭[ҥ V\499yԩ:R ˎbDIꊮc3X[[h u& ֎Y[[@;J XYYhRoؠynv{U-⼣z@;J'gc3TUU%&&j vjnӎ:?ZjN-`?y@ `xۇ,LV__"T':YSr@a߭&R+`hKK Ў(>o붽F:rkse#e%/;oeeEGvTQ111䠮:6V r椙;wTe;ˎt՜Z.]ּs}B@QIEI X>wƿ7W15===il!4b8---<<zbҎZ[[C;J***޽;e]W6/\af$>zW^׊Q;*fϞ/Zdҥr\jxbMM&9+]` |JA?lj  BMϙt=90l K:ϟGEE9~Ŗ&V‚)& pvv0aVP+[kov ^1cBjEQݻw߿۷WXadddii:7& 8QЎv(ccc]W5G8D|477WLCd ^?3c\D"tww^t꧄> +уKѷvrr҆EwGqrrJHHظq_R__EŀD"%Co߾Ўv555A" 9;r5VG@ڜ꺭-M 6RiVVP(tvvW1ΝK,\㷞6TRT s-{>k, $>|wFnD嫤u`a_rIH#n u;4o޼ {{wVWW޽7ڳx@ǮC v\[iÛ x<^TTV NhZnn.9gNhii@ݎ4裏>?nܸQwNkGݲ#'_2)FW\Z>83gwZlZN=zͳD}ahuy6P(at "i'$͙PQQ1Ęu%q^^CO~J Rȇ511ٽ{X,njj111QLCd h}ѹW 8ګ2[ltQHw/0B[`kV΋f/Ҽ'MM;ry<."C+u]G"WHukf# (Gu1z?R"R+Jep%_]SMhcޙs3FtW`D[U~khGΚ'_+ ` @PLJ47{6zܸwzK\uCHߐG'n8Z 2"|rd zSh>jߋLMM 2dȐ0,%%e׏K/<MLjHg7ީcw~6lCCå˗Μ:sw1x G_`tݨA)S&D>@7]@lvd8aϟ??Ǎy5#AXxN* ##iM 5N1NjGX[[Ot0] |[6n&M6OVt -7dhAAKW~)jo-7 (ۏzv,j١F‰nƍl0BEEů~=S}&-F}쓏.>h4qꈩk)TQm֮̎?|d `t<oE\,D~m̙֎֞pt?0 ԐUu뵭.b9e昙>>>և| . 6@;a8Ƶ֯>)w^^u;| ,:lw67l~ɍ߬ {u h]]<`^KqGuyhޓQ q+q='mF3P ]OB:zfG$?y!~sїbk*@Q]t/̈c^5F V;wٳJ !c0<40$DWOgv<455ru:_rb bBs+x v̎Wtt4ޕcBBj#g (m>PJvW@!Q ! 1++KEI (u1iGA;JD"ѓ'OxdXvTo֓DWױ,,,<==Z :FRsjzv<_W+JRױ t"Hb.I&AvԐ((9ֳiu.Q*vi 2V(c\P(|IddP=ϕذaPE39AV;jff{4__߄mXGhGUmcaa1h ]ׂP-((`W)?lXG?~ٳg;+@HII7n\=VXqv#w=x 11144MH mf,C Ú?!u_[D"A2WիWd2TjjjZVV"˛_OSSv sÙ={^ެ]t7|caaeb"olsέ\R1qQQѵkduuu<mƚuǣC[YY)eH@zANcfP. 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VbXgoy<UCJJ@ hii),,Jfׯ8q㙚*&ŕaY=YM>۷oذW^2,22rΝ z ***fϞӌ_~СC{챳px޽/;pVPUUdɒ@H߿fРA$33sŊϞ={ɓ'݉+V;vlrr?b۽999nݺuرO?-%%eIǏݻwa>Ғg-]433ĉ[l>|x.]hE͛[o=zh߾}+VիWsssxxxbb" BaLL֭[G6mڰan޼yQ[[[mԐ< ?(:nܸu?󄄄Ww999D7n466geepMެׯϙ3gݺu%%%O޼y_|4vXD"¤Rbb /^5Z|yhhH$>}P(۷ڵkcbbRRRNڵk׶mے 0hРI&oW\5jͦMlrȑtAԭ B |||֬YxϜ93((($$ADFF˗/,hG_[777… `ѢEfffPaXcc @&OQL8qƍ @Hlccf; 0L&q\H$H>|0tБ#G`ff~J"J;w?~<QBFb dAlmmd2P(ҥ\\܂ ԭW5,,,CD" ݻ{nooYfq\")x]d 5330W^{޷o_eeH$D-^e˖SN&M0l񙙙D∈k׮[X阧ˎ5j͚5Æ ۴ia/ӧe2D"ڵkהMWka}Ӌ-[p-[o޼̟?.---66%::0\f͚ݻw;w.>>|ZҥK|ܹs,Y2dȐSNѣG:ujСDbz 0___.((a 2:͛7O<:͝;wϟ(DWױW\:MvvԩSQtoaz{F*vUE𰱱!2d2Y^^^Uy⅑8rVVV^A ެYt5wGiޝ/)`GPP(b_(mһ;_އvQ( Q{AQڤw vJ-(P:4 ~I~yZQhGt,hGi hGiޝ/)>ЎBXЎ,6Ў&;_S}hhGұYl7 Mzw`ЎB; cA;J`o @;J|NvJǂvf@/v6/C ?f[ endstream endobj 401 0 obj << /Type /Page /Parent 3 0 R /Annots [ 403 0 R 405 0 R 409 0 R 411 0 R 413 0 R 415 0 R 417 0 R 419 0 R 421 0 R 423 0 R 427 0 R 429 0 R 431 0 R 433 0 R 435 0 R 437 0 R 439 0 R 441 0 R 445 0 R 447 0 R 449 0 R 451 0 R 453 0 R 455 0 R ] /Contents 402 0 R >> endobj 402 0 obj << /Length 23401 >> stream q 15.000 21.864 577.500 755.136 re W n 0.965 0.965 0.965 rg 26.250 730.777 555.000 46.223 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 730.777 m 581.250 730.777 l 581.250 731.527 l 26.250 731.527 l f q 35.250 742.027 537.000 34.973 re W n 0.271 0.267 0.267 rg BT 35.250 766.011 Td /F4 9.8 Tf [(Figure 2. Results from simulation data.)] TJ ET BT 215.128 766.011 Td /F1 9.8 Tf [( The proportion of correct assignments for haplotypes and locations are )] TJ ET BT 35.250 752.275 Td /F1 9.8 Tf [(represented as boxplots.)] TJ ET Q BT 26.250 713.754 Td /F1 9.8 Tf [(Having tested that the method satisfactorily assigned the correct ancestral locations on simulated data, we applied the )] TJ ET BT 537.286 713.754 Td /F5 9.8 Tf [(SeqTrack)] TJ ET BT 26.250 701.849 Td /F1 9.8 Tf [(algorithm to a dataset of 279 near-complete hemagglutinin \(HA\) sequences collected between the 3 )] TJ ET BT 458.711 705.737 Td /F1 8.7 Tf [(rd)] TJ ET BT 466.416 701.849 Td /F1 9.8 Tf [( of March and the 18 )] TJ ET BT 558.553 705.737 Td /F1 8.7 Tf [(th)] TJ ET BT 565.781 701.849 Td /F1 9.8 Tf [( of )] TJ ET BT 26.250 689.944 Td /F1 9.8 Tf [(June 2009. While no sequences are available for the first confirmed cases \(La Gloria, 15 )] TJ ET BT 409.922 693.832 Td /F1 8.7 Tf [(th)] TJ ET BT 417.150 689.944 Td /F1 9.8 Tf [( February; )] TJ ET 0.267 0.267 0.267 rg BT 464.292 689.944 Td /F1 9.8 Tf [([22])] TJ ET 0.271 0.267 0.267 rg BT 480.555 689.944 Td /F1 9.8 Tf [( \), the time window )] TJ ET BT 26.250 678.039 Td /F1 9.8 Tf [(defined by the collection dates extends from the early stages of the outbreak to the global pandemic, which was officially )] TJ ET BT 26.250 666.135 Td /F1 9.8 Tf [(declared by the WHO on the 11th June 2009. In figure 2, we represent the reconstruction by our method of the spatiotemporal )] TJ ET BT 26.250 654.230 Td /F1 9.8 Tf [(dynamics of the 2009 H1N1 pandemic split into three major stages: \(i\) initial spread in Mexico and the US \(Fig. 3a\), \(ii\) )] TJ ET BT 26.250 642.325 Td /F1 9.8 Tf [(sustained transmission within North America and spread to the rest of the world \(Fig. 3b\) and \(iii\) further worldwide spread and )] TJ ET BT 26.250 630.420 Td /F1 9.8 Tf [(secondary outbreaks outside the Americas \(Fig. 3c\).)] TJ ET 0.965 0.965 0.965 rg 26.250 251.149 555.000 369.390 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 620.539 m 581.250 620.539 l 581.250 619.789 l 26.250 619.789 l f 26.250 251.149 m 581.250 251.149 l 581.250 251.899 l 26.250 251.899 l f q 123.000 0 0 225.000 35.250 385.789 cm /I188 Do Q q 35.250 262.399 537.000 117.390 re W n 0.271 0.267 0.267 rg BT 35.250 368.800 Td /F4 9.8 Tf [(Figure 3. Maps of inferred ancestries of the swine-origin A/H1N1 flu pandemic, based on 279 hemagglutinin \(HA\) )] TJ ET BT 35.250 355.064 Td /F4 9.8 Tf [(DNA sequences available on Genbank as of the 26/06/2009.)] TJ ET BT 309.449 355.064 Td /F1 9.8 Tf [( Arrows represent inferred ancestries, with colors indicating )] TJ ET BT 35.250 341.328 Td /F1 9.8 Tf [(the statistical support \(Equation 2\). Local transmissions are shown as dots for single events, and sunflowers for multiple )] TJ ET BT 35.250 327.592 Td /F1 9.8 Tf [(transmissions. The inset histogram displays the number of strains analyzed by collection date. Dates are provided as days )] TJ ET BT 35.250 313.855 Td /F1 9.8 Tf [(since the most recent common ancestor \(MRCA\), estimated as the 21/01/2009 )] TJ ET 0.267 0.267 0.267 rg BT 377.183 313.855 Td /F1 9.8 Tf [([22])] TJ ET 0.271 0.267 0.267 rg BT 393.445 313.855 Td /F1 9.8 Tf [( . The three different panels display )] TJ ET BT 35.250 300.119 Td /F1 9.8 Tf [(successive stages of the pandemic \(corresponding time frame highlighted in the inset\): a\) transmissions from Mexico to the )] TJ ET BT 35.250 286.383 Td /F1 9.8 Tf [(US, b\) transmissions within the US, and beginning of world-wide spread, and c\) further worldwide spread, likely from )] TJ ET BT 35.250 272.647 Td /F1 9.8 Tf [(unobserved outbreaks outside the Americas.)] TJ ET Q BT 26.250 234.126 Td /F1 9.8 Tf [(The initial stage ending around the 20 )] TJ ET BT 192.097 238.014 Td /F1 8.7 Tf [(th)] TJ ET BT 199.326 234.126 Td /F1 9.8 Tf [( of April is characterized by transmissions from Mexico to the US as well as some local )] TJ ET BT 26.250 222.221 Td /F1 9.8 Tf [(transmissions both within Mexico and the US \(Fig. 3a\). This pattern gives further support to the A/H1N1 having originated in )] TJ ET BT 26.250 210.316 Td /F1 9.8 Tf [(Mexico. Secondary outbreaks within the US become widespread during the second phase while Mexico and the US also start )] TJ ET BT 26.250 198.411 Td /F1 9.8 Tf [(seeding the rest of the world \(Fig. 3b\). It is also during this stage that we infer the first case of a within-country transmission )] TJ ET BT 26.250 186.507 Td /F1 9.8 Tf [(outside the Americas \(France on the 1 )] TJ ET BT 194.243 190.395 Td /F1 8.7 Tf [(st)] TJ ET BT 200.985 186.507 Td /F1 9.8 Tf [( of May\). Many of the ancestries over large geographic distances are well supported, )] TJ ET BT 26.250 174.602 Td /F1 9.8 Tf [(suggesting that the intercontinental inferred ancestries accurately capture the actual pattern of transmission from the Americas )] TJ ET BT 26.250 162.697 Td /F1 9.8 Tf [(to Europe, Asia, and Australia. Conversely, the fraction of transmissions with low associated statistical support may represent )] TJ ET BT 26.250 150.792 Td /F1 9.8 Tf [(cases where intermediate stages in the ancestry path have not been sampled. This is also likely to be the case during the third )] TJ ET BT 26.250 138.888 Td /F1 9.8 Tf [(phase, where many transmissions originating from Mexico, the US, and Canada are characterized by faint statistical support. )] TJ ET BT 26.250 126.983 Td /F1 9.8 Tf [(Conversely, the increasing number of local transmissions in Asia, Russia and Australia are characterised by high statistical )] TJ ET BT 26.250 115.078 Td /F1 9.8 Tf [(support and point to the emergence of multiple secondary outbreaks.)] TJ ET BT 26.250 95.673 Td /F1 9.8 Tf [(Flight traffic is widely recognized as an important determinant for the spread of seasonal and pandemic influenza at large )] TJ ET BT 26.250 83.769 Td /F1 9.8 Tf [(geographic scales )] TJ ET 0.267 0.267 0.267 rg BT 107.536 83.769 Td /F1 9.8 Tf [([1])] TJ ET BT 118.378 83.769 Td /F1 9.8 Tf [([2])] TJ ET BT 129.220 83.769 Td /F1 9.8 Tf [([3])] TJ ET BT 140.062 83.769 Td /F1 9.8 Tf [([23])] TJ ET BT 156.325 83.769 Td /F1 9.8 Tf [([24])] TJ ET 0.271 0.267 0.267 rg BT 172.588 83.769 Td /F1 9.8 Tf [( . Thus, we evaluated the relationship between passenger-flow and the number of inferred )] TJ ET BT 26.250 71.864 Td /F1 9.8 Tf [(transmissions between countries. Both quantities were fairly correlated \( )] TJ ET BT 339.449 71.864 Td /F5 9.8 Tf [(r)] TJ ET BT 342.696 71.864 Td /F1 9.8 Tf [( = 0.54; )] TJ ET BT 378.206 71.864 Td /F5 9.8 Tf [(t)] TJ ET BT 380.916 71.864 Td /F1 9.8 Tf [( -test: )] TJ ET BT 408.011 71.864 Td /F5 9.8 Tf [(t)] TJ ET BT 410.722 71.864 Td /F1 9.8 Tf [( = 3.75; df = 34; P = 3.3 x 10 )] TJ ET BT 536.760 75.752 Td /F1 8.7 Tf [(-4)] TJ ET BT 544.465 71.864 Td /F1 9.8 Tf [( \), but )] TJ ET BT 26.250 59.959 Td /F1 9.8 Tf [(this correlation was largely driven by the high connectivity of the US with Mexico and Canada. A far more remarkable aspect of )] TJ ET BT 26.250 48.054 Td /F1 9.8 Tf [(the spatiotemporal reconstruction of the 2009 A/H1N1 pandemic is the near-absence of implausible transmission events \(Fig. )] TJ ET BT 26.250 36.150 Td /F1 9.8 Tf [(3\). The only possible exceptions to this pattern are two Mexican sequences which trace their ancestry back to the US. However, )] TJ ET Q q 15.000 21.864 577.500 755.136 re W n 0.965 0.965 0.965 rg 26.250 730.777 555.000 46.223 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 730.777 m 581.250 730.777 l 581.250 731.527 l 26.250 731.527 l f q 35.250 742.027 537.000 34.973 re W n 0.271 0.267 0.267 rg BT 35.250 766.011 Td /F4 9.8 Tf [(Figure 2. Results from simulation data.)] TJ ET BT 215.128 766.011 Td /F1 9.8 Tf [( The proportion of correct assignments for haplotypes and locations are )] TJ ET BT 35.250 752.275 Td /F1 9.8 Tf [(represented as boxplots.)] TJ ET Q BT 26.250 713.754 Td /F1 9.8 Tf [(Having tested that the method satisfactorily assigned the correct ancestral locations on simulated data, we applied the )] TJ ET BT 537.286 713.754 Td /F5 9.8 Tf [(SeqTrack)] TJ ET BT 26.250 701.849 Td /F1 9.8 Tf [(algorithm to a dataset of 279 near-complete hemagglutinin \(HA\) sequences collected between the 3 )] TJ ET BT 458.711 705.737 Td /F1 8.7 Tf [(rd)] TJ ET BT 466.416 701.849 Td /F1 9.8 Tf [( of March and the 18 )] TJ ET BT 558.553 705.737 Td /F1 8.7 Tf [(th)] TJ ET BT 565.781 701.849 Td /F1 9.8 Tf [( of )] TJ ET BT 26.250 689.944 Td /F1 9.8 Tf [(June 2009. While no sequences are available for the first confirmed cases \(La Gloria, 15 )] TJ ET BT 409.922 693.832 Td /F1 8.7 Tf [(th)] TJ ET BT 417.150 689.944 Td /F1 9.8 Tf [( February; )] TJ ET 0.267 0.267 0.267 rg BT 464.292 689.944 Td /F1 9.8 Tf [([22])] TJ ET 0.271 0.267 0.267 rg BT 480.555 689.944 Td /F1 9.8 Tf [( \), the time window )] TJ ET BT 26.250 678.039 Td /F1 9.8 Tf [(defined by the collection dates extends from the early stages of the outbreak to the global pandemic, which was officially )] TJ ET BT 26.250 666.135 Td /F1 9.8 Tf [(declared by the WHO on the 11th June 2009. In figure 2, we represent the reconstruction by our method of the spatiotemporal )] TJ ET BT 26.250 654.230 Td /F1 9.8 Tf [(dynamics of the 2009 H1N1 pandemic split into three major stages: \(i\) initial spread in Mexico and the US \(Fig. 3a\), \(ii\) )] TJ ET BT 26.250 642.325 Td /F1 9.8 Tf [(sustained transmission within North America and spread to the rest of the world \(Fig. 3b\) and \(iii\) further worldwide spread and )] TJ ET BT 26.250 630.420 Td /F1 9.8 Tf [(secondary outbreaks outside the Americas \(Fig. 3c\).)] TJ ET 0.965 0.965 0.965 rg 26.250 251.149 555.000 369.390 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 620.539 m 581.250 620.539 l 581.250 619.789 l 26.250 619.789 l f 26.250 251.149 m 581.250 251.149 l 581.250 251.899 l 26.250 251.899 l f q 123.000 0 0 225.000 35.250 385.789 cm /I190 Do Q q 35.250 262.399 537.000 117.390 re W n 0.271 0.267 0.267 rg BT 35.250 368.800 Td /F4 9.8 Tf [(Figure 3. Maps of inferred ancestries of the swine-origin A/H1N1 flu pandemic, based on 279 hemagglutinin \(HA\) )] TJ ET BT 35.250 355.064 Td /F4 9.8 Tf [(DNA sequences available on Genbank as of the 26/06/2009.)] TJ ET BT 309.449 355.064 Td /F1 9.8 Tf [( Arrows represent inferred ancestries, with colors indicating )] TJ ET BT 35.250 341.328 Td /F1 9.8 Tf [(the statistical support \(Equation 2\). Local transmissions are shown as dots for single events, and sunflowers for multiple )] TJ ET BT 35.250 327.592 Td /F1 9.8 Tf [(transmissions. The inset histogram displays the number of strains analyzed by collection date. Dates are provided as days )] TJ ET BT 35.250 313.855 Td /F1 9.8 Tf [(since the most recent common ancestor \(MRCA\), estimated as the 21/01/2009 )] TJ ET 0.267 0.267 0.267 rg BT 377.183 313.855 Td /F1 9.8 Tf [([22])] TJ ET 0.271 0.267 0.267 rg BT 393.445 313.855 Td /F1 9.8 Tf [( . The three different panels display )] TJ ET BT 35.250 300.119 Td /F1 9.8 Tf [(successive stages of the pandemic \(corresponding time frame highlighted in the inset\): a\) transmissions from Mexico to the )] TJ ET BT 35.250 286.383 Td /F1 9.8 Tf [(US, b\) transmissions within the US, and beginning of world-wide spread, and c\) further worldwide spread, likely from )] TJ ET BT 35.250 272.647 Td /F1 9.8 Tf [(unobserved outbreaks outside the Americas.)] TJ ET Q BT 26.250 234.126 Td /F1 9.8 Tf [(The initial stage ending around the 20 )] TJ ET BT 192.097 238.014 Td /F1 8.7 Tf [(th)] TJ ET BT 199.326 234.126 Td /F1 9.8 Tf [( of April is characterized by transmissions from Mexico to the US as well as some local )] TJ ET BT 26.250 222.221 Td /F1 9.8 Tf [(transmissions both within Mexico and the US \(Fig. 3a\). This pattern gives further support to the A/H1N1 having originated in )] TJ ET BT 26.250 210.316 Td /F1 9.8 Tf [(Mexico. Secondary outbreaks within the US become widespread during the second phase while Mexico and the US also start )] TJ ET BT 26.250 198.411 Td /F1 9.8 Tf [(seeding the rest of the world \(Fig. 3b\). It is also during this stage that we infer the first case of a within-country transmission )] TJ ET BT 26.250 186.507 Td /F1 9.8 Tf [(outside the Americas \(France on the 1 )] TJ ET BT 194.243 190.395 Td /F1 8.7 Tf [(st)] TJ ET BT 200.985 186.507 Td /F1 9.8 Tf [( of May\). Many of the ancestries over large geographic distances are well supported, )] TJ ET BT 26.250 174.602 Td /F1 9.8 Tf [(suggesting that the intercontinental inferred ancestries accurately capture the actual pattern of transmission from the Americas )] TJ ET BT 26.250 162.697 Td /F1 9.8 Tf [(to Europe, Asia, and Australia. Conversely, the fraction of transmissions with low associated statistical support may represent )] TJ ET BT 26.250 150.792 Td /F1 9.8 Tf [(cases where intermediate stages in the ancestry path have not been sampled. This is also likely to be the case during the third )] TJ ET BT 26.250 138.888 Td /F1 9.8 Tf [(phase, where many transmissions originating from Mexico, the US, and Canada are characterized by faint statistical support. )] TJ ET BT 26.250 126.983 Td /F1 9.8 Tf [(Conversely, the increasing number of local transmissions in Asia, Russia and Australia are characterised by high statistical )] TJ ET BT 26.250 115.078 Td /F1 9.8 Tf [(support and point to the emergence of multiple secondary outbreaks.)] TJ ET BT 26.250 95.673 Td /F1 9.8 Tf [(Flight traffic is widely recognized as an important determinant for the spread of seasonal and pandemic influenza at large )] TJ ET BT 26.250 83.769 Td /F1 9.8 Tf [(geographic scales )] TJ ET 0.267 0.267 0.267 rg BT 107.536 83.769 Td /F1 9.8 Tf [([1])] TJ ET BT 118.378 83.769 Td /F1 9.8 Tf [([2])] TJ ET BT 129.220 83.769 Td /F1 9.8 Tf [([3])] TJ ET BT 140.062 83.769 Td /F1 9.8 Tf [([23])] TJ ET BT 156.325 83.769 Td /F1 9.8 Tf [([24])] TJ ET 0.271 0.267 0.267 rg BT 172.588 83.769 Td /F1 9.8 Tf [( . Thus, we evaluated the relationship between passenger-flow and the number of inferred )] TJ ET BT 26.250 71.864 Td /F1 9.8 Tf [(transmissions between countries. Both quantities were fairly correlated \( )] TJ ET BT 339.449 71.864 Td /F5 9.8 Tf [(r)] TJ ET BT 342.696 71.864 Td /F1 9.8 Tf [( = 0.54; )] TJ ET BT 378.206 71.864 Td /F5 9.8 Tf [(t)] TJ ET BT 380.916 71.864 Td /F1 9.8 Tf [( -test: )] TJ ET BT 408.011 71.864 Td /F5 9.8 Tf [(t)] TJ ET BT 410.722 71.864 Td /F1 9.8 Tf [( = 3.75; df = 34; P = 3.3 x 10 )] TJ ET BT 536.760 75.752 Td /F1 8.7 Tf [(-4)] TJ ET BT 544.465 71.864 Td /F1 9.8 Tf [( \), but )] TJ ET BT 26.250 59.959 Td /F1 9.8 Tf [(this correlation was largely driven by the high connectivity of the US with Mexico and Canada. A far more remarkable aspect of )] TJ ET BT 26.250 48.054 Td /F1 9.8 Tf [(the spatiotemporal reconstruction of the 2009 A/H1N1 pandemic is the near-absence of implausible transmission events \(Fig. )] TJ ET BT 26.250 36.150 Td /F1 9.8 Tf [(3\). The only possible exceptions to this pattern are two Mexican sequences which trace their ancestry back to the US. However, )] TJ ET Q q 15.000 21.864 577.500 755.136 re W n 0.965 0.965 0.965 rg 26.250 730.777 555.000 46.223 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 730.777 m 581.250 730.777 l 581.250 731.527 l 26.250 731.527 l f q 35.250 742.027 537.000 34.973 re W n 0.271 0.267 0.267 rg BT 35.250 766.011 Td /F4 9.8 Tf [(Figure 2. Results from simulation data.)] TJ ET BT 215.128 766.011 Td /F1 9.8 Tf [( The proportion of correct assignments for haplotypes and locations are )] TJ ET BT 35.250 752.275 Td /F1 9.8 Tf [(represented as boxplots.)] TJ ET Q BT 26.250 713.754 Td /F1 9.8 Tf [(Having tested that the method satisfactorily assigned the correct ancestral locations on simulated data, we applied the )] TJ ET BT 537.286 713.754 Td /F5 9.8 Tf [(SeqTrack)] TJ ET BT 26.250 701.849 Td /F1 9.8 Tf [(algorithm to a dataset of 279 near-complete hemagglutinin \(HA\) sequences collected between the 3 )] TJ ET BT 458.711 705.737 Td /F1 8.7 Tf [(rd)] TJ ET BT 466.416 701.849 Td /F1 9.8 Tf [( of March and the 18 )] TJ ET BT 558.553 705.737 Td /F1 8.7 Tf [(th)] TJ ET BT 565.781 701.849 Td /F1 9.8 Tf [( of )] TJ ET BT 26.250 689.944 Td /F1 9.8 Tf [(June 2009. While no sequences are available for the first confirmed cases \(La Gloria, 15 )] TJ ET BT 409.922 693.832 Td /F1 8.7 Tf [(th)] TJ ET BT 417.150 689.944 Td /F1 9.8 Tf [( February; )] TJ ET 0.267 0.267 0.267 rg BT 464.292 689.944 Td /F1 9.8 Tf [([22])] TJ ET 0.271 0.267 0.267 rg BT 480.555 689.944 Td /F1 9.8 Tf [( \), the time window )] TJ ET BT 26.250 678.039 Td /F1 9.8 Tf [(defined by the collection dates extends from the early stages of the outbreak to the global pandemic, which was officially )] TJ ET BT 26.250 666.135 Td /F1 9.8 Tf [(declared by the WHO on the 11th June 2009. In figure 2, we represent the reconstruction by our method of the spatiotemporal )] TJ ET BT 26.250 654.230 Td /F1 9.8 Tf [(dynamics of the 2009 H1N1 pandemic split into three major stages: \(i\) initial spread in Mexico and the US \(Fig. 3a\), \(ii\) )] TJ ET BT 26.250 642.325 Td /F1 9.8 Tf [(sustained transmission within North America and spread to the rest of the world \(Fig. 3b\) and \(iii\) further worldwide spread and )] TJ ET BT 26.250 630.420 Td /F1 9.8 Tf [(secondary outbreaks outside the Americas \(Fig. 3c\).)] TJ ET 0.965 0.965 0.965 rg 26.250 251.149 555.000 369.390 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 620.539 m 581.250 620.539 l 581.250 619.789 l 26.250 619.789 l f 26.250 251.149 m 581.250 251.149 l 581.250 251.899 l 26.250 251.899 l f q 123.000 0 0 225.000 35.250 385.789 cm /I192 Do Q q 35.250 262.399 537.000 117.390 re W n 0.271 0.267 0.267 rg BT 35.250 368.800 Td /F4 9.8 Tf [(Figure 3. Maps of inferred ancestries of the swine-origin A/H1N1 flu pandemic, based on 279 hemagglutinin \(HA\) )] TJ ET BT 35.250 355.064 Td /F4 9.8 Tf [(DNA sequences available on Genbank as of the 26/06/2009.)] TJ ET BT 309.449 355.064 Td /F1 9.8 Tf [( Arrows represent inferred ancestries, with colors indicating )] TJ ET BT 35.250 341.328 Td /F1 9.8 Tf [(the statistical support \(Equation 2\). Local transmissions are shown as dots for single events, and sunflowers for multiple )] TJ ET BT 35.250 327.592 Td /F1 9.8 Tf [(transmissions. The inset histogram displays the number of strains analyzed by collection date. Dates are provided as days )] TJ ET BT 35.250 313.855 Td /F1 9.8 Tf [(since the most recent common ancestor \(MRCA\), estimated as the 21/01/2009 )] TJ ET 0.267 0.267 0.267 rg BT 377.183 313.855 Td /F1 9.8 Tf [([22])] TJ ET 0.271 0.267 0.267 rg BT 393.445 313.855 Td /F1 9.8 Tf [( . The three different panels display )] TJ ET BT 35.250 300.119 Td /F1 9.8 Tf [(successive stages of the pandemic \(corresponding time frame highlighted in the inset\): a\) transmissions from Mexico to the )] TJ ET BT 35.250 286.383 Td /F1 9.8 Tf [(US, b\) transmissions within the US, and beginning of world-wide spread, and c\) further worldwide spread, likely from )] TJ ET BT 35.250 272.647 Td /F1 9.8 Tf [(unobserved outbreaks outside the Americas.)] TJ ET Q BT 26.250 234.126 Td /F1 9.8 Tf [(The initial stage ending around the 20 )] TJ ET BT 192.097 238.014 Td /F1 8.7 Tf [(th)] TJ ET BT 199.326 234.126 Td /F1 9.8 Tf [( of April is characterized by transmissions from Mexico to the US as well as some local )] TJ ET BT 26.250 222.221 Td /F1 9.8 Tf [(transmissions both within Mexico and the US \(Fig. 3a\). This pattern gives further support to the A/H1N1 having originated in )] TJ ET BT 26.250 210.316 Td /F1 9.8 Tf [(Mexico. Secondary outbreaks within the US become widespread during the second phase while Mexico and the US also start )] TJ ET BT 26.250 198.411 Td /F1 9.8 Tf [(seeding the rest of the world \(Fig. 3b\). It is also during this stage that we infer the first case of a within-country transmission )] TJ ET BT 26.250 186.507 Td /F1 9.8 Tf [(outside the Americas \(France on the 1 )] TJ ET BT 194.243 190.395 Td /F1 8.7 Tf [(st)] TJ ET BT 200.985 186.507 Td /F1 9.8 Tf [( of May\). Many of the ancestries over large geographic distances are well supported, )] TJ ET BT 26.250 174.602 Td /F1 9.8 Tf [(suggesting that the intercontinental inferred ancestries accurately capture the actual pattern of transmission from the Americas )] TJ ET BT 26.250 162.697 Td /F1 9.8 Tf [(to Europe, Asia, and Australia. Conversely, the fraction of transmissions with low associated statistical support may represent )] TJ ET BT 26.250 150.792 Td /F1 9.8 Tf [(cases where intermediate stages in the ancestry path have not been sampled. This is also likely to be the case during the third )] TJ ET BT 26.250 138.888 Td /F1 9.8 Tf [(phase, where many transmissions originating from Mexico, the US, and Canada are characterized by faint statistical support. )] TJ ET BT 26.250 126.983 Td /F1 9.8 Tf [(Conversely, the increasing number of local transmissions in Asia, Russia and Australia are characterised by high statistical )] TJ ET BT 26.250 115.078 Td /F1 9.8 Tf [(support and point to the emergence of multiple secondary outbreaks.)] TJ ET BT 26.250 95.673 Td /F1 9.8 Tf [(Flight traffic is widely recognized as an important determinant for the spread of seasonal and pandemic influenza at large )] TJ ET BT 26.250 83.769 Td /F1 9.8 Tf [(geographic scales )] TJ ET 0.267 0.267 0.267 rg BT 107.536 83.769 Td /F1 9.8 Tf [([1])] TJ ET BT 118.378 83.769 Td /F1 9.8 Tf [([2])] TJ ET BT 129.220 83.769 Td /F1 9.8 Tf [([3])] TJ ET BT 140.062 83.769 Td /F1 9.8 Tf [([23])] TJ ET BT 156.325 83.769 Td /F1 9.8 Tf [([24])] TJ ET 0.271 0.267 0.267 rg BT 172.588 83.769 Td /F1 9.8 Tf [( . Thus, we evaluated the relationship between passenger-flow and the number of inferred )] TJ ET BT 26.250 71.864 Td /F1 9.8 Tf [(transmissions between countries. Both quantities were fairly correlated \( )] TJ ET BT 339.449 71.864 Td /F5 9.8 Tf [(r)] TJ ET BT 342.696 71.864 Td /F1 9.8 Tf [( = 0.54; )] TJ ET BT 378.206 71.864 Td /F5 9.8 Tf [(t)] TJ ET BT 380.916 71.864 Td /F1 9.8 Tf [( -test: )] TJ ET BT 408.011 71.864 Td /F5 9.8 Tf [(t)] TJ ET BT 410.722 71.864 Td /F1 9.8 Tf [( = 3.75; df = 34; P = 3.3 x 10 )] TJ ET BT 536.760 75.752 Td /F1 8.7 Tf [(-4)] TJ ET BT 544.465 71.864 Td /F1 9.8 Tf [( \), but )] TJ ET BT 26.250 59.959 Td /F1 9.8 Tf [(this correlation was largely driven by the high connectivity of the US with Mexico and Canada. A far more remarkable aspect of )] TJ ET BT 26.250 48.054 Td /F1 9.8 Tf [(the spatiotemporal reconstruction of the 2009 A/H1N1 pandemic is the near-absence of implausible transmission events \(Fig. )] TJ ET BT 26.250 36.150 Td /F1 9.8 Tf [(3\). The only possible exceptions to this pattern are two Mexican sequences which trace their ancestry back to the US. However, )] TJ ET Q q 123.000 0 0 225.000 35.250 385.789 cm /I194 Do Q q 0.000 0.000 0.000 rg BT 291.710 19.825 Td /F1 11.0 Tf [(4)] TJ ET BT 25.000 19.825 Td /F1 11.0 Tf [(PLOS Currents Influenza)] TJ ET Q endstream endobj 403 0 obj << /Type /Annot /Subtype /Link /A 404 0 R /Border [0 0 0] /H /I /Rect [ 464.2915 689.0423 480.5545 698.9629 ] >> endobj 404 0 obj << /Type /Action >> endobj 405 0 obj << /Type /Annot /Subtype /Link /A 406 0 R /Border [0 0 0] /H /I /Rect [ 35.2500 385.7895 158.2500 610.7895 ] >> endobj 406 0 obj << /Type /Action /S /URI /URI (http://currents.plos.org/influenza/files/2009/08/figure2.png) >> endobj 407 0 obj << /Type /XObject /Subtype /Image /Width 164 /Height 300 /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 1 /Columns 164 /BitsPerComponent 8>> /ColorSpace /DeviceGray /BitsPerComponent 8 /Length 312>> stream x ?B.du`RR)TJ*%JIRR)TJ*%JIRR)TJ*%JIRR)TJ*%JIRR)TJ*%JIRR)TJ*%JIRR)TJ*%JIRR)TJ*%JIRR)TJ*%JIRR)TJ*%JIRR)TJ*%JIRR)TJ*%JIRR)TJ*%JIRR)TJ*%JIRR)TJ*%JIRR)TJ*%JIRR)TJ*%JIRR)TJ*%JIRR)TJ*l endstream endobj 408 0 obj << /Type /XObject /Subtype /Image /Width 164 /Height 300 /SMask 407 0 R /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 3 /Columns 164 /BitsPerComponent 8>> /ColorSpace /DeviceRGB /BitsPerComponent 8 /Length 58632>> stream xwu'9Ot1  @$@1+j%[6d'Y:Zd[֮$۔ehI14H`r =sH}o{znݺι"}W yJs(^1³R1W^ SJP`H"RY抂I!^mFZ* UY%H)B:!2ST2@+Q|U`K0 (J0 Y)TK1HoKBZ)B)Vg1N(%IȚB_3`u[l#9uYvho^ZZ[\bLIik-5[UE֊'oVpZ˫@ jvZZ %=juiQ xR(bm$MF lJd# 5YoYf ,p)T(H=">M_2">Ζ8 -yo/Mey@׃ #q2\.ڶBPSyHXP[oŷ1*gO<'X[F}uH8ݻ>|Lc~ݻvRk4 bKb2gߎvyc}o[6uo?(5JzDB2dBHEa,}ꬊгl ,AE@& Q ?0 +<A('JLc(itW8awyܔAgvfw~Jw. bl;E~=٫٤"Qe|J%߃7#HBoPujtŻ>"l ]*͂J8.Z7憬[R!( xNa0hcm\OP(MoO|苰{T@|&bIŕ;BWf"; @cTM./3Nt'D} tVeSF ڹ]̃y:!.2຿=2uD]|7E\b2}sT뾴z:dH9v`8qٗ_]06&K8ajW^eIB*t0% ,=xYʕFa qgm&"'Dhi Rz(1O\h;J;oWFȨ4a6t:tC. 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The inference of at least one implausible )] TJ ET BT 26.250 755.571 Td /F1 9.8 Tf [(event from the US to Mexico was inescapable as the oldest sequences present in the dataset were all sampled in the US. The )] TJ ET BT 26.250 743.667 Td /F1 9.8 Tf [(absence of implausible transmissions during the later stages of the pandemic is particularly surprising as we expected )] TJ ET BT 536.702 743.667 Td /F5 9.8 Tf [(SeqTrack)] TJ ET BT 26.250 731.762 Td /F1 9.8 Tf [(to struggle with the increasingly sparse sampling of the extant viral strains. Over the time period analyzed, the available )] TJ ET BT 26.250 719.857 Td /F1 9.8 Tf [(samples become less representative of the global viral population; A/H1N1 cases have been increasing essentially )] TJ ET BT 26.250 707.952 Td /F1 9.8 Tf [(exponentially but the sequencing effort has diminished from the end of April.)] TJ ET BT 26.250 671.350 Td /F4 12.0 Tf [(Discussion)] TJ ET BT 26.250 651.396 Td /F1 9.8 Tf [(We have introduced a new methodological paradigm for the analysis of genetic data sampled during an outbreak. We )] TJ ET BT 26.250 639.491 Td /F1 9.8 Tf [(developed a method rooted in this paradigm which behaves satisfactorily on simulated data and reconstructs a highly plausible )] TJ ET BT 26.250 627.586 Td /F1 9.8 Tf [(global scenario for the early stages of the 2009 A/H1N1 pandemic. We reconstruct an initial outbreak in Mexico, and a rapid )] TJ ET BT 26.250 615.681 Td /F1 9.8 Tf [(spread to the US. At a later stage, Mexico and the US act as the principal source for the worldwide diffusion of the virus, with )] TJ ET BT 26.250 603.777 Td /F1 9.8 Tf [(secondary foci of infection becoming increasingly common with time outside the Americas. However, there is considerable )] TJ ET BT 26.250 591.872 Td /F1 9.8 Tf [(potential for methodological developments and improvements of the )] TJ ET BT 321.597 591.872 Td /F5 9.8 Tf [(SeqTraq)] TJ ET BT 358.988 591.872 Td /F1 9.8 Tf [( algorithm, both in the short and the long term.)] TJ ET BT 26.250 572.467 Td /F1 9.8 Tf [(In this paper we used maximum parsimony because the origin of A/H1N1 is sufficiently recent for homoplasies \(recombination )] TJ ET BT 26.250 560.562 Td /F1 9.8 Tf [(or back mutations\) to be safely ignored. However, )] TJ ET BT 243.548 560.562 Td /F5 9.8 Tf [(SeqTrack)] TJ ET BT 285.269 560.562 Td /F1 9.8 Tf [( genealogies could be optimized on other criteria, such as genetic )] TJ ET BT 26.250 548.658 Td /F1 9.8 Tf [(distances or log-likelihoods based on complex models of sequence evolution \(see Methods\). Another development of immediate )] TJ ET BT 26.250 536.753 Td /F1 9.8 Tf [(interest relates to the use of diverse genetic information. All analyzes were conducted on the hemagglutinin \(HA\) segment. The )] TJ ET BT 26.250 524.848 Td /F1 9.8 Tf [(influenza genome comprises eight segments each harbouring one gene. As the A/H1N1 sequencing effort was undertaken )] TJ ET BT 26.250 512.943 Td /F1 9.8 Tf [(independently by a large number of labs, the available genetic information is extremely heterogeneous. Sequences deposited )] TJ ET BT 26.250 501.039 Td /F1 9.8 Tf [(on Genbank for various strains range from small fragments of specific genes to complete genomes, including a majority of )] TJ ET BT 26.250 489.134 Td /F1 9.8 Tf [(strains for which an essentially random combination of segments were sequenced. This translates in a considerable loss of )] TJ ET BT 26.250 477.229 Td /F1 9.8 Tf [(information. )] TJ ET BT 79.894 477.229 Td /F5 9.8 Tf [(S)] TJ ET BT 86.398 477.229 Td /F1 9.8 Tf [( uch heterogeneous information could be accommodated by averaging genetic differentiation across segments, )] TJ ET BT 26.250 465.324 Td /F1 9.8 Tf [(using appropriate weights to account for different substitution rates and segment lengths.)] TJ ET BT 26.250 445.920 Td /F1 9.8 Tf [(However, including a large fraction of strains with heterogeneous sequencing coverage would require accurate estimates of )] TJ ET BT 26.250 434.015 Td /F1 9.8 Tf [(substitution rates, which can be difficult to obtain for emerging pathogens. Another possible concern is that different segments )] TJ ET BT 26.250 422.110 Td /F1 9.8 Tf [(may exhibit incongruent genealogies due to different selective pressures, reassortments and/or intra-genomic interactions )] TJ ET 0.267 0.267 0.267 rg BT 552.974 422.110 Td /F1 9.8 Tf [([4])] TJ ET BT 563.816 422.110 Td /F1 9.8 Tf [([25])] TJ ET BT 26.250 410.205 Td /F1 9.8 Tf [([26])] TJ ET BT 42.513 410.205 Td /F1 9.8 Tf [([27])] TJ ET BT 58.776 410.205 Td /F1 9.8 Tf [([28])] TJ ET 0.271 0.267 0.267 rg BT 75.039 410.205 Td /F1 9.8 Tf [( . Some other developments would require more effort. It would in particular be desirable to consider the various )] TJ ET BT 26.250 398.301 Td /F1 9.8 Tf [(parameters of the model from a probabilistic perspective. For instance, the date of probable transmission could be better )] TJ ET BT 26.250 386.396 Td /F1 9.8 Tf [(captured by a distribution of the time during which a specific sequence remains unaltered rather than a fixed collection date. )] TJ ET BT 26.250 374.491 Td /F1 9.8 Tf [(Moreover, a probabilistic framework would also allow incorporating information besides genetic sequences and collection dates, )] TJ ET BT 26.250 362.586 Td /F1 9.8 Tf [(such as prevalence data or spatial connectivity between locations.)] TJ ET BT 26.250 343.182 Td /F1 9.8 Tf [(The 2009 A/H1N1 influenza pandemic is the fourth in modern history. 20 )] TJ ET BT 341.107 347.070 Td /F1 8.7 Tf [(th)] TJ ET BT 348.335 343.182 Td /F1 9.8 Tf [( century pandemics occurred in 1918, 1957 and )] TJ ET BT 26.250 331.277 Td /F1 9.8 Tf [(1968. In all three previous cases, the newly emerged strain replaced the strain that was circulating and causing seasonal )] TJ ET BT 26.250 319.372 Td /F1 9.8 Tf [(\(winter\) epidemics. The current seasonal influenza is a descendent of the 1968 H3N2 pandemic and has been co-circulating )] TJ ET BT 26.250 307.467 Td /F1 9.8 Tf [(with a less virulent H1N1 strain at lower frequencies since 1977 )] TJ ET 0.267 0.267 0.267 rg BT 302.604 307.467 Td /F1 9.8 Tf [([4])] TJ ET 0.271 0.267 0.267 rg BT 313.446 307.467 Td /F1 9.8 Tf [( . Whether the 2009 A/H1N1 will fully displace the current )] TJ ET BT 26.250 295.563 Td /F1 9.8 Tf [(seasonal influenza strains remains to be seen. Seasonal influenza strains have strongly cyclical dynamics, with the majority of )] TJ ET BT 26.250 283.658 Td /F1 9.8 Tf [(cases observed during the winter in both hemispheres. The epidemics in the Northern and Southern hemisphere are believed to )] TJ ET BT 26.250 271.753 Td /F1 9.8 Tf [(be essentially independent but both are seeded most years from Southeast Asia which acts as a reservoir for flu )] TJ ET 0.267 0.267 0.267 rg BT 511.810 271.753 Td /F1 9.8 Tf [([4])] TJ ET BT 522.652 271.753 Td /F1 9.8 Tf [([5])] TJ ET 0.271 0.267 0.267 rg BT 533.494 271.753 Td /F1 9.8 Tf [( . The )] TJ ET BT 26.250 259.848 Td /F1 9.8 Tf [(factors underlying seasonal dynamics are poorly understood despite decades of research )] TJ ET 0.267 0.267 0.267 rg BT 414.261 259.848 Td /F1 9.8 Tf [([29])] TJ ET 0.271 0.267 0.267 rg BT 430.524 259.848 Td /F1 9.8 Tf [( . There is considerable )] TJ ET BT 26.250 247.944 Td /F1 9.8 Tf [(disagreement over the importance of climatic variables such as temperature and humidity in driving the seasonal patterns )] TJ ET BT 26.250 236.039 Td /F1 9.8 Tf [(worldwide )] TJ ET 0.267 0.267 0.267 rg BT 72.299 236.039 Td /F1 9.8 Tf [([30])] TJ ET BT 88.562 236.039 Td /F1 9.8 Tf [([31])] TJ ET 0.271 0.267 0.267 rg BT 104.825 236.039 Td /F1 9.8 Tf [( . An additional confounding effect arises from school holidays, which are also believed to be important drivers )] TJ ET BT 26.250 224.134 Td /F1 9.8 Tf [(of seasonality in influenza )] TJ ET 0.267 0.267 0.267 rg BT 140.598 224.134 Td /F1 9.8 Tf [([32])] TJ ET BT 156.861 224.134 Td /F1 9.8 Tf [([33])] TJ ET 0.271 0.267 0.267 rg BT 173.124 224.134 Td /F1 9.8 Tf [( .)] TJ ET BT 26.250 204.729 Td /F1 9.8 Tf [(In principle, our method would be ideal to shed further light on the effect of human travel, climate and additional factors such as )] TJ ET BT 26.250 192.825 Td /F1 9.8 Tf [(timing of school holidays on the underlying factors behind the spread of the 2009 A/H1N1 pandemic. However, the main )] TJ ET BT 26.250 180.920 Td /F1 9.8 Tf [(difficulty stems from the current limitation of the available data. The ratio between the number of confirmed and actual cases is )] TJ ET BT 26.250 169.015 Td /F1 9.8 Tf [(likely to vary greatly between countries. Moreover, the number of strains that have been sequenced for each country is )] TJ ET BT 26.250 157.110 Td /F1 9.8 Tf [(uncorrelated with the number of confirmed cases. This leads to considerable difficulties for disentangling the main factors )] TJ ET BT 26.250 145.206 Td /F1 9.8 Tf [(behind the spread of the 2009 A/H1N1 pandemic. What is certain is that human travel must be important. The majority of long )] TJ ET BT 26.250 133.301 Td /F1 9.8 Tf [(distance movement is likely to be mediated by airline travel both for seasonal and pandemic flu )] TJ ET 0.267 0.267 0.267 rg BT 437.554 133.301 Td /F1 9.8 Tf [([1])] TJ ET BT 448.396 133.301 Td /F1 9.8 Tf [([2])] TJ ET BT 459.238 133.301 Td /F1 9.8 Tf [([3])] TJ ET BT 470.080 133.301 Td /F1 9.8 Tf [([23])] TJ ET BT 486.343 133.301 Td /F1 9.8 Tf [([25])] TJ ET BT 502.606 133.301 Td /F1 9.8 Tf [([34])] TJ ET 0.271 0.267 0.267 rg BT 518.869 133.301 Td /F1 9.8 Tf [( . Despite the )] TJ ET BT 26.250 121.396 Td /F1 9.8 Tf [(limitations of the genetic dataset, we observe a highly significant correlation between flight traffic and the routes inferred by )] TJ ET BT 26.250 109.491 Td /F5 9.8 Tf [(SeqTrack)] TJ ET BT 67.970 109.491 Td /F1 9.8 Tf [( . At this stage, we are unable to provide a quantitative estimate of the effect of climate. However, the sustained )] TJ ET BT 26.250 97.587 Td /F1 9.8 Tf [(spread of the 2009 A/H1N1 strain in the Northern hemisphere during the spring and summer suggests it may be less sensitive )] TJ ET BT 26.250 85.682 Td /F1 9.8 Tf [(to climatic conditions than the seasonal influenza strains currently in circulation.)] TJ ET BT 26.250 66.277 Td /F1 9.8 Tf [(The )] TJ ET BT 45.760 66.277 Td /F5 9.8 Tf [(SeqTrack)] TJ ET BT 87.480 66.277 Td /F1 9.8 Tf [( algorithm has been specifically developed to model the spatiotemporal dynamics of the 2009 A/H1N1 pandemic. )] TJ ET BT 26.250 54.372 Td /F1 9.8 Tf [(However, the approach should be applicable to essentially any genetic data collected during the early stages of an outbreak. )] TJ ET BT 26.250 42.468 Td /F1 9.8 Tf [(This could include localised outbreaks within a school or a community but also epidemics at much larger geographical scale. As )] TJ ET Q q 15.000 28.182 577.500 748.818 re W n 0.271 0.267 0.267 rg BT 26.250 767.476 Td /F1 9.8 Tf [(the statistical support was very low in both cases with likelihoods of 2.110-7 and 0.11. The inference of at least one implausible )] TJ ET BT 26.250 755.571 Td /F1 9.8 Tf [(event from the US to Mexico was inescapable as the oldest sequences present in the dataset were all sampled in the US. The )] TJ ET BT 26.250 743.667 Td /F1 9.8 Tf [(absence of implausible transmissions during the later stages of the pandemic is particularly surprising as we expected )] TJ ET BT 536.702 743.667 Td /F5 9.8 Tf [(SeqTrack)] TJ ET BT 26.250 731.762 Td /F1 9.8 Tf [(to struggle with the increasingly sparse sampling of the extant viral strains. Over the time period analyzed, the available )] TJ ET BT 26.250 719.857 Td /F1 9.8 Tf [(samples become less representative of the global viral population; A/H1N1 cases have been increasing essentially )] TJ ET BT 26.250 707.952 Td /F1 9.8 Tf [(exponentially but the sequencing effort has diminished from the end of April.)] TJ ET BT 26.250 671.350 Td /F4 12.0 Tf [(Discussion)] TJ ET BT 26.250 651.396 Td /F1 9.8 Tf [(We have introduced a new methodological paradigm for the analysis of genetic data sampled during an outbreak. We )] TJ ET BT 26.250 639.491 Td /F1 9.8 Tf [(developed a method rooted in this paradigm which behaves satisfactorily on simulated data and reconstructs a highly plausible )] TJ ET BT 26.250 627.586 Td /F1 9.8 Tf [(global scenario for the early stages of the 2009 A/H1N1 pandemic. We reconstruct an initial outbreak in Mexico, and a rapid )] TJ ET BT 26.250 615.681 Td /F1 9.8 Tf [(spread to the US. At a later stage, Mexico and the US act as the principal source for the worldwide diffusion of the virus, with )] TJ ET BT 26.250 603.777 Td /F1 9.8 Tf [(secondary foci of infection becoming increasingly common with time outside the Americas. However, there is considerable )] TJ ET BT 26.250 591.872 Td /F1 9.8 Tf [(potential for methodological developments and improvements of the )] TJ ET BT 321.597 591.872 Td /F5 9.8 Tf [(SeqTraq)] TJ ET BT 358.988 591.872 Td /F1 9.8 Tf [( algorithm, both in the short and the long term.)] TJ ET BT 26.250 572.467 Td /F1 9.8 Tf [(In this paper we used maximum parsimony because the origin of A/H1N1 is sufficiently recent for homoplasies \(recombination )] TJ ET BT 26.250 560.562 Td /F1 9.8 Tf [(or back mutations\) to be safely ignored. However, )] TJ ET BT 243.548 560.562 Td /F5 9.8 Tf [(SeqTrack)] TJ ET BT 285.269 560.562 Td /F1 9.8 Tf [( genealogies could be optimized on other criteria, such as genetic )] TJ ET BT 26.250 548.658 Td /F1 9.8 Tf [(distances or log-likelihoods based on complex models of sequence evolution \(see Methods\). Another development of immediate )] TJ ET BT 26.250 536.753 Td /F1 9.8 Tf [(interest relates to the use of diverse genetic information. All analyzes were conducted on the hemagglutinin \(HA\) segment. The )] TJ ET BT 26.250 524.848 Td /F1 9.8 Tf [(influenza genome comprises eight segments each harbouring one gene. As the A/H1N1 sequencing effort was undertaken )] TJ ET BT 26.250 512.943 Td /F1 9.8 Tf [(independently by a large number of labs, the available genetic information is extremely heterogeneous. Sequences deposited )] TJ ET BT 26.250 501.039 Td /F1 9.8 Tf [(on Genbank for various strains range from small fragments of specific genes to complete genomes, including a majority of )] TJ ET BT 26.250 489.134 Td /F1 9.8 Tf [(strains for which an essentially random combination of segments were sequenced. This translates in a considerable loss of )] TJ ET BT 26.250 477.229 Td /F1 9.8 Tf [(information. )] TJ ET BT 79.894 477.229 Td /F5 9.8 Tf [(S)] TJ ET BT 86.398 477.229 Td /F1 9.8 Tf [( uch heterogeneous information could be accommodated by averaging genetic differentiation across segments, )] TJ ET BT 26.250 465.324 Td /F1 9.8 Tf [(using appropriate weights to account for different substitution rates and segment lengths.)] TJ ET BT 26.250 445.920 Td /F1 9.8 Tf [(However, including a large fraction of strains with heterogeneous sequencing coverage would require accurate estimates of )] TJ ET BT 26.250 434.015 Td /F1 9.8 Tf [(substitution rates, which can be difficult to obtain for emerging pathogens. Another possible concern is that different segments )] TJ ET BT 26.250 422.110 Td /F1 9.8 Tf [(may exhibit incongruent genealogies due to different selective pressures, reassortments and/or intra-genomic interactions )] TJ ET 0.267 0.267 0.267 rg BT 552.974 422.110 Td /F1 9.8 Tf [([4])] TJ ET BT 563.816 422.110 Td /F1 9.8 Tf [([25])] TJ ET BT 26.250 410.205 Td /F1 9.8 Tf [([26])] TJ ET BT 42.513 410.205 Td /F1 9.8 Tf [([27])] TJ ET BT 58.776 410.205 Td /F1 9.8 Tf [([28])] TJ ET 0.271 0.267 0.267 rg BT 75.039 410.205 Td /F1 9.8 Tf [( . Some other developments would require more effort. It would in particular be desirable to consider the various )] TJ ET BT 26.250 398.301 Td /F1 9.8 Tf [(parameters of the model from a probabilistic perspective. For instance, the date of probable transmission could be better )] TJ ET BT 26.250 386.396 Td /F1 9.8 Tf [(captured by a distribution of the time during which a specific sequence remains unaltered rather than a fixed collection date. )] TJ ET BT 26.250 374.491 Td /F1 9.8 Tf [(Moreover, a probabilistic framework would also allow incorporating information besides genetic sequences and collection dates, )] TJ ET BT 26.250 362.586 Td /F1 9.8 Tf [(such as prevalence data or spatial connectivity between locations.)] TJ ET BT 26.250 343.182 Td /F1 9.8 Tf [(The 2009 A/H1N1 influenza pandemic is the fourth in modern history. 20 )] TJ ET BT 341.107 347.070 Td /F1 8.7 Tf [(th)] TJ ET BT 348.335 343.182 Td /F1 9.8 Tf [( century pandemics occurred in 1918, 1957 and )] TJ ET BT 26.250 331.277 Td /F1 9.8 Tf [(1968. In all three previous cases, the newly emerged strain replaced the strain that was circulating and causing seasonal )] TJ ET BT 26.250 319.372 Td /F1 9.8 Tf [(\(winter\) epidemics. The current seasonal influenza is a descendent of the 1968 H3N2 pandemic and has been co-circulating )] TJ ET BT 26.250 307.467 Td /F1 9.8 Tf [(with a less virulent H1N1 strain at lower frequencies since 1977 )] TJ ET 0.267 0.267 0.267 rg BT 302.604 307.467 Td /F1 9.8 Tf [([4])] TJ ET 0.271 0.267 0.267 rg BT 313.446 307.467 Td /F1 9.8 Tf [( . Whether the 2009 A/H1N1 will fully displace the current )] TJ ET BT 26.250 295.563 Td /F1 9.8 Tf [(seasonal influenza strains remains to be seen. Seasonal influenza strains have strongly cyclical dynamics, with the majority of )] TJ ET BT 26.250 283.658 Td /F1 9.8 Tf [(cases observed during the winter in both hemispheres. The epidemics in the Northern and Southern hemisphere are believed to )] TJ ET BT 26.250 271.753 Td /F1 9.8 Tf [(be essentially independent but both are seeded most years from Southeast Asia which acts as a reservoir for flu )] TJ ET 0.267 0.267 0.267 rg BT 511.810 271.753 Td /F1 9.8 Tf [([4])] TJ ET BT 522.652 271.753 Td /F1 9.8 Tf [([5])] TJ ET 0.271 0.267 0.267 rg BT 533.494 271.753 Td /F1 9.8 Tf [( . The )] TJ ET BT 26.250 259.848 Td /F1 9.8 Tf [(factors underlying seasonal dynamics are poorly understood despite decades of research )] TJ ET 0.267 0.267 0.267 rg BT 414.261 259.848 Td /F1 9.8 Tf [([29])] TJ ET 0.271 0.267 0.267 rg BT 430.524 259.848 Td /F1 9.8 Tf [( . There is considerable )] TJ ET BT 26.250 247.944 Td /F1 9.8 Tf [(disagreement over the importance of climatic variables such as temperature and humidity in driving the seasonal patterns )] TJ ET BT 26.250 236.039 Td /F1 9.8 Tf [(worldwide )] TJ ET 0.267 0.267 0.267 rg BT 72.299 236.039 Td /F1 9.8 Tf [([30])] TJ ET BT 88.562 236.039 Td /F1 9.8 Tf [([31])] TJ ET 0.271 0.267 0.267 rg BT 104.825 236.039 Td /F1 9.8 Tf [( . An additional confounding effect arises from school holidays, which are also believed to be important drivers )] TJ ET BT 26.250 224.134 Td /F1 9.8 Tf [(of seasonality in influenza )] TJ ET 0.267 0.267 0.267 rg BT 140.598 224.134 Td /F1 9.8 Tf [([32])] TJ ET BT 156.861 224.134 Td /F1 9.8 Tf [([33])] TJ ET 0.271 0.267 0.267 rg BT 173.124 224.134 Td /F1 9.8 Tf [( .)] TJ ET BT 26.250 204.729 Td /F1 9.8 Tf [(In principle, our method would be ideal to shed further light on the effect of human travel, climate and additional factors such as )] TJ ET BT 26.250 192.825 Td /F1 9.8 Tf [(timing of school holidays on the underlying factors behind the spread of the 2009 A/H1N1 pandemic. However, the main )] TJ ET BT 26.250 180.920 Td /F1 9.8 Tf [(difficulty stems from the current limitation of the available data. The ratio between the number of confirmed and actual cases is )] TJ ET BT 26.250 169.015 Td /F1 9.8 Tf [(likely to vary greatly between countries. Moreover, the number of strains that have been sequenced for each country is )] TJ ET BT 26.250 157.110 Td /F1 9.8 Tf [(uncorrelated with the number of confirmed cases. This leads to considerable difficulties for disentangling the main factors )] TJ ET BT 26.250 145.206 Td /F1 9.8 Tf [(behind the spread of the 2009 A/H1N1 pandemic. What is certain is that human travel must be important. The majority of long )] TJ ET BT 26.250 133.301 Td /F1 9.8 Tf [(distance movement is likely to be mediated by airline travel both for seasonal and pandemic flu )] TJ ET 0.267 0.267 0.267 rg BT 437.554 133.301 Td /F1 9.8 Tf [([1])] TJ ET BT 448.396 133.301 Td /F1 9.8 Tf [([2])] TJ ET BT 459.238 133.301 Td /F1 9.8 Tf [([3])] TJ ET BT 470.080 133.301 Td /F1 9.8 Tf [([23])] TJ ET BT 486.343 133.301 Td /F1 9.8 Tf [([25])] TJ ET BT 502.606 133.301 Td /F1 9.8 Tf [([34])] TJ ET 0.271 0.267 0.267 rg BT 518.869 133.301 Td /F1 9.8 Tf [( . Despite the )] TJ ET BT 26.250 121.396 Td /F1 9.8 Tf [(limitations of the genetic dataset, we observe a highly significant correlation between flight traffic and the routes inferred by )] TJ ET BT 26.250 109.491 Td /F5 9.8 Tf [(SeqTrack)] TJ ET BT 67.970 109.491 Td /F1 9.8 Tf [( . At this stage, we are unable to provide a quantitative estimate of the effect of climate. However, the sustained )] TJ ET BT 26.250 97.587 Td /F1 9.8 Tf [(spread of the 2009 A/H1N1 strain in the Northern hemisphere during the spring and summer suggests it may be less sensitive )] TJ ET BT 26.250 85.682 Td /F1 9.8 Tf [(to climatic conditions than the seasonal influenza strains currently in circulation.)] TJ ET BT 26.250 66.277 Td /F1 9.8 Tf [(The )] TJ ET BT 45.760 66.277 Td /F5 9.8 Tf [(SeqTrack)] TJ ET BT 87.480 66.277 Td /F1 9.8 Tf [( algorithm has been specifically developed to model the spatiotemporal dynamics of the 2009 A/H1N1 pandemic. )] TJ ET BT 26.250 54.372 Td /F1 9.8 Tf [(However, the approach should be applicable to essentially any genetic data collected during the early stages of an outbreak. )] TJ ET BT 26.250 42.468 Td /F1 9.8 Tf [(This could include localised outbreaks within a school or a community but also epidemics at much larger geographical scale. As )] TJ ET Q q 15.000 28.182 577.500 748.818 re W n 0.271 0.267 0.267 rg BT 26.250 767.476 Td /F1 9.8 Tf [(the statistical support was very low in both cases with likelihoods of 2.110-7 and 0.11. The inference of at least one implausible )] TJ ET BT 26.250 755.571 Td /F1 9.8 Tf [(event from the US to Mexico was inescapable as the oldest sequences present in the dataset were all sampled in the US. The )] TJ ET BT 26.250 743.667 Td /F1 9.8 Tf [(absence of implausible transmissions during the later stages of the pandemic is particularly surprising as we expected )] TJ ET BT 536.702 743.667 Td /F5 9.8 Tf [(SeqTrack)] TJ ET BT 26.250 731.762 Td /F1 9.8 Tf [(to struggle with the increasingly sparse sampling of the extant viral strains. Over the time period analyzed, the available )] TJ ET BT 26.250 719.857 Td /F1 9.8 Tf [(samples become less representative of the global viral population; A/H1N1 cases have been increasing essentially )] TJ ET BT 26.250 707.952 Td /F1 9.8 Tf [(exponentially but the sequencing effort has diminished from the end of April.)] TJ ET BT 26.250 671.350 Td /F4 12.0 Tf [(Discussion)] TJ ET BT 26.250 651.396 Td /F1 9.8 Tf [(We have introduced a new methodological paradigm for the analysis of genetic data sampled during an outbreak. We )] TJ ET BT 26.250 639.491 Td /F1 9.8 Tf [(developed a method rooted in this paradigm which behaves satisfactorily on simulated data and reconstructs a highly plausible )] TJ ET BT 26.250 627.586 Td /F1 9.8 Tf [(global scenario for the early stages of the 2009 A/H1N1 pandemic. We reconstruct an initial outbreak in Mexico, and a rapid )] TJ ET BT 26.250 615.681 Td /F1 9.8 Tf [(spread to the US. At a later stage, Mexico and the US act as the principal source for the worldwide diffusion of the virus, with )] TJ ET BT 26.250 603.777 Td /F1 9.8 Tf [(secondary foci of infection becoming increasingly common with time outside the Americas. However, there is considerable )] TJ ET BT 26.250 591.872 Td /F1 9.8 Tf [(potential for methodological developments and improvements of the )] TJ ET BT 321.597 591.872 Td /F5 9.8 Tf [(SeqTraq)] TJ ET BT 358.988 591.872 Td /F1 9.8 Tf [( algorithm, both in the short and the long term.)] TJ ET BT 26.250 572.467 Td /F1 9.8 Tf [(In this paper we used maximum parsimony because the origin of A/H1N1 is sufficiently recent for homoplasies \(recombination )] TJ ET BT 26.250 560.562 Td /F1 9.8 Tf [(or back mutations\) to be safely ignored. However, )] TJ ET BT 243.548 560.562 Td /F5 9.8 Tf [(SeqTrack)] TJ ET BT 285.269 560.562 Td /F1 9.8 Tf [( genealogies could be optimized on other criteria, such as genetic )] TJ ET BT 26.250 548.658 Td /F1 9.8 Tf [(distances or log-likelihoods based on complex models of sequence evolution \(see Methods\). Another development of immediate )] TJ ET BT 26.250 536.753 Td /F1 9.8 Tf [(interest relates to the use of diverse genetic information. All analyzes were conducted on the hemagglutinin \(HA\) segment. The )] TJ ET BT 26.250 524.848 Td /F1 9.8 Tf [(influenza genome comprises eight segments each harbouring one gene. As the A/H1N1 sequencing effort was undertaken )] TJ ET BT 26.250 512.943 Td /F1 9.8 Tf [(independently by a large number of labs, the available genetic information is extremely heterogeneous. Sequences deposited )] TJ ET BT 26.250 501.039 Td /F1 9.8 Tf [(on Genbank for various strains range from small fragments of specific genes to complete genomes, including a majority of )] TJ ET BT 26.250 489.134 Td /F1 9.8 Tf [(strains for which an essentially random combination of segments were sequenced. This translates in a considerable loss of )] TJ ET BT 26.250 477.229 Td /F1 9.8 Tf [(information. )] TJ ET BT 79.894 477.229 Td /F5 9.8 Tf [(S)] TJ ET BT 86.398 477.229 Td /F1 9.8 Tf [( uch heterogeneous information could be accommodated by averaging genetic differentiation across segments, )] TJ ET BT 26.250 465.324 Td /F1 9.8 Tf [(using appropriate weights to account for different substitution rates and segment lengths.)] TJ ET BT 26.250 445.920 Td /F1 9.8 Tf [(However, including a large fraction of strains with heterogeneous sequencing coverage would require accurate estimates of )] TJ ET BT 26.250 434.015 Td /F1 9.8 Tf [(substitution rates, which can be difficult to obtain for emerging pathogens. Another possible concern is that different segments )] TJ ET BT 26.250 422.110 Td /F1 9.8 Tf [(may exhibit incongruent genealogies due to different selective pressures, reassortments and/or intra-genomic interactions )] TJ ET 0.267 0.267 0.267 rg BT 552.974 422.110 Td /F1 9.8 Tf [([4])] TJ ET BT 563.816 422.110 Td /F1 9.8 Tf [([25])] TJ ET BT 26.250 410.205 Td /F1 9.8 Tf [([26])] TJ ET BT 42.513 410.205 Td /F1 9.8 Tf [([27])] TJ ET BT 58.776 410.205 Td /F1 9.8 Tf [([28])] TJ ET 0.271 0.267 0.267 rg BT 75.039 410.205 Td /F1 9.8 Tf [( . Some other developments would require more effort. It would in particular be desirable to consider the various )] TJ ET BT 26.250 398.301 Td /F1 9.8 Tf [(parameters of the model from a probabilistic perspective. For instance, the date of probable transmission could be better )] TJ ET BT 26.250 386.396 Td /F1 9.8 Tf [(captured by a distribution of the time during which a specific sequence remains unaltered rather than a fixed collection date. )] TJ ET BT 26.250 374.491 Td /F1 9.8 Tf [(Moreover, a probabilistic framework would also allow incorporating information besides genetic sequences and collection dates, )] TJ ET BT 26.250 362.586 Td /F1 9.8 Tf [(such as prevalence data or spatial connectivity between locations.)] TJ ET BT 26.250 343.182 Td /F1 9.8 Tf [(The 2009 A/H1N1 influenza pandemic is the fourth in modern history. 20 )] TJ ET BT 341.107 347.070 Td /F1 8.7 Tf [(th)] TJ ET BT 348.335 343.182 Td /F1 9.8 Tf [( century pandemics occurred in 1918, 1957 and )] TJ ET BT 26.250 331.277 Td /F1 9.8 Tf [(1968. In all three previous cases, the newly emerged strain replaced the strain that was circulating and causing seasonal )] TJ ET BT 26.250 319.372 Td /F1 9.8 Tf [(\(winter\) epidemics. The current seasonal influenza is a descendent of the 1968 H3N2 pandemic and has been co-circulating )] TJ ET BT 26.250 307.467 Td /F1 9.8 Tf [(with a less virulent H1N1 strain at lower frequencies since 1977 )] TJ ET 0.267 0.267 0.267 rg BT 302.604 307.467 Td /F1 9.8 Tf [([4])] TJ ET 0.271 0.267 0.267 rg BT 313.446 307.467 Td /F1 9.8 Tf [( . Whether the 2009 A/H1N1 will fully displace the current )] TJ ET BT 26.250 295.563 Td /F1 9.8 Tf [(seasonal influenza strains remains to be seen. Seasonal influenza strains have strongly cyclical dynamics, with the majority of )] TJ ET BT 26.250 283.658 Td /F1 9.8 Tf [(cases observed during the winter in both hemispheres. 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An additional confounding effect arises from school holidays, which are also believed to be important drivers )] TJ ET BT 26.250 224.134 Td /F1 9.8 Tf [(of seasonality in influenza )] TJ ET 0.267 0.267 0.267 rg BT 140.598 224.134 Td /F1 9.8 Tf [([32])] TJ ET BT 156.861 224.134 Td /F1 9.8 Tf [([33])] TJ ET 0.271 0.267 0.267 rg BT 173.124 224.134 Td /F1 9.8 Tf [( .)] TJ ET BT 26.250 204.729 Td /F1 9.8 Tf [(In principle, our method would be ideal to shed further light on the effect of human travel, climate and additional factors such as )] TJ ET BT 26.250 192.825 Td /F1 9.8 Tf [(timing of school holidays on the underlying factors behind the spread of the 2009 A/H1N1 pandemic. However, the main )] TJ ET BT 26.250 180.920 Td /F1 9.8 Tf [(difficulty stems from the current limitation of the available data. The ratio between the number of confirmed and actual cases is )] TJ ET BT 26.250 169.015 Td /F1 9.8 Tf [(likely to vary greatly between countries. Moreover, the number of strains that have been sequenced for each country is )] TJ ET BT 26.250 157.110 Td /F1 9.8 Tf [(uncorrelated with the number of confirmed cases. This leads to considerable difficulties for disentangling the main factors )] TJ ET BT 26.250 145.206 Td /F1 9.8 Tf [(behind the spread of the 2009 A/H1N1 pandemic. What is certain is that human travel must be important. The majority of long )] TJ ET BT 26.250 133.301 Td /F1 9.8 Tf [(distance movement is likely to be mediated by airline travel both for seasonal and pandemic flu )] TJ ET 0.267 0.267 0.267 rg BT 437.554 133.301 Td /F1 9.8 Tf [([1])] TJ ET BT 448.396 133.301 Td /F1 9.8 Tf [([2])] TJ ET BT 459.238 133.301 Td /F1 9.8 Tf [([3])] TJ ET BT 470.080 133.301 Td /F1 9.8 Tf [([23])] TJ ET BT 486.343 133.301 Td /F1 9.8 Tf [([25])] TJ ET BT 502.606 133.301 Td /F1 9.8 Tf [([34])] TJ ET 0.271 0.267 0.267 rg BT 518.869 133.301 Td /F1 9.8 Tf [( . Despite the )] TJ ET BT 26.250 121.396 Td /F1 9.8 Tf [(limitations of the genetic dataset, we observe a highly significant correlation between flight traffic and the routes inferred by )] TJ ET BT 26.250 109.491 Td /F5 9.8 Tf [(SeqTrack)] TJ ET BT 67.970 109.491 Td /F1 9.8 Tf [( . At this stage, we are unable to provide a quantitative estimate of the effect of climate. However, the sustained )] TJ ET BT 26.250 97.587 Td /F1 9.8 Tf [(spread of the 2009 A/H1N1 strain in the Northern hemisphere during the spring and summer suggests it may be less sensitive )] TJ ET BT 26.250 85.682 Td /F1 9.8 Tf [(to climatic conditions than the seasonal influenza strains currently in circulation.)] TJ ET BT 26.250 66.277 Td /F1 9.8 Tf [(The )] TJ ET BT 45.760 66.277 Td /F5 9.8 Tf [(SeqTrack)] TJ ET BT 87.480 66.277 Td /F1 9.8 Tf [( algorithm has been specifically developed to model the spatiotemporal dynamics of the 2009 A/H1N1 pandemic. )] TJ ET BT 26.250 54.372 Td /F1 9.8 Tf [(However, the approach should be applicable to essentially any genetic data collected during the early stages of an outbreak. )] TJ ET BT 26.250 42.468 Td /F1 9.8 Tf [(This could include localised outbreaks within a school or a community but also epidemics at much larger geographical scale. As )] TJ ET Q q 0.000 0.000 0.000 rg BT 291.710 19.825 Td /F1 11.0 Tf [(5)] TJ ET BT 25.000 19.825 Td /F1 11.0 Tf [(PLOS Currents Influenza)] TJ ET Q endstream endobj 461 0 obj << /Type /Annot /Subtype /Link /A 462 0 R /Border [0 0 0] /H /I /Rect [ 552.9742 421.2083 563.8162 431.1290 ] >> endobj 462 0 obj << /Type /Action >> endobj 463 0 obj << /Type /Annot /Subtype /Link /A 464 0 R /Border [0 0 0] /H /I /Rect [ 563.8162 421.2083 580.0793 431.1290 ] >> endobj 464 0 obj << /Type /Action >> endobj 465 0 obj << /Type /Annot /Subtype /Link /A 466 0 R /Border [0 0 0] /H /I /Rect [ 26.2500 409.3036 42.5130 419.2242 ] >> endobj 466 0 obj << /Type /Action >> endobj 467 0 obj << /Type /Annot /Subtype /Link /A 468 0 R /Border [0 0 0] /H /I /Rect [ 42.5130 409.3036 58.7760 419.2242 ] >> endobj 468 0 obj << /Type /Action >> endobj 469 0 obj << /Type /Annot /Subtype /Link /A 470 0 R /Border [0 0 0] /H /I /Rect [ 58.7760 409.3036 75.0390 419.2242 ] >> endobj 470 0 obj << /Type /Action >> endobj 471 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it should prove effective in bacteria and fungi, in addition to )] TJ ET BT 26.250 755.571 Td /F1 9.8 Tf [(viruses. A straightforward application would be the reconstruction of the global spread of the fungus )] TJ ET BT 457.629 755.571 Td /F5 9.8 Tf [(Batrachochytrium )] TJ ET BT 26.250 743.667 Td /F5 9.8 Tf [(dendrobatidis)] TJ ET BT 84.779 743.667 Td /F1 9.8 Tf [( , which is driving amphibian populations to extinction worldwide )] TJ ET 0.267 0.267 0.267 rg BT 362.762 743.667 Td /F1 9.8 Tf [([35])] TJ ET 0.271 0.267 0.267 rg BT 379.024 743.667 Td /F1 9.8 Tf [( . We hope that the performance of the )] TJ ET BT 26.250 731.762 Td /F1 9.8 Tf [(method, together with its wide applicability, flexibility, computational speed and free availability within the )] TJ ET BT 478.728 731.762 Td /F5 9.8 Tf [(adegenet)] TJ ET BT 519.385 731.762 Td /F1 9.8 Tf [( package )] TJ ET 0.267 0.267 0.267 rg BT 561.661 731.762 Td /F1 9.8 Tf [([15])] TJ ET 0.271 0.267 0.267 rg BT 26.250 719.857 Td /F1 9.8 Tf [(will convince infectious disease epidemiologists to adopt it as an integral part of the toolkit for disease outbreak analysis. More )] TJ ET BT 26.250 707.952 Td /F1 9.8 Tf [(generally, we hope that the novel paradigm it is based upon will open a whole new field in the statistical genetics of emerging )] TJ ET BT 26.250 696.048 Td /F1 9.8 Tf [(pathogens.)] TJ ET BT 26.250 659.445 Td /F4 12.0 Tf [(Acknowledgments)] TJ ET BT 26.250 639.491 Td /F1 9.8 Tf [(We are most grateful to all our colleagues who sequenced strains from the 2009 influenza A/H1N1 pandemic and made them )] TJ ET BT 26.250 627.586 Td /F1 9.8 Tf [(publicly available. We feel particularly indebted towards Nancy Cox, Mark Greenway, Naomi Komadina, Andreas Nitsche, John )] TJ ET BT 26.250 615.681 Td /F1 9.8 Tf [(Pasick, Tomas Pumarola and Pilaipan Puthavathana for their willingness to provide additional information on sequences they )] TJ ET BT 26.250 603.777 Td /F1 9.8 Tf [(submitted on Genbank. We address many thanks to Vicente Acua for providing insights about the graph theory, and to William )] TJ ET BT 26.250 591.872 Td /F1 9.8 Tf [(Hanage for commenting on the earlier version of the work.)] TJ ET BT 26.250 555.269 Td /F4 12.0 Tf [(Funding information)] TJ ET BT 26.250 535.315 Td /F1 9.8 Tf [(FB acknowledges financial support from the BBSRC and the MRC.)] TJ ET BT 26.250 498.713 Td /F4 12.0 Tf [(Competing interests)] TJ ET BT 26.250 478.758 Td /F1 9.8 Tf [(The authors have declared that no competing interests exist.)] TJ ET BT 26.250 442.156 Td /F4 12.0 Tf [(References)] TJ ET BT 26.250 414.702 Td /F1 9.8 Tf [(1.)] TJ ET BT 38.132 414.702 Td /F1 9.8 Tf [(Cooper BS, Pitman RJ, Edmunds WJ, Gay NJ \(2006\) Delaying the International Spread of Pandemic Influenza. 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Genetic Epidemiology 33, 281-289.)] TJ ET BT 26.250 250.654 Td /F1 9.8 Tf [(7.)] TJ ET BT 38.132 250.654 Td /F1 9.8 Tf [(Cottam EM, Thebaud G, Wadsworth J, et al. \(2008\) Integrating genetic and epidemiological data to determine transmission )] TJ ET BT 26.250 238.749 Td /F1 9.8 Tf [(pathways of foot-and-mouth disease virus. Proceedings of the Royal Society B-Biological Sciences 275, 887-895.)] TJ ET BT 26.250 219.345 Td /F1 9.8 Tf [(8.)] TJ ET BT 38.132 219.345 Td /F1 9.8 Tf [(Drummond AJ, Rambaut A \(2007\) BEAST: Bayesian evolutionary analysis by sampling trees. Bmc Evolutionary Biology 7, 8.)] TJ ET BT 26.250 199.940 Td /F1 9.8 Tf [(9.)] TJ ET BT 38.132 199.940 Td /F1 9.8 Tf [(Grenfell BT, Pybus OG, Gog JR, et al. \(2004\) Unifying the Epidemiological and Evolutionary Dynamics of Pathogens. )] TJ ET BT 26.250 188.035 Td /F1 9.8 Tf [(Science 303, 327-332.)] TJ ET BT 26.250 168.630 Td /F1 9.8 Tf [(10.)] TJ ET BT 43.553 168.630 Td /F1 9.8 Tf [(Templeton AR \(1998\) Nested clade analyses of phylogeographic data: testing hypotheses about gene flow and population )] TJ ET BT 26.250 156.726 Td /F1 9.8 Tf [(history. Molecular Ecology 7, 381-397.)] TJ ET BT 26.250 137.321 Td /F1 9.8 Tf [(11.)] TJ ET BT 43.553 137.321 Td /F1 9.8 Tf [(Garten RJ, Davis CT, Russell CA, et al. \(2009\) Antigenic and Genetic Characteristics of Swine-Origin 2009 A\(H1N1\) )] TJ ET BT 26.250 125.416 Td /F1 9.8 Tf [(Influenza Viruses Circulating in Humans. Science, 325, 197-201.)] TJ ET BT 26.250 106.011 Td /F1 9.8 Tf [(12.)] TJ ET BT 43.553 106.011 Td /F1 9.8 Tf [(Smith G, Vijaykrishna D, Bahl J, et al. \(2009\) Origins and evolutionary genomics of the 2009 swine-origin H1N1 influenza A )] TJ ET BT 26.250 94.107 Td /F1 9.8 Tf [(epidemic. Nature. 459, 1122-1127.)] TJ ET BT 26.250 74.702 Td /F1 9.8 Tf [(13.)] TJ ET BT 43.553 74.702 Td /F1 9.8 Tf [(Chu YJ, Liu TH \(1965\) On the Shortest Arborescence of a Directed Graph. Science Sinica 14, 1396-1400.)] TJ ET BT 26.250 55.297 Td /F1 9.8 Tf [(14.)] TJ ET BT 43.553 55.297 Td /F1 9.8 Tf [(Edmonds J \(1967\) Optimum Branchings. J. Res. Nat. Bur. Standards 9, 233-240.)] TJ ET Q q 15.000 45.416 577.500 731.584 re W n 0.271 0.267 0.267 rg BT 26.250 767.476 Td /F1 9.8 Tf [(the method does not require extensive genetic polymorphism it should prove effective in bacteria and fungi, in addition to )] TJ ET BT 26.250 755.571 Td /F1 9.8 Tf [(viruses. A straightforward application would be the reconstruction of the global spread of the fungus )] TJ ET BT 457.629 755.571 Td /F5 9.8 Tf [(Batrachochytrium )] TJ ET BT 26.250 743.667 Td /F5 9.8 Tf [(dendrobatidis)] TJ ET BT 84.779 743.667 Td /F1 9.8 Tf [( , which is driving amphibian populations to extinction worldwide )] TJ ET 0.267 0.267 0.267 rg BT 362.762 743.667 Td /F1 9.8 Tf [([35])] TJ ET 0.271 0.267 0.267 rg BT 379.024 743.667 Td /F1 9.8 Tf [( . We hope that the performance of the )] TJ ET BT 26.250 731.762 Td /F1 9.8 Tf [(method, together with its wide applicability, flexibility, computational speed and free availability within the )] TJ ET BT 478.728 731.762 Td /F5 9.8 Tf [(adegenet)] TJ ET BT 519.385 731.762 Td /F1 9.8 Tf [( package )] TJ ET 0.267 0.267 0.267 rg BT 561.661 731.762 Td /F1 9.8 Tf [([15])] TJ ET 0.271 0.267 0.267 rg BT 26.250 719.857 Td /F1 9.8 Tf [(will convince infectious disease epidemiologists to adopt it as an integral part of the toolkit for disease outbreak analysis. More )] TJ ET BT 26.250 707.952 Td /F1 9.8 Tf [(generally, we hope that the novel paradigm it is based upon will open a whole new field in the statistical genetics of emerging )] TJ ET BT 26.250 696.048 Td /F1 9.8 Tf [(pathogens.)] TJ ET BT 26.250 659.445 Td /F4 12.0 Tf [(Acknowledgments)] TJ ET BT 26.250 639.491 Td /F1 9.8 Tf [(We are most grateful to all our colleagues who sequenced strains from the 2009 influenza A/H1N1 pandemic and made them )] TJ ET BT 26.250 627.586 Td /F1 9.8 Tf [(publicly available. We feel particularly indebted towards Nancy Cox, Mark Greenway, Naomi Komadina, Andreas Nitsche, John )] TJ ET BT 26.250 615.681 Td /F1 9.8 Tf [(Pasick, Tomas Pumarola and Pilaipan Puthavathana for their willingness to provide additional information on sequences they )] TJ ET BT 26.250 603.777 Td /F1 9.8 Tf [(submitted on Genbank. We address many thanks to Vicente Acua for providing insights about the graph theory, and to William )] TJ ET BT 26.250 591.872 Td /F1 9.8 Tf [(Hanage for commenting on the earlier version of the work.)] TJ ET BT 26.250 555.269 Td /F4 12.0 Tf [(Funding information)] TJ ET BT 26.250 535.315 Td /F1 9.8 Tf [(FB acknowledges financial support from the BBSRC and the MRC.)] TJ ET BT 26.250 498.713 Td /F4 12.0 Tf [(Competing interests)] TJ ET BT 26.250 478.758 Td /F1 9.8 Tf [(The authors have declared that no competing interests exist.)] TJ ET BT 26.250 442.156 Td /F4 12.0 Tf [(References)] TJ ET BT 26.250 414.702 Td /F1 9.8 Tf [(1.)] TJ ET BT 38.132 414.702 Td /F1 9.8 Tf [(Cooper BS, Pitman RJ, Edmunds WJ, Gay NJ \(2006\) Delaying the International Spread of Pandemic Influenza. PLoS Med 3, )] TJ ET BT 26.250 402.797 Td /F1 9.8 Tf [(e212.)] TJ ET BT 26.250 383.392 Td /F1 9.8 Tf [(2.)] TJ ET BT 38.132 383.392 Td /F1 9.8 Tf [(Ferguson NM, Cummings DAT, Fraser C, et al. \(2006\) Strategies for mitigating an influenza pandemic. Nature 442, 448-452.)] TJ ET BT 26.250 363.987 Td /F1 9.8 Tf [(3.)] TJ ET BT 38.132 363.987 Td /F1 9.8 Tf [(Germann TC, Kadau K, Longini IM, Macken CA \(2006\) Mitigation strategies for pandemic influenza in the United States. 103, )] TJ ET BT 26.250 352.083 Td /F1 9.8 Tf [(5935-5940.)] TJ ET BT 26.250 332.678 Td /F1 9.8 Tf [(4.)] TJ ET BT 38.132 332.678 Td /F1 9.8 Tf [(Rambaut A, Pybus OG, Nelson MI, et al. \(2008\) The genomic and epidemiological dynamics of human influenza A virus. )] TJ ET BT 26.250 320.773 Td /F1 9.8 Tf [(Nature 453, 615-U612.)] TJ ET BT 26.250 301.368 Td /F1 9.8 Tf [(5.)] TJ ET BT 38.132 301.368 Td /F1 9.8 Tf [(Russell CA, Jones TC, Barr IG, et al. \(2008\) The Global Circulation of Seasonal Influenza A \(H3N2\) Viruses. Science 320, )] TJ ET BT 26.250 289.464 Td /F1 9.8 Tf [(340-346.)] TJ ET BT 26.250 270.059 Td /F1 9.8 Tf [(6.)] TJ ET BT 38.132 270.059 Td /F1 9.8 Tf [(Sloan CD, Duell EJ, Shi X, et al. \(2009\) Ecogeographic genetic epidemiology. Genetic Epidemiology 33, 281-289.)] TJ ET BT 26.250 250.654 Td /F1 9.8 Tf [(7.)] TJ ET BT 38.132 250.654 Td /F1 9.8 Tf [(Cottam EM, Thebaud G, Wadsworth J, et al. \(2008\) Integrating genetic and epidemiological data to determine transmission )] TJ ET BT 26.250 238.749 Td /F1 9.8 Tf [(pathways of foot-and-mouth disease virus. Proceedings of the Royal Society B-Biological Sciences 275, 887-895.)] TJ ET BT 26.250 219.345 Td /F1 9.8 Tf [(8.)] TJ ET BT 38.132 219.345 Td /F1 9.8 Tf [(Drummond AJ, Rambaut A \(2007\) BEAST: Bayesian evolutionary analysis by sampling trees. 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A straightforward application would be the reconstruction of the global spread of the fungus )] TJ ET BT 457.629 755.571 Td /F5 9.8 Tf [(Batrachochytrium )] TJ ET BT 26.250 743.667 Td /F5 9.8 Tf [(dendrobatidis)] TJ ET BT 84.779 743.667 Td /F1 9.8 Tf [( , which is driving amphibian populations to extinction worldwide )] TJ ET 0.267 0.267 0.267 rg BT 362.762 743.667 Td /F1 9.8 Tf [([35])] TJ ET 0.271 0.267 0.267 rg BT 379.024 743.667 Td /F1 9.8 Tf [( . We hope that the performance of the )] TJ ET BT 26.250 731.762 Td /F1 9.8 Tf [(method, together with its wide applicability, flexibility, computational speed and free availability within the )] TJ ET BT 478.728 731.762 Td /F5 9.8 Tf [(adegenet)] TJ ET BT 519.385 731.762 Td /F1 9.8 Tf [( package )] TJ ET 0.267 0.267 0.267 rg BT 561.661 731.762 Td /F1 9.8 Tf [([15])] TJ ET 0.271 0.267 0.267 rg BT 26.250 719.857 Td /F1 9.8 Tf [(will convince infectious disease epidemiologists to adopt it as an integral part of the toolkit for disease outbreak analysis. More )] TJ ET BT 26.250 707.952 Td /F1 9.8 Tf [(generally, we hope that the novel paradigm it is based upon will open a whole new field in the statistical genetics of emerging )] TJ ET BT 26.250 696.048 Td /F1 9.8 Tf [(pathogens.)] TJ ET BT 26.250 659.445 Td /F4 12.0 Tf [(Acknowledgments)] TJ ET BT 26.250 639.491 Td /F1 9.8 Tf [(We are most grateful to all our colleagues who sequenced strains from the 2009 influenza A/H1N1 pandemic and made them )] TJ ET BT 26.250 627.586 Td /F1 9.8 Tf [(publicly available. We feel particularly indebted towards Nancy Cox, Mark Greenway, Naomi Komadina, Andreas Nitsche, John )] TJ ET BT 26.250 615.681 Td /F1 9.8 Tf [(Pasick, Tomas Pumarola and Pilaipan Puthavathana for their willingness to provide additional information on sequences they )] TJ ET BT 26.250 603.777 Td /F1 9.8 Tf [(submitted on Genbank. We address many thanks to Vicente Acua for providing insights about the graph theory, and to William )] TJ ET BT 26.250 591.872 Td /F1 9.8 Tf [(Hanage for commenting on the earlier version of the work.)] TJ ET BT 26.250 555.269 Td /F4 12.0 Tf [(Funding information)] TJ ET BT 26.250 535.315 Td /F1 9.8 Tf [(FB acknowledges financial support from the BBSRC and the MRC.)] TJ ET BT 26.250 498.713 Td /F4 12.0 Tf [(Competing interests)] TJ ET BT 26.250 478.758 Td /F1 9.8 Tf [(The authors have declared that no competing interests exist.)] TJ ET BT 26.250 442.156 Td /F4 12.0 Tf [(References)] TJ ET BT 26.250 414.702 Td /F1 9.8 Tf [(1.)] TJ ET BT 38.132 414.702 Td /F1 9.8 Tf [(Cooper BS, Pitman RJ, Edmunds WJ, Gay NJ \(2006\) Delaying the International Spread of Pandemic Influenza. PLoS Med 3, )] TJ ET BT 26.250 402.797 Td /F1 9.8 Tf [(e212.)] TJ ET BT 26.250 383.392 Td /F1 9.8 Tf [(2.)] TJ ET BT 38.132 383.392 Td /F1 9.8 Tf [(Ferguson NM, Cummings DAT, Fraser C, et al. \(2006\) Strategies for mitigating an influenza pandemic. Nature 442, 448-452.)] TJ ET BT 26.250 363.987 Td /F1 9.8 Tf [(3.)] TJ ET BT 38.132 363.987 Td /F1 9.8 Tf [(Germann TC, Kadau K, Longini IM, Macken CA \(2006\) Mitigation strategies for pandemic influenza in the United States. 103, )] TJ ET BT 26.250 352.083 Td /F1 9.8 Tf [(5935-5940.)] TJ ET BT 26.250 332.678 Td /F1 9.8 Tf [(4.)] TJ ET BT 38.132 332.678 Td /F1 9.8 Tf [(Rambaut A, Pybus OG, Nelson MI, et al. \(2008\) The genomic and epidemiological dynamics of human influenza A virus. )] TJ ET BT 26.250 320.773 Td /F1 9.8 Tf [(Nature 453, 615-U612.)] TJ ET BT 26.250 301.368 Td /F1 9.8 Tf [(5.)] TJ ET BT 38.132 301.368 Td /F1 9.8 Tf [(Russell CA, Jones TC, Barr IG, et al. \(2008\) The Global Circulation of Seasonal Influenza A \(H3N2\) Viruses. Science 320, )] TJ ET BT 26.250 289.464 Td /F1 9.8 Tf [(340-346.)] TJ ET BT 26.250 270.059 Td /F1 9.8 Tf [(6.)] TJ ET BT 38.132 270.059 Td /F1 9.8 Tf [(Sloan CD, Duell EJ, Shi X, et al. \(2009\) Ecogeographic genetic epidemiology. 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PLoS Med 6, e1000085.)] TJ ET BT 26.250 470.691 Td /F1 9.8 Tf [(25.)] TJ ET BT 43.553 470.691 Td /F1 9.8 Tf [(Viboud C, Bjornstad ON, Smith DL, et al. \(2006\) Synchrony, Waves, and Spatial Hierarchies in the Spread of Influenza. )] TJ ET BT 26.250 458.786 Td /F1 9.8 Tf [(Science 312, 447-451.)] TJ ET BT 26.250 439.381 Td /F1 9.8 Tf [(26.)] TJ ET BT 43.553 439.381 Td /F1 9.8 Tf [(Ferguson NM, Galvani AP, Bush RM \(2003\) Ecological and immunological determinants of influenza evolution. Nature 422, )] TJ ET BT 26.250 427.476 Td /F1 9.8 Tf [(428-433.)] TJ ET BT 26.250 408.072 Td /F1 9.8 Tf [(27.)] TJ ET BT 43.553 408.072 Td /F1 9.8 Tf [(Holmes EC, Ghedin E, Miller N, et al. \(2005\) Whole-Genome Analysis of Human Influenza A Virus Reveals Multiple )] TJ ET BT 26.250 396.167 Td /F1 9.8 Tf [(Persistent Lineages and Reassortment among Recent H3N2 Viruses. PLoS Biol 3, e300.)] TJ ET BT 26.250 376.762 Td /F1 9.8 Tf [(28.)] TJ ET BT 43.553 376.762 Td /F1 9.8 Tf [(Young JF, Palese P \(1979\) Evolution of human influenza A viruses in nature: recombination contributes to genetic variation )] TJ ET BT 26.250 364.857 Td /F1 9.8 Tf [(of H1N1 strains. Proceedings of the National Academy of Sciences of the United States of America 76, 6547-6551.)] TJ ET BT 26.250 345.453 Td /F1 9.8 Tf [(29.)] TJ ET BT 43.553 345.453 Td /F1 9.8 Tf [(Mitnaul LJ, Matrosovich MN, Castrucci MR, et al. \(2000\) Balanced Hemagglutinin and Neuraminidase Activities Are Critical )] TJ ET BT 26.250 333.548 Td /F1 9.8 Tf [(for Efficient Replication of Influenza A Virus. J. Virol. 74, 6015-6020.)] TJ ET BT 26.250 314.143 Td /F1 9.8 Tf [(30.)] TJ ET BT 43.553 314.143 Td /F1 9.8 Tf [(Earn, D.J.D., Dushoff, J., and Levin, S.A., 2002. Ecology and evolution of the flu. Trends in Ecology & Evolution 17, 334-340.)] TJ ET BT 26.250 294.738 Td /F1 9.8 Tf [(31.)] TJ ET BT 43.553 294.738 Td /F1 9.8 Tf [(Dushoff, J., Plotkin, J.B., Levin, S.A., and Earn, D.J.D., 2004. Dynamical resonance can account for seasonality of influenza )] TJ ET BT 26.250 282.834 Td /F1 9.8 Tf [(epidemics. Proceedings of the National Academy of Sciences of the United States of America 101, 16915-16916.)] TJ ET BT 26.250 263.429 Td /F1 9.8 Tf [(32.)] TJ ET BT 43.553 263.429 Td /F1 9.8 Tf [(Shaman, J., and Kohn, M., 2009. Absolute humidity modulates influenza survival, transmission, and seasonality. )] TJ ET BT 26.250 251.524 Td /F1 9.8 Tf [(Proceedings of the National Academy of Sciences of the United States of America 106, 3243-3248.)] TJ ET BT 26.250 232.119 Td /F1 9.8 Tf [(33.)] TJ ET BT 43.553 232.119 Td /F1 9.8 Tf [(Cauchemez, S., Valleron, A.-J., Boelle, P.-Y., Flahault, A., and Ferguson, N.M., 2008. Estimating the impact of school )] TJ ET BT 26.250 220.215 Td /F1 9.8 Tf [(closure on influenza transmission from Sentinel data. Nature 452, 750-754.)] TJ ET BT 26.250 200.810 Td /F1 9.8 Tf [(34.)] TJ ET BT 43.553 200.810 Td /F1 9.8 Tf [(Heymann, A., Chodick, G., Reichman, B., Kokia, E., and Laufer, J., 2004. Influence of school closure on the incidence of )] TJ ET BT 26.250 188.905 Td /F1 9.8 Tf [(viral respiratory diseases among children and on health care utilization. Pediatric Infectious Disease Journal 23, 675-677.)] TJ ET BT 26.250 169.500 Td /F1 9.8 Tf [(35.)] TJ ET BT 43.553 169.500 Td /F1 9.8 Tf [(Brownstein, J.S., Wolfe, C.J., and Mandl, K.D., 2006. Empirical Evidence for the Effect of Airline Travel on Inter-Regional )] TJ ET BT 26.250 157.596 Td /F1 9.8 Tf [(Influenza Spread in the United States. PLoS Med 3, e401.)] TJ ET BT 26.250 138.191 Td /F1 9.8 Tf [(36.)] TJ ET BT 43.553 138.191 Td /F1 9.8 Tf [(James TY, Litvintseva AP, Vilgalys R, et al. 2009. Rapid Global Expansion of the Fungal Disease Chytridiomycosis into )] TJ ET BT 26.250 126.286 Td /F1 9.8 Tf [(Declining and Healthy Amphibian Populations. Plos Pathogens 5, 12.)] TJ ET Q q 15.000 108.905 577.500 668.095 re W n 0.271 0.267 0.267 rg BT 26.250 759.976 Td /F1 9.8 Tf [(15.)] TJ ET BT 43.553 759.976 Td /F1 9.8 Tf [(Jombart T \(2008\) adegenet: a R package for the multivariate analysis of genetic markers. Bioinformatics 24, 1403-1405.)] TJ ET BT 26.250 740.571 Td /F1 9.8 Tf [(16.)] TJ ET BT 43.553 740.571 Td /F1 9.8 Tf [(R Development Core Team \(2009\) R: A language and environment for statistical computing. R Foundation for Statistical )] TJ ET BT 26.250 728.667 Td /F1 9.8 Tf [(Computing, Vienna.)] TJ ET BT 26.250 709.262 Td /F1 9.8 Tf [(17.)] TJ ET BT 43.553 709.262 Td /F1 9.8 Tf [(Benson DA, Karsch-Mizrachi I, Lipman DJ, Ostell J, Wheeler DL \(2007\) GenBank. Nucl. Acids Res., S1, D21-D25.)] TJ ET BT 26.250 689.857 Td /F1 9.8 Tf [(18.)] TJ ET BT 43.553 689.857 Td /F1 9.8 Tf [(Bush RM, Smith CB, Cox NJ, Fitch WM \(2000\) Effects of passage history and sampling bias on phylogenetic reconstruction )] TJ ET BT 26.250 677.952 Td /F1 9.8 Tf [(of human influenza A evolution. Proceedings of the National Academy of Sciences of the United States of America 97, 6974-)] TJ ET BT 26.250 666.048 Td /F1 9.8 Tf [(6980.)] TJ ET BT 26.250 646.643 Td /F1 9.8 Tf [(19.)] TJ ET BT 43.553 646.643 Td /F1 9.8 Tf [(Larkin MA, Blackshields G, Brown NP, et al. \(2007\) Clustal W and Clustal X version 2.0. Bioinformatics 23, 2947-2948.)] TJ ET BT 26.250 627.238 Td /F1 9.8 Tf [(20.)] TJ ET BT 43.553 627.238 Td /F1 9.8 Tf [(Waterhouse AM, Procter JB, Martin DMA, Clamp M, Barton GJ \(2009\) Jalview Version 2--a multiple sequence alignment )] TJ ET BT 26.250 615.333 Td /F1 9.8 Tf [(editor and analysis workbench. Bioinformatics 25, 1189-1191.)] TJ ET BT 26.250 595.929 Td /F1 9.8 Tf [(21.)] TJ ET BT 43.553 595.929 Td /F1 9.8 Tf [(Paradis E, Claude J, Strimmer K \(2004\) APE: Analyses of Phylogenetics and Evolution in R language. Bioinformatics 20, )] TJ ET BT 26.250 584.024 Td /F1 9.8 Tf [(289-290.)] TJ ET BT 26.250 564.619 Td /F1 9.8 Tf [(22.)] TJ ET BT 43.553 564.619 Td /F1 9.8 Tf [(Fraser C, Donnelly CA, Cauchemez S, et al. \(2009\) Pandemic Potential of a Strain of Influenza A \(H1N1\) : Early Findings. )] TJ ET BT 26.250 552.714 Td /F1 9.8 Tf [(Science. 324, 1557-1561.)] TJ ET BT 26.250 533.310 Td /F1 9.8 Tf [(23.)] TJ ET BT 43.553 533.310 Td /F1 9.8 Tf [(Viboud CC, Bjornstad ON, Smith DL, et al. \(2006\) Synchrony, Waves, and Spatial Hierarchies in the Spread of Influenza. )] TJ ET BT 26.250 521.405 Td /F1 9.8 Tf [(Science 312, 447-451.)] TJ ET BT 26.250 502.000 Td /F1 9.8 Tf [(24.)] TJ ET BT 43.553 502.000 Td /F1 9.8 Tf [(Wu JT, Leung GM, Lipsitch M, Cooper BS, Riley S \(2009\) Hedging against Antiviral Resistance during the Next Influenza )] TJ ET BT 26.250 490.095 Td /F1 9.8 Tf [(Pandemic Using Small Stockpiles of an Alternative Chemotherapy. PLoS Med 6, e1000085.)] TJ ET BT 26.250 470.691 Td /F1 9.8 Tf [(25.)] TJ ET BT 43.553 470.691 Td /F1 9.8 Tf [(Viboud C, Bjornstad ON, Smith DL, et al. \(2006\) Synchrony, Waves, and Spatial Hierarchies in the Spread of Influenza. )] TJ ET BT 26.250 458.786 Td /F1 9.8 Tf [(Science 312, 447-451.)] TJ ET BT 26.250 439.381 Td /F1 9.8 Tf [(26.)] TJ ET BT 43.553 439.381 Td /F1 9.8 Tf [(Ferguson NM, Galvani AP, Bush RM \(2003\) Ecological and immunological determinants of influenza evolution. Nature 422, )] TJ ET BT 26.250 427.476 Td /F1 9.8 Tf [(428-433.)] TJ ET BT 26.250 408.072 Td /F1 9.8 Tf [(27.)] TJ ET BT 43.553 408.072 Td /F1 9.8 Tf [(Holmes EC, Ghedin E, Miller N, et al. \(2005\) Whole-Genome Analysis of Human Influenza A Virus Reveals Multiple )] TJ ET BT 26.250 396.167 Td /F1 9.8 Tf [(Persistent Lineages and Reassortment among Recent H3N2 Viruses. PLoS Biol 3, e300.)] TJ ET BT 26.250 376.762 Td /F1 9.8 Tf [(28.)] TJ ET BT 43.553 376.762 Td /F1 9.8 Tf [(Young JF, Palese P \(1979\) Evolution of human influenza A viruses in nature: recombination contributes to genetic variation )] TJ ET BT 26.250 364.857 Td /F1 9.8 Tf [(of H1N1 strains. Proceedings of the National Academy of Sciences of the United States of America 76, 6547-6551.)] TJ ET BT 26.250 345.453 Td /F1 9.8 Tf [(29.)] TJ ET BT 43.553 345.453 Td /F1 9.8 Tf [(Mitnaul LJ, Matrosovich MN, Castrucci MR, et al. \(2000\) Balanced Hemagglutinin and Neuraminidase Activities Are Critical )] TJ ET BT 26.250 333.548 Td /F1 9.8 Tf [(for Efficient Replication of Influenza A Virus. J. Virol. 74, 6015-6020.)] TJ ET BT 26.250 314.143 Td /F1 9.8 Tf [(30.)] TJ ET BT 43.553 314.143 Td /F1 9.8 Tf [(Earn, D.J.D., Dushoff, J., and Levin, S.A., 2002. Ecology and evolution of the flu. Trends in Ecology & Evolution 17, 334-340.)] TJ ET BT 26.250 294.738 Td /F1 9.8 Tf [(31.)] TJ ET BT 43.553 294.738 Td /F1 9.8 Tf [(Dushoff, J., Plotkin, J.B., Levin, S.A., and Earn, D.J.D., 2004. Dynamical resonance can account for seasonality of influenza )] TJ ET BT 26.250 282.834 Td /F1 9.8 Tf [(epidemics. Proceedings of the National Academy of Sciences of the United States of America 101, 16915-16916.)] TJ ET BT 26.250 263.429 Td /F1 9.8 Tf [(32.)] TJ ET BT 43.553 263.429 Td /F1 9.8 Tf [(Shaman, J., and Kohn, M., 2009. Absolute humidity modulates influenza survival, transmission, and seasonality. )] TJ ET BT 26.250 251.524 Td /F1 9.8 Tf [(Proceedings of the National Academy of Sciences of the United States of America 106, 3243-3248.)] TJ ET BT 26.250 232.119 Td /F1 9.8 Tf [(33.)] TJ ET BT 43.553 232.119 Td /F1 9.8 Tf [(Cauchemez, S., Valleron, A.-J., Boelle, P.-Y., Flahault, A., and Ferguson, N.M., 2008. Estimating the impact of school )] TJ ET BT 26.250 220.215 Td /F1 9.8 Tf [(closure on influenza transmission from Sentinel data. Nature 452, 750-754.)] TJ ET BT 26.250 200.810 Td /F1 9.8 Tf [(34.)] TJ ET BT 43.553 200.810 Td /F1 9.8 Tf [(Heymann, A., Chodick, G., Reichman, B., Kokia, E., and Laufer, J., 2004. Influence of school closure on the incidence of )] TJ ET BT 26.250 188.905 Td /F1 9.8 Tf [(viral respiratory diseases among children and on health care utilization. Pediatric Infectious Disease Journal 23, 675-677.)] TJ ET BT 26.250 169.500 Td /F1 9.8 Tf [(35.)] TJ ET BT 43.553 169.500 Td /F1 9.8 Tf [(Brownstein, J.S., Wolfe, C.J., and Mandl, K.D., 2006. Empirical Evidence for the Effect of Airline Travel on Inter-Regional )] TJ ET BT 26.250 157.596 Td /F1 9.8 Tf [(Influenza Spread in the United States. PLoS Med 3, e401.)] TJ ET BT 26.250 138.191 Td /F1 9.8 Tf [(36.)] TJ ET BT 43.553 138.191 Td /F1 9.8 Tf [(James TY, Litvintseva AP, Vilgalys R, et al. 2009. Rapid Global Expansion of the Fungal Disease Chytridiomycosis into )] TJ ET BT 26.250 126.286 Td /F1 9.8 Tf [(Declining and Healthy Amphibian Populations. Plos Pathogens 5, 12.)] TJ ET Q q 15.000 108.905 577.500 668.095 re W n 0.271 0.267 0.267 rg BT 26.250 759.976 Td /F1 9.8 Tf [(15.)] TJ ET BT 43.553 759.976 Td /F1 9.8 Tf [(Jombart T \(2008\) adegenet: a R package for the multivariate analysis of genetic markers. Bioinformatics 24, 1403-1405.)] TJ ET BT 26.250 740.571 Td /F1 9.8 Tf [(16.)] TJ ET BT 43.553 740.571 Td /F1 9.8 Tf [(R Development Core Team \(2009\) R: A language and environment for statistical computing. R Foundation for Statistical )] TJ ET BT 26.250 728.667 Td /F1 9.8 Tf [(Computing, Vienna.)] TJ ET BT 26.250 709.262 Td /F1 9.8 Tf [(17.)] TJ ET BT 43.553 709.262 Td /F1 9.8 Tf [(Benson DA, Karsch-Mizrachi I, Lipman DJ, Ostell J, Wheeler DL \(2007\) GenBank. Nucl. Acids Res., S1, D21-D25.)] TJ ET BT 26.250 689.857 Td /F1 9.8 Tf [(18.)] TJ ET BT 43.553 689.857 Td /F1 9.8 Tf [(Bush RM, Smith CB, Cox NJ, Fitch WM \(2000\) Effects of passage history and sampling bias on phylogenetic reconstruction )] TJ ET BT 26.250 677.952 Td /F1 9.8 Tf [(of human influenza A evolution. Proceedings of the National Academy of Sciences of the United States of America 97, 6974-)] TJ ET BT 26.250 666.048 Td /F1 9.8 Tf [(6980.)] TJ ET BT 26.250 646.643 Td /F1 9.8 Tf [(19.)] TJ ET BT 43.553 646.643 Td /F1 9.8 Tf [(Larkin MA, Blackshields G, Brown NP, et al. \(2007\) Clustal W and Clustal X version 2.0. Bioinformatics 23, 2947-2948.)] TJ ET BT 26.250 627.238 Td /F1 9.8 Tf [(20.)] TJ ET BT 43.553 627.238 Td /F1 9.8 Tf [(Waterhouse AM, Procter JB, Martin DMA, Clamp M, Barton GJ \(2009\) Jalview Version 2--a multiple sequence alignment )] TJ ET BT 26.250 615.333 Td /F1 9.8 Tf [(editor and analysis workbench. Bioinformatics 25, 1189-1191.)] TJ ET BT 26.250 595.929 Td /F1 9.8 Tf [(21.)] TJ ET BT 43.553 595.929 Td /F1 9.8 Tf [(Paradis E, Claude J, Strimmer K \(2004\) APE: Analyses of Phylogenetics and Evolution in R language. Bioinformatics 20, )] TJ ET BT 26.250 584.024 Td /F1 9.8 Tf [(289-290.)] TJ ET BT 26.250 564.619 Td /F1 9.8 Tf [(22.)] TJ ET BT 43.553 564.619 Td /F1 9.8 Tf [(Fraser C, Donnelly CA, Cauchemez S, et al. \(2009\) Pandemic Potential of a Strain of Influenza A \(H1N1\) : Early Findings. )] TJ ET BT 26.250 552.714 Td /F1 9.8 Tf [(Science. 324, 1557-1561.)] TJ ET BT 26.250 533.310 Td /F1 9.8 Tf [(23.)] TJ ET BT 43.553 533.310 Td /F1 9.8 Tf [(Viboud CC, Bjornstad ON, Smith DL, et al. \(2006\) Synchrony, Waves, and Spatial Hierarchies in the Spread of Influenza. )] TJ ET BT 26.250 521.405 Td /F1 9.8 Tf [(Science 312, 447-451.)] TJ ET BT 26.250 502.000 Td /F1 9.8 Tf [(24.)] TJ ET BT 43.553 502.000 Td /F1 9.8 Tf [(Wu JT, Leung GM, Lipsitch M, Cooper BS, Riley S \(2009\) Hedging against Antiviral Resistance during the Next Influenza )] TJ ET BT 26.250 490.095 Td /F1 9.8 Tf [(Pandemic Using Small Stockpiles of an Alternative Chemotherapy. PLoS Med 6, e1000085.)] TJ ET BT 26.250 470.691 Td /F1 9.8 Tf [(25.)] TJ ET BT 43.553 470.691 Td /F1 9.8 Tf [(Viboud C, Bjornstad ON, Smith DL, et al. \(2006\) Synchrony, Waves, and Spatial Hierarchies in the Spread of Influenza. )] TJ ET BT 26.250 458.786 Td /F1 9.8 Tf [(Science 312, 447-451.)] TJ ET BT 26.250 439.381 Td /F1 9.8 Tf [(26.)] TJ ET BT 43.553 439.381 Td /F1 9.8 Tf [(Ferguson NM, Galvani AP, Bush RM \(2003\) Ecological and immunological determinants of influenza evolution. Nature 422, )] TJ ET BT 26.250 427.476 Td /F1 9.8 Tf [(428-433.)] TJ ET BT 26.250 408.072 Td /F1 9.8 Tf [(27.)] TJ ET BT 43.553 408.072 Td /F1 9.8 Tf [(Holmes EC, Ghedin E, Miller N, et al. \(2005\) Whole-Genome Analysis of Human Influenza A Virus Reveals Multiple )] TJ ET BT 26.250 396.167 Td /F1 9.8 Tf [(Persistent Lineages and Reassortment among Recent H3N2 Viruses. PLoS Biol 3, e300.)] TJ ET BT 26.250 376.762 Td /F1 9.8 Tf [(28.)] TJ ET BT 43.553 376.762 Td /F1 9.8 Tf [(Young JF, Palese P \(1979\) Evolution of human influenza A viruses in nature: recombination contributes to genetic variation )] TJ ET BT 26.250 364.857 Td /F1 9.8 Tf [(of H1N1 strains. Proceedings of the National Academy of Sciences of the United States of America 76, 6547-6551.)] TJ ET BT 26.250 345.453 Td /F1 9.8 Tf [(29.)] TJ ET BT 43.553 345.453 Td /F1 9.8 Tf [(Mitnaul LJ, Matrosovich MN, Castrucci MR, et al. \(2000\) Balanced Hemagglutinin and Neuraminidase Activities Are Critical )] TJ ET BT 26.250 333.548 Td /F1 9.8 Tf [(for Efficient Replication of Influenza A Virus. J. Virol. 74, 6015-6020.)] TJ ET BT 26.250 314.143 Td /F1 9.8 Tf [(30.)] TJ ET BT 43.553 314.143 Td /F1 9.8 Tf [(Earn, D.J.D., Dushoff, J., and Levin, S.A., 2002. Ecology and evolution of the flu. Trends in Ecology & Evolution 17, 334-340.)] TJ ET BT 26.250 294.738 Td /F1 9.8 Tf [(31.)] TJ ET BT 43.553 294.738 Td /F1 9.8 Tf [(Dushoff, J., Plotkin, J.B., Levin, S.A., and Earn, D.J.D., 2004. Dynamical resonance can account for seasonality of influenza )] TJ ET BT 26.250 282.834 Td /F1 9.8 Tf [(epidemics. Proceedings of the National Academy of Sciences of the United States of America 101, 16915-16916.)] TJ ET BT 26.250 263.429 Td /F1 9.8 Tf [(32.)] TJ ET BT 43.553 263.429 Td /F1 9.8 Tf [(Shaman, J., and Kohn, M., 2009. Absolute humidity modulates influenza survival, transmission, and seasonality. )] TJ ET BT 26.250 251.524 Td /F1 9.8 Tf [(Proceedings of the National Academy of Sciences of the United States of America 106, 3243-3248.)] TJ ET BT 26.250 232.119 Td /F1 9.8 Tf [(33.)] TJ ET BT 43.553 232.119 Td /F1 9.8 Tf [(Cauchemez, S., Valleron, A.-J., Boelle, P.-Y., Flahault, A., and Ferguson, N.M., 2008. Estimating the impact of school )] TJ ET BT 26.250 220.215 Td /F1 9.8 Tf [(closure on influenza transmission from Sentinel data. Nature 452, 750-754.)] TJ ET BT 26.250 200.810 Td /F1 9.8 Tf [(34.)] TJ ET BT 43.553 200.810 Td /F1 9.8 Tf [(Heymann, A., Chodick, G., Reichman, B., Kokia, E., and Laufer, J., 2004. Influence of school closure on the incidence of )] TJ ET BT 26.250 188.905 Td /F1 9.8 Tf [(viral respiratory diseases among children and on health care utilization. Pediatric Infectious Disease Journal 23, 675-677.)] TJ ET BT 26.250 169.500 Td /F1 9.8 Tf [(35.)] TJ ET BT 43.553 169.500 Td /F1 9.8 Tf [(Brownstein, J.S., Wolfe, C.J., and Mandl, K.D., 2006. Empirical Evidence for the Effect of Airline Travel on Inter-Regional )] TJ ET BT 26.250 157.596 Td /F1 9.8 Tf [(Influenza Spread in the United States. PLoS Med 3, e401.)] TJ ET BT 26.250 138.191 Td /F1 9.8 Tf [(36.)] TJ ET BT 43.553 138.191 Td /F1 9.8 Tf [(James TY, Litvintseva AP, Vilgalys R, et al. 2009. Rapid Global Expansion of the Fungal Disease Chytridiomycosis into )] TJ ET BT 26.250 126.286 Td /F1 9.8 Tf [(Declining and Healthy Amphibian Populations. 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