The tree of life of fishes is in a state of flux because we still lack a comprehensive phylogeny that includes all major groups. The situation is most critical for a large clade of spiny-finned fishes, traditionally referred to as percomorphs, whose uncertain relationships have plagued ichthyologists for over a century. Most of what we know about the higher-level relationships among fish lineages has been based on morphology, but rapid influx of molecular studies is changing many established systematic concepts. We report a comprehensive molecular phylogeny for bony fishes that includes representatives of all major lineages. DNA sequence data for 21 molecular markers (one mitochondrial and 20 nuclear genes) were collected for 1410 bony fish taxa, plus four tetrapod species and two chondrichthyan outgroups (total 1416 terminals). Bony fish diversity is represented by 1093 genera, 369 families, and all traditionally recognized orders. The maximum likelihood tree provides unprecedented resolution and high bootstrap support for most backbone nodes, defining for the first time a global phylogeny of fishes. The general structure of the tree is in agreement with expectations from previous morphological and molecular studies, but significant new clades arise. Most interestingly, the high degree of uncertainty among percomorphs is now resolved into nine well-supported supraordinal groups. The order Perciformes, considered by many a polyphyletic taxonomic waste basket, is defined for the first time as a monophyletic group in the global phylogeny. A new classification that reflects our phylogenetic hypothesis is proposed to facilitate communication about the newly found structure of the tree of life of fishes. Finally, the molecular phylogeny is calibrated using 60 fossil constraints to produce a comprehensive time tree. The new time-calibrated phylogeny will provide the basis for and stimulate new comparative studies to better understand the evolution of the amazing diversity of fishes.

Despite the prominence of “tree-thinking” among contemporary systematists and evolutionary biologists, the biological meaning of different mathematical representations of phylogenies may still be muddled. We compare two basic kinds of discrete mathematical models used to portray phylogenetic relationships among species and higher taxa: stem-based trees and node-based trees. Each model is a tree in the sense that is commonly used in mathematics; the difference between them lies in the biological interpretation of their vertices and edges. Stem-based and node-based trees carry exactly the same information and the biological interpretation of each is similar. Translation between these two kinds of trees can be accomplished by a simple algorithm, which we provide. With the mathematical representation of stem-based and node-based trees clarified, we argue for a distinction between types of trees and types of names. Node-based and stem-based trees contain exactly the same information for naming clades. However, evolutionary concepts, such as monophyly, are represented as different mathematical substructures in the two models. For a given stem-based tree, one should employ stem-based names, whereas for a given node-based tree, one should use node-based names, but applying a node-based name to a stem-based tree is not logical because node-based names cannot exist on a stem-based tree and visa versa. Authors might use node-based and stem-based concepts of monophyly for the same representation of a phylogeny, yet, if so, they must recognize that such a representation differs from the graphical models used for computing in phylogenetic systematics.