O O Ta Tb Tc Td Te Tf

Figure 1 Summary of the comparative approach for inferring phenotypic evolution. a, Phylogenetic systematics (i.e., tree building): reconstruction of genealogical interrelationships among taxa (extant and/or fossil) using morphological and/or molecular sequence data. Taxa are species or clades (monophyletic groups of species): phylogeny includes six ingroup terminal taxa (TA-TF) and two outgroup taxa (O1 and O2). b, Character state optimization at internal nodes (branching points or hypothesized speciation events). Observed trait values at tips of the tree. Seven internal tree nodes represented by ancestral taxa (AG-AM) with trait values estimated by linear parsimony. c, Evolution: tracing the history of phenotypic changes along branches of the tree. Numbers indicate absolute amount of trait change on the branch.

A tree-shaped branching diagram conveys two kinds of information (whether they are intended or not): the tree topology, or the sequential order in which the taxa branch from one another, and the lengths of the individual branches (Figure 2). These two aspects of a tree correspond to the cladogenesis and the anagenesis of Rensch (1959). The tree topology (branching order) is reconstructed from the distribution of shared-derived traits among taxa. The traits examined may be morphological novelties or nucleotide substitutions. Branch lengths may be reconstructed from one or more sources of information, including alternative models (or modes) of character evolution, or from empirical data. Under models of constant (or near constant) evolution (e.g., molecular clocks), all terminal taxa are treated as equidistant from the root (or base) of the tree. Terminal taxa are those at the tips of the tree, as opposed to ancestral taxa at internal nodes (branching points) within the tree. Under models of punctuated equilibrium, all (or most) character evolution occurs at branching points (nodes), and all branches are therefore of equal (or almost equal) length. Branch lengths derived from empirical data sets may be treated as proportional to the amount of character state change on that particular tree topology, or from stochastic models of evolution assuming that DNA nucleotide substitutions occur at an equal rate (Sanderson, 2002). The constant evolution and punctuated equilibrium models represent extremes of branch-length heterogeneity, between which branch lengths derived from empirical data sets usually fall. Branch lengths for clades with known fossilized members can also be estimated from the geological age of these fossils (Benton et al., 2000; Near and Sanderson, 2004). Calibrations based on molecular sequence divergence or fossil data can take one of two forms: assignment of a fixed age to a node, or enforcement of a minimum or maximum age constraint on a node. The latter option is generally a better reflection of the information content of fossil evidence.

It is important to recognize an analytical difference in the two kinds of information represented in a phylogeny: whereas the tree topology is transitive, the branch lengths are not. In the language of formal logic, 'transitive' means that a relationship necessarily holds across (i.e., it transcends) the particularity of data sets. In the case of phylogenetic trees, the branching order derived from analysis of one data set is expected to predict the branching order of independent data sets (e.g., those derived from different genes, genes and morphology, osteology and neurology). Branch lengths, however, are intransitive, meaning the branch length values derived from one data set are not expected to predict those of other data sets. The reason for this is that we believe there has been a single phylogenetic history of life; a unique sequence of speciation events that gave rise to the species richness of the modern world. This single history underlies the evolution of all aspects of organismal phenotypes. There are, however, no such expectations of homogeneity in the rates of phenotypic (or gene sequence) evolution; in fact,

Outgroup 1 Outgroup 2

Taxon A Taxon B Taxon C Taxon D

Taxon E Taxon F

Outgroup 1 — Outgroup 2

Taxon D Taxon E Taxon F (b)

Outgroup 1 Outgroup 2

Taxon A

Taxon B Taxon C

Taxon D

Taxon E

Taxon F

Figure 2 Alternative branch length models. a, Molecular clock: all terminal taxa equidistant from root to from an ultrametric tree. b, Equal branch lengths: all character evolution (anagenesis) occurs at branching events, as in punctuated equilibrium. c, Empirical: branch lengths proportional to amount of character evolution and/or geological ages determined from fossils. Note: tree topology is transitive; branch lengths are not.

the differential effects of directional and stabilizing selection on different phenotypes may be expected to result in longer or shorter branches for some traits than others.

1.03.3 Methods

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