Fitting macroevolutionary models to phylogenies: an example using vertebrate body sizes

How do traits change through time and with speciation? We present a simple and generally applicable method for comparing various models of the macroevolution of traits within a maximum likelihood framework. We illustrate four such models: 1) variance among species accumulates in direct proportion to time separating them (gradual model); 2) variation accumulates with the number of speciation events separating them (speciational model); 3) differences between species are unrelated to phylogenetic relatedness (pitchfork model); and 4) a free model where the trait evolves at its own idiosyncratic rate among lineages. Using species-specific body size, we compare the four models across two data sets: twenty-one clades of vertebrate species, and two clades of bird families. For the twenty-one vertebrate trees, the pitchfork model is most successful, though not significantly, and the most successful by far for the youngest clades. The speciational model seems to be preferred for older clades. For both clades of bird families, the speciational model offers the best fit to family-level body size evolution. However, the pitchfork model does much worse for one clade than for the other, suggesting a difference in the relationship between diversification and body-size evolution in the two groups. These examples highlight some possibilities afforded by this simple approach.