Divergent vertebral formulae shape the evolution of axial complexity in mammals.

Complexity, defined as the number of parts and their degree of differentiation, is a poorly explored aspect of macroevolutionary dynamics. The maximum anatomical complexity of organisms has undoubtedly increased through evolutionary time. However, it is unclear whether this increase is a purely diffusive process or whether it is at least partly driven, occurring in parallel in most or many lineages and with increases in the minima as well as the means. Highly differentiated and serially repeated structures, such as vertebrae, are useful systems with which to investigate these patterns. We focus on the serial differentiation of the vertebral column in 1,136 extant mammal species, using two indices that quantify complexity as the numerical richness and proportional distribution of vertebrae across presacral regions and a third expressing the ratio between thoracic and lumbar vertebrae. We address three questions. First, we ask whether the distribution of complexity values in major mammal groups is similar or whether clades have specific signatures associated with their ecology. Second, we ask whether changes in complexity throughout the phylogeny are biased towards increases and whether there is evidence of driven trends. Third, we ask whether evolutionary shifts in complexity depart from a uniform Brownian motion model. Vertebral counts, but not complexity indices, differ significantly between major groups and exhibit greater within-group variation than recognized hitherto. We find strong evidence of a trend towards increasing complexity, where higher values propagate further increases in descendant lineages. Several increases are inferred to have coincided with major ecological or environmental shifts. We find support for multiple-rate models of evolution for all complexity metrics, suggesting that increases in complexity occurred in stepwise shifts, with evidence for widespread episodes of recent rapid divergence. Different subclades evolve more complex vertebral columns in different configurations and probably under different selective pressures and constraints, with widespread convergence on the same formulae. Further work should therefore focus on the ecological relevance of differences in complexity and a more detailed understanding of historical patterns.