Ancestral State Reconstruction, Rate Heterogeneity, and the Evolution of Reptile Viviparity

Abstract

Virtually all models for reconstructing ancestral states for discrete characters make the crucial assumption that the trait of interest evolves at a uniform rate across the entire tree. However, this assumption is unlikely to hold in many situations, particularly as ancestral state reconstructions are being performed on increasingly large phylogenies. Here, we show how failure to account for such variable evolutionary rates can cause highly anomalous (and likely incorrect) results, while three methods that accommodate rate variability yield the opposite, more plausible, and more robust reconstructions. The random local clock method, implemented in BEAST, estimates the position and magnitude of rate changes on the tree; split BiSSE estimates separate rate parameters for pre-specified clades; and the hidden rates model partitions each character state into a number of rate categories. Simulations show the inadequacy of traditional models when characters evolve with both asymmetry (different rates of change between states within a character) and heterotachy (different rates of character evolution across different clades). The importance of accounting for rate heterogeneity in ancestral state reconstruction is highlighted empirically with a new analysis of the evolution of viviparity in squamate reptiles, which reveal a predominance of forward (oviparous-viviparous) transitions and very few reversals.

Introgression and repeated co-option facilitated the recurrent emergence of C4photosynthesis among close relatives

“…2012; Niemiller et al. 2013; Igic and Busch 2013; King and Lee 2015). In the case of photosynthetic transitions within Alloteropsis depicted here, considering the photosynthetic type as a binary character would lead to a single C 4 origin as the most plausible scenario (Ibrahim et al.…”

“…2012), particularly when some character states affect the rates of speciation and/or extinction, when rates of transitions are high and asymmetrical, or variable among clades and through time (Maddison 2006; Goldberg and Igic 2008; Beaulieu et al. 2013; Igic and Busch 2013; King and Lee 2015). Indeed, transition rates might be higher in taxonomic groups possessing evolutionary precursors that increase the likelihood of evolving a specific trait (Blount et al.…”

Minimal effects of latitude on present-day speciation rates in New World birds

“…State-dependent models of diversification are known to be sensitive to violations of this assumption. We do not fully understand the consequences of violating these assumptions, but unaccommodated rate heterogeneity can result in inflated Type I error rates [41,42] and severely biased ancestral state estimates [43].…”

Epoch‐based likelihood models reveal no evidence for accelerated evolution of viviparity in squamate reptiles in response to cenozoic climate change

“…The ages of the origins of viviparity were taken from those generated by the focal BEAST analysis in King and Lee (), which used the tree in Pyron and Burbrink (). This analysis is reproduced as Figure S1 here; other analyses using the best‐supported models gave similar results.…”

“…In the first, the asymmetry between “forward” (oviparous‐to‐viviparous) and “reverse” (viviparous‐to‐oviparous) transitions was empirically estimated from the data. In the second, asymmetry was fixed to the value estimated in King and Lee (), that is, 5.51:1 in favor of forward changes. For each of the four analyses, stepping‐stone sampling (Xie et al, ) was used to compare each epoch model with the simpler model (strict clock, equivalent to a single‐epoch model).…”