Quantifying the effects of anagenetic and cladogenetic evolution

Abstract

An ongoing debate in evolutionary biology is whether phenotypic change occurs predominantly around the time of speciation or whether it instead accumulates gradually over time. In this work I propose a general framework incorporating both types of change, quantify the effects of speciational change via the correlation between species and attribute the proportion of change to each type. I discuss results of parameter estimation of Hominoid body size in this light. I derive mathematical formulae related to this problem, the probability generating functions of the number of speciation events along a randomly drawn lineage and from the most recent common ancestor of two randomly chosen tip species for a conditioned Yule tree. Additionally I obtain in closed form the variance of the distance from the root to the most recent common ancestor of two randomly chosen tip species.

Keywords: Branching diffusion process; Conditioned branching process; Phyletic gradualism; Punctuated equilibrium; Quadratic variation; Yule–Ornstein–Uhlenbeck with jumps process.