Adventures in Stochastic Processes: Modelling the Macroevolution of Quantitative Traits using Diffusion Equations

Stochastic processes are commonly used to model various aspects of the evolution of organisms, both at the level of the population (e.g. gene frequencies), and at the level of the species (e.g. traits). This is because stochastic processes allow us to model both the deterministic aspects of evolution, such as selection, as well as the stochastic aspects of evolution, such as genetic drift and other sources of “randomness” in the same modelling framework. Indeed, the development of modern phylogenetic comparative methods has focussed attention on the need for explicit models of evolution in order to test hypotheses about the phenotypic correlations among traits, and correlations between traits and environments. Further, explicit models of evolution are necessary in order to understand the dynamics of trait change and disparity through “deep” time.

In this talk I will discuss the mathematical structure of some commonly-used stochastic process models of evolution (diffusions). I will discuss similarities and differences among models and introduce two new evolutionary models that may be of use particularly when traits are “non-Gaussian”, that is, when traits do not follow a Normal distribution. I will discuss the implementation of software in order to fit such diffusion models to trait data on phylogenies. Pitfalls and issues associated with testing hypotheses about model parameters will also be addressed, as will directions for future research.


Simone Blomberg started out as a lizard ecologist (PhD with R. Shine (USyd) at the same time as Scott Keogh). After a successful postdoc on phylogenetic comparative methods in the USA with T. Garland and A. Ives (U. Wisconsin, Madison and U. California, Riverside), Simone returned to Australia without a job. After trying (and failing) to obtain a position as a lizard ecologist, Simone re-trained, gaining a Masters degree in Applied Statistics from the ANU (2004). After working as an applied statistician with D. Lindenmayer (ANU), in 2007 Simone was appointed to a lectureship in the School of Biological Sciences at the University of Queensland, with a special focus on providing a statistical consulting service to academic staff and postgraduate students. She has been there ever since, researching the interface between statistics and evolutionary theory, supervising postgraduate students, teaching undergraduates and working to further increase the quality of science produced by the UQ School of Biological Sciences.