STOCHASTIC ECO-EVOLUTIONARY DYNAMICS OF MULTIVARIATE TRAITS: A Framework for Modeling Population Processes Illustrated by the Study of Drifting G-Matrices

I derive a novel stochastic equation for the evolution of the additive genetic variance-covariance matrix G in response to mutation, selection, drift, and fluctuating population size. Common wisdom holds that G should respond to drift only as a scaled reduction. In contrast, I find that drift causes drastic and predictable shifts in the orientation of G by driving genetic correlations to their extremes. Biologically, this is a consequence of linkage build-up introduced by drift. I compare these theoretical results to empirical observations based on experiments conducted by Phillips et. al. (2001). Additionally, to derive the model of G -matrix evolution, I developed a novel synthetic framework for modelling ecological and evolutionary dynamics of populations carrying multivariate traits. By striking a balance between genetic detail and analytical tractability, and by minimizing requisite technical background, this framework is optimized for deriving new models across a wide range of topics in population biology. Foundations of the framework are formalized by the theory of measure-valued processes, but application of the framework only requires multivariate calculus, and heuristics are presented in the main text for making additional calculations involving stochastic processes. Collectively, this work establishes a powerful framework enabling efficient formal analysis of integrated population processes across evolution and ecology, and its potential for making new discoveries is illustrated by novel findings on fundamental aspects of G -matrix evolution.