Stochastic eco-evolutionary dynamics of multivariate traits: A framework for modeling population processes illustrated by the study of drifting <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si17.svg"> <mml:mi mathvariant="bold">G</

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 the effect of drift on G is simply to reduce each of its entries by a common proportional amount while preserving its orientation. In contrast, I find that drift causes significant and directional 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. 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.