"Eco-evolutionary dynamics for finite populations and the noise-induced reversal of selection"Bhat, ShikharaTheoretical studies from diverse areas of population biology have shown that demographic stochasticity can substantially impact evolutionary dynamics in finite populations, including scenarios where traits that are disfavored by natural selection can nevertheless increase in frequency through the course of evolution. Historically, most general analytic frameworks have either restricted themselves to models with constant or deterministically varying total population size or have resorted to dynamically insufficient formulations. Here, we analytically describe the eco-evolutionary dynamics of finite populations from demographic first principles to investigate how noise-induced effects can alter the evolutionary fate of populations in which total population size may vary stochastically over time. Starting from a generic birth-death process describing a finite population of individuals with discrete traits, we derive a set of stochastic differential equations (SDEs) that recover well-known descriptions of evolutionary dynamics such as the replicator-mutator equation, the Price equation, and Fisher's fundamental theorem in the infinite population limit. For finite populations, our SDEs reveal how stochasticity can induce a directional evolutionary force termed `noise-induced selection' via two distinct mechanisms, one that operates over relatively faster (ecological) timescales and another that is only apparent over longer (evolutionary) timescales. Despite arising from the stochasticity of finite systems, the effects of noise-induced selection are predictable and may oppose natural selection. In some cases, noise-induced selection can even reverse the direction of evolution predicted by natural selection. By extending and generalizing some standard equations of population genetics, we thus describe how noise-induced selection appears alongside and interacts with the more well-understood forces of natural selection, neutral drift, and transmission effects (mutation/migration) to determine the eco-evolutionary dynamics of finite populations of non-constant size. |
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