A white noise approach to evolutionary ecology

Although the evolutionary response to random genetic drift is classically modelled as a sampling process for populations with fixed abundance, abundances of in wild fluctuate over time. Furthermore, since exhibit demographic stochasticity and part due stochasticity, theoretical approaches are needed understand role eco-evolutionary dynamics. Here we close this gap quantitative characters evolving continuously reproducing by providing framework track stochastic dynamics abundance density across phenotypic space using partial differential equations. In develop set heuristics operationalize powerful, but abstract theory white noise diffusion-limits individual-based models. Applying these heuristics, obtain ordinary equations that generalize classical expressions ecological genetics. particular, supplying growth rate reproductive variance functions densities trait values, population size, mean additive responding mutation, drift, deterministic selection noise-induced selection. We demonstrate utility our approach formulating model diffuse coevolution mediated exploitative competition continuum resources. addition distributions, predicts interaction networks defined niche-overlap, coefficients, or gradients. Using high-richness approximation, find linear gradients coefficients uncorrelated, magnitudes quadratic both positively correlated coefficients. Hence, competing species strongly affect each other’s tend also impose on one another, directionality not predicted. This contributes development synthetic ecology formalizing first principle derivations models tracking feedbacks biological processes patterns diversity they produce.