A white noise approach to evolutionary ecology

Area of Science:

• Evolutionary Ecology
• Theoretical Ecology
• Population Genetics

Background:

• Classical models of genetic drift assume fixed population sizes, which is unrealistic for wild populations.
• Wild populations experience demographic stochasticity, a key driver of random genetic drift.
• Existing theoretical approaches do not fully capture the interplay between demographic stochasticity and eco-evolutionary dynamics.

Purpose of the Study:

• To develop a theoretical framework for tracking the stochastic dynamics of quantitative traits in populations with fluctuating abundances.
• To integrate demographic stochasticity into models of eco-evolutionary dynamics.
• To generalize classical quantitative genetics by incorporating realistic population fluctuations and stochasticity.

Main Methods:

• Utilized stochastic partial differential equations to model abundance density across phenotypic space.
• Developed heuristics to translate abstract white noise and diffusion-limit theories into practical models.
• Derived stochastic ordinary differential equations generalizing ecological quantitative genetics expressions.

Main Results:

• The derived equations track population size, mean trait, and additive genetic variance under mutation, demographic stochasticity, genetic drift, and selection.
• A model of diffuse coevolution via exploitative competition was formulated, predicting trait and abundance distributions.
• Analysis revealed correlations between selection gradients and competition coefficients in competing species, though directionality was not determined.

Conclusions:

• The framework provides a robust method for studying eco-evolutionary dynamics in fluctuating populations.
• It offers a more realistic approach to understanding the interplay of ecological and evolutionary processes.
• This work contributes to a synthetic theory of evolutionary ecology by formalizing stochastic models of biological feedbacks and diversity patterns.