Stochastic dynamics of adaptive trait and neutral marker driven by eco-evolutionary feedbacks

Area of Science:

• Evolutionary Biology
• Population Genetics
• Eco-evolutionary Dynamics

Background:

• Understanding how selection and adaptation influence neutral genetic diversity is crucial in evolutionary biology.
• Eco-evolutionary frameworks integrate ecological dynamics with evolutionary processes to study trait variation and its consequences.

Purpose of the Study:

• To investigate the impact of selection and adaptation on neutral diversity within an eco-evolutionary context.
• To develop a mathematical model describing the interplay between trait evolution and neutral genetic variation.

Main Methods:

• A continuous-time, finite population model incorporating selection on a trait and a linked neutral marker.
• Analysis of population dynamics driven by births, deaths, mutations, and competition.
• Mathematical derivation of the Substitution Fleming-Viot Process (SFVP) from an individual-based model in the large population limit.

Main Results:

• The study proves the convergence to the SFVP, a novel measure-valued diffusive process with jumps.
• Identified hitchhiking of neutral markers during the invasion of favorable mutations, leading to genetic bottlenecks.
• Established conditions for time-scale separation, approximating marker distribution by Fleming-Viot distribution between trait substitutions.

Conclusions:

• The SFVP provides a framework for understanding neutral diversity dynamics under eco-evolutionary feedbacks.
• Mutations, ecological parameters, and trait values jointly regulate the restoration of neutral diversity post-selective sweep.
• The model highlights the importance of considering the interplay between ecological and evolutionary processes.