Analysis of disruptive selection in subdivided populations

Area of Science:

• Evolutionary biology
• Population genetics
• Ecological modeling

Background:

• Existing analytical methods for evolutionarily stable strategies (ESS) do not fully account for small patch sizes and limited dispersal.
• Disruptive selection dynamics near a candidate ESS require refined models considering population structure.

Purpose of the Study:

• To derive local stability conditions for ESS that incorporate the consequences of small and constant patch sizes.
• To interpret these conditions using inclusive fitness theory and analyze dispersal and competition models.
• To bridge the gap between existing modeling frameworks (Rm concept) and inclusive fitness theory.

Main Methods:

• Derivation of local stability conditions based on Rm, the production of successful emigrants from a patch.
• Interpretation of results through the lens of inclusive fitness theory, considering relatedness between genes.
• Analysis of basic models of dispersal and resource competition using the derived conditions.

Main Results:

• Local stability conditions were derived, accounting for small, constant patch sizes.
• The condition for convergence to an ESS is proportional to inclusive fitness expressions.
• Evolutionary stability stricto sensu considers selection on relatedness, including three-gene relationships.
• Analysis revealed cases of global instability despite local stability in resource competition models.

Conclusions:

• The derived results identify and analyze the relative importance of different selective pressures.
• The study connects the Rm concept with inclusive fitness theory in population dynamics.
• The findings are applicable to haploid island models and potentially more general dispersal scenarios.