Multilocus selection in subdivided populations I. Convergence properties for weak or strong migration

Area of Science:

• Population Genetics
• Evolutionary Biology
• Mathematical Biology

Background:

• Understanding population dynamics requires modeling evolutionary forces like selection, migration, and recombination.
• Previous models often simplified interactions between these forces.
• Deterministic models provide a framework for analyzing complex genetic structures.

Purpose of the Study:

• To analyze the dynamics and equilibrium structure of a deterministic population-genetic model.
• To investigate the interplay of migration, selection, and recombination on multiple loci.
• To identify predictable outcomes in population genetic trajectories.

Main Methods:

• Developed a deterministic model for diploid individuals across discrete demes.
• Incorporated migration, selection varying across demes, and recombination between loci.
• Analyzed convergence properties and limiting cases of the evolutionary forces.

Main Results:

• In the absence of selection, populations converge to a state of global linkage equilibrium with uniform allele frequencies.
• When migration and recombination are strong relative to selection, dynamics approximate a weak-selection limit, preserving equilibrium properties.
• When migration is weak relative to recombination, equilibria perturb those of a non-migratory system, maintaining stability and quasi-linkage equilibrium.

Conclusions:

• Population genetic models with strong migration and recombination exhibit predictable convergence to equilibria.
• Complex dynamics like cycling are absent, with trajectories consistently leading to stable states.
• The study simplifies understanding of evolutionary forces' combined effects on genetic diversity.