The diffusion model for migration and selection in a dioecious population

Area of Science:

• Population Genetics
• Evolutionary Biology
• Mathematical Biology

Background:

• Existing population genetics models often focus on monoecious populations.
• Understanding genetic processes in dioecious (two-sex) populations is crucial for evolutionary studies.
• Subdivided populations with migration and selection present complex dynamics.

Purpose of the Study:

• To derive and analyze the diffusion approximation for migration and selection in a multiallelic, dioecious population structure.
• To generalize existing models to include dioecious populations and arbitrary migration ranges.
• To demonstrate the applicability of cline theory and wave of advance models to dioecious systems.

Main Methods:

• Derivation of the diffusion approximation for discrete, non-overlapping generations in a lattice of panmictic colonies.
• Analysis of both autosomal and X-linked loci.
• Generalization of unidimensional models to include dioecious populations and symmetric migration of finite range.

Main Results:

• The diffusion approximation successfully models migration and selection in dioecious populations.
• Ploidy-weighted averages allow allelic frequencies to satisfy monoecious population equations.
• Transition conditions for population barriers are shown to hold for dioecious populations, extending cline theory.

Conclusions:

• The mathematical framework for clines and the wave of advance of favorable alleles is directly applicable to dioecious populations.
• This work unifies theoretical approaches for monoecious and dioecious systems under diffusion approximation.
• Provides a robust model for studying allele frequency dynamics in structured dioecious populations.