Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
7380573 | Physica A: Statistical Mechanics and its Applications | 2014 | 13 Pages |
Abstract
We discuss a minimalist model of assortative mating for sexually reproducing haploid individuals with two biallelic loci. Assortativeness is introduced in the model by preventing mating between individuals whose alleles differ at both loci. Using methods of dynamical systems and population genetics we provide a full description of the evolution of the system for the case of very large populations. We derive the equations governing the evolution of haplotype frequencies and study the equilibrium solutions, stability, and speed of convergence to equilibrium. We find a constant of motion which allows us to introduce a geometrical construction that makes it straightforward to predict the fate of initial conditions. Finally, we discuss the consequences of this class of assortative mating models, including their possible extensions and implications for sympatric and topopatric speciation.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
David M. Schneider, Eduardo do Carmo, Ayana B. Martins, Marcus A.M. de Aguiar,