Derivation of Several SDE Systems in One- and Two-Locus Population Genetics

Abstract

A direct approach is described for deriving stochastic differential equations (SDEs) for the dynamics of evolving populations. Itô SDEs are presented and compared for populations of haploid and diploid individuals with one or more alleles at one locus undergoing pure genetic drift. The results agree with previous investigations in mathematical genetics using diffusion approximations. Furthermore, a stochastic differential equation model is derived for diploid populations with two alleles at two loci. The derived SDE systems provide unifying, consistent models.

Keywords:

• Stochastic partial differential equation
• Population genetics
• Itô system
• Stochastic model

Mathematics Subject Classification:

• 60H10
• 60H15
• 92D25
• 65C30

Additional information

Funding

This investigation was partly funded by NSF grant DMS-0718302.