###
A finite locus effect diffusion model for the evolution
of a quantitative trait

* with J.R. Miller and M.B. Hamilton*
appeared in
the Journal of Mathematical Biology
52(2006)6:761-787

### Abstract

A diffusion model is constructed for the joint distribution of
absolute locus effect sizes and allele frequencies for loci
contributing to an additive quantitative trait under selection in a
haploid, panmictic population. The model is designed to approximate
a discrete model exactly in the limit as both population size and
the number of loci affecting the trait tend to infinity. For the
case when all loci have the same absolute effect size, formal
multiple-timescale asymptotics are used to predict the long-time
response of the population trait mean to selection. For the case
where loci can take on either of two distinct effect sizes, not
necessarily with equal probability, numerical solutions of the
system indicate that response to selection of a quantitative trait
is insensitive to the variability of the distribution of effect
sizes when mutation is negligible.

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