If ten genes affect an individual's height and one has a population with average height 6'5" that is forced to live in low-ceilinged caves, how might this selective pressure act at the genetic level of individuals? What happens if the different genes have different magnitudes of effect?

A nonlocal diffusion model is constructed and studied for the joint distribution of absolute gene effect sizes and allele frequencies for genes contributing to an quantitative trait in a haploid population where there is a selection pressure on the quantitative trait.

The model is designed to approximate a discrete model exactly in the limit as both population size and the number of genes affecting the trait tend to infinity. For the case where genes can take on either of two distinct effect sizes, numerical simulations indicate that response to selection depends on the variability of the distribution of absolute effect sizes as well as the mean effect size.

This is joint work with Judy Miller and Matt Hamilton of Georgetown University.