Inferring multi-locus selection strengths from measured allele frequencies in a bacterial population

by Magnus Ekeberg (KTH)

Tuesday 2 Jun 2015, 13:30 → 14:30 Europe/Stockholm

122:026

Simple selection can be traced to allele types at just one locus (allele type '1' leads to higher survival and reproduction rates than type '2'), while more complex traits can require particular allele-type combinations across several loci to be present for evolutionary pressure to arise. This talk presents a novel framework for uncovering such selection effects in a population of haploid individuals when given repeated observations of allele frequencies at L loci.

Our starting point is a many-locus Wright-Fisher model, a diffusion approximation of which yields a high-dimensional Fokker-Planck equation governing the probability of the population being in a certain state of allele frequencies. We derive, under weak assumptions, the stationary distribution of this diffusion equation. By presuming that the experimental observations are roughly independent samples from this distribution, we can cast the selection detection problem as a conventional maximum-likelihood inference. We also address and resolve several computational issues related to this inference, such as restricting higher-order selection to pairs of loci to reduce the complexity of certain prohibitively large sums, and the derivation of a pseudo-likelihood objective to allow for efficient numerical execution even at large L.