How genealogies are affected by the speed of evolution

Abstract

In a series of recent works it has been shown that a class of simple models of evolving populations under selection leads to genealogical trees whose statistics are given by the Bolthausen-Sznitman coalescent rather than by the well-known Kingman coalescent in the case of neutral evolution. Here we show that when conditioning the genealogies on the speed of evolution, one finds a one-parameter family of tree statistics which interpolates between the Bolthausen-Sznitman and Kingman coalescents. This interpolation can be calculated explicitly for one specific version of the model, the exponential model. Numerical simulations of another version of the model and a phenomenological theory indicate that this one-parameter family of tree statistics could be universal. We compare this tree structure with those appearing in other contexts, in particular in the mean field theory of spin glasses. © 2012 Copyright Taylor and Francis Group, LLC.