Genealogies in simple models of evolution

TL;DR

This paper reviews the statistical properties of genealogies in simple evolutionary models, highlighting how selection influences coalescence times and the underlying coalescent processes, with distinctions between asexual and sexual reproduction.

Contribution

It provides a comparative analysis of genealogical statistics under different models, emphasizing the impact of selection and the transition from Kingman to Bolthausen-Sznitman coalescent.

Findings

Selection causes coalescence times to grow logarithmically with population size.

Genealogies often follow the Bolthausen-Sznitman coalescent rather than Kingman.

In neutral models, the time to common ancestors is logarithmic in population size.

Abstract

We review the statistical properties of the genealogies of a few models of evolution. In the asexual case, selection leads to coalescence times which grow logarithmically with the size of the population in contrast with the linear growth of the neutral case. Moreover for a whole class of models, the statistics of the genealogies are those of the Bolthausen-Sznitman coalescent rather than the Kingman coalescent in the neutral case. For sexual reproduction, the time to reach the first common ancestors to the whole population and the time for all individuals to have all their ancestors in common are also logarithmic in the neutral case, as predicted by Chang []. We discuss how these times are modified in a simple way of introducing selection.