Sample genealogies and genetic variation in populations of variable size

TL;DR

This paper analyzes how variable population sizes affect genealogical structures and genetic variation, providing a general mathematical framework for understanding the impact of population dynamics on genetic diversity.

Contribution

It introduces a general expression for the moments of total branch lengths in genealogies under variable population sizes, extending coalescent theory.

Findings

Population size variations influence genealogical branch length distributions.

Population heterogeneity affects mutation distribution and homozygosity.

The model applies to arbitrary smooth changes in population size.

Abstract

We consider neutral evolution of a large population subject to changes in its population size. For a population with a time-variable carrying capacity we have computed the distributions of the total branch lengths of its sample genealogies. Within the coalescent approximation we have obtained a general expression, Eq. (27), for the moments of these distributions for an arbitrary smooth dependence of the population size on time. We investigate how the frequency of population-size variations alters the distributions. This allows us to discuss their influence on the distribution of the number of mutations, and on the population homozygosity in populations with variable size.