Genealogical distance under selection

TL;DR

This paper investigates how natural selection influences genealogical distances in populations, showing that selection tends to reduce these distances compared to neutral evolution, with convergence results under certain conditions.

Contribution

It provides mathematical proofs that selection shortens genealogical distances and demonstrates convergence to neutral distances as selection strength increases.

Findings

Genealogical distance is stochastically smaller under selection.

Distances converge to neutral case as selection parameter tends to infinity.

Results hold in large populations and equilibrium conditions.

Abstract

We study the genealogical distance of two randomly chosen individuals in a population that evolves according to a two type Moran model with mutation and selection. We prove that this distance is stochastically smaller than the corresponding distance in the neutral model, when the population size is large. Moreover, we prove convergence of the genealogical distance under selection to the distance in the neutral case, when the system is in equilibrium and the selection parameter tends to infinity.