Noisy traveling waves: effect of selection on genealogies

TL;DR

This paper investigates how selection influences genealogical structures in evolving populations modeled by noisy traveling waves, revealing a logarithmic scaling of coalescence times and connections to spin glass theory.

Contribution

It introduces a novel analysis linking noisy traveling wave models of evolution to genealogical time scales and spin glass statistics, providing new theoretical predictions and simulations.

Findings

Coalescence times scale as log^α N, differing from neutral models.

The predicted α matches simulation results.

Exact solutions relate genealogies to mean-field spin glass models.

Abstract

For a family of models of evolving population under selection, which can be described by noisy traveling wave equations, the coalescence times along the genealogical tree scale like $\log^\alpha N$, where $N$ is the size of the population, in contrast with neutral models for which they scale like $N$. An argument relating this time scale to the diffusion constant of the noisy traveling wave leads to a prediction for $\alpha$ which agrees with our simulations. An exactly soluble case gives trees with statistics identical to those predicted for mean-field spin glasses in Parisi's theory.