Neutral Aggregation in Finite Length Genotype space

TL;DR

This paper analyzes the distribution of genetic differences among individuals in genome space under neutrality, revealing how population size, mutation rate, and migration influence genetic clustering.

Contribution

It provides a theoretical framework for understanding neutral aggregation in finite genome spaces, extending to geographically dispersed populations.

Findings

Neutral aggregation dominates when Nν<1/L, leading to clustering.

Individuals are dispersed when Nν>1, indicating randomness.

The model applies to ecological systems to test neutrality hypotheses.

Abstract

The advent of modern genome sequencing techniques allows for a more stringent test of the neutrality hypothesis of Darwinian evolution, where all individuals have the same fitness. Using the individual based model of Wright and Fisher, we compute the amplitude of neutral aggregation in the genome space, i.e., the probability of finding two individuals at genetic (hamming) distance k as a function of genome size L, population size N and mutation probability per base \nu. In well mixed populations, we show that for N\nu\textless{}1/L, neutral aggregation is the dominant force and most individuals are found at short genetic distances from each other. For N\nu\textgreater{}1 on the contrary, individuals are randomly dispersed in genome space. The results are extended to geographically dispersed population, where the controlling parameter is shown to be a combination of mutation and migration probability. The theory we develop can be used to test the neutrality hypothesis in various ecological and evolutionary systems.