Molecular Clock on a Neutral Network

TL;DR

This paper develops a formalism to analyze the distribution of accumulated mutations in populations evolving on neutral networks, demonstrating that overdispersion of the molecular clock naturally arises under certain network conditions.

Contribution

It introduces a graph-based formalism to compute all cumulants of mutation distributions and proves overdispersion in the molecular clock for generic neutral networks.

Findings

Overdispersion is proven to occur in neutral networks.

High sparsity and large fluctuations in neutrality lead to overdispersion.

Results can help infer network topology from mutation data.

Abstract

The number of fixed mutations accumulated in an evolving population often displays a variance that is significantly larger than the mean (the overdispersed molecular clock). By examining a generic evolutionary process on a neutral network of high-fitness genotypes, we establish a formalism for computing all cumulants of the full probability distribution of accumulated mutations in terms of graph properties of the neutral network, and use the formalism to prove overdispersion of the molecular clock. We further show that significant overdispersion arises naturally in evolution when the neutral network is highly sparse, exhibits large global fluctuations in neutrality, and small local fluctuations in neutrality. The results are also relevant for elucidating the topological structure of a neutral network from empirical measurements of the substitution process.