Randomness versus selection in genome evolution

TL;DR

This paper models genome evolution using a Markov chain, revealing how randomness and selection influence allele frequencies, with the number of 1's converging to a Gaussian distribution centered around the expected value.

Contribution

It introduces a Markov chain model for genome evolution that captures the interplay between randomness and selection in allele frequency dynamics.

Findings

Number of 1's converges to a Gaussian distribution

Randomness and selection balance each other out

Even with selective advantage, the chain rarely reaches all 1's

Abstract

We propose a Markov chain approach for the evolution of a genealogical line of genomes. Our idealized genome has $N$ sites and each site can be in state $0$ or $1$. At each time step we pick a site at random. If the site is in state $0$ we flip it to state 1 with probability $p$ or we keep it in state $0$ with probability $1-p$. If the site is in state $1$ we flip it to state 0 with probability $1-p$ or we keep it in state $1$ with probability $p$. Even when state 1 has a selective advantage (i.e. $p>1/2$) the Markov chain is quite unlikely to approach the most fit allele (i.e. all 1's). In fact, randomness (i.e. which site is picked for a possible mutation) and selection (i.e. the value of $p$) balance each other out so that the number of $1$'s in the genome converges to a Gaussian distribution centered around $Np$.