A basic model of mutations

TL;DR

This paper introduces a fundamental mutation model and derives exact formulas for key evolutionary metrics, revealing connections to classical Markov models like Ehrenfest's.

Contribution

It provides new exact analytical expressions for mutation-related times in a basic mutation model, linking to established Markov processes.

Findings

Exact mean discovery time for the master sequence

Mean return times to initial state and Hamming classes

Connections to Ehrenfest model formulas

Abstract

We study a basic model for mutations. We derive exact formulae for the mean time needed to discover the master sequence, the mean returning time to the initial state, or to any Hamming class. These last two formulae are the same than the formulae obtained by Mark Kac for the Ehrenfest model.