Finite genome length corrections for the mean fitness and gene probabilities in evolution models

TL;DR

This paper derives finite genome length corrections for mean fitness and gene probabilities in evolution models using Hamilton-Jacobi equations, validated by numerical solutions, applicable to various nonlinear Markov models.

Contribution

It introduces a Hamilton-Jacobi equation approach to compute 1/L corrections in genome evolution models, extending analysis to general fitness landscapes.

Findings

Analytic expressions for finite-size corrections derived

Numerical solutions confirm the accuracy of the corrections

Method applicable to nonlinear Markov models

Abstract

Using the Hamilton-Jacobi equation approach to study genomes of length $L$, we obtain 1/L corrections for the steady state population distributions and mean fitness functions for horizontal gene transfer model, as well as for the diploid evolution model with general fitness landscapes. Our numerical solutions confirm the obtained analytic equations. Our method could be applied to the general case of nonlinear Markov models.