Biological Evolution in a Multidimensional Fitness Landscape

TL;DR

This paper models biological evolution across a multidimensional fitness landscape, analyzing the effects of recombination, mutation, and lethal mutations on mean fitness in both infinite and finite populations, with implications for viruses and statistical mechanics.

Contribution

It introduces a multidimensional fitness landscape model with a theorem on population dynamics, extending previous models to include recombination and lethal mutations.

Findings

Derived mean fitness formulas for infinite populations.

Formulated a finite population model with lethal mutations.

Provided insights into virus evolution and connections to statistical mechanics.

Abstract

We considered a {multi-block} molecular model of biological evolution, in which fitness is a function of the mean types of alleles located at different parts (blocks) of the genome. We formulated an infinite population model with selection and mutation, and calculated the mean fitness. For the case of recombination, we formulated a model with a multidimensional fitness landscape (the dimension of the space is equal to the number of blocks) and derived a theorem about the dynamics of initially narrow distribution. We also considered the case of lethal mutations. We also formulated the finite population version of the model in the case of lethal mutations. Our models, derived for the virus evolution, are interesting also for the statistical mechanics and the Hamilton-Jacobi equation as well.