Semiconservative quasispecies equations for polysomic genomes: The general case

TL;DR

This paper extends quasispecies equations to model polysomic, semiconservative genomes, including diploid and polyploid cases, with a focus on perfect lesion repair, revealing increased analytical complexity compared to haploid models.

Contribution

It generalizes quasispecies equations to polysomic genomes, maintaining formal similarity to haploid models, and explores the impact of different chromosome segregation mechanisms.

Findings

Equations are formally identical to haploid case with proper classification.

Analytical solutions for mean fitness are more complex in polyploid genomes.

Solutions are obtained for perfect lesion repair scenarios.

Abstract

This paper develops a formulation of the quasispecies equations appropriate for polysomic, semiconservatively replicating genomes. This paper is an extension of previous work on the subject, which considered the case of haploid genomes. Here, we develop a more general formulation of the quasispecies equations that is applicable to diploid and even polyploid genomes. Interestingly, with an appropriate classification of population fractions, we obtain a system of equations that is formally identical to the haploid case. As with the work for haploid genomes, we consider both random and immortal DNA strand chromosome segregation mechanisms. However, in contrast to the haploid case, we have found that an analytical solution for the mean fitness is considerably more difficult to obtain for the polyploid case. Accordingly, whereas for the haploid case we obtained expressions for the mean fitness for the case of an analogue of the single-fitness-peak landscape for arbitrary lesion repair probabilities (thereby allowing for non-complementary genomes), here we solve for the mean fitness for the restricted case of perfect lesion repair.