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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.