Diploidy, homologous recombination repair, and the selective advantage for sexual reproduction in unicellular organisms

This paper develops mathematical models describing the evolutionary dynamics of both asexually and sexually reproducing populations of diploid unicellular organisms. The asexual and sexual life cycles are based on the asexual and sexual life cycles in Saccharomyces cerevisiae, or Baker’s yeast, which normally reproduces by asexual budding, but switches to sexual reproduction when stressed. The mathematical models consider three reproduction pathways: (1) Asexual reproduction. (2) Self-fertilization (3) Sexual reproduction. We also consider two forms of genome organization. In one case, we assume that the genome consists of two multi-gene chromosomes, while in the second case we consider the opposite extreme and assume that each gene defines a separate chromosome, which we call the multi-chromosome genome. These two cases are considered in order to explore the role that recombination has on the mutation-selection balance and the selective advantage of the various reproduction strategies. We assume that the purpose of diploidy is to provide redundancy, so that damage to a gene may be repaired using the other, presumably undamaged copy (a process known as homologous recombination repair). As a result, we assume that the fitness of the organism only depends on the number of homologous gene pairs that contain at least one functional copy of a given gene. If the organism has at least one functional copy of every gene in the genome, we assume a fitness of 1, and we assume that each homologous gene pair without a functional copy of a given gene induces a fitness penalty of α. However, we assume that, even among organisms with at least one functional copy of every gene, there is an effective fitness penalty for having faulty copies of genes. This fitness penalty arises as a result of the repair of a damaged functional gene when its homologue has a fixed mutation. The repair process can lead to the mutation being transferred to the functional gene, leading to the loss of functionality of both copies of a given gene. For nearly all of the reproduction strategies we consider, we find that the mean fitnesses have an upper bound of max{2e−N − 1, 0}, where N is the number of genes in the haploid set of the genome, and is the probability that a given DNA template strand of a given gene produces a mutated daughter during replication. The only exceptions are the twoand multi-chromosome sexual reproduction pathways. These strategies are found to have a mean fitness that can exceed the mean fitness of all of the other strategies, provided that N is sufficiently large. The critical value of N beyond which the sexual pathways have a higher mean fitness than the other strategies decreases as α approaches 1. Furthermore, while the other reproduction strategies experience a total loss of viability due to the steady accumulation of deleterious mutations once N exceeds ln 2, the transition in the sexual pathways may be delayed to arbitrarily high values of N provided that α is sufficiently close to 1. We explicitly allow for mitotic recombination in this work, which has been found, using previous models, to provide an identical selective advantage as sexual reproduction. With the models used in this study, we do not find any advantage for mitotic recombination over other reproduction strategies. However, sexual reproduction with random mating does have a selective advantage over other reproduction strategies. The results of this paper suggest that sex provides a selective advantage by acting on “non-essential” genes, i.e., genes that confer a fitness advantage to the organism, but are not necessary for the organism to grow and reproduce. The more “non-essential” the genes, as measured by how close α is to 1 in our model, the stronger the selective advantage for sex. The results of this paper also suggest an explanation for why unicellular organisms such as Saccharomyces cerevisiae (Baker’s yeast) switch to a sexual mode of reproduction when stressed. Finally, while the results of this paper are based on modeling mutation-propagation in unicellular organisms, they nevertheless suggest that, in more complex organisms with significantly larger genomes, sex is necessary to prevent the loss of viability of a population due to genetic drift.