Selective advantage for sexual reproduction

This paper develops a simplified model for sexual reproduction within the quasispecies formalism. The model assumes a diploid genome consisting of two chromosomes, where the fitness is determined by the number of chromosomes that are identical to a given master sequence. We also assume that there is a cost to sexual reproduction, given by a characteristic time ${\tau }_{\mathit{\text{seek}}}$ during which haploid cells seek out a mate with which to recombine. If the mating strategy is such that only viable haploids can mate, then when ${\tau }_{\mathit{\text{seek}}}=0$, it is possible to show that sexual reproduction will always out compete asexual reproduction. However, as ${\tau }_{\mathit{\text{seek}}}$ increases, sexual reproduction only becomes advantageous at progressively higher mutation rates. Once the time cost for sex reaches a critical threshold, the selective advantage for sexual reproduction disappears entirely. The results of this paper suggest that sexual reproduction is not advantageous in small populations per se, but rather in populations with low replication rates. In this regime, the cost for sex is sufficiently low that the selective advantage obtained through recombination leads to the dominance of the strategy. In fact, at a given replication rate and for a fixed environment volume, sexual reproduction is selected for in high populations because of the reduced time spent finding a reproductive partner.

Figure 1

(Color online) Comparison of the sexual and asexual replication pathways considered in this paper.

Figure 2

(Color online) The various replication pathways and their associated probabilities. The factor of 2 in the second pathway comes from the fact that either the top or bottom parent “$V$” chromosome can form a daughter “$U$” chromosome.

Figure 3

Comparison of $\overline{\kappa }(\tau =\infty )∕\kappa$ for both sexual and asexual replication, with $\kappa =0$ and $\alpha =1∕2$. Note that sexual replication outcompetes asexual replication for all mutation regimes.

Figure 4

${\kappa }_{=}$ versus $p$ for $\alpha =1∕4,1∕2,3∕4$. A graph of ${\kappa }_{\mathit{crit}}\left(\alpha \right)$ is included as well.