  This paper develops a simplified model for sexual replication within the
quasispecies formalism. We assume that the genomes of the replicating organisms
are two-chromosomed and diploid, and that 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 replication, given by a characteristic
time $ \tau_{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_{seek} = 0 $, it is possible to show that sexual replication
will always outcompete asexual replication. However, as $ \tau_{seek} $
increases, sexual replication only becomes advantageous at progressively higher
mutation rates. Once the time cost for sex reaches a critical threshold, the
selective advantage for sexual replication disappears entirely. The results of
this paper suggest that sexual replication 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
replication is selected for in high populations because of the reduced time
spent finding a reproductive partner.
