  This paper develops mathematical models describing the evolutionary dynamics
of both asexually and sexually reproducing populations of diploid unicellular
organisms. We 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 assume that each gene defines a separate chromosome. If the organism
has $ l $ homologous pairs that lack a functional copy of the given gene, then
the fitness of the organism is $ \kappa_l $. The $ \kappa_l $ are assumed to be
monotonically decreasing, so that $ \kappa_0 = 1 > \kappa_1 > \kappa_2 > ... >
\kappa_{\infty} = 0 $. For nearly all of the reproduction strategies we
consider, we find, in the limit of large $ N $, that the mean fitness at
mutation-selection balance is $ \max\{2 e^{-\mu} - 1, 0\} $, where $ N $ is the
number of genes in the haploid set of the genome, $ \epsilon $ is the
probability that a given DNA template strand of a given gene produces a mutated
daughter during replication, and $ \mu = N \epsilon $. The only exception is
the sexual reproduction pathway for the multi-chromosomed genome. Assuming a
multiplicative fitness landscape where $ \kappa_l = \alpha^{l} $ for $ \alpha
\in (0, 1) $, this strategy is found to have a mean fitness that exceeds the
mean fitness of all of the other strategies. Furthermore, while the other
reproduction strategies experience a total loss of viability due to the steady
accumulation of deleterious mutations once $ \mu $ exceeds $ \ln 2 $, no such
transition occurs in the sexual pathway. The results of this paper demonstrate
a selective advantage for sexual reproduction with fewer and much less
restrictive assumptions than previous work.
