  This paper develops models describing asexual and sexual replication in
sporulating organisms. Replication via sporulation is the replication strategy
for all multicellular life, and may even be observed in unicellular life (such
as with budding yeast). We consider diploid populations replicating via one of
two possible sporulation mechanisms: (1) Asexual sporulation, whereby adult
organisms produce single-celled diploid spores that grow into adults
themselves. (2) Sexual sporulation, whereby adult organisms produce
single-celled diploid spores that divide into haploid gametes. The haploid
gametes enter a haploid "pool", where they may recombine with other haploids to
form a diploid spore that then grows into an adult. We consider a haploid
fusion rate given by second-order reaction kinetics. We work with a simplified
model where the diploid genome consists of only two chromosomes, each of which
may be rendered defective with a single point mutation of the wild-type. We
find that the asexual strategy is favored when the rate of spore production is
high compared to the characteristic growth rate from a spore to a reproducing
adult. Conversely, the sexual strategy is favored when the rate of spore
production is low compared to the characteristic growth rate from a spore to a
reproducing adult. As the characteristic growth time increases, or as the
population density increases, the critical ratio of spore production rate to
organism growth rate at which the asexual strategy overtakes the sexual one is
pushed to higher values. Therefore, the results of this model suggest that, for
complex multicellular organisms, sexual replication is favored at high
population densities, and low growth and sporulation rates.
