This study presents a mathematical model in which a single beneficial
mutation arises in a very large population that is subject to frequent
deleterious mutations. The results suggest that, if the population is
sexual, then the deleterious mutations will have little effect on the
ultimate fate of the beneficial mutation. However, if most offspring
are produced asexually, then the probability that the beneficial mutat
ion will be lost from the population may be greatly enhanced by the de
leterious mutations. Thus, sexual populations may adapt much more quic
kly than populations where most reproduction is asexual. Some of the r
esults were produced using computer simulation methods, and a techniqu
e was developed that allows treatment of arbitrarily large numbers of
individuals in a reasonable amount of computer time. This technique ma
y be of prove useful for the analysis of a wide variety of models, tho
ugh there are some constraints on its applicability. For example, the
technique requires that reproduction can be described by Poisson proce
sses.