Fixation probabilities for advantageous mutants: a note on multiplication and sampling

If the average number of gametes produced by the individual is small, as may be the case for haploid organisms, then sampling with and without replacement can lead to considerable differences in the fixation probabilities of mutant alleles. As a function of the population size N, these probabilities converge quickly to the survival probabilities given by branching processes with Poisson or Bernoulli offspring distributions.