We derive a basic result for the loss of heterozygosity in a single generation of a haploid population and the limiting heterozygosity for the model after a large number of generations. The model used is based on a Galton-Watson branching process. For populations with a mean growth rate greater than one, heterozygosity does not approach zero, as would occur under the Wright-Fisher model [Kimura 1983]. We show that Sewall Wright's result [Wright 1938] on the effective population size of a diploid population with a range of variances in offspring number can be considered as a special case of a significantly more general result and use this as an example of the care that needs to be taken with the concept of effective population size. Our results provide some indication as to how and under what circumstances questions in coalescent theory for diploid populations can be reduced to problems in haploid coalescent theory. We then introduce mutation in the form of infinite-alleles and finite-alleles models and demonstrate that for populations with a mean growth rate greater than one, the concept of a balance between mutation and drift is not generally applicable during growth. Finally, we consider a limitation on the practical application of single-locus neutral population genetic models that does not appear to have been widely considered, namely the influence of selection on the wider genotype (cf. [Felsenstein 1974]).

- Wright S 1938. Size of population and breeding structure in relation to evolution. Science 87, 430-431.
- Kimura M 1983. The Neutral Theory of Molecular Evolution. Cambridge:Cambridge University Press.
- Felsenstein J 1974. The evolutionary advantage of recombination. Genetics 78: 737–756.