Allele Frequency Spectra as a General Tool for Modeling Genetic Diversity

In this paper we study genetic variation at a highly polymorphic locus of a monoecious or dioecious population whose census and effective sizes differ and possibly vary independently over time. More specifically, we develop a general framework for the allele frequency spectrum (AFS) at this locus, and functions of the AFS. Examples of such functions are number of alleles, number of common and rare alleles, allelic diversity, gene diversity, higher order gene diversity and Hill numbers. We develop exact recursions for the expected AFS, and its functionals, with particular interest in populations that experience a rapid (a few generations) bottleneck followed by approaching a new equilibrium between mutation and drift. A grid-based numerical algorithm is developed, which is exact for small populations and approximate for large populations. This algorithm is exemplified with exact calculations for small populations that undergo a bottleneck, and approximate calculations for a moderately large population that rapidly decreases in size.