A class of models of selectively neutral alleles

Abstract

Using exchangeability as a statistical analog of neutrality, we derive a generalized sampling distribution for neutral alleles. The distribution depends upon a parameter that determines the underlying marginal distribution of the number of copies of a neutral allele and that can range from zero to infinity. The sampling model of Ewens (1972) is a special case characterized by an extreme value (0) of this parameter. Two other special cases are considered, one of which seems to be applicable to populations with a structure like that of the Yanomama Indians of South America. We then investigate the expected frequency spectra under these three special cases and discover that all three models yield a broad range of possible spectra with overlap between the special cases. We finally show that Ewens' sampling model cannot be used to construct tests of neutrality versus selection tending to maintain polymorphisms, but it can be used to construct tests of directional selection versus neutrality plus selection tending to yield polymorphic states.