Sampling theory for alleles in a random environment

A MAJOR effort in theoretical population genetics has been aimed at developing statistical tests to distinguish between various explanations of observed patterns of enzyme variation1. Perhaps the most useful result to emerge from this effort is Ewens' sampling theory of neutral alleles2. This theory allows one to use the number and configuration of alleles in a sample to test for departures from neutrality. Watterson3 has derived the analogous sampling distribution for a finite population subject to the joint effects of mutation and symmetric heterotic selection. It differs from the neutral sampling theory, providing a stronger hypothesis-testing situation than has previously been available. In this note I present a third sampling distribution. It applies to an infinite population in which the selective coefficients fluctuate at random through time and space. Quite unexpectedly, the sampling distribution turns out to be identical to that for the neutral model, indicating that agreement of data with Ewens' sampling distribution does not rule out the possibility that natural selection is responsible for the genetic variation in the sample. Furthermore, the properties of random-selection populations at equilibrium are indistinguishable from neutral-allele populations for observations made at a single time point. This result calls into question the claim that agreement of data with predictions of the neutral model argues against natural selection as an important factor for the maintenance of genetic variation.