LIKELIHOOD RATIOS FOR THE INFINITE ALLELES MODEL

The stationary distribution for the population frequencies under an in finite alleles model is described as a random sequence (x1, x2,...) su ch that SIGMA x(i) = 1. Likelihood ratio theory is developed for rando m samples drawn from such populations. As a result of the theory, it i s shown that any parameter distinguishing an infinite alleles model wi th selection from the neutral infinite alleles model cannot be consist ently estimated based on gene frequencies at a single locus. Furthermo re, the likelihood ratio (neutral versus selection) converges to a non -trivial random variable under both hypotheses. This shows that if one wishes to test a completely specified infinite alleles model with sel ection against neutrality, the test will not obtain power 1 in the lim it.