Monte Carlo algorithms for Hardy-Weinberg proportions

The Hardy-Weinberg law is among the most important principles in the study of biological systems (Crow, 1988, Genetics 119, 473-476). Given its importance, many tests have been devised to determine whether a finite population follows Hardy-Weinberg proportions. Because asymptotic tests can fail, Guo and Thompson (1992, Biometrics 48, 36.1-372) developed an exact test; unfortunately, the Monte Carlo method they proposed to evaluate their test has a running time that grows linearly in the size of the population N. Here, we propose a new algorithm whose expected running time is linear in the size of the table produced, and completely independent of N. In practice, this new algorithm can be considerably faster than the original method.