Meiotic recombination, one of the central biological processes studied in population genetics, comes in two known forms: crossovers and gene conversions. A number of previous studies have shown that when one of these two events is nonexistent in the genealogical model, the point estimation of the corresponding recombination rate by population genetic methods tends to be inflated. Therefore, it has become necessary to obtain statistical evidence from population genetic data about whether one of the two recombination events is absent.
In this paper, we formulate this problem in a hypothesis testing framework and devise a testing procedure based on the likelihood ratio test (LRT). However, because the null value (i.e., zero) lies on the boundary of the parameter space, the regularity conditions for the large-sample approximation to the distribution of the LRT statistic do not apply. In turn, the standard chi-squared approximation is inaccurate. To address this critical issue, we propose a parametric bootstrap procedure to obtain an approximate p-value for the observed test statistic. Coalescent simulations are conducted to show that our approach yields accurate null p-values that closely follow the theoretical prediction while the estimated alternative p-values tend to concentrate closer to zero. Finally, the method is demonstrated on a real biological data set from the telomere of the X chromosome of African Drosophila melanogaster.
Our methodology provides a necessary complement to the existing procedures of estimating meiotic recombination rates from population genetic data.