Estimating the frequency distribution of crossovers during meiosis from recombination data

Estimation of tetrad crossover frequency distributions from genetic recombination data is a classic problem dating back to Weinstein (1936, Genetics 21, 155-199). But a number of important issues, such as how to specify the maximum number of crossovers, how to construct confidence intervals for crossover probabilities, and how to obtain correct p-values for hypothesis tests, have never been adequately addressed. In this article, we obtain some properties of the maximum likelihood estimate (MLE) for crossover probabilities that imply guidelines for choosing the maximum number of crossovers. We give these results for both normal meiosis and meiosis with nondisjunction. We also develop an accelerated EM algorithm to find the MLE more efficiently. We propose bootstrap-based methods to find confidence intervals and p-values and conduct simulation studies to check the validity of the bootstrap approach.