Estimating the frequency distribution of crossovers during meiosis from recombination data

Estimation of tetrad crossover frequency distributions from genetic recombi nation data is a classic problem dating back to Weinstein (1936, Genetics 2 1, 155-199). But a number of important issues, such as how to specify the m aximum number of crossovers, how to construct confidence intervals for cros sover probabilities, and how to obtain correct p-values for hypothesis test s, have never been adequately addressed. In this article, we obtain some pr operties of tile maximum likelihood estimate (MLE) for crossover probabilit ies 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 efficien tly. We propose bootstrap-based methods to find confidence intervals and p- values and conduct simulation studies to check the validity of the bootstra p approach.