Methods for analyzing the spatial distribution of chiasmata during meiosis based on recombination data

Using genetic recombination data to make inferences about chiasmata oil the tetrad during meiosis is a classic problem dating back to Weinstein's paper in 1936 (Genetics 21, 155-199). In the last few years, Weinstein's methods have been revived and applied to new problems, but a number of important statistical issues remain unresolved. Recently, we developed improved statistical methods for studying the frequency distribution of the number of chiasmata (Yu and Feingold, 2001, Biometrics 57, 427-434). In the current article, we develop methods for the complementary issue of studying the spatial distribution of chiasmata. Somewhat different statistical approaches are needed for the spatial problem than for the frequency problem because different scientific questions are of interest. We explore the properties of the maximum likelihood estimate (MLE) for chiasma spatial distributions and propose improvements to the estimation procedures. We develop a class of statistical tests for comparing chiasma patterns in tetrads that have undergone normal meiosis and tetrads that have had a nondisjunction event. Finally, we propose an EM algorithm to rind the MLE when the observed data is ambiguous, as is often the case in human datasets. We apply our improved methods to reanalyze a dataset from the literature studying the association between crossover location and meiotic nondisjunction of chromosome 21.