Statistical analysis of crossover interference using the chi-square model

Abstract

The chi-square model (also known as the gamma model with integer shape parameter) for the occurrence of crossover along a chromosome was first proposed in the 1940's as a description of interference that was mathematically tractable but without biological basis. Recently, the chi- square model has been reintroduced into the literature from a biological perspective. It arises as a result of certain hypothesized constraints on the resolution of randomly distributed crossover intermediates. In this paper under the assumption of no chromatid interference, the probability for any single or tetrad joint recombination pattern is derived under the chi-square model. The method of maximum likelihood is then used to estimate the chi- square parameters m and genetic distances among marker loci. We discuss how to interpret the goodness-of-fit statistics appropriately when there are some recombination classes that have only a small number of observations. Finally, comparisons are made between the chi-square model and some other tractable models in the literature.