STATISTICAL-ANALYSIS OF CROSSOVER INTERFERENCE USING THE CHI-SQUARE MODEL

The chi-square model (also known as the gamma model with integer shape parameter) for the occurrence of crossovers along a chromosome was fi rst proposed in the 1940's as a description of interference that was m athematically tractable but without biological basis. Recently, the ch i-square model has been reintroduced into the literature from a biolog ical perspective. It arises as a result of certain hypothesized constr aints on the resolution of randomly distributed crossover intermediate s. In this paper under the assumption of no chromatid interference, th e probability for any single spore or tetrad joint recombination patte rn is derived under the chi-square model. The method of maximum likeli hood is then used to estimate the chi-square parameter m and genetic d istances among marker loci. We discuss how to interpret the goodness-o f-fit statistics appropriately when there are some recombination class es 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.