The Poisson-skip model of crossing-over

Abstract

The Poisson-skip model introduced in this paper generalizes the chi-square model of crossover interference. Both models are constructed from the random points of a Poisson process occurring along a meiotic bundle of four chromatids. The points of the Poisson process are divided into $\chi$ points and o points, with $\chi$ points corresponding to crossovers. In the chi-square model, a fixed number of o points intervene between every adjacent pair of $\chi$ points; in the Poisson-skip model, a random number of o points intervene. Both of these renewal models permit reasonably straightforward calculation of gamete and tetrad probabilities for multiple linked markers. We illustrate the data analysis possibilities of the Poisson-skip model by fitting it to classical recombination data on Drosophila, the mouse, and Neurospora. We also describe conditions on the discrete skip distribution that guarantee positive interference.