Stochastic modeling of the crossover process during meiosis

Abstract

During meiosis, homologous chromosomes pair and each of the paired chromosomes duplicates, resulting in a bundle of four homologous chromatids. Exchanges take place after the formation of this four-strand structure, with each crossover involving two nonsister chromatids, i.e. chromatids originating from homologous chromosomes. Crossovers are precise breakage-and-reunion events which are essential for proper segregation, and can promote genetic variation. A good model for the crossover process is important to the understanding of crossing over mechanisms, to the construction of genetic maps, and to the strategy of finding disease genes. Usually randominvolvement of different pairs of chromatids (no chromatid interference) and random occurrence of crossovers on the four strand bundle (no chiasma interference) are assumed in genetic mappings, although crossover interference has been observed in many organisms. In this paper, we discuss Markov models for both chromatid interference and chiasma interference. Under these Markov models, there exists closed form expression for the probability of any data pattern that can result from the genetic studies considered in this paper. Map functions under different chromatid and chiasma interference models are compared.