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May 1997 The Poisson-skip model of crossing-over
Kenneth Lange, Terence P. Speed, Hongyu Zhao
Ann. Appl. Probab. 7(2): 299-313 (May 1997). DOI: 10.1214/aoap/1034625332


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.


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Kenneth Lange. Terence P. Speed. Hongyu Zhao. "The Poisson-skip model of crossing-over." Ann. Appl. Probab. 7 (2) 299 - 313, May 1997.


Published: May 1997
First available in Project Euclid: 14 October 2002

zbMATH: 0876.92018
MathSciNet: MR1442314
Digital Object Identifier: 10.1214/aoap/1034625332

Primary: 92D10
Secondary: 60K05

Keywords: Genetic recombination , interference , Markov chain , Poisson process , reliability theory , Renewal process

Rights: Copyright © 1997 Institute of Mathematical Statistics


Vol.7 • No. 2 • May 1997
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