Title: A Stochastic Model of Autosomal Chromosome Size Evolution: Modification of a Sankoff-Ferretti Model

Abstract

Motivated by results from Nadeau and Taylor (1984), Sankoff and Ferretti (1996) proposed a stochastic model of chromosome size evolution via random reciprocal translocations. Comparison of their model to data revealed a problem: the predicted lengths of the smallest and largest chromosomes were grossly inaccurate. To alleviate this difficulty, a generalized Sankoff-Ferretti proportional model (probability of choosing chromosomes is proportional to length) will be considered. An advantage of the generalized proportional model is that a simple formula for the stationary distribution can be determined. The generalized model makes more accurate predictions of chromosome size than the proportional model of Sankoff and Ferretti, but still predicts the smallest and largest chromosomes inaccurately. By considering modifications to the generalized model, chromosome size predictions improve in accuracy. This work was conducted in a National Science Foundation "Research Experience for Undergraduates" program at Cornell University with the effort of Michael Ferguson and Suzanne Sindi, undergraduates at Cornell and Cal State Fullerton, respectively, and supervision of Dr. Richard Durrett, professor in the Mathematics Department at Cornell.