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The equilibrium distribution for a generalized Sankoff-Ferretti model accurately predicts chromosome size distributions in a wide variety of species

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Arkendra De ,
Michael Ferguson ,
Suzanne Sindi  and
Richard Durrett
Arkendra De
Affiliation:
Purdue University
Michael Ferguson
Affiliation:
Cornell University
Suzanne Sindi
Affiliation:
California State University, Fullerton
Richard Durrett*
Affiliation:
Cornell University
*
∗∗∗∗ Postal address: Department of Mathematics, Cornell University, Ithaca, NY 14853, USA. Email address: rtd1@cornell.edu
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Abstract

Sankoff and Ferretti (1996) introduced several models of the evolution of chromosome size by reciprocal translocations, where for simplicity they ignored the existence of centromeres. However, when they compared the models to data on six organisms they found that their short chromosomes were too short, and their long chromosomes were too long. Here, we consider a generalization of their proportional model with explicit chromosome centromeres and introduce fitness functions based on recombination probabilities and on the length of the longest chromosome arm. We find a simple formula for the stationary distribution for our model which fits the data on chromosome lengths in many, but not all, species.

Keywords

reciprocal translocationchromosome size modelMarkov chain

MSC classification

Primary: 60J05: Discrete-time Markov processes on general state spaces
Secondary: 92D10: Genetics
Type
Research Papers
Information
Journal of Applied Probability , Volume 38 , Issue 2 , June 2001 , pp. 324 - 334
Copyright
Copyright © Applied Probability Trust 2001 

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Footnotes

∗

Current address: 1704 White Ash Drive, Carmel, IN 46033, USA.

∗∗

Current address: 10512 Pilla Terra Court, Laurel, MD 20723, USA.

∗∗∗

Current address: 1387 Burgundy Way, Placentia, CA 92870, USA.

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