Branching process models for mutant genes in nonstationary populations

Theoretical Population Biology
K Lange, R Z Fan

Abstract

A deleterious gene achieves a population balance between the opposing forces of selection and mutation. In this paper we explore the nature of this stochastic balance when the surrounding normal population is not at equilibrium. Assuming that new mutations occur according to a Poisson process and thereafter evolve by the rules of a continuous time branching process, we derive explicit formulas and recurrence relations determining the probability distribution of the current number of mutant individuals. In fact, we compute expectations for a variety of interesting random variables for genetic models involving autosomal dominant and X-linked diseases. We can also handle haplotype information on linked markers. This feature will be especially helpful in understanding the linkage disequilibrium strategy of positional cloning in population isolates. In the presence of exponential growth of the normal population, our formulas reduce to the evaluation of certain Laplace transforms.

References

Oct 1, 1978·Theoretical Population Biology·K Gladstien, K Lange
Jan 1, 1986·Cold Spring Harbor Symposia on Quantitative Biology·W F Bodmer
Jul 1, 1981·Social Science & Medicine. Part B, Medical Anthropology·E K Feierman
Aug 1, 1980·Theoretical Population Biology·K Lange, K Gladstien

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Citations

Jul 31, 2008·Journal of the Royal Society, Interface·Z Patwa, L M Wahl
Mar 1, 2006·Theoretical Population Biology·Amaury Lambert
Jul 29, 1998·Theoretical Population Biology·R Fan, K Lange
Mar 10, 2000·Theoretical Population Biology·S W Guo, K Lange
Aug 30, 2001·Trends in Genetics : TIG·D E Reich, E S Lander
Nov 15, 2003·Journal of Theoretical Biology·Susanna C ManrubiaEster Lázaro

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