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- W3104253094 abstract "We consider two processes that have been used to study gene duplication, Watterson’s [Genetics 105 (1983) 745–766] double recessive null model and Lynch and Force’s [Genetics 154 (2000) 459–473] subfunctionalization model. Though the state spaces of these diffusions are two and six-dimensional, respectively, we show in each case that the diffusion stays close to a curve. Using ideas of Katzenberger [Ann. Probab. 19 (1991) 1587–1628] we show that one-dimensional projections converge to diffusion processes, and we obtain asymptotics for the time to loss of one gene copy. As a corollary we find that the probability of subfunctionalization decreases exponentially fast as the population size increases. This rigorously confirms a result Ward and Durrett [Theor. Pop. Biol. 66 (2004) 93–100] found by simulation that the likelihood of subfunctionalization for gene duplicates decays exponentially fast as the population size increases." @default.
- W3104253094 created "2020-11-23" @default.
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- W3104253094 date "2009-02-01" @default.
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- W3104253094 title "Degenerate diffusions arising from gene duplication models" @default.
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- W3104253094 doi "https://doi.org/10.1214/08-aap530" @default.
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