Degenerate diffusions arising from gene duplication models

Published

Journal Article

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. © Institute of Mathematical Statistics, 2009.

Full Text

Duke Authors

Cited Authors

  • Durrett, R; Popovic, L

Published Date

  • February 1, 2009

Published In

Volume / Issue

  • 19 / 1

Start / End Page

  • 15 - 48

Electronic International Standard Serial Number (EISSN)

  • 1050-5164

International Standard Serial Number (ISSN)

  • 1050-5164

Digital Object Identifier (DOI)

  • 10.1214/08-AAP530

Citation Source

  • Scopus