Degenerate diffusions arising from gene duplication models
| dc.creator | Durrett, Rick | |
| dc.creator | Popovic, Lea | |
| dc.date | 2009-02-27 | |
| dc.date.accessioned | 2026-07-07T12:47:33Z | |
| dc.date.available | 2026-07-07T12:47:33Z | |
| dc.description | 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. | |
| dc.description | Published in at http://dx.doi.org/10.1214/08-AAP530 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/0902.4780 | |
| dc.identifier | http://arxiv.org/abs/0902.4780 | |
| dc.identifier | Annals of Applied Probability 2009, Vol. 19, No. 1, 15-48 | |
| dc.identifier | doi:10.1214/08-AAP530 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/221760 | |
| dc.subject | Probability | |
| dc.subject | 60J60, 60J70, 92D15, 92D20 (Primary) | |
| dc.title | Degenerate diffusions arising from gene duplication models | |
| dc.type | text |