We consider the stepping stone model on the torus of side L in ℤ2 in the limit L→∞, and study the time it takes two lineages tracing backward in time to coalesce. Our work fills a gap between the finite range migration case of [Ann. Appl. Probab. 15 (2005) 671–699] and the long range case of [Genetics 172 (2006) 701–708], where the migration range is a positive fraction of L. We obtain limit theorems for the intermediate case, and verify a conjecture in [Probability Models for DNA Sequence Evolution (2008) Springer] that the model is homogeneously mixing if and only if the migration range is of larger order than (log L)1/2.
Publié le : 2010-06-15
Classification:
Stepping stone model,
torus random walk,
hitting times,
coalescence times,
60K35,
60G50,
92D10,
82C41
@article{1276867297,
author = {Cox, J. Theodore},
title = {Intermediate range migration in the two-dimensional stepping stone model},
journal = {Ann. Appl. Probab.},
volume = {20},
number = {1},
year = {2010},
pages = { 785-805},
language = {en},
url = {http://dml.mathdoc.fr/item/1276867297}
}
Cox, J. Theodore. Intermediate range migration in the two-dimensional stepping stone model. Ann. Appl. Probab., Tome 20 (2010) no. 1, pp. 785-805. http://gdmltest.u-ga.fr/item/1276867297/