We propose two models of the evolution of a pair of competing populations. Both are lattice based. The first is a compromise between fully spatial models, which do not appear amenable to analytic results, and interacting particle system models, which do not, at present, incorporate all of the competitive strategies that a population might adopt. The second is a simplification of the first, in which competition is only supposed to act within lattice sites and the total population size within each lattice point is a constant. In a special case, this second model is dual to a branching annihilating random walk. For each model, using a comparison with oriented percolation, we show that for certain parameter values, both populations will coexist for all time with positive probability. As a corollary, we deduce survival for all time of branching annihilating random walk for sufficiently large branching rates. We also present a number of conjectures relating to the rôle of space in the survival probabilities for the two populations.
Publié le : 2007-10-15
Classification:
Competing species,
coexistence,
branching annihilating random walk,
interacting diffusions,
regulated population,
heteromyopia,
stepping stone model,
survival,
Feller diffusion,
Wright–Fisher diffusion,
60K35,
60J80,
60J85,
60J70,
92D25
@article{1191419173,
author = {Blath, Jochen and Etheridge, Alison and Meredith, Mark},
title = {Coexistence in locally regulated competing populations and survival of branching annihilating random walk},
journal = {Ann. Appl. Probab.},
volume = {17},
number = {1},
year = {2007},
pages = { 1474-1507},
language = {en},
url = {http://dml.mathdoc.fr/item/1191419173}
}
Blath, Jochen; Etheridge, Alison; Meredith, Mark. Coexistence in locally regulated competing populations and survival of branching annihilating random walk. Ann. Appl. Probab., Tome 17 (2007) no. 1, pp. 1474-1507. http://gdmltest.u-ga.fr/item/1191419173/