A SIMPLE EVOLUTIONARY GAME ARISING FROM THE STUDY OF THE ROLE OF IGF-II IN PANCREATIC CANCER
成果类型：
Article
署名作者：
Ma, Ruibo; Durrett, Rick
署名单位：
Duke University
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/17-AAP1378
发表日期：
2018
页码：
2896-2921
关键词：
摘要：
We study an evolutionary game in which a producer at x gives birth at rate 1 to an offspring sent to a randomly chosen point in x + N-c, while a cheater at x gives birth at rate lambda > 1 times the fraction of producers in x + N-d and sends its offspring to a randomly chosen point in x + N-c. We first study this game on the d-dimensional torus (Z mod L)(d) with N-d = (Z mod L)(d) and N-c = the 2d nearest neighbors. If we let L -> infinity then t -> infinity the fraction of producers converges to 1/lambda. In d >= 3 the limiting finite dimensional distributions converge as t -> infinity to the voter model equilibrium with density 1/lambda. We next reformulate the system as an evolutionary game with birthdeath updating and take N-c = N-d = N. Using results for voter model perturbations we show that in d = 3 with N = the six nearest neighbors, the density of producers converges to (2/lambda) - 0.5 for 4/3 < lambda < 4. Producers take over the system when lambda < 4/3 and die out when lambda > 4. In d = 2 with N = [-c,root logN, c root logN](2) there are similar phase transitions, with coexistence occurring when (1 + 2 theta)/(1 + theta) < lambda < (1 + 2 theta)/theta where = theta = (e(3/(pi c2)) - 1)/2.