期刊
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS
卷 18, 期 8, 页码 1381-1403出版社
TAYLOR & FRANCIS LTD
DOI: 10.1080/10236198.2011.628662
关键词
applications of Markov chains and discrete-time Markov processes on general state spaces; population dynamics (general); stochastic difference equations
资金
- National Science Foundation [DMS-0517987, DMS-1022639]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1022639] Funding Source: National Science Foundation
Understanding under what conditions populations, whether they be plants, animals or viral particles, persist is an issue of theoretical and practical importance in population biology. Both biotic interactions and environmental fluctuations are key factors that can facilitate or disrupt persistence. One approach to examining the interplay between these deterministic and stochastic forces is the construction and analysis of stochastic difference equations Xt+1 = F(X-t, xi(t+1)), where X-t is an element of R-k represents the state of the populations and xi(1), xi(2), . . . is a sequence of random variables representing environmental stochasticity. In the analysis of these stochastic models, many theoretical population biologists are interested in whether the models are bounded and persistent. Here, boundedness asserts that asymptotically X-t tends to remain in compact sets. In contrast, persistence requires that X-t tends to be 'repelled' by some 'extinction set' S-0 subset of R-k. Here, results on both of these proprieties are reviewed for single species, multiple species and structured population models. The results are illustrated with applications to stochastic versions of the Hassell and Ricker single species models, Ricker, Beverton-Holt, lottery models of competition, and lottery models of rock-paper-scissor games. A variety of conjectures and suggestions for future research are presented.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据