Stochastic population growth in spatially heterogeneous environments: the density-dependent case.
Stochastic population growth in spatially heterogeneous environments: the density-dependent case.
复制标题
空间异质环境中的随机人口增长：密度依赖性情况。
DOI：
10.1007/s00285-017-1153-2
复制
发表时间：
2018-03
影响因子：
1.9
通讯作者：
Yin G
中科院分区：
文献类型：
--
作者：
Hening A;Nguyen DH;Yin G
这项工作致力于研究受环境随机性、资源竞争、时空异质性和分散性综合影响的结构化人口的动态。种群分布在 n 个斑块中，其种群丰度被建模为位于 上的非线性随机微分方程组的解。我们证明，r，即在没有竞争的情况下总人口的随机增长率，决定了人口的长期行为。参数 r 可以表示为相关线性化随机微分方程组的 Lyapunov 指数。详细分析表明，如果 ，种群丰度以多项式方式快速收敛到 上的唯一不变概率测度，而当 时，斑块的种群丰度几乎肯定以指数方式快速收敛到 0。这概括并扩展了埃文斯等人的结果。 （J Math Biol 66(3):423–476,）并证明了他们的猜想之一。与最近的发展相比，我们的模型包含了非常普遍的依赖于密度的增长率和竞争条件。此外，我们证明持久性对于环境噪声的增长率、分散矩阵和协方差矩阵的小扰动（可能与密度相关）是稳健的。我们还表明，随机增长率持续取决于系数。我们的工作让环境噪音驱动我们的系统退化。从生物学的角度来看，这是相关的，因为例如不同斑块的环境可以完全相关。我们展示了如何使非简并结果适应简并设置。作为一个例子，我们充分分析了两个补丁的情况， ，并表明随机增长率是离散率的递减函数。特别是，与 Evans 等人处理的非退化设置的结果相反，耦合两个汇块永远不会产生持久性。这表明有时通过分散耦合可以使系统持久存在。
This work is devoted to studying the dynamics of a structured population that is subject to the combined effects of environmental stochasticity, competition for resources, spatio-temporal heterogeneity and dispersal. The population is spread throughout n patches whose population abundances are modeled as the solutions of a system of nonlinear stochastic differential equations living on . We prove that r, the stochastic growth rate of the total population in the absence of competition, determines the long-term behaviour of the population. The parameter r can be expressed as the Lyapunov exponent of an associated linearized system of stochastic differential equations. Detailed analysis shows that if , the population abundances converge polynomially fast to a unique invariant probability measure on , while when , the population abundances of the patches converge almost surely to 0 exponentially fast. This generalizes and extends the results of Evans et al. (J Math Biol 66(3):423–476,) and proves one of their conjectures. Compared to recent developments, our model incorporates very general density-dependent growth rates and competition terms. Furthermore, we prove that persistence is robust to small, possibly density dependent, perturbations of the growth rates, dispersal matrix and covariance matrix of the environmental noise. We also show that the stochastic growth rate depends continuously on the coefficients. Our work allows the environmental noise driving our system to be degenerate. This is relevant from a biological point of view since, for example, the environments of the different patches can be perfectly correlated. We show how one can adapt the nondegenerate results to the degenerate setting. As an example we fully analyze the two-patch case, , and show that the stochastic growth rate is a decreasing function of the dispersion rate. In particular, coupling two sink patches can never yield persistence, in contrast to the results from the non-degenerate setting treated by Evans et al. which show that sometimes coupling by dispersal can make the system persistent.
登录
查看更多内容
影响因子：
2.9
作者：
Bascompte, J;Possingham, HP;Roughgarden, J
通讯作者：
Roughgarden, J
影响因子：
1.9
作者：
Evans, Steven N.;Hening, Alexandru;Schreiber, Sebastian J.
通讯作者：
Schreiber, Sebastian J.
影响因子：
1.9
作者：
HARDIN, DP;TAKAC, P;WEBB, GF
通讯作者：
WEBB, GF
影响因子：
1.9
作者：
HARDIN, DP;TAKAC, P;WEBB, GF
通讯作者：
WEBB, GF
影响因子：
2
作者：
ASSING, S;MANTHEY, R
通讯作者：
MANTHEY, R