Stochastic population growth in spatially heterogeneous environments.
Stochastic population growth in spatially heterogeneous environments.
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DOI：
10.1007/s00285-012-0514-0
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发表时间：
2013-02
影响因子：
1.9
通讯作者：
Sen, Arnab
中科院分区：
文献类型：
--
作者：
Evans, Steven N.;Ralph, Peter L.;Schreiber, Sebastian J.;Sen, Arnab
关键词：
经典生态学理论预测，环境随机性通过降低人口的人均增长率来增加灭绝风险。对于空间均匀但时间可变的环境中的定居种群，一个简单的种群增长模型是随机微分方程dZt = μZtdt + σ ZtdWt，t ≥ 0，其中Zt+Δt − Zt的条件律给定Zt = z，当时间增量Δt很小时，均值和方差近似为zμΔt和z2σ2Δt。长期随机增长率limt→∞ t−1 log Zt等于。然而，大多数人口都经历了空间和时间的变化。为了理解环境随机性、空间异质性和扩散对种群增长的相互作用，我们研究了一个类似的模型，t ≥ 0，用于n个斑块中的种群丰度：给定Xt = x，Xt+Δt的条件律使得的条件均值近似为[xiμi +∑j（xj Dji − xi Dij）]Δt其中μi是第i个斑块的人均增长率，Dij是从第i个斑块到第j个斑块的扩散率，对于某个协方差矩阵<$i =（σij），和的条件协方差近似为xixjσijΔt。我们证明了对于这样一个空间扩展的种群，如果表示总种群丰度，则斑块比例矢量Yt = Xt /St在t → ∞时按规律收敛到随机矢量Y∞，并且随机增长率limt→∞ t−1 log St等于种群经历的时空平均人均增长率减去种群经历的时空平均时间变化的一半。利用随机增长率的这个特征，我们导出了生活在两个斑块中的种群的随机增长率的显式表达式，确定了对于自由分散的种群，分散矩阵D的哪些选择产生了最大的随机增长率，导出了对于分散有限的种群的随机增长率的解析近似，并使用群论技术来近似生活在多尺度景观中的种群的随机增长率（例如岛屿上草地上植物上的昆虫）。我们的研究结果提供了基本的见解“理想的自由”运动的不确定性，耦合汇人口的持久性，扩散率的演变，以及在保护生物学的单个大或几个小（SLOSS）的辩论。例如，我们的分析意味着，即使在没有密度依赖的反馈，理想的自由分散占据多个补丁在空间异质环境提供的环境波动足够强，足够弱的空间相关。相反，对于生活在相似环境中的扩散扩散种群，中间扩散率使其随机增长率最大化。
Classical ecological theory predicts that environmental stochasticity increases extinction risk by reducing the average per-capita growth rate of populations. For sedentary populations in a spatially homogeneous yet temporally variable environment, a simple model of population growth is a stochastic differential equation dZt = μZtdt + σ ZtdWt, t ≥ 0, where the conditional law of Zt+Δt − Zt given Zt = z has mean and variance approximately zμΔt and z2σ2Δt when the time increment Δt is small. The long-term stochastic growth rate limt→∞ t−1 log Zt for such a population equals . Most populations, however, experience spatial as well as temporal variability. To understand the interactive effects of environmental stochasticity, spatial heterogeneity, and dispersal on population growth, we study an analogous model , t ≥ 0, for the population abundances in n patches: the conditional law of Xt+Δt given Xt = x is such that the conditional mean of is approximately [xiμi +∑j (xj Dji − xi Dij)]Δt where μi is the per capita growth rate in the ith patch and Dij is the dispersal rate from the ith patch to the jth patch, and the conditional covariance of and is approximately xixjσijΔt for some covariance matrix Σ = (σij). We show for such a spatially extended population that if denotes the total population abundance, then Yt = Xt /St, the vector of patch proportions, converges in law to a random vector Y∞ as t → ∞, and the stochastic growth rate limt→∞ t−1 log St equals the space-time average per-capita growth rate experienced by the population minus half of the space-time average temporal variation experienced by the population. Using this characterization of the stochastic growth rate, we derive an explicit expression for the stochastic growth rate for populations living in two patches, determine which choices of the dispersal matrix D produce the maximal stochastic growth rate for a freely dispersing population, derive an analytic approximation of the stochastic growth rate for dispersal limited populations, and use group theoretic techniques to approximate the stochastic growth rate for populations living in multi-scale landscapes (e.g. insects on plants in meadows on islands). Our results provide fundamental insights into “ideal free” movement in the face of uncertainty, the persistence of coupled sink populations, the evolution of dispersal rates, and the single large or several small (SLOSS) debate in conservation biology. For example, our analysis implies that even in the absence of density-dependent feedbacks, ideal-free dispersers occupy multiple patches in spatially heterogeneous environments provided environmental fluctuations are sufficiently strong and sufficiently weakly correlated across space. In contrast, for diffusively dispersing populations living in similar environments, intermediate dispersal rates maximize their stochastic growth rate.
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影响因子：
2.9
作者：
Bascompte, J;Possingham, HP;Roughgarden, J
通讯作者：
Roughgarden, J
影响因子：
4.3
作者：
Cantrell, Robert Stephen;Cosner, Chris;Lou, Yuan
通讯作者：
Lou, Yuan
DOI：
10.1017/s030821050001876x
发表时间：
1989-01-01
影响因子：
1.3
作者：
CANTRELL, RS;COSNER, C
通讯作者：
COSNER, C
影响因子：
6.3
作者：
FOLEY, P
通讯作者：
FOLEY, P
影响因子：
1.9
作者：
Dockery, J;Hutson, V;Pernarowski, M
通讯作者：
Pernarowski, M