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首页> 外文期刊>Proceedings of the National Academy of Sciences of the United States of America >Space and stochasticity in population dynamics
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Space and stochasticity in population dynamics

机译：人口动态中的空间和随机性

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摘要

Organisms interact with each other mostly over local scales, so the local density experienced by an individual is of greater importance than the mean density in a population. This simple observation poses a tremendous challenge to theoretical ecology, and because nonlinear stochastic and spatial models cannot be solved exactly, much effort has been spent in seeking effective approximations. Several authors have observed that spatial population systems behave like deterministic nonspatial systems if dispersal averages the dynamics over a sufficiently large scale. We exploit this fact to develop an exact series expansion, which allows one to derive approximations of stochastic individual-based models without resorting to heuristic assumptions. Our approach makes it possible to calculate the corrections to mean-field models in the limit where the interaction range is large, and it provides insight into the performance of moment closure methods. With this approach, we demonstrate how the buildup of spatiotemporal correlations slows down the spread of an invasion, prolongs time lags associated with extinction debt, and leads to locally oscillating but globally stable coexistence of a host and a parasite.
机译：生物彼此之间的相互作用主要是在局部尺度上进行的，因此，个体所经历的局部密度比种群中的平均密度更为重要。这种简单的观察对理论生态提出了巨大的挑战，并且由于非线性随机和空间模型无法精确求解，因此在寻求有效逼近上花费了很多精力。几位作者观察到，如果分散在足够大的范围内平均动力学，则空间种群系统的行为将像确定性非空间系统一样。我们利用这一事实来开发一种精确的级数展开式，该展开式允许在不依靠启发式假设的情况下得出基于随机个体的模型的近似值。我们的方法使得可以在相互作用范围较大的极限中计算对均值场模型的校正，并且可以深入了解力矩闭合方法的性能。通过这种方法，我们证明了时空相关性的建立如何减缓入侵的扩散，延长与灭绝债务相关的时间滞后，并导致宿主和寄生虫在本地振荡但在全球范围内稳定并存。

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