Local interactions among individual members of a population can generate intricate small-scale spatial structure, which can strongly influence population dynamics. The two-way interplay between local interactions and population dynamics is well understood in the relatively simple case where the population occupies a fixed domain with a uniform average density. However, the situation where the average population density is spatially varying is less well understood. This situation includes ecologically important scenarios such as species invasions, range shifts, and moving population fronts. Here, we investigate the dynamics of the spatial stochastic logistic model in a scenario where an initially confined population subsequently invades new, previously unoccupied territory. This simple model combines density-independent proliferation with dispersal, and density-dependent mortality via competition with other members of the population. We show that, depending on the spatial scales of dispersal and competition, either a clustered or a regular spatial structure develops over time within the invading population. In the short-range dispersal case, the invasion speed is significantly lower than standard predictions of the mean-field model. We conclude that mean-field models, even when they account for non-local processes such as dispersal and competition, can give misleading predictions for the speed of a moving invasion front.

中文翻译：

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小型空间结构影响大型入侵率

人口个体成员之间的局部相互作用可以生成复杂的小规模空间结构，这可以极大地影响人口动态。在相对简单的情况下，局部交互作用和种群动态之间的双向相互作用是众所周知的，在这种情况下，种群占据具有均匀平均密度的固定域。但是，人们对平均人口密度在空间上变化的情况了解得很少。这种情况包括具有重要生态意义的场景，例如物种入侵，范围转移和迁徙的人口前沿。在这里，我们调查了在最初受限的人口随后入侵新的，先前未被占用的领土的情况下空间随机逻辑模型的动力学。这个简单的模型结合了密度无关的扩散和扩散，与人口中其他成员的竞争所致的密度依赖性死亡率。我们表明，根据扩散和竞争的空间规模，在入侵人口中，随着时间的推移会发展成集群的或规则的空间结构。在短距离扩散情况下，入侵速度明显低于平均场模型的标准预测。我们得出的结论是，即使平均域模型考虑了分散和竞争等非局部过程，也可以对移动战线的速度做出误导性的预测。在短距离扩散情况下，入侵速度明显低于平均场模型的标准预测。我们得出的结论是，即使平均域模型考虑了分散和竞争等非局部过程，也可能对入侵前沿的速度给出误导性的预测。在短距离扩散情况下，入侵速度明显低于平均场模型的标准预测。我们得出的结论是，即使平均域模型考虑了分散和竞争等非局部过程，也可能对入侵前沿的速度给出误导性的预测。