There is growing evidence that ecological interactions are often nonlocal. Correspondingly, increasing attention is paid to mathematical models with nonlocal terms as such models may provide a more realistic description of ecological dynamics. Here we consider a nonlocal prey-predator model where the movement of both species is described by the standard Fickian diffusion, and hence is local, but the intra-specific competition of prey is nonlocal and is described by a convolution-type term with the ‘top-hat’ (piecewise-constant) kernel. The prey growth rate also includes the strong Allee effect. The system is studied using a combination of analytical tools and extensive numerical simulations. We obtain that nonlocality makes possible the pattern formation due to the Turing instability, which is not possible in the corresponding local model. We also obtain that the nonlocality creates bistability: it depends on the initial conditions which of the two spatially heterogeneous distributions emerges. Finally, we show that the bifurcation structure of the system is less sensitive to the choice of parametrization than it is in the corresponding nonspatial case, suggesting that nonlocality may decrease the structural sensitivity of the system.

越来越多的证据表明，生态相互作用通常是非本地的。相应地，越来越多地关注具有非局部项的数学模型，因为这样的模型可以提供对生态动力学的更现实的描述。在这里，我们考虑了一个非本地的猎物-捕食者模型，其中两个物种的运动都由标准的Fickian扩散描述，因此是局部的，但是种内种的竞争不是局部的，而是由卷积型术语描述，即“顶帽”（分段恒定）内核。猎物的增长率还包括强大的Allee效应。使用分析工具和广泛的数值模拟相结合的方法对系统进行了研究。我们发现由于图灵不稳定性，非局部性使得图案形成成为可能，而这在相应的局部模型中是不可能的。我们还获得了非局部性产生双稳态的能力：它取决于初始条件，两个空间异质性分布中哪个出现。最后，我们表明系统的分叉结构对参数化的选择比在相应的非空间情况下更不敏感，这表明非局部性可能会降低系统的结构敏感性。