Department of Applied Mathematics, University of Calcutta, 92 APC Road, Kolkata 700009, India.
Chaos. 2021 May;31(5):053108. doi: 10.1063/5.0040844.
In ecology, the intra- and inter-specific competition between individuals of mobile species for shared resources is mostly non-local; i.e., competition at any spatial position will not only be dependent on population at that position, but also on population in neighboring regions. Therefore, models that assume competition to be restricted to the individuals at that position only are actually oversimplifying a crucial physical process. For the past three decades, researchers have established the necessity of considering spatial non-locality while modeling ecological systems. Despite this ecological importance, studies incorporating this non-local nature of resource competition in an aquatic ecosystem are surprisingly scarce. To this end, the celebrated Scheffer's tri-trophic minimal model has been considered here as a base model due to its efficacy in describing the pelagic ecosystem with least complexity. It is modified into an integro-reaction-diffusion system to include the effect of non-local competition by introducing a weighted spatial average with a suitable influence function. A detailed analysis shows that the non-locality may have a destabilizing effect on underlying nutrient-plankton-fish dynamics. A local system in a stable equilibrium state can lose its stability through spatial Hopf and Turing bifurcations when strength of a non-local interaction is strong enough, which eventually generates a large range of spatial patterns. The relationship between a non-local interaction and fish predation has been established, which shows that fish predation contributes in damping of plankton oscillations. Overall, results obtained here manifest the significance of non-locality in aquatic ecosystems and its possible contribution to the phenomena of "spatial patchiness."
在生态学中，移动物种个体之间为共享资源而产生的种内和种间竞争大多是非局部的；也就是说，任何空间位置的竞争不仅取决于该位置的种群，还取决于邻近区域的种群。因此，那些仅假设竞争局限于该位置个体的模型实际上过于简化了一个关键的物理过程。在过去的三十年里，研究人员已经确定了在建模生态系统时必须考虑空间非局部性。尽管这在生态学上很重要，但在水生生态系统中纳入资源竞争的这种非局部性质的研究却出奇地少。为此，由于其在描述浮游生态系统时具有最小复杂性的功效，著名的 Scheffer 三营养最小模型被视为基础模型。通过引入具有合适影响函数的加权空间平均值，将其修改为积分反应扩散系统，以包括非局部竞争的影响。详细分析表明，非局部性可能对基础养分-浮游生物-鱼类动态产生不稳定性影响。当地系统在稳定平衡状态下可以通过空间 Hopf 和 Turing 分岔失去稳定性，当非局部相互作用的强度足够强时，最终会产生大范围的空间模式。建立了非局部相互作用与鱼类捕食之间的关系，表明鱼类捕食有助于减缓浮游生物的波动。总的来说，这里得到的结果表明了非局部性在水生生态系统中的重要性及其对“空间斑块化”现象的可能贡献。
