School of Mathematical Science, Yangzhou University, Yangzhou 225002 China.
Department of Mathematics, University of York, York YO10 5DD, UK.
J Theor Biol. 2021 May 21;517:110631. doi: 10.1016/j.jtbi.2021.110631. Epub 2021 Feb 16.
Size-spectrum models are a recent class of models describing the dynamics of a whole community based on a description of individual organisms. The models are motivated by marine ecosystems where they cover the size range from multicellular plankton to the largest fish. We propose to extend the size-spectrum model with spatial components. The spatial dynamics is governed by a random motion and a directed movement in the direction of increased fitness, which we call 'fitness-taxis'. We use the model to explore whether spatial irregularities of marine communities can occur due to the internal dynamics of predator-prey interactions and spatial movements. This corresponds to a pattern-formation analysis generalized to an entire ecosystem but is not limited to one prey and one predator population. The analyses take the form of Fourier analysis and numerical experiments. Results show that diffusion always stabilizes the equilibrium but fitness-taxis destabilizes it, leading to non-stationary spatially inhomogeneous population densities, which are travelling in size. However, there is a strong asymmetry between fitness-induced destabilizing effects and diffusion-induced stabilizing effects with the latter dominating over the former. These findings reveal that fitness taxis acts as a possible mechanism behind pattern formations in ecosystems with high diversity of organism sizes, which can drive the emergence of spatial heterogeneity even in a spatially homogeneous environment.
尺寸谱模型是一类新兴的模型，它基于对个体生物的描述来描述整个群落的动态。这些模型的灵感来自海洋生态系统，它们涵盖了从多细胞浮游生物到最大鱼类的大小范围。我们建议扩展具有空间分量的尺寸谱模型。空间动态由随机运动和沿适应度增加的方向的定向运动控制，我们称之为“适应度偏导”。我们使用该模型来探索由于捕食者-猎物相互作用和空间运动的内部动态，海洋群落的空间不规则性是否可能发生。这对应于广义到整个生态系统的模式形成分析，但不限于一种猎物和一种捕食种群。分析采用傅里叶分析和数值实验的形式。结果表明，扩散总是稳定平衡但适应度偏导会使其失稳，导致非定常的、空间不均匀的种群密度，它们在大小上移动。然而，适应度引起的不稳定性与扩散引起的稳定性之间存在强烈的不对称性，后者占主导地位。这些发现表明，适应度偏导可能是具有高生物体大小多样性的生态系统中模式形成的潜在机制，它甚至可以在空间均匀的环境中驱动空间异质性的出现。
