Dutta Partha Sharathi, Kooi Bob W, Feudel Ulrike
Department of Mathematics, Indian Institute of Technology Ropar, Punjab 140 001, India.
Department of Theoretical Biology, VU University, De Boelelaan 1087, NL 1081 HV Amsterdam, The Netherlands.
J Theor Biol. 2017 Mar 21;417:28-42. doi: 10.1016/j.jtbi.2017.01.020. Epub 2017 Jan 17.
We study the effects of predation on the competition of prey populations for two resources in a chemostat. We investigate a variety of small food web compositions: the bi-trophic food web (two resources-two competing prey) and the three-trophic food web (two resources-two prey-generalist predator) comparing different model formulations: substitutable resources and essential resources, namely Liebig's minimum law model (perfect essential resources) and complementary resources formulations. The prediction of the outcome of competition is solely based on bifurcation analysis in which the inflow of resources into the chemostat is used as the bifurcation parameter. We show that the results for different bi-trophic food webs are very similar, as only equilibria are involved in the long-term dynamics. In the three-trophic food web, the outcome of competition is manifested largely by non-equilibrium dynamics, i.e., in oscillatory behavior. The emergence of predator-prey cycles leads to strong deviations between the predictions of the outcome of competition based on Liebig's minimum law and the complementary resources. We show that the complementary resources formulation yields a stabilization of the three-trophic food web by decreasing the existence interval of oscillations. Furthermore, we find an exchange of a region of oscillatory co-existence of all three species in Liebig's formulation by a region of bistability of two limit cycles containing only one prey and the predator in the complementary formulation.
我们研究了在恒化器中捕食对猎物种群争夺两种资源的竞争的影响。我们调查了多种小型食物网组成：双营养级食物网（两种资源 - 两种竞争猎物）和三营养级食物网（两种资源 - 两种猎物 - 泛化捕食者），并比较了不同的模型公式：可替代资源和必需资源，即利比希最小定律模型（完美必需资源）和互补资源公式。竞争结果的预测完全基于分岔分析，其中进入恒化器的资源流入被用作分岔参数。我们表明，不同双营养级食物网的结果非常相似，因为长期动态仅涉及平衡态。在三营养级食物网中，竞争结果主要由非平衡动态表现出来，即表现为振荡行为。捕食者 - 猎物循环的出现导致基于利比希最小定律和互补资源的竞争结果预测之间存在强烈偏差。我们表明，互补资源公式通过缩短振荡的存在区间使三营养级食物网得到稳定。此外，我们发现在利比希公式中所有三个物种振荡共存的区域，在互补公式中被仅包含一种猎物和捕食者的两个极限环的双稳态区域所取代。
