Graduate School of Science and Technology, Shizuoka University, 3-5-1 Johoku, Naka-ku, Hamamatsu, 432-8561, Japan.
Mathematics Division, Institute of Mathematical Sciences and Physics, University of the Philippines Los Baños, College, Laguna, 4031, Philippines.
Sci Rep. 2018 Jan 19;8(1):1198. doi: 10.1038/s41598-017-19044-9.
Classical Lotka-Volterra (LV) competition equation has shown that coexistence of competitive species is only possible when intraspecific competition is stronger than interspecific competition, i.e., the species inhibit their own growth more than the growth of the other species. Note that density effect is assumed to be linear in a classical LV equation. In contrast, in wild populations we can observed that mortality rate often increases when population density is very high, known as crowding effects. Under this perspective, the aggregation models of competitive species have been developed, adding the additional reduction in growth rates at high population densities. This study shows that the coexistence of a few species is promoted. However, an unsolved question is the coexistence of many competitive species often observed in natural communities. Here, we build an LV competition equation with a nonlinear crowding effect. Our results show that under a weak crowding effect, stable coexistence of many species becomes plausible, unlike the previous aggregation model. An analysis indicates that increased mortality rate under high density works as elevated intraspecific competition leading to the coexistence. This may be another mechanism for the coexistence of many competitive species leading high species diversity in nature.
经典的洛特卡-沃尔泰拉（Lotka-Volterra，LV）竞争方程表明，只有当种内竞争强于种间竞争时，即一个物种对自身生长的抑制作用大于对其他物种生长的抑制作用，竞争物种才能共存。请注意，经典 LV 方程中假设密度效应是线性的。相比之下，在野生种群中，我们可以观察到当种群密度非常高时，死亡率经常会增加，这被称为拥挤效应。在这种观点下，已经开发出了竞争物种的聚集模型，即在高种群密度下增加了生长速率的额外降低。本研究表明，这促进了少数物种的共存。然而，一个悬而未决的问题是，在自然群落中经常观察到许多竞争物种的共存。在这里，我们建立了一个具有非线性拥挤效应的 LV 竞争方程。我们的结果表明，在弱拥挤效应下，许多物种的稳定共存变得合理，这与之前的聚集模型不同。分析表明，高密度下死亡率的增加起到了提高种内竞争的作用，从而导致了共存。这可能是导致自然界中许多竞争物种共存并具有高物种多样性的另一种机制。
