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.

中文翻译：

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Lotka-Volterra竞争系统中具有拥挤效应的多物种共存。

经典的Lotka-Volterra（LV）竞争方程表明，竞争物种的共存只有在种内竞争比种间竞争强的情况下才有可能，即种比其他种的生长更能抑制自身的生长。注意，在经典的LV方程中，密度效应被认为是线性的。相反，在野生种群中，我们可以观察到，当种群密度很高时，死亡率通常会增加，这被称为拥挤效应。在这种情况下，已经开发了竞争性物种的聚集模型，增加了人口密度高时增长率的进一步降低。这项研究表明，促进了几种物种的共存。但是，一个尚未解决的问题是自然界中经常观察到的许多竞争物种并存。在这里，我们建立了具有非线性拥挤效应的LV竞争方程。我们的结果表明，与以前的聚集模型不同，在较弱的拥挤效应下，许多物种的稳定共存变得合理。分析表明，高密度下的死亡率升高是种内竞争加剧导致共存的原因。这可能是许多竞争物种共存的另一种机制，导致自然界中物种高度多样性。