Multi-species coexistence in Lotka-Volterra competitive systems with crowding effects

Maica Krizna A Gavina,Satoru Morita,Takashi Nagatani,Hiromu Ito,Genki Ichinose,Kei-Ichi Tainaka,Takeru Tahara,Jin Yoshimura,Tatsuya Togashi,Takuya Okabe

doi:10.1038/s41598-017-19044-9

Abstract

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.

Highlights

Competition is one of the fundamental ecological interactions between species[1]
Using our modified LV competition model with nonlinear crowding effect, we show that multiple species are generally possible to coexist using LV system with crowding effect
Setting dxi/dt = 0, we obtain the zero isoclines for the modified Lotka-Volterra (LV) competition equations with nonlinear crowding effect rate mi. These isoclines are straight lines in the classical LV competition equation when we sketch the graph of the population density 1 with respect to the population density 2 (Fig. 1, dotted lines)

Summary

Introduction

Competition is one of the fundamental ecological interactions between species[1]. We can observe that coexisting species are competing for the same resources[2]. We suspect that there should be some mechanisms for coexistence of competitive species, e.g., spatial structures[5,6] These models, introduce an additional complexity into the mathematical models of classical LV systems. To consider the nonlinear density effects, aggregation models have been developed and studied extensively introducing ‘mean crowding’[8,9,10,15,16]. These models show the coexistence of a few species, but not many species. This coexistence dynamics should be applicable to insect or animal species

Methods

Results

Conclusion