Spatial dynamics of a Lotka-Volterra model with a shifting habitat

Yueding Yuan,Xingfu Zou,Yang Wang

doi:10.3934/dcdsb.2019076

Abstract

In this paper, we study a Lotka-Volterra competition-diffusion model that describes the growth, spread and competition of two species in a shifting habitat. Our results show that (Ⅰ) if the competition between the two species are either mutually strong or mutually weak against each other, the spatial dynamics mainly depend on environment worsening speed c and the spreading speed of each species in the absence of the other in the best possible environment; (Ⅱ) if one species is a strong competitor and the other is a weak competitor, then the interplay of the species' competing strengths and the spreading speeds also has an effect on the spatial dynamics. Particularly, we find that a strong but slower competitor can co-persist with a weak but faster competitor, provided that the environment worsening speed is not too fast.

Highlights

It is well known that spatial heterogeneity and diffusion play an important role when considering the interaction of biological species that can diffuse in the real world
We develop a new approach that enables us to obtain the spatial dynamics of the model (6) subject to the strong competition
As mentioned in Remark 2, under the weak competition condition ai ∈ (0, 1), i = 1, 2, c < c∗(∞) is a sufficient condition for the two species to copersist by spreading toward the right

Summary

Introduction

It is well known that spatial heterogeneity and diffusion play an important role when considering the interaction of biological species that can diffuse in the real world (see, e.g., [5, 6, 7, 16, 26, 34, 35]). The following result shows that if the two species initially live only on a bounded domain and their respective spreading speed is less than the habitat’s worsening speed c, both species will go to extinction, regardless of the competition strength.

Results

Conclusion