Global dynamics of a two-species competition patch model in a Y-shaped river network

TL;DR

This study analyzes a two-species competition model in a Y-shaped river network, revealing conditions for species exclusion and highlighting the influence of dispersal and drift rates on species survival.

Contribution

It introduces a novel two-species competition model on a Y-shaped river network and characterizes conditions for competitive exclusion and the impact of dispersal rates.

Findings

Competition exclusion occurs under certain conditions.

Equal dispersal rates favor the species with smaller drift.

Small drift rates are advantageous for species survival.

Abstract

In this paper, we investigate a two-species Lotka-Volterra competition patch model in a Y-shaped river network, where the two species are assumed to be identical except for their random and directed movements. We show that competition exclusion can occur under certain conditions, i.e., one of the semi-trivial equilibrium is globally asymptotically stable. Especially, if the random dispersal rates of the two species are equal, the species with a smaller drift rate will drive the other species to extinction, which suggests that small drift rates are favored.