Direct and indirect effects of toxins on competition dynamics of species in an aquatic environment

Abstract

When two competing species are simultaneously exposed in a polluted environment, one species may be more vulnerable to toxins than the other. To study the impact of environmental toxins on competition dynamics of two species, we develop a toxin-dependent competition model that incorporates both direct and indirect toxic effects on the species. The direct effects of toxins typically reduce population abundance by increasing mortality and reducing reproduction. However, the indirect effects, which are mediated through competitive interactions, may lead to counterintuitive effects. We investigate the toxin-dependent competition model and explore the impact of the interplay between environmental toxins and distinct toxic tolerance of two species on the competition outcomes. The results of theoretical analysis and numerical studies reveal that while high level of toxins is harmful to both species, possibly leading to extirpation of both species, intermediate level of toxins, plus different vulnerabilities of two species to toxins, affect competition outcomes in many counterintuitive ways. It turns out that sublethal toxins may boost coexistence of two species (hence keep species diversity in ecosystems) by reducing the abundance of the predominant species; sublethal toxins may overturn and exchange roles of winner and loser in competition; sublethal toxins may also induce different types of bistability of the competition dynamics, where the competition outcome is doomed to exclusion or coexistence, depending on initial population densities. The theory developed here provides a sound foundation for understanding competitive interactions between two species in a polluted aquatic environment.

The impact of toxins on competition dynamics of three species in a polluted aquatic environment

“…It should be noted that in some senses, our three-species competition model (2) extends the two-species toxin-mediated competition model by Shan and Huang [25], whereas there are two main differences between the two models. In the first place, model (2) considers the fact that the death from interspecific competition leads to the loss of toxin in the population, which was overlooked in the two-species competition model in [25]. In the second place, if there is no toxin or inter-specific competition, the population growth model of single species in model (2) reduces to…”

“…The model was used to shed light on the effects of varying toxin concentration on long-term dynamics of organisms at different trophic levels. Recently, in order to further study the impact of environmental toxins on population interactions, Shan and Huang [25] developed a toxin-dependent competition model for two species that are simultaneously exposed to a polluted aquatic environment. The model was then utilized to scrutinize how the interplay between direct and indirect effects of environmental toxins determines competition outcomes of two species.…”

“…The main purpose of this work is to study how environmental toxins affect the competition dynamics of three species in a polluted aquatic ecosystem. To this end, we develop a toxin-mediated competition model which extends the two-species competition model by Shan and Huang [25]. Our model is composed of a six ordinary differential equations.…”

“…We use x i (t)(i = 1, 2, 3) to represent the concentration of biomass of species at time t. Let u i be the concentration of toxin in species i at time t. Let y i (t) be the body burden of species i. See section 2 in [25] for more precise definitions of x i , u i , and y i . The mathematical model that describes the toxin-mediated competition dynamics of the three species in a polluted aquatic environment is given by…”

“…The term (k i y i + m i + c ii x i + j =i c ij x j )u i describes the loss of toxin in the population due to mortality (including toxin-dependent mortality and competition mortality). (Note that the two-species competition model studied in [25] ignores the loss of toxin contained in the population due to death from competition.) Finally, equation (1c) defines the body burden -toxin concentration per unit species biomass.…”