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Journal of Mathematical Biology

, Volume 78, Issue 3, pp 739–766 | Cite as

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

  • Chunhua Shan
  • Qihua HuangEmail author
Article
  • 189 Downloads

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.

Keywords

Toxin Competition Fast-slow dynamics Coexistence Exclusion Bistability 

Mathematics Subject Classification

92Bxx 37N25 34C23 

Notes

Acknowledgements

The authors thank Gunog Seo (Colgate University) for fruitful discussions. The authors gratefully acknowledge two anonymous referees for careful reading and insightful comments which greatly improve the manuscript.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsThe University of ToledoToledoU.S.A.
  2. 2.School of Mathematical and Statistical SciencesSouthwest UniversityChongqingChina

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