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.
Similar content being viewed by others
References
CCME (2003) The Canadian Council of Ministers of the Environment, Canadian water quality guidelines for the protection of aquatic life: guidance on the site-specific application of water quality guidelines in Canada: procedures for deriving numerical water quality objectives. http://ceqg-rcqe.ccme.ca/download/en/221
Cody ML, Diamond JM (1975) Ecology and evolution of communities. Belknap Press of Harvard University Press, Cambridge
Fenichel N (1971) Persistence and smoothness of invariant manifolds for flows. Indiana Univ Math J 21:193–226
Fenichel N (1979) Geometric singular perturbation theory for ordinary differential equations. J Diff Equ 31:53–98
Forbes V, Hommen U, Thorbek P, Heimbach F, den Brink PV, J Wogram HT, Grimm V (2009) Ecological models in support of regulatory risk assessments of pesticides: developing a strategy for the future. Integr Environ Asses Manag 5:167–172
Forbes V, Sibly R, Calow P (2001) Toxicant impacts on density-limited populations: a critical review of theory, practice, and results. Ecol Appl 11:1249–1257
Freedman HI, Shukla JB (1991) Models for the effect of toxicant in single-species and predator–prey systems. J Math Biol 30:15–30
Grover JP (1997) Resource competition. Chapman & Hall, London
Hallam TG, Clark CE (1983) Effect of toxicants on populations: a qualitative approach. I. Equilibrium environmental exposure. Ecol Model 18:291–304
Hallam TG, Clark CE, Jordan GS (1983) Effect of toxicants on populations: a qualitative approach. II. First order kinetics. J Math Biol 18:25–37
Hallam TG, Luna JD (1984) Extinction and persistence in models of population-toxicant interactions. Ecol Model 22:13–20
Hallam TG, Luna JD (1990) Toxicant-induced mortality in models of daphnia populations. Environ Toxicol Chem 9:597–621
Huang Q, Parshotam L, Wang H, Bampfylde C, Lewis M (2013) A model of the impact of contaminants on fish population dynamics. J Theor Biol 334:71–79
Huang Q, Wang H, Lewis MA (2015) The impact of environmental toxins on predator–prey dynamics. J Theor Biol 378:12–30
Kot M (2001) Elements of mathematical ecology. Cambridge University Press, Cambridge
Luna JT, Hallam TG (1987) Effect of toxicants on populations: a qualitative approach. IV. Resource-consumer-toxiocant models. Ecol Model 35:249–273
McElroy AE, Barron MG, Beckvar N, Driscoll SBK, Meador JP, Parkerton TF, Preuss TG, Steevens JA (2010) A review of the tissue residue approach for organic and organometallic compounds in aquatic organisms. Integr Environ Assess Manag 7:50–74
Schoener TW (1982) The controversy over interspecific competition: despite spirited criticism, competition continues to occupy a major domain in ecological thought. Am Sci 70:586–595
Smith H (1995) Monotone dynamical systems. An introduction to the theory of competitive and cooperative systems. Mathematical surveys and monographs, vol 41. American Mathematical Society, Providence
Thieme HR (2003) Mathematics in population biology. Princeton University Press, Princeton
Thomas DM, Snell TW, Jaffar SM (1996) A control problem in a polluted environment. Math Biosci 133:139–163
USNARA (2013) US national archives and records administration, code of federal regulations, title 40-protection of environment, Appendix A to part 423–126 priority pollutants
Waltman P (1983) Competition models in population biology. SIAM, Philadelphia
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
C. Shan: The research of C. Shan was partially supported by the startup fund 110799 from the University of Toledo and the Simons Foundation-Collaboration Grants for Mathematicians 523360.
Q. Huang: The research of Q. Huang was partially supported by the faculty startup fund 20710948 from Southwest University and the Fundamental Research Funds for the Central Universities XDJK2018B031.
Rights and permissions
About this article
Cite this article
Shan, C., Huang, Q. Direct and indirect effects of toxins on competition dynamics of species in an aquatic environment. J. Math. Biol. 78, 739–766 (2019). https://doi.org/10.1007/s00285-018-1290-2
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00285-018-1290-2