Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

Mechanistically derived Toxicant-mediated predator-prey model under Stoichiometric constraints

Department of Mathematics and Statistics,Texas Tech University,Lubbock, TX 79409, USA

Studies in ecological stoichiometry highlight that grazer dynamics are affected by insufficient food nutrient content (low phosphorus (P)/carbon (C) ratio) as well as excess food nutrient content (high P:C). Contaminant stressors affect all levels of the biological hierarchy, from cells to organs to organisms to populations to entire ecosystems. Eco-toxicological modeling under the framework of ecological stoichiometry predicts the risk of bio-accumulation of a toxicant under stoichiometric constraints. In this paper, we developed and analyzed a Lotka–Volterra type predator– prey model which explicitly tracks the environmental toxicant as well as the toxicant in the populations under stoichiometric constraints. Analytic, numerical, slow-fast steady state and bifurcation theory are employed to predict the risk of toxicant bio-accumulation under varying food conditions. In some cases, our model predicts different population dynamics, including wide amplitude limit cycles where producer densities exhibit very low values and may be in danger of stochastic extinction.
  Figure/Table
  Supplementary
  Article Metrics

Keywords predator–prey model; ecological stoichiometry; ecotoxicology

Citation: Md Nazmul Hassan, Angela Peace. Mechanistically derived Toxicant-mediated predator-prey model under Stoichiometric constraints. Mathematical Biosciences and Engineering, 2020, 17(1): 349-365. doi: 10.3934/mbe.2020019

References

  • 1. W. X. Wang and N. S. Fisher, Assimilation of trace elements and carbon by the mussel mytilus edulis:effects of food composition, Limnol. Oceanogr., 41 (1996), 197-207.
  • 2. R. Ashauer and C. D. Brown, Toxicodynamic assumptions in ecotoxicological hazard models, Environ. Toxicol. Chem., 27 (2008), 1817-1821.
  • 3. Q. Huang, L. Parshotam, H. Wang, et al., A model for the impact ofcontaminants on fish population dynamics. J. Theor. Biol., 334 (2013), 71-79.
  • 4. Q. Huang, H. Wang and M. Lewis, Development of a toxin-mediated predator-prey model applicable to aquatic environments in the athabasca oil sands region, Osrin Report no. Tech. rep., (2014), TR-59. 59 pp. Available from: http://hdl.handle.net/10402/era.40140.
  • 5. M. Danger and F. Maunoury-Danger, Ecological stoichiometry. In: Encyclopedia of Aquatic Ecotoxicology, Springer, (2013), 317-326.
  • 6. O. Ieromina, W. J. Peijnenburg, G. de Snoo, et al., Impact of imidacloprid on daphnia magna under different food quality regimes, Environ. Toxicol. Chem., 33 (2014), 621-631.
  • 7. C. R. Lessard and P. C. Frost, Phosphorus nutrition alters herbicide toxicity on Daphnia magna, Sci. Total Environ., 421 (2012), 124-128.
  • 8. R. Karimi, C. Chen, P. Pickhardt, et al., Stoichiometric controls of mercury dilution by growth, P. Natl. Acad. Sci. USA, 104 (2007), 7477-7482.
  • 9. A. Peace, M. Poteat and H. Wang, Somatic growth dilution of a toxicant in a predator-prey model under stoichiometric constraints, J. Theo. Biol., 407 (2016), 198-211.
  • 10. M. N. Hassan, K. Thompson, G. Mayer, et al., Effect of excess food nutrient on producer-grazer model under stoichiometric and toxicological constraints, Math. Biosci. Eng., 16 (2018), 150-167.
  • 11. R. W. Sterner and J. J. Elser, Ecological stoichiometry: the biology of elements from molecules to the biosphere, Princeton University Press, (2002).
  • 12. A. Peace, Y. Zhao, I. Loladze, et al., A stoichiometric producer-grazer model incorporating the effects of excess food-nutrient content on consumer dynamics, Math. Biosci., 244 (2013), 107- 115.
  • 13. F. J. Miller, P. M. Schlosser, D. B. Janszen, Haber's rule: a special case in a family of curves relating concentration and duration of exposure to a fixed level of response for a given endpoint, Toxicology, 149 (2000), 21-34.
  • 14. T. Andersen, Pelagic nutrient cycles: herbivores as sources and sinks, Springer Science & Business Media, 129, 2013.
  • 15. R. W. Vocke, K. L. Sears, J. J. O'Toole, et al., Growth responses of selected freshwater algae to trace elements and scrubber ash slurry generated by coal-fired power plants, Water Res., 14 (1980), 141-150.
  • 16. K. E. Biesinger, L. E. Anderson and J. G. Eaton, Chronic effects of inorganic and organic mercury ondaphnia magna: Toxicity, accumulation, and loss, Arch. Environ. Con. Tox., 11 (1982), 769-774.
  • 17. W. R. Hill and I. L. Larsen, Growth dilution of metals in microalgal biofilms, Environ. Sci. Technol., 39 (2005), 1513-1518.
  • 18. M. T. Tsui and W. X. Wang, Uptake and elimination routes of inorganic mercury and methylmercury in daphnia magna, Environ. Sci. Technol., 38 (2004), 808-816.
  • 19. B. Kooi, D. Bontje, G. Van Voorn, et al., Sublethal toxic effects in a simple aquatic foodchain, Ecol. Model., 212 (2008), 304-318.
  • 20. I. Loladze, Y. Kuang and J. J. Elser, Stoichiometry in producer-grazer systems: Linking energy flow with element cycling, Bull. Math. Bio., 62L (2000), 1137-1162.
  • 21. X. Li, H. Wang and Y. Kuang, Global analysis of a stoichiometric producer-grazer model withholling type functional responses, J. Math. Biol., 63 (2011), 901-932.
  • 22. T. Xie, X. Yang, X. Li, et al., Complete global and bifurcation analysis of a stoichiometricpredator-prey model, J. Dyn. Differ. Equ., 30 (2018), 447-472.
  • 23. G. A. Van Voorn, B. W. Kooi and M. P. Boer, Ecological consequences of global bifurcations in somefood chain models, Math. Biosci., 226 (2010), 120-133.
  • 24. A. Peace, H. Wang and Y. Kuang, Dynamics of a producer-grazer model incorporating the effects of excess food nutrient content on grazers growth, Bull. Math. Biol., 76 (2014), 2175-2197.
  • 25. X. Yang, X. Li, H. Wang, et al., Stability and bifurcation in a stoichiometric producer-grazermodel with knife edge, SIAM J. Appl. Dyn. Syst., 15 (2016), 2051-2077.    
  • 26. M. G. Neubert and H. Caswell, Alternatives to resilience for measuring the responses of ecologicalsystems to perturbations, Ecology, 78 (1997), 653-665.
  • 27. S. Rinaldi, S. Muratori and Y. Kuznetsov, Multiple attractors, catastrophes and chaos in seasonallyperturbed predator-prey communities, Bull Math. Biol., 55 (1993), 15-35.
  • 28. S. M. Henson and J. M. Cushing, The effect of periodic habitat fluctuations on a nonlinear insectpopulation model, J. Math. Biol., 36 (1997), 201-226.
  • 29. M. N. Hassan, L. Asik, J. Kulik, et al., Environmental seasonality on predator-preysystems under nutrient and toxicant constraints, J. Theor. Biol., 480 (2019), 71-80.
  • 30. R. Vesipa and L. Ridolfi, Impact of seasonal forcing on reactive ecological systems, J. Theor. Biol., 419 (2017), 23-35.

 

Reader Comments

your name: *   your email: *  

© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved