Effect of Excess Food Nutrient on Producer-Grazer Model under Stoichiometric and Toxicological Constraints

Md Nazmul Hassan; Kelsey Thompson; Gregory Mayer; Angela Peace; Md Nazmul Hassan; Kelsey Thompson; Gregory Mayer; Angela Peace

doi:10.3934/mbe.2019008

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 1: 150-167. doi: 10.3934/mbe.2019008

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Effect of Excess Food Nutrient on Producer-Grazer Model under Stoichiometric and Toxicological Constraints

1.
Department of Mathematics and Statistics,Texas Tech University,Lubbock, TX 79409, USA
2.
Institute of Environmental and Human Health, Texas Tech University,Lubbock, TX 79409, USA

Received: 10 September 2018 Accepted: 24 September 2018 Published: 11 December 2018

Accurately assessing the risks of contaminants requires more than an understanding of the effects of contaminants on individual organism, but requires further understanding of complex ecological interactions, elemental cycling, and the interactive effects of natural stressors, such as resource limitations, and contaminant stressors. There is increasing evidence that organisms experience interactive effects of contaminant stressors and food conditions, such as resource stoichiometry, availability and excess of nutrient. Here, we develop and analyze the first producer-grazer population model that incorporates the effects of excess nutrients, as well as nutrient limitations on grazer exposed to toxicants. We use analytical, numerical and bifurcation analysis to reduce and explore model parameterized for an aquatic system of algae and zooplankton exposed to methylmercury under varying phosphorus conditions. Under certain environmental conditions, our models predict higher toxicity than previous models that neglect the consequences excess nutrient conditions can have on grazer populations.
- ecotoxicology,
- ecological stoichiometry,
- stoichiometric knife edge
Citation: Md Nazmul Hassan, Kelsey Thompson, Gregory Mayer, Angela Peace. Effect of Excess Food Nutrient on Producer-Grazer Model under Stoichiometric and Toxicological Constraints[J]. Mathematical Biosciences and Engineering, 2019, 16(1): 150-167. doi: 10.3934/mbe.2019008

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Abstract

Accurately assessing the risks of contaminants requires more than an understanding of the effects of contaminants on individual organism, but requires further understanding of complex ecological interactions, elemental cycling, and the interactive effects of natural stressors, such as resource limitations, and contaminant stressors. There is increasing evidence that organisms experience interactive effects of contaminant stressors and food conditions, such as resource stoichiometry, availability and excess of nutrient. Here, we develop and analyze the first producer-grazer population model that incorporates the effects of excess nutrients, as well as nutrient limitations on grazer exposed to toxicants. We use analytical, numerical and bifurcation analysis to reduce and explore model parameterized for an aquatic system of algae and zooplankton exposed to methylmercury under varying phosphorus conditions. Under certain environmental conditions, our models predict higher toxicity than previous models that neglect the consequences excess nutrient conditions can have on grazer populations.

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