Somatic Growth Dilution of a toxicant in a predator-prey model under stoichiometric constraints

The development of aquatic food chain models that incorporate both the effects of nutrient availability, as well as, track toxicants through trophic levels will shed light on ecotoxicological processes and ultimately help improve risk assessment efforts. Here we develop a stoichiometric aquatic food chain model of two trophic levels that investigates concurrent nutrient and toxic stressors in order to improve our understanding of the processes governing the trophic transfer for nutrients, energy, and toxicants. Analytical analysis of positive invariance, local stability of boundary equilibria, numerical simulations, and bifurcation analysis are presented. The model captures and explores a phenomenon called the Somatic Growth Dilution (SGD) effect recently observed empirically, where organisms experience a greater than proportional gain in biomass relative to toxicant concentrations when consuming food with high nutritional content vs. low quality food.