Stoichiometry in producer-grazer systems: Linking energy flow with elementcycling

All organisms are composed of multiple chemical elements such as carbon, ni trogen and phosphorus. While energy flow and element cycling are two fundam ental and unifying principles in ecosystem theory, population models usuall y ignore the latter. Such models implicitly assume chemical homogeneity of all trophic levels by concentrating on a single constituent, generally an e quivalent of energy. In this paper, we examine ramifications of an explicit assumption that both producer and grazer are composed of two essential ele ments: carbon and phosphorous. Using stoichiometric principles, we construc t a two-dimensional Lotka-Volterra type model that incorporates chemical he terogeneity of the first two trophic levels of a food chain. The analysis s hows that indirect competition between two populations for phosphorus can s hift predator-prey interactions from a (+, -) type to an unusual (-, -) cla ss. This leads to complex dynamics with multiple positive equilibria, where bistability and deterministic extinction of the grazer are possible. We de rive simple graphical tests for the local stability of all equilibria and s how that system dynamics are confined to a bounded region. Numerical simula tions supported by qualitative analysis reveal that Rosenzweig's paradox of enrichment holds only in the part of the phase plane where the grazer is e nergy limited; a new phenomenon, the paradox of energy enrichment, arises i n the other parr, where the grazer is phosphorus limited. A bifurcation dia gram shows that energy enrichment of producer-grazer systems differs radica lly from nutrient enrichment. Hence, expressing producer-grazer interaction s in stoichiometrically realistic terms reveals qualitatively new dynamical behavior. (C) 2000 Society for Mathematical Biology.