Stoichiometry in producer-grazer systems: Linking energy flow with element cycling |
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Authors: | Irakli Loladze Yang Kuang James J Elser |
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Institution: | (1) Department of Mathematics, Arizona State University, Tempe, AZ 85287-1804, USA;(2) Department of Biology, Arizona State University, Tempe, AZ 85287-1501l, USA |
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Abstract: | All organisms are composed of multiple chemical elements such as carbon, nitrogen and phosphorus. While energy flow and element cycling are two fundamental and unifying principles in ecosystem theory, population models usually ignore the latter. Such models
implicitly assume chemical homogeneity of all trophic levels by concentrating on a single constituent, generally an equivalent
of energy. In this paper, we examine ramifications of an explicit assumption that both producer and grazer are composed of
two essential elements: carbon and phosphorous. Using stoichiometric principles, we construct a two-dimensional Lotka-Volterra
type model that incorporates chemical heterogeneity of the first two trophic levels of a food chain. The analysis shows that
indirect competition between two populations for phosphorus can shift predator—prey interactions from a (+, −) type to an
unusual (−, −) class. This leads to complex dynamics with multiple positive equilibria, where bistability and deterministic
extinction of the grazer are possible. We derive simple graphical tests for the local stability of all equilibria and show
that system dynamics are confined to a bounded region. Numerical simulations supported by qualitative analysis reveal that
Rosenzweig’s paradox of enrichment holds only in the part of the phase plane where the grazer is energy limited; a new phenomenon,
the paradox of energy enrichment, arises in the other part, where the grazer is phosphorus limited. A bifurcation diagram
shows that energy enrichment of producer—grazer systems differs radically from nutrient enrichment. Hence, expressing producer—grazer
interactions in stoichiometrically realistic terms reveals qualitatively new dynamical behavior. |
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