TY - JOUR

T1 - Stoichiometry in producer-grazer systems

T2 - Linking energy flow with element cycling

AU - Loladze, Irakli

AU - Kuang, Yang

AU - Elser, James

N1 - Funding Information:
The authors express their gratitude to T. Andersen for insightful discussions. We are grateful to W. F. Fagan, S. G. Fisher, H. Thieme and two anonymous referees for valuable comments and suggestions on an earlier version of this paper. This work was supported by National Science Foundation grant DEB-9725867.

PY - 2000

Y1 - 2000

N2 - 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. (C) 2000 Society for Mathematical Biology.

AB - 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. (C) 2000 Society for Mathematical Biology.

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U2 - 10.1006/bulm.2000.0201

DO - 10.1006/bulm.2000.0201

M3 - Article

C2 - 11127517

AN - SCOPUS:0033646273

VL - 62

SP - 1137

EP - 1162

JO - The Bulletin of Mathematical Biophysics

JF - The Bulletin of Mathematical Biophysics

SN - 0092-8240

IS - 6

ER -