Freshwater Biology (1997) 38, 447–471 A model approach to planktonic stoichiometry and consumer-resource stability DAG O. HESSEN* AND BIRGER BJERKENG² *University of Oslo, Department of Biology, PO Box 1027 Blindern, N-0316 Oslo, Norway ²Norwegian Institute for Water Research, PO Box 173 Kjelsås, N-0411 Oslo, Norway SUMMARY 1. The model explores stoichiometric feedback effects between an alga and a grazer (Daphnia) in a simplified chemostat-type system in stagnant conditions or with fixed dilution rate. 2. When running the model with fixed stoichiometry and P-sufficient food, the grazer with highest requirements for phosphorus (P) will exert the most efficient control of algal biomass owing to more P being allocated to zooplankton biomass and less P recycled. 3. When including potential P-limitation of the grazer, the grazer with high P requirements (high P : C ratio) will be the least efficient grazer in a system with fluctuating and temporarily low P : C ratio in algae (Q a ). 4. Qualitatively deficient food will yield decreased growth efficiency in zooplankton. As Q a decreases, the grazer isocline for zero net growth is shifted upwards, and the required algal biomass for positive growth increases. There may then be a critical level of Q a below which the grazer with high P : C suffers negative population growth regardless of algal biomass. In cases with low minimum Q a and a P-demanding grazer, this may cause the system to enter an irreversible stage with high biomass of P-deficient phytoplankton which do not support zooplankton growth. 5. Cumulative primary production for scenarios with continuous P input is, in general, higher the more Q a is allowed to drop below saturation values, and highest when this is combined with a grazer with a high P : C ratio. The lower growth rate of P-deficient phytoplankton was compensated for by reduced success of the P-limited grazer, yielding low grazing pressure and resulting in larger phytoplankton biomass. Introduction Models of autotroph–herbivore interactions, from Lotka–Volterra models and onwards, traditionally focus on direct interactions and biomasses and flows in terms of carbon (C). In the grazing process there is a strong recirculation component embedded, however, which may be an important regulating factor for primary production and thus imply important feed- backs for the grazer itself. Recent works underscore that foodweb dynamics depend on more than the direct interactions between trophic levels, populations or individuals, and that there is a strong stoichiometric component in foodweb interactions (Reiners, 1986; DeAngelis et al., 1989; Sterner, Elser & Hessen, 1992; © 1997 Blackwell Science Ltd 447 Sterner & Hessen, 1994). A grazer (or predator) will probably extract a maximum amount of whatever biochemical compounds and elements that are in short supply relative to its own demands. Surplus components will be released in some proportion to their relative abundance in food (Olsen et al., 1986; Hessen & Andersen, 1992). The release of the nutrient elements phosphorus (P) and nitrogen (N) calls for special attention because they are the most important limiting elements for primary production in aquatic and terrestrial ecosystems (Hecky & Kilham, 1988; Vitousek & Howarth, 1991). The quantitative role of nutrient release from grazers is well recognized in