Grazing limitation and nutrient limitation in marine ecosystems: Steady state solutions of an ecosystem model with multiple food chains

Here I develop a model with multiple phytoplankton-zooplankton food chains where each food chain is based on a different size class of algae. Model parameters were chosen to allow food chains based on smaller algal size classes to dominate under oligotrophic conditions, with larger size classes being added sequentially with increased nutrient loading. The model makes use of allometric relations among size classes to minimize the number of free parameters, facilitating numerical exploration of its steady state behavior. The model is simple, yet it is complex enough to allow simultaneous predator limitation of algal size classes (or species) and nutrient limitation of total phytoplankton biomass. This perspective, not obtainable from models with single phytoplankton and zooplankton size classes, is applied to the particular case of elevated nitrate levels in the equatorial Pacific. The model shows clearly that it is possible for each phytoplankton size class to be limited by its herbivores, while at the same time micronutrient (notably iron) dcliciency may limit the number of size classes that can exist in the community and hence the total phytoplankton biomass that can be supported. Empirical evidence and theoretical argument suggest that a common ecosystem structure is one wherein the density of each plant species is limited by its herbivores while total plant biomass is limited by the availability of space or nutrients (Hairston et al. 1960; Power 1992; Strong 1992). Marine ecosystem models containing a single “phytoplankton” variable and a single “zooplankton” variable cannot easily convey this distinction, however, since the phytoplankton variable in such models simultaneously represents a single phytoplankton species and the entire phytoplankton trophic level, confounding the limitation of species’ population sizes with the limitation of total algal abundance. The inability of models with single phytoplankton (P) and single zooplankton (Z) variables (1 P 1Z models) to convey this distinction limits their utility in exploring important empirical questions. Consider, for example, the discussion by Frost and Franzen (1992) of simultaneous nutrient limitation and grazing control of phyAcknowledgments I thank Steve Carson, Jorge Sarmiento, and Robbie Toggweiler for helpful suggestions on the manuscript. This research was funded in part by grant NA26RGO 10201 from the National Oceanic and Atmospheric Administration. Additional support was provided by NASA grant NAGW-3 137 and NSF grant OCE 9012333 to J. L. Sarmiento. toplankton standing stock and growth rates in the equatorial Pacific. Frost and Franzen rely on a simple model of pelagic food chain to observe that nutrient limitation acting alone would result in algal standing stocks that are too high and algal growth rates that are too low. Then they rely on verbal arguments to further conclude that limitation by micronutrients may be necessary to account for growth rates that seem low by a factor of two (Cullen et al. 1992) as well as to account for the absence of large algal species, which are thought to be more sensitive to low micronutrient levels than species smaller are (Hudson and Morel 1990; Morel et al. 1991). This reliance on verbal arguments to account for the absence of large phytoplankton size classes underscores the incompleteness of their 1 P 1Z model: it would be more satisfying, and more instructive, if the model were capable of portraying not only the simultaneous effects of herbivory and nutrient limitation on resident phytoplankton populations but could also account naturally for the absence of larger size classes. Here, I develop a more complete model that allows the interaction of nutrient control and grazing control to be examined more directly. This model is a simplified version of the model of Moloney and Field (199 1). The model consists of multiple food chains, each based on a different size class of algae. The parameters of