Trophic model closure influences ecosystem response to enrichment

Abstract

There exists considerable uncertainty about the most appropriate functional form to describe mortality at the highest trophic level (the closure problem). Although linear and quadratic formulations predict strongly different dynamics, it is unclear which of these formulations is more realistic. We introduce an implicit predator population feeding on the highest trophic level, parameterized through a Holling Type II functional response and empirically observed predator–prey scaling relations. Thus, we arrive at a hyperbolic mortality formulation that is a hybrid between the linear and quadratic forms. Subsequently, we investigate the impact of this formulation on the modeled population dynamics. In particular, we compare the stability properties of simple food-chain models with a hyperbolic mortality and a linear mortality. Contrary to classical theory, the model with a hyperbolic mortality does not exhibit destabilization due to nutrient enrichment. For this model, we find that limit cycles are rather associated with a top-heavy ecosystem structure (high predator, low prey densities). The weak response to enrichment emerges because populations of both the predator and prey increase with nutrient supply, consistent with observations. We discuss the mechanism behind the relationship between top-heaviness and instability from an ecological and a mathematical perspective.