Enrichment and stability: a phenomenological coupling of energy value and carrying capacity

Simple predator-prey models with a prey-dependent functional response predict that enrichment (increased carrying capacity) destabilizes community dynamics: this is the 'paradox of enrichment'. However, the energy value of prey is very important in this context. The intraspecific chemical composition of prey species determines its energy value as a food for the potential predator. Theoretical and experimental studies establish that variable chemical composition of prey affects the predator-prey dynamics. Recently, experimental and theoretical approaches have been made to incorporate explicitly the stoichiometric heterogeneity of simple predator-prey systems. Following the results of the previous experimental and theoretical advances, in this article we propose a simple phenomenological formulation of the variation of energy value at increased level of carrying capacity. Results of our study demonstrate that coupling the parameters representing the phenomenological energy value and carrying capacity in a realistic way, may avoid destabilization of community dynamics following enrichment. Additionally, under such coupling the producer-grazer system persists for only an intermediate zone of production--a result consistent with recent studies. We suggest that, while addressing the issue of enrichment in a general predator-prey model, the phenomenological relationship that we propose here might be applicable to avoid Rosenzweig's paradox.