The stability of ecosystems: a brief overview of the paradox of enrichment

In theory, enrichment of resource in a predator-prey model leads to destabilization of the system, thereby collapsing the trophic interaction, a phenomenon referred to as "the paradox of enrichment". After it was first proposed by Rosenzweig (1971), a number of subsequent studies were carried out on this dilemma over many decades. In this article, we review these theoretical and experimental works and give a brief overview of the proposed solutions to the paradox. The mechanisms that have been discussed are modifications of simple predator-prey models in the presence of prey that is inedible, invulnerable, unpalatable and toxic. Another class of mechanisms includes an incorporation of a ratio-dependent functional form, inducible defence of prey and density-dependent mortality of the predator. Moreover, we find a third set of explanations based on complex population dynamics including chaos in space and time. We conclude that, although any one of the various mechanisms proposed so far might potentially prevent destabilization of the predator-prey dynamics following enrichment, in nature different mechanisms may combine to cause stability, even when a system is enriched. The exact mechanisms, which may differ among systems, need to be disentangled through extensive field studies and laboratory experiments coupled with realistic theoretical models

Coevolution in a One Predator–Two Prey System

Background: Our understanding of coevolution in a predator–prey system is based mostly on pair-wise interactions. Methodology and Principal Findings: Here I analyze a one-predator–two-prey system in which the predator’s attack ability and the defense abilities of the prey all evolve. The coevolutionary consequences can differ dramatically depending on the initial trait value and the timing of the alternative prey’s invasion into the original system. If the invading prey species has relatively low defense ability when it invades, its defense is likely to evolve to a lower level, stabilizing the population dynamics. In contrast, if when it invades its defense ability is close to that of the resident prey, its defense can evolve to a higher level and that of the resident prey may suddenly cease to evolve, destabilizing the population dynamics. Destabilization due to invasion is likely when the invading prey is adaptively superior (evolution of its defense is less constrained and fast), and it can also occur in a broad condition even when the invading prey is adaptively inferior. In addition, invasion into a resident system far from equilibrium characterized by population oscillations is likely to cause further destabilization

Unpalatable prey resolves the paradox of enrichment

Enrichment is an increasingly serious trend in natural ecosystems. A theoretical model of a predator–prey system with a natural assumption of satiation in predation predicts that enrichment causes the populations to fluctuate to stochastic extinction. However, this 'paradox of enrichment' does not always occur in experimental and natural communities. Here we present a theoretical model that describes a novel mechanism for resolving the paradox in the case of a predator with optimal selective feeding. Specifically, a less profitable but edible (thus `unpalatable') prey species sharply reduces the amplitude of population oscillations and firmly prevents the minimum abundances of species from falling below certain values. The presence of such an unpalatable prey thus guarantees the robustness of the system against enrichment