Ecosystem Resilience and Productivity: Are Predictions Possible?

Abstract

The notion of ecosystem stability has a long history in ecology. The classical question is whether some systems are more stable than others, and if so, what makes them more stable. The stability concept as such has been intensively debated and the confusion about its meaning has led to opposite conclusions about the relationship between food web structure and its dynamic properties (Pimm 1991). A recurrent problem focuses on ecosystem responses to increased productivity. Notwithstanding the far from solved problem of exactly how should be represented in food web models, many attempts have been made to predict how dynamic stability properties change with changes in (Rosenzweig 1971, Nakajima and DeAngelis 1989, DeAngelis 1992, Abrams and Roth 1994, Rosenzweig 1995 for review), how food web structure itself is affected by levels of (Fretwell 1977, Oksanen et al. 1981, DeAngelis et al. 1989, Rosenzweig 1995), and how population interactions within the food web best should be modeled (e.g., the preyvs ratio-dependent debate; Arditi and Ginzburg 1989, Berryman 1992, Ginzburg and Akvakaya 1992, Oksanen et al. 1992, Abrams 1994, Lundberg and Fryxell 1995). Recently, Stone et al. (1996) addressed the relationship between ecosystem resilience and by formally analyzing the return time in single-species models in discrete time and a predator-prey model in continuous time. The return time of the system is the speed at which the equilibrium is approached after disturbance. Ecosystem resilience is therefore inversely proportional to return time. In single-species models, the return time is unambiguously determined by r, the maximum per capita growth rate of the population (given that we follow conventional notation). The maximum per capita growth rate is a quite plausible parameter relating population responses to productivity, although we may wonder (biologically, not mathematically) what happened to population carrying capacity (K). In systems with two or more species, the carrying capacity potentially matters, depending on what model one chooses to work with and how is defined in terms of the parameters of the model. We here extend the work by Stone et al. (1996) and we show that the conclusion about effects on ecosystem resilience is 1) strongly model dependent and 2) dependent on the fundamental assumption of how productivity is defined in terms of the parameters of the model. We will thus reinforce Stone et al.'s suggestion that it will be difficult to find any universal relationship between stability (here resilience) and productivity. Stone et al. (1996) showed that in a two-species predator-prey system, return time (TR) by and large increases as maximum per capita growth rate increases. Given that r is a fair representation of system productivity, this conclusion is not generally valid. To illustrate this, we used two familiar predator-prey models that differ from the model that Stone et al. used (shown in Murray 1990). The first one is the well-known Rosenzweig-MacArthur model