Material Cycling and the Stability of Ecosystems

The cycling of matter in the form of nutrients, such as nitrogen or phosphorus, is an integral part of every ecosystem. As such, it is usually included in descriptive ecosystem models. Yet it has been ignored in most heuristic theoretical models, which have focused on communities rather than ecosystems (see, e.g., May 1974). A number of theoretical studies, however, have now been carried out on the effect of nutrient cycling on ecosystem stability (Jordan et al. 1972; Austin and Cook 1974; Webster et al. 1975; Nisbet and Gurney 1976; Harwell et al. 1977, 1981; Sjoberg 1977; Parker 1978; Harwell and Ragsdale 1979; DeAngelis 1980; Harrison and Fekete 1980; Nisbet et al. 1983; DeAngelis et al. 1989a; Nakajima and DeAngelis 1989). These studies, as well as many empirical investigations, have recently been reviewed extensively by DeAngelis and colleagues (DeAngelis et al. 1989b; DeAngelis 1992). They have led to the following conclusions: material cycling in model ecosystems that are closed with respect to matter increases the probability that these systems will be locally stable, but an increased degree of material cycling (i.e., an increased closure of the system) in open systems decreases their resilience, that is, the rate at which they return to their locally stable, steady state following a perturbation (DeAngelis et al. 1989b). An especially clear and general demonstration of this tendency toward decreased resilience with tighter recycling was provided by DeAngelis (1980). The latter conclusion, however, seems to some extent to contradict he former: if resilience decreases with tighter recycling, how can closed systems be stable? It seems also to contradict the view of pioneer ecologists, who hypothesized that the tighter material cycling during the course of ecosystem succession might increase homeostasis (Odum 1969). A partial resolution of this paradox lies in the fact that a decrease in resilience may be accompanied by a concomitant increase in resistance (Webster et al. 1975; Harrison and Fekete 1980). Resistance to perturbations indeed approaches the concept of homeostasis much more than does resilience. My purpose here is to go further by laying a bridge between the conclusions from closed and open systems and clarifying the meaning of resilience as it has been investigated so far. I reexamine the general nonlinear model used by DeAngelis (1980) and show that resilience decreases with tighter material cycling only in a restricted sense; that is, what decreases is only the resilience of the total quantity of matter within the ecosystem, but not the resilience of its internal structure. I then discuss the implications of this fact.