Understanding the role of intermediate time scales on the stability of classical food web modules

Background/Question/Methods

Ecologists have long sought to understand what biological attributes impart stability to an ecosystem. Although at first the intuitive notion of stability appears straightforward, researchers have developed a bewildering number of metrics for describing ecological stability.  This preponderance of stability metrics has frequently caused confusion, requiring a synthesis that generates a coherent theory elucidating the mechanisms and timescales associated with the different aspects of ecological stability.

Here, we seek to resolve some of the confusion by unfolding the dynamics of a simple consumer-resource interaction module (hereafter, C-R interactions) to show that even the most common empirical stability metric, the coefficient of variation (CV), obfuscates two different underlying aspects of ecological stability. While stability has been frequently discussed in the ecological literature, we are unaware of the use of bifurcation theory to organize different metrics of stability. This is surprising given that bifurcations act as organizing centers for understanding the qualitative dynamics of all dynamical systems, and so should delineate zones of dynamics that may be vulnerable to different kinds of instability. One reason bifurcations may have not been considered is the fact that bifurcation theory in ecology has tended to be employed on deterministic systems, and yet instability and collapse in real system take place within a time dependent stochastic setting.

Results/Conclusions

In what follows, we first review common dynamical metrics of stability (CV, minima, eigenvalues). We then argue using the classical type II C-R model as an example where the frequently used empirical metric, CV, hides two different, but important aspects of stability: (i) stability due to mean population density processes, and; (ii) stability due to population density variance processes. We then employ a simple stochastic C-R framework in order to elucidate: (i) when we expect these two different processes to arise in ecological systems, and importantly; (ii) highlight the fact that these two stability processes respond differentially, but predictably, to changes in fundamental parameters that govern biomass flux and loss in any C-R interaction (e.g., attack rates, carrying capacity, mortality). Using this framework we are able to show how general ecological predictions on the interactions of deterministic cycles and be extended to the interaction between deterministic and stochastic cycles to generate chaos in a food chain.