Coexistence in a temporally varying environment is predicted to arise when species differ in their temporal patterns of resource consumption. However, key to this outcome is coupling of resource consumption and resource availability. High resource consumption rates, due to favorable environmental conditions, are expected to draw down resources, causing high competition. The phenomenon is called covariance between environment and competition (covEC). For coexistence to occur, covEC must be weaker for a species perturbed to low density (an “invader”) compared to an unperturbed species (a “resident”). However, these outcomes have not been thoroughly investigated in models. Instead, the formulation of models often implicitly includes them. Thus, the theory is incomplete because there is no satisfactory theory of this key component, covEC. Moreover, it has been suggested detecting covEC in nature provides a powerful means of testing coexistence by the storage effect. The phenomenon of covEC therefore requires a thorough theoretical understanding. Here we extend the MacArthur consumer-resource model to varying environments. The explicit resource dynamics in the MacArthur model allow a theory of covEC to be developed. Our approach was to develop quantitative measures of factors contributing to covEC, and studying their effects in computer simulations.
Results/Conclusions
We found that relative speeds of resource consumption, consumer dynamics and environmental variation have major effects on covEC. Resource speed by far had the dominant effect and can be divided into two major components, resource amplitude, and resource phase relative to consumers. Resident covEC is maximal when resource amplitude is greatest and phase relative consumer is zero, and this is achieved when resources turn over rapidly, most strongly promoting coexistence by the storage effect. These results allow us to address the fundamental ideas of Hutchinson’s Paradox of the Plankton. While they do show that seasonal environmental variation can promote coexistence of consumers on limited resources, it produces very different predictions about time scales of environmental change and consumer dynamics compared with Hutchinson. Contrary to Hutchinson’s predictions we find that slow consumer dynamics are favorable to coexistence and do not lead to averaging of environment fluctuations, nullifying their effects. Critical to coexistence is factors strengthening covEC for residents, found here to be fast resource dynamics, not intermediate consumer dynamics.