In the face of global warming it is imperative to understand how temperature affects trophic dynamics and energy flow through ecosystems. While most theoretical studies of the effects of temperature on predator–prey interactions are based on the same generic model, they nevertheless predict a wide range of seemingly inconsistent effects of warming including decreased stability, increased stability, extinctions, or more complex responses. A major source of variation among these studies stems from a lack of consensus on the temperature dependence of process rates and model parameters. Our study extends previous work in three ways. First, instead of making a priori assumptions on the temperature dependence of prey carrying capacity, we describe prey growth as a function of a limiting resource, the dynamics of which are explicitly modeled. The temperature dependence of prey carrying capacity thus emerges as a dynamic property. Second, instead of assuming exclusively monotonous temperature dependencies of model parameters, we address the entire physiologically tolerable temperature range over which several rate parameters show unimodal relationships to temperature. Third, instead of restricting the predator’s functional response to type II, we allow for a type III response. The model was parameterized for a pelagic grazer–algae system.
Results/Conclusions
Depending on the modes of resource supply and recycling, the model predicts that the temperature dependence of prey carrying capacity can range from near-independence to monotonically declining to strongly hump-shaped. Yet, the qualitative influences of temperature and resource enrichment on predator–prey dynamics are independent of the mode of resource supply, and a very general and robust picture arises. When plotted in resource supply-temperature space, persistence and stability boundaries are U-shaped functions of temperature when the predator has a type II response; i.e. lower resource enrichment is required to support the predator – but also to destabilize predator–prey dynamics – at intermediate than at both low and high temperatures. If the functional response is of type III, the persistence boundary is also U-shaped but a potentially large region of stability opens up at intermediate temperatures. Warming can thus predictably increase or decrease stability and predator persistence, depending on current temperature, resource supply and the predator’s functional response. The results of most published studies can be mapped onto the persistence and stability boundaries in resource supply-temperature space, suggesting that previous, contrasting predictions can be described as special cases in different regions of parameter space.