Apparent competition occurs when two species that do not interact directly negatively impact each other through a shared enemy. It is a key component of most communities be they natural or agricultural. Most species that engage in apparent competition are ectotherms, species whose body temperature depends on the environmental temperature. Investigating how temperature variation, particularly warming, influences apparent competition is therefore a key research priority. Recent theory on temperature effects on competitive and trophic interactions suggest that cold-adapted species tend to be both superior competitors and less susceptible to predation. Given this precedent, we hypothesize that the more cold-adapted apparent competitors will be less susceptible to the common predator than warm-adapted apparent competitors. Previous theory, however, has been based on unstructured models that do not take into account the developmental delays that characterize the complex life cycles of multi-cellular ectotherms. Here we present a mathematical framework based on delay differential equations that both incorporates temperature-dependent developmental delays and mechanistic descriptions of trait responses to temperature derived from first principles of thermodynamics. We use the model to investigate whether cold-adapted apparent competitors have an advantage over their warm-adapted counterparts.
Results/Conclusions
In an unstructured model without developmental delays, a more cold-adapted apparent competitor can indeed tolerate a higher abundance of the shared predator. Incorporating developmental delays however, alters this expectation in significant ways. Because the developmental delay is longer (maturation rate is lower) at lower temperatures, cold-adapted prey species suffer greater juvenile mortality and hence produce fewer adults, reducing their total birth rate relative to the death rate. Warm-adapted prey species have higher birth rates during periods when developmental delays are shorter, therefore experiencing smaller overall juvenile mortality and producing larger adult cohorts, in turn subsidizing the predator and strengthening its detrimental effects on the cold-adapted prey species. Interestingly, the prey species' developmental delays have little or no effects on the predator, while the predator's delay decreases its persistence through mortality during development. We are conducting numerical simulations of the delay model both under typical seasonal variation and recent IPCC warming scenarios to determine whether the predictions based on a constant thermal environment still hold for variable environments. Given that apparent competition is an integral component of natural and agricultural communities, this work has implications for climate warming effects on both biodiversity and pest control.