Persistence of tri-trophic interactions in seasonal environments.

The interplay between species interactions and environmental variation is well-understood for pairwise interactions but not for multi-trophic interactions. Understanding how such interactions persist in a thermally variable environment is particularly important given that most biodiversity on the planet consists of ectotherms whose body temperature depends on the environmental temperature. Here we present a trait-based mathematical framework for investigating how tri-trophic food chains persist in seasonal environments. We report two key findings. First, the persistence of the tri-trophic interaction is enhanced if species at upper trophic levels (e.g. top predators) are more cold-adapted than those at lower levels (e.g. basal resources) by virtue of lower thermal optima, wider response breadths and lower mortality within the favourable temperature range. The important implication is that the assembly and persistence of multi-trophic interactions requires that species at lower trophic levels be somewhat maladapted to their ambient thermal environment, as in the case of recent invasions. Second, differential sensitivity to thermally varying environments provides a mechanistic explanation for the conflict of interest between the intermediate consumer and top predator. The same cold-adaptations that increase the consumer's ability to increase when rare deter the predator's ability to do so. Thus, being well-adapted to its thermal environment makes the intermediate consumer better able to acquire resources and avoid predators. We predict that the hierarchy in cold-adaptation should constrain the number of trophic levels that can be supported in a given thermal environment, and that ectotherm food chain lengths should increase with increasing latitude because larger-amplitude seasonal fluctuations generate more opportunities for species to diverge in their thermal optima.