Bottom-up and top-down effects in food chains depend on functional dependence: an explicit framework

Observed stock changes in perturbed ecosystems sometimes, but not always, are smaller than predicted by the trophic cascade hypothesis. These varying outcomes can be explained by (1) using detailed analysis of trophic-level interactions within the standard energy-based linear food-chain model, or (2) invoking web models and/or non-energy interactions between organisms. Previously I developed an analytic approach for the linear chain for a press-type perturbation and applied it to ratio-dependent functional relationships. Here I extend the linear chain analysis to a more general functional relationship which allows independent variation of prey dependence and intra-level interference. I find that different combinations of prey dependence and interference lead to large or small cascading effects. Generally, large top-down effects require weak interference, while large bottom-up effects require both weak interference and strong prey dependence.