A unified quantitative approach to trophic cascade and bottom-up: top-down hypotheses

A general analytic approach is developed to predict how perturbing one level of a food chain affects the stocks in other levels. (The comparison is between initial and final steady states.) This yields qualitative and quantitative predictions of the trophic cascade hypothesis and the bottom-up: top-down hypothesis, respectively. For a wide range of reasonable ratio-dependent functional relationships between trophic levels in a food chain, the quantitative approach predicts that perturbation effects should propagate up the chain with the same sign and roughly constant strength, but down the chain with alternating sign and diminishing strength. There is less diminishment for the case of trophic levels with a low ratio of energy losses (metabolism, mortality) to input. The trophic cascade model’s prediction of the sign of compartmental stock changes is based on a linear food chain model and does not necessarily hold for food webs. Both points are illustrated by simulating perturbation responses in models of two ecosystems (one representing a chain and one a web). The approach can be used for a wide range of functional responses connecting trophic levels besides ratio dependence.