Propagation of permanent perturbations in food chains and food webs - van den Berg, Hugo Antontus (Ecological modelling, 1998)
Fluxes of matter through an ecosystem are subject to influences arising in its external surroundings. Variations of these influences lead to changes in the flux pattern of the ecosystem. Straightforward application of the Chain Rule shows how the sensitivity of the steady state can be resolved into a matrix containing the direct external influences on the ecosystem's fluxes premultiplied by the inverse of the community matrix. An example of this formalism is given, and various ways to model flux functions are briefly reviewed. The formalism is applied to trophic cascades theory, which was later assimilated into the Bottom up:top-down theory. A consistency check on this model is given. The concept of ratio-dependence has been put forward as an explanation of why trophic cascades must peter out, away from the locus of direct perturbation. It is shown that ratio-dependence achieves this by virtue of satisfying a more general condition on so-called `coupling strengths'.