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I will discuss results and applications of an ongoing collaboration with theoretical biochemists on how to model and analyse trophic cascades in ecological foodwebs. This work is inspired by metabolic control analysis (MCA) and its application to biochemical networks. A critical compenent of this work is how best to represent general models of trophic cascades and then apply sensitivity analyses of steady state solutions, representing long term average population levels, to perturbations in scalings of feeding (i.e. functional responses) and growth rate functions in the differential equations modeling the trophic cascade. I will present so-called control coefficient connectivity relationships of the normalized sensitivity coefficients in terms of local elasticity coefficients (i.e. the percentage change in feeding and growth rates for percentage changes in population levels) for two broad classes of trophic cascades: those that have linear and those that have nonlinear growth functions. I will then demonstrate how these connectivity relationships can be applied to more specific classes of trophic cascades, including hyperbolic growth functions used in metaphysiological models. The analysis provides a formula for computing the degree to which control by the feeding and growth functions is top-down versus bottom-up at any level in a trophic cascade. Trophic control analysis provides a framework for articulating the degree to which equilibria---or, more usefully, long term average---population levels are influenced by the different rate functions in terms of local elasticity functions. An example of a statement that can be made in this framework is: Assume that the per capita growth rates of a prey and predator are proportional to their feeding rates minus losses to predation for the prey and to natural mortality for the predator. Then the effects of unit changes in these rates on predator density are positive with respect to prey feeding on a buffered resource and negative with respect to a predator feeding only on the prey. Further, these effects are approximately equal in magnitude when, at steady-state, the prey is satiated but the predator is food limited.

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