Control analysis of trophic chains

Inspired by the application of metabolic control analysis (MCA) to biochemical networks, we conduct a generalized sensitivity analysis of the equilibrium of a set of differential equations used to model trophic chains. We focus on changes in the equilibrium to perturbations of feeding (i.e. functional responses) and growth rate functions. So-called control coefficient connectivity relationships are derived for two broad classes of trophic chains: those governed by linear and those governed by nonlinear growth functions. These connectivity relationships link global sensitivity coefficients to local elasticities represented by the normalized partial derivatives of the rate functions. We derive results for specific classes of trophic chains, including hyperbolic growth functions used in metaphysiological models. Our results provide formulae for computing the degree to which control by the feeding and growth functions is top-down versus bottom-up at any level in any given trophic chain. Control analysis provides a framework for articulating the degree to which equilibrium—or, more usefully, long term average—population levels are influenced by the different rate functions in terms of local elasticity functions. Control Analysis also provides techniques for probing the trophic cascade hypothesis.