Sensitivity analysis of a simple model food chain

Abstract

Parameter sensitivities of steady-state population densities of a simple Lotka-Volterra food chain are studied analytically. It is shown that a high percentage of parameter sensitivities is zero, and that the distribution of zero sensitivities along the food chain exhibits a characteristically regular pattern. The pattern implies that the sensitivity of a given population with respect to parameters of another population depends non-monotonically upon the distance of the two populations within the chain. Moreover, the complete sensitivity structure depends drastically on whether the total number of populations in the food chain is odd or even. The sensitivity pattern is shown to be identical to that of the inverse of the community matrix of the food chain. These results provide characterisation of the model food chain in addition to that in terms of steady states and their stability properties.