Dynamic trophic cascade

In a previous article, I developed, and demonstrated with simulations, an analytical approach for predicting and analyzing effects of press (step-function) perturbations on food chains [Ecol. Model. 171 (2004) 21]. The method allows explicit variation of the functional dependence connecting trophic levels. Here I extend that analysis to perturbations sinusoidal in time. The sinusoid partially bridges the gap between the idealized press-type experiment (which assumes initial and final steady states, but is doubtful experimentally) and a totally dynamic situation (which is daunting analytically but closer to reality). I find that the effect of a sinusoidal perturbation is to multiply the previous press result by a factor that diminishes both up and down the food chain. The factor depends on perturbing frequency approximately as 1/(1+(ωτi)2)1/2, where τi is the characteristic time of affected level i. This frequency-dependent diminution is another potential reason why bottom-up and top-down cascade effects are hard to detect.