The Time-Scale Problem in Exploiter-Victim Models: Does the Solution Lie in Ratio-Dependent Exploitation?

Standard exploiter-victim models assume an instantaneous connection between foraging and population dynamics. However, in nature this connection is inevitably time-delayed: it takes time to convert food into offspring. R. Arditi and L. R. Ginzburg proposed that this time delay implies ratio-dependent exploitation. Models with ratio-dependent exploitation predict that primary productivity has no impact on food chain length and that the standing crop of all trophic levels increases linearly with increasing primary productivity. Conversely, the traditional victim-dependent models imply that food chain length increases with increasing primary productivity and that only top trophic levels and trophic levels that are an even number of links below the top respond positively to increasing primary productivity. We study the impact of time-delayed numerical responses on predator isoclines, and we do not find support of the theoretical arguments of Arditi and Ginzburg. We also review data on biomass patterns in plants and herbivores, which seem to support the predictions of the victim-dependent model.