When is a type III functional response stabilizing? Theory and practice of predicting plankton dynamics under enrichment

The curvature of generalized Holling type functional response curves is controlled by a shape parameter b yielding hyperbolic type II (b = 1) to increasingly sigmoid type III (b > 1) responses. Empirical estimates of b vary considerably across taxa. Larger consumer-resource body mass ratios have been suggested to generate more pronounced type III responses and therefore to promote dynamic stability. The dependence of consumer-resource stability on b has, however, not been systematically explored, and the accurate empirical determination of b is challenging. Specifically, the shape of the functional response of the pelagic grazer Daphnia feeding on phytoplankton, and its consequences for stability, remain controversial. We derive a novel analytical condition relating b to local stability of consumer-resource interactions and use it to predict stability of empirically parameterized models of Daphnia and phytoplankton under enrichment. Functional response parameters were experimentally derived for two species of Daphnia feeding separately on single cultures of two different phytoplankton species. All experimentally studied Daphnia-algae systems exhibited type III responses. Parameterized type III responses are predicted to stabilize the modeled Daphnia-phytoplankton dynamics in some species pairs but not in others. Remarkably, stability predictions differ depending on whether functional response parameters are derived from clearance vs. ingestion rates. Accurate parameter estimation may therefore require fitting to both rates. In addition, our estimates of b for filter-feeding Daphnia are much smaller than predicted for actively hunting predators at similar consumer-resource body mass ratios. This suggests that the relationship between functional response shape and body mass ratios may vary with predation mode.