Allometric functional response model: body masses constrain interaction strengths.

1. Functional responses quantify the per capita consumption rates of predators depending on prey density. The parameters of these nonlinear interaction strength models were recently used as successful proxies for predicting population dynamics, food-web topology and stability. 2. This study addressed systematic effects of predator and prey body masses on the functional response parameters handling time, instantaneous search coefficient (attack coefficient) and a scaling exponent converting type II into type III functional responses. To fully explore the possible combinations of predator and prey body masses, we studied the functional responses of 13 predator species (ground beetles and wolf spiders) on one small and one large prey resulting in 26 functional responses. 3. We found (i) a power-law decrease of handling time with predator mass with an exponent of -0.94; (ii) an increase of handling time with prey mass (power-law with an exponent of 0.83, but only three prey sizes were included); (iii) a hump-shaped relationship between instantaneous search coefficients and predator-prey body-mass ratios; and (iv) low scaling exponents for low predator-prey body mass ratios in contrast to high scaling exponents for high predator-prey body-mass ratios. 4. These scaling relationships suggest that nonlinear interaction strengths can be predicted by knowledge of predator and prey body masses. Our results imply that predators of intermediate size impose stronger per capita top-down interaction strengths on a prey than smaller or larger predators. Moreover, the stability of population and food-web dynamics should increase with increasing body-mass ratios in consequence of increases in the scaling exponents. 5. Integrating these scaling relationships into population models will allow predicting energy fluxes, food-web structures and the distribution of interaction strengths across food web links based on knowledge of the species' body masses.