Prey body mass and richness underlie the persistence of a top predator

Predators and prey often differ in body mass. The ratio of predator to prey body mass influences the predator's functional response (how consumption varies with prey density), and therefore, the strength and stability of the predator-prey interaction. The persistence of food chains is maximized when prey species are neither too big nor too small relative to their predator. Nonetheless, we do not know if (i) food web persistence requires that all predator-prey body mass ratios are intermediate, nor (ii) if this constraint depends on prey diversity. We experimentally quantified the functional response for a single predator consuming prey species of different body masses. We used the resultant allometric functional response to parametrize a food web model. We found that predator persistence was maximized when the minimum prey size in the community was intermediate, but as prey diversity increased, the minimum body size could take a broader range of values. This last result occurs because of Jensen's inequality: the average handling time for multiple prey of different sizes is higher than the handling time of the average sized prey. Our results demonstrate that prey diversity mediates how differences between predators and prey in body mass determine food web stability.