Effects of Predator–prey Body Size Ratios on the Stability of Food Chains

Abstract

The effects of predator-prey body size ratios on the resilience and probability of stability in linear Lotka–Volterra food chains have been analysed. The prey per capita interaction strengths of the model is assumed to be negatively correlated to the relative size difference between a predator and its prey. The relationship between prey interaction strength and predator–prey body size ratios is motivated by energetical arguments. Analytical results show that, given this assumption (on prey interaction strengths) and if average (relative) size differences between predators and their prey decrease with the trophic position of the consumer (as found in a large number of “real food webs”) the probability of local stability in model food chains is increased (when compared to model chains with a constant predator–prey body size ratio). Numerical simulations show that in most cases, the effect on the probability of stability is accompanied by an increase in resilience. For example, as model food chain length is increased from two to three trophic levels in one simulation, the return time increases by more than two orders of magnitude with a constant predator–prey body mass ratio while chains longer than four are not feasible. With a decreasing predator–prey body mass ratio on the other hand, the return time does not increase as rapidly and feasible equilibria exist for longer chains. The relationship between resilience and food chain length is, in this model, affected by the relationship between the predator–prey body mass ratio and the trophic position of the predator, that is, how fast this ratio decreases with increasing trophic height. The effect of body mass on consumer mortality rates, and subsequently on the probability of stability and resilience is also analysed. Decreasing mortality rates with increasing body size does not change the results qualitatively, it only increases the probability that an equilibrium is feasible.