EFFECTS OF PREDATOR-PREY BODY-SIZE RATIOS ON THE STABILITY OF FOOD-CHAINS

The effects of predator-prey body size ratios on the resilience and pr obability of stability in linear Lotka-Volterra food chains have been analysed. The prey per capita interaction strengths of the model is as sumed to be negatively correlated to the relative size difference betw een a predator and its prey. The relationship between prey interaction strength and predator-prey body size ratios is motivated by energetic al 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 o f 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 rati o). Numerical simulations show that in most cases, the effect on the p robability of stability is accompanied by an increase in resilience. F or example, as model food chain length is increased from two to three trophic levers in one simulation, the return time increases by more th an two orders of magnitude with a constant predator-prey body mass rat io while chains longer than four are not feasible. With a decreasing p redator-prey body mass ratio on the other hand, the return time does n ot increase as rapidly and feasible equilibria exist for longer chains . The relationship between resilience and food chain length is, in thi s model, affected by the relationship between the predator-prey body m ass ratio and the trophic position of the predator, that is, how fast this ratio decreases with increasing trophic height. The effect of bod y mass on consumer mortality rates, and subsequently on the probabilit y of stability and resilience is also analysed. Decreasing mortality r ates with increasing body size do not change the results qualitatively , it only increases the probability that an equilibrium is feasible. ( C) 1998 Academic Press.