Resistance of a food chain to invasion by a top predator

We study the invasion of a top predator into a food chain in a chemostat. F or each trophic level, a bioenergetic model is used in which maintenance an d energy reserves are taken into account. Bifurcation analysis is performed on the set of nonlinear ordinary differential equations which describe the dynamic behaviour of the food chain. In this paper, we analyse how the abi lity of a top predator to invade the food chain depends on the values of tw o control parameters: the dilution rate and the concentration of the substr ate in the input. We investigate invasion by studying the long-term behavio ur after introduction of a small amount of top predator. To that end we loo k at the stability of the boundary attractors; equilibria, limit cycles as well as chaotic attractors using bifurcation analysis. It will be shown tha t the invasibility criterion is the positiveness of the Lyapunov exponent a ssociated with the change of the biomass of the top predator. It appears th at the region in the control parameter space where a predator can invade in creases with its growth rate. The resulting system becomes more resistant t o further invasion when the top predator grows faster. This implies that sh ort food chains with moderate growth rate of the top predator are liable to be invaded by fast growing invaders which consume the top predator. There may be, however, biological constraints on the top predator's growth rate. Predators are generally larger than prey while larger organisms commonly gr ow slower. As a result, the growth rate generally decreases with the trophi c level. This may enable short food chains to be resistant to invaders. We will relate these results to ecological community assembly and the debate o n the length of food chains in nature. (C) 1999 Elsevier Science Inc. All r ights reserved.