YIELD AND DYNAMICS OF TRITROPHIC FOOD-CHAINS

Strong relationships between yield and dynamic behavior of tritrophic food chains are pointed out by analyzing the classical Rosenzweig-MacA rthur model. On the one hand, food chains are subdivided into undersup plied and oversupplied categories, the first being those in which a ma rginal increase of nutrient supply to the bottom produces a marginal i ncrease of mean yield al the top. On the other hand, a detailed bifurc ation analysis proves that dynamic complexity first increases with nut rient supply (from stationary to a low-frequency cyclic regime and, fi nally, to chaos) and then decreases (from chaos to a high-frequency cy clic regime). A careful comparison of the two analyses supports the co nclusion that food chains cycling at high frequency are oversupplied, while all others are undersupplied. A straightforward consequence of t his result is that maximization of food yield requires a chaotic regim e. This regime turns out to be very often on the edge of a potential c atastrophic collapse of the top component of the food chain. In other words, optimality implies very complex and dangerous dynamics, as intu itively understood long ago for ditrophic food chains by Rosenzweig in his famous article on the paradox of enrichment.