info:oai:pure.iiasa.ac.at:4952info:ofi/fmt:xml:xsd:oai_dc https://pure.iiasa.ac.at/id/eprint/4952/ Yield and Dynamics of Tri-Trophic Food Chains Feo, O. de Rinaldi, S. Strong relationships between top productivity and dynamic behavior of tri-trophic food chains are pointed out by analyzing the classical Rosenzweig-MacArthur model. On one hand, food chains are subdivided into under-supplied and over-supplied, the first being those in which a marginal increase of nutrient supply to the bottom produces a marginal increase of mean top productivity. On the other hand, a detailed bifurcation analysis proves that dynamics complexity first increases with nutrient supply (from stationary to low-frequency cyclic regime and, finally, to chaos) and then decreases (from chaos to high-frequency cyclic regime). A careful comparison of the two analyses supports the conclusion that food chains cycling at high-frequency are over-supplied, while all others are under-supplied. A straightforward consequence of this result is that maximization of top productivity requires a chaotic regime. This regime turns out to be very often on the edge of a potential catastrophic collapse of food yield. In other words, optimality implies very complex and dangerous dynamics, as stated long ago for di-trophic food chains by Rosenzweig in his famous paper on the paradox of enrichment. WP-96-075 1996-07 Monograph NonPeerReviewed text en https://pure.iiasa.ac.at/id/eprint/4952/1/WP-96-075.pdf Feo, O. de & Rinaldi, S. <https://pure.iiasa.ac.at/view/iiasa/253.html> (1996). Yield and Dynamics of Tri-Trophic Food Chains. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-96-075