?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=https%3A%2F%2Fpure.iiasa.ac.at%2Fid%2Feprint%2F4952%2F&rft.title=Yield+and+Dynamics+of+Tri-Trophic+Food+Chains&rft.creator=Feo%2C+O.+de&rft.creator=Rinaldi%2C+S.&rft.description=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%2C+food+chains+are+subdivided+into+under-supplied+and+over-supplied%2C+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%2C+a+detailed+bifurcation+analysis+proves+that+dynamics+complexity+first+increases+with+nutrient+supply+(from+stationary+to+low-frequency+cyclic+regime+and%2C+finally%2C+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%2C+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%2C+optimality+implies+very+complex+and+dangerous+dynamics%2C+as+stated+long+ago+for+di-trophic+food+chains+by+Rosenzweig+in+his+famous+paper+on+the+paradox+of+enrichment.&rft.publisher=WP-96-075&rft.date=1996-07&rft.type=Monograph&rft.type=NonPeerReviewed&rft.format=text&rft.language=en&rft.identifier=https%3A%2F%2Fpure.iiasa.ac.at%2Fid%2Feprint%2F4952%2F1%2FWP-96-075.pdf&rft.identifier=++Feo%2C+O.+de+%26+Rinaldi%2C+S.+%3Chttps%3A%2F%2Fpure.iiasa.ac.at%2Fview%2Fiiasa%2F253.html%3E++(1996).++Yield+and+Dynamics+of+Tri-Trophic+Food+Chains.+++IIASA+Working+Paper.+IIASA%2C+Laxenburg%2C+Austria%3A+WP-96-075+++++