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ANALYSIS OF MULTI-SPECIES ECOLOGICAL AND EVOLUTIONARY DYNAMICS

ANALYSIS OF MULTI-SPECIES ECOLOGICAL AND EVOLUTIONARY DYNAMICS. 3. The Rosenzweig-MacArthur prey -predator model (S. Rinaldi)

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ANALYSIS OF MULTI-SPECIES ECOLOGICAL AND EVOLUTIONARY DYNAMICS

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  1. ANALYSIS OF MULTI-SPECIES ECOLOGICAL AND EVOLUTIONARY DYNAMICS 3. The Rosenzweig-MacArthurprey-predator model (S. Rinaldi) Evidence of prey-predator cycles in Nature. Analysis of the Rosenzweig-MacArthurprey-predator model. Predator extinction, stationarycoexistence, and cycliccoexistence. Hopfbifurcation. Furtherreadings Analysis of EvolutionaryProcesses, Princeton Univ. Press, 2008, pp. 256-258 Ecole Normale Supérieure, Paris December 9-13, 2013

  2. Borealforestecosystem

  3. Canadian Lynx and SnowshoeHare

  4. Prey-predator models

  5. Most common assumptions

  6. Derivation of Hollingtype II

  7. The Rosenzweig-MacArthur model

  8. Remarks

  9. Remarks

  10. Lowefficiency

  11. Medium Efficiency Transcriticalbifurcation

  12. High efficiency Hopf

  13. Conclusions III H II TC I For eachvalue of the efficiencythereis a uniquemode of behavior: I Predator extinction (lowefficiency) II Stationarycoexistence (medium efficiency) III Cycliccoexistence (high efficiency)

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