Analysis of multi species ecological and evolutionary dynamics
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ANALYSIS OF MULTI-SPECIES ECOLOGICAL AND EVOLUTIONARY DYNAMICS PowerPoint PPT Presentation


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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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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


Borealforestecosystem


Canadian Lynx and SnowshoeHare


Prey-predator models


Most common assumptions


Derivation of Hollingtype II


The Rosenzweig-MacArthur model


Remarks


Remarks


Lowefficiency


Medium Efficiency

Transcriticalbifurcation


High efficiency

Hopf


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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