Analysis of multi species ecological and evolutionary dynamics
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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

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


Boreal forest ecosystem

Borealforestecosystem


Canadian lynx and snowshoe h are

Canadian Lynx and SnowshoeHare


Prey predator models

Prey-predator models


Most common assumptions

Most common assumptions


Derivation of holling type ii

Derivation of Hollingtype II


The rosenzweig macarthur model

The Rosenzweig-MacArthur model


Remarks

Remarks


Analysis of multi species ecological and evolutionary dynamics

Remarks


Low efficiency

Lowefficiency


Medium efficiency

Medium Efficiency

Transcriticalbifurcation


High efficiency

High efficiency

Hopf


Conclusions

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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