Predator-Prey Dynamics

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Lectures 13-14

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Lotka-Voltera predator-prey equations

  • N=prey number

  • P=predator number

  • r=prey growth rate

  • m=predator mortality

  • a=predator efficiency

  • E=predator individuals produced per prey object

<ul><li><p>N=prey number</p></li><li><p>P=predator number</p></li><li><p>r=prey growth rate</p></li><li><p>m=predator mortality</p></li><li><p>a=predator efficiency</p></li><li><p>E=predator individuals produced per prey object</p></li></ul><p></p>
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Lotka-Voltera prey isocline

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Lotka-Voltera predator isocline

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Critique of Lotka-Voltera predator-prey model

Initial conditions seem to determine outcome

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Changes to the Lotka-Voltera Model made by Rosenzweig-MacArthur

  • Density-dependent prey growth

  • F is Holling Type II

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Rosenzweig-MacArthur equations

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Rosenzweig-MacArthur isoclines

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Stable equilibrium for Rosenzweig-MacArthur

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Unstable equilibrium for Rosenzweig-MacArthur

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Enrichment-effects

  • Destabilizing

  • Increases K

  • Prey isocline is affected

  • Predator isocline is not affected