Lecture 29-cwo-LVpred

Lecture 29-cwo-LVpred - Outline: PredatorPrey Systems 1....

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1. Text gives examples 1. Lotka-Volterra models 1. Modifications 1. DDT 1. Pest control Outline: Predator- Prey Systems
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Competition: aP r P a r Ndt dN caN N a r Pdt dP NP N PN P - = + = + - = + = / / μ 1 a12 2 a21 a11 a22 Predation: P aN P N aP N Notation differs from text μ is death rate of predator, a is attack rate c is conversion rate r is prey growth w/o predation
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N P Phase planes: r/a Putting it together… dN/Ndt=0 μ /ca dP/Pdt=0 The equilibrium is neutrally stable
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Dynamics: N P 1 2 3 4 1 2 3 4 1 2 3 2 3 4 Out of phase by ¼ cycle. “Time-lags” (numeric not parameters).
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1. Interference among predators 2. Competition among prey 3. Predator functional response 4. Spatial heterogeneity Stability: How can we stabilize this system? P aNP N aPN
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N P Predator interference: r/a dN/Ndt=0 dP/Pdt=0 The equilibrium is stable
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N P Functional response: dN/Ndt=0 dP/Pdt=0 I: neutral II: destabilizing III: depends
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N P Paradox of enrichment: dN/Ndt=0 dP/Pdt=0 Combine Type II functional response and prey competition Stable limit cycle
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Lecture 29-cwo-LVpred - Outline: PredatorPrey Systems 1....

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