lecture_12_November_4_without_questions

lecture_12_November_4_without_questions - E EM B 120 I ntr...

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EEMB 120 – Introduction to Ecology November 4, 2010 Reminder: No discussion sections next week Midterm Tuesday Nov. 9, no lecture Thursday Nov. 11 (Veteran’s Day Holiday)
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Midterm #2 – Tuesday Nov. 9 Lecture material : October 14 – November 2 Section material: Papers by Durant (Oct. 25) and Almany (Nov. 1) Make-ups will only be granted for those with medical or family emergencies. Sample questions posted on the website REVIEW SESSION – Sunday Nov. 7, time and room TBA No calculators
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L-V Predator-Prey Model Develop 2 linked equations, one for prey and one for predator Solve them for equilibrium (no growth) Plot results on a phase plane Graphical analysis to determine stability and ask questions about outcome of predator-prey interactions
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Lotka-Volterra Predator-Prey Model Predatio n dN / dt = rN – α NP dP / dt = f α NP - qP Where : r = per capita birth rate for prey α = predator attack rate (capture efficiency) f = predator conversion efficiency q = per capita death rate for predators
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Assumptions of the Lotka-Volterra Predator-Prey Model 1. Closed populations – no immigration or emigration 2. Prey and predator do not have K 3. Prey population growth limited only by the predator 4. Predator only eats one prey type and will starve if no prey are present 5. Individual predators can consume an infinite number of prey – no interference or cooperation among predators 6. Random encounters between predators and prey, no spatial refuges for prey
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L-V Predator-Prey Model Develop 2 linked equations, one for prey and one for predator Solve them for equilibrium (no growth) Plot results on a phase plane Graphical analysis to determine stability and ask questions about outcome of predator-prey interactions
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Lotka-Volterra Predator-Prey Model Predatio n Equilibrium Solution for Prey Set dN / dt equal to O (Prey population not changing) : 0 = rN - α NP True if – 1) N = 0 So, when the predator population = r / α prey population is at equilibrium 2) P = r / α α NP = rN P = r / α Call this predator population size P *
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Lotka-Volterra Predator-Prey Model Predatio n Equilibrium Solution for Prey The number of predators needed to keep the prey population from growing (P * ) is determined by the ratio of the prey growth rate and the predator attack rate P * = r / α P N P * = r/ α dN / dt = 0 Too many P Too few P
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