lecture_12_November_4_without_questions

lecture_12_November_4_without_questions - EEMB 120 – I...

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Unformatted text preview: EEMB 120 – I ntroduction to Ecology November 4, 2010 Reminder: No discussion sections next week Midterm Tuesday Nov. 9, no lecture Thursday Nov. 11 (Veteran’s Day Holiday) 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 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 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 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. I ndividual 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 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 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 * 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 Lotka-Volterra Predator-Prey Model...
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This note was uploaded on 11/11/2010 for the course EEMB 120 taught by Professor Nisbet during the Fall '08 term at UCSB.

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lecture_12_November_4_without_questions - EEMB 120 – I...

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