Lecture12Handout

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EEMB 120 – Introduction to Ecology November 8, 2007 Reminder: No Sections Next Week (Nov. 12-16) Veteran’s Day campus holiday Monday, Nov. 12 Got it! A sandperch following capture of a juvenile damselfish

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Midterm #2 – Tuesday Nov. 13 Lecture material : October 16 – November 8 Section material: Papers by (1) Fujiwara & Caswell (week of Oct. 15) (2) Packer et al. (week of Oct. 22) (3) Durant (week of Oct. 29) Make-ups will only be granted for those with medical or family emergencies. Last year’s second midterm posted on our website. REVIEW SESSION – Thursday Nov. 8, 6:30-8:00 PM GIRVETZ 1004 (NOT HERE!) Sally Holbrook – Office hours Friday Nov. 9, 11:00-12:00

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Predation Remember, We defined a + - species interaction as “Predation” Covers a wide range of relationships and effects Lethal effects Predators directly affect prey mortality rates through total consumption Prey directly affect predator birth/death rates Form modeled by L-V predator/prey model

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Sub-lethal effects Predators may directly affect prey birth/mortality rates through partial consumption (herbivory or parasitism) Predators may indirectly affect prey birth/mortality rates through effects on prey behavior Can alter : Habitat use Diel activity patterns Immediate behavior (stop and watch) Predation Results in decreased fecundity due to : Poorer feeding Smaller overall body size Results in increased mortality due to : Slower body growth rate Increased time in vulnerable sizes Models very complex

L-V Predator-Prey Model: 

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 Predation Commonly used model to predict outcome of predator-prey interactions – analogous approach to L-V model of interspecific competition Some notation: N represents number of Prey So, dN / dt represents change in prey pop. abundance over time P represents number of Predators So, dP / dt represents change in predator pop. abundance over time

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Lotka-Volterra Predator-Prey Model Predation Building the model: the prey equation Assumptions - 1) Prey limited only by predators (no carrying capacity) dN / dt = rN (Exponential growth) rN = Total number of prey births r = Prey per capita birth rate (density independent)

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Lotka-Volterra Predator-Prey Model Predation Building the model: the prey equation Assumptions - 2) Number of prey consumed is proportional to the encounter rate between predators and prey dN / dt = rN - aNP a = attack rate (capture efficiency) aNP = intensity of predation (total number of prey eaten)

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Lotka-Volterra Predator-Prey Model Predation Building the model: the predator equation Assumptions - 4) Predators decline exponentially in the absence of prey dP / dt = - qP (Exponential decline) qP = Total number of predator deaths q = Predator per capita death rate (density independent) 3) Predators eat only single species of prey

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Lotka-Volterra Predator-Prey Model Predation Building the model: the predator equation Assumptions - 5) Increases in predator population equals number of prey consumed multiplied by a conversion efficiency dP / dt = faNP - qP f = conversion efficiency (prey into baby predators) faNP = total number of predator births

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Lotka-Volterra Predator-Prey Model Predation dN / dt = rN – aNP dP / dt = faNP - qP Where : r = per capita birth rate for prey a = predator attack rate (capture efficiency) f = predator conversion efficiency q = per capita death rate for predators

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Lotka-Volterra Predator-Prey Model Predation Equilibrium Solution for Prey Set dN / dt equal to O (Prey population not changing) : 0 = rN - aNP True if – 1) N = 0 So, when the predator population = r / a prey population is at equilibrium 2) P = r / a Call this predator population size P*

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Lotka-Volterra Predator-Prey Model Predation 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 / a P N P* = r/a dN / dt = 0

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Lotka-Volterra Predator-Prey Model Predation Equilibrium Solution for Predator Set dP / dt equal to O (Predator population not changing) : 0 = faNP - qP True if – 1) P = 0 So, when the prey population = q / fa predator population is at equilibrium 2) N = q / fa Call this prey population size N*

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Lotka-Volterra Predator-Prey Model Predation Equilibrium Solution for Predator The number of prey needed to keep the predator population from growing (N*) is determined by the ratio of the predator mortality rate and the overall efficiency of the predators N* = q / fa P N dP / dt = 0 N* = q/fa

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L-V Predator-Prey Model – the no-growth isoclines plotted on a phase plane P* = r/a N* = q/fa

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Lotka-Volterra Predator-Prey Model Predation Prey Predators Time Population Size Disturbances Neutrally Stable 1 cycle 1 cycle N*, P* 1/4 cycle

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Lotka-Volterra Predator-Prey Model Predation P N P* = r/a N* = q/fa What happens if we alter values for r ? Changing prey birth rate alters P* not N* r P*

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Lotka-Volterra Predator-Prey Model Predation P N P* = r/a N* = q/fa What happens if we alter values for q ? Changing predator death rate alters N* not P* q N*