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Ecology Modeling

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Ecology Modeling

February 25-March 4, 2010

- Models are not the whole picture
- They use assumptions

- Exponential growth
- Exponential growth
- Logistic growth

- Competition models
- Lotka-Volterra

- Predator-prey models
- Predator-prey
- Theta Logistic

Exponential Growth

- dN/dt=rN
- r=intrinsic rate of increase
- N=population size

- Why is this unrealistic?
- In 24 hrs one bacteria would turn to 1024

Logistic Growth

- dN/dt=rN(K-N/K)
- Carrying capacity

- Continuous growth
- Overlapping generations (humans)

- Discrete growth
- No overlapping generations (some insects)

Lotka-Volterra

- Two species using each other’s resources
- Not directly hurting each other

- Pg 50 has equations
- What do dN/dt, r, N and K mean? (from last week)

- Negative-negative interaction

- Competition coefficient
- How many of species 1 is equal to species 2
- α and β
- When α and β are 0, we have logistic growth

- To visualize we use isoclines

K1/α12

K2

K1/alpha12

k2

Predator-Prey

- Growth of prey only limited by predation
- Assumptions
- Predator specialist that only exists with prey
- Individual predators consume infinite prey
- Prey and predators encounter each other randomly

- Prey
- dN/dt=rN-CNP

- Predator
- dN/dt=gCNP-dP

- r=rate of increase for prey
- N=population size of prey
- C=constant rate of prey being captured
- P=population size of predator
- d=exponential death rate for predator (predator starvation rate for the stupid or diseased ones)
- g=a constant depicting conversion of captured prey to predator population growth
- Does not include a carrying capacity

- Incorporates carrying capacity
- Assumptions for theta-logistic
- Predator population density does not affect an individual predator’s chances of birth and death directly
- Number of surviving offspring produced by a predator is directly proportional to the amount of prey it consumes

- Prey
- dN/dt=rN{1-(N/K)θ}-fP

- Predator
- dP/dt=gP[f-D]

- K=carrying capacity
- θ=how birth and death change with changing population size prey
- f=number of prey eaten based on prey density
- g=minimum prey needed by predator to survive
- d=minimum per capita prey intake for stable predator population

f uses C and h