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## PowerPoint Slideshow about ' Ecology Modeling' - alesia

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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

- r=intrinsic rate of increase
- N=population size
- Why is this unrealistic?
- In 24 hrs one bacteria would turn to 1024

- Carrying capacity
- Continuous growth
- Overlapping generations (humans)
- Discrete growth
- No overlapping generations (some insects)

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

- 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

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

- 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

- 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

Theta-Logistic Predator-Prey
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