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# Ecology Modeling PowerPoint PPT Presentation

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. Ecology Models. Exponential Growth. dN/dt=rN

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

### Lotka-Volterra Competition

• 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

### Predator-prey assumptions

• 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

### Predator Prey Relationships

• 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

### Theta-logistic

• 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