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Ecology Modeling

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

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Ecology Modeling

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  1. Ecology Modeling February 25-March 4, 2010

  2. 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

  3. Exponential Growth

  4. dN/dt=rN • r=intrinsic rate of increase • N=population size • Why is this unrealistic? • In 24 hrs one bacteria would turn to 1024 Exponential Growth

  5. Logistic Growth

  6. dN/dt=rN(K-N/K) • Carrying capacity • Continuous growth • Overlapping generations (humans) • Discrete growth • No overlapping generations (some insects) Logistic Population Growth

  7. Lotka-Volterra

  8. 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

  9. 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 Competition coefficients

  10. Species 1

  11. Species 2

  12. K1/α12 K2 4 competition scenarios

  13. Case 1: Species 1outcompetes species 2

  14. K1/alpha12 k2 Case 2: species 2outcompetes species 1

  15. Stable Equilibrium

  16. Unstable Equilibrium

  17. Predator-Prey

  18. 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

  19. 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

  20. 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

  21. 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 Theta-Logistic Predator-Prey

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