Logistic Growth of Wolf Population in Yellowstone

by William Mashburn

Submitted : Spring 2009

The logistic equation is used as a continuous density-dependent mathematical model to generalize gray wolf (canis lupus) population growth in Yellowstone National Park, U.S. Observed data from Yellowstone fits the logistic curve when the growth parameter K is equal to 170. It is determined that any negative value of the growth rate parameter r over a short time span will result in a decline in population size until extinction occurs or until the growth parameter increases to be > 0. The minimum initial value of population size N required for canis lupus to go extinct in Yellowstone is 1. The average growth rate parameter r is calculated for a fourteen year period following reintroduction of canis lupus to be 0.34. Using this parameter, the amount of time t required for the population to grow as high as theoretically possible before it reaches the projected carrying capacity, K, is found to be 20.84 years. This amount of time corresponds to the time following the spring breeding season of 2015. The carrying capacity, when theoretically lowered, produces damped oscillations of population size until population size N is approximately equal to K, and a steady state results.

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