Description:
ABOUT YELLOWSTONE NP BISON POPULATION, 1902-1931
Populations of organisms often show an S-shaped growth pattern, where population grows rapidly in an early stage, then slows to little or no growth in a later stage. S-shaped or sigmoidal growth can be caused by a number of factors, however a common interpretation involves an external limit to growth based on environmental factors. Populations might be limited to some value (often referred to as the carrying capacity) because of finite food resources, space, water, etc.
Data on North American bison (aka "buffalo") in Yellowstone National Park between 1902 and 1931 show an S-shaped curve of population as a function of time. One might question how these data were obtained, given the rugged terrain of the park, and at what time or times of the year (bison often die in the winter and spring). Bison wander in and out of the park boundaries; is there really a "park population"?
Sigmoidal growth curves are often modeled using a modified exponential model, the logistic model, where the growth rate decreases as the population increases. The bison data fit a logistic model very well. To fit the data with a discrete logistic model, students must determine reasonable values for the initial population and initial time, the carrying capacity, and the initial growth rate; none of these parameters are given in the actual data set.
The bison data suggest a carrying capacity of approximately X for Yellowstone National Park, however the current bison population is approximately 2X. Is the model wrong, or did something else happen?
