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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?

Reference: we have not yet obtained the original citation for these data. The numbers were found at a Carroll College website devoted to the Intermath/ILAP project. We highly recommend: http://web.carroll.edu/mvanisko/ilaps/yellowstone.html

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 Carroll College Intermath/ILAP website, no citation Yellowstone NP bison population, 1902-1931 year population 1902 44 1903 47 1904 51 1905 74 1906 1907 84 1908 95 1909 118 1910 149 1911 168 1912 192 1913 215 1914 1915 270 1916 348 1917 397 1918 1919 504 1920 501 1921 602 1922 647 1923 748 1924 1925 830 1926 931 1927 1008 1928 1057 1929 1109 1930 1124 1931 1192

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