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Data Set #015

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About the Data

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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