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Sampling Properties of a Family of Diversity Measures
Woollcott Smith and J. Frederick Grassle
Vol. 33, No. 2 (Jun., 1977), pp. 283-292
Published by: International Biometric Society
Stable URL: http://www.jstor.org/stable/2529778
Page Count: 10
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A family of species diversity measures proposed by Hurlbert (1971) is defined as the expected number of species in a random sample of m individuals from a population. For m = 2 this measure is equivalent to Simpson's diversity index. For larger m, the measure is increasingly sensitive to rare species. In this paper we use unbiased estimation theory to obtain a minimum variance unbiased estimator for this family of diversity measures. An unbiased estimator of the sampling variance is also obtained. These results are then used to partition the variation in sample diversity between random sampling error and local variation community diversity.
Biometrics © 1977 International Biometric Society