Sampling Properties of a Family of Diversity Measures

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Abstract
A family of species diversity measures proosed 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. An unbiased estimation theory is used 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 diveristy between random sampling error and local variation community diversity.

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