Sampling Properties of a Family of Diversity Measures

A Jamlily oJfspecies diversity mceasures proposed by Hurlbert (1971) is defined as the expected niumiiber oJ species in a random sample of m individuals Jrom a population. For m = 2 this miieasure is equivalent to Simpson 's diversity index. For larger m, the mneasure is increasingly sensitive to rare species. In this paper we use unbiased estimation theory to obtain a minimum variance unbiased estimwator Jor this family of diversity measures. A n unbiased estimator oJ the samiipling varianice is also obtained. These results are then used to partition the variation in sam^ple diversity betweeni randomii samiipling error and local variation community diversity.

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