In a local biodiversity inventory the locally rare species are of particular importance. The main problem of sample-based inventories is that many species are so rare that they will not be observed. The observed frequencies of species in the sample provide an estimate of the species proportion in the population. This may be used to estimate the number of species which exist in the population, but which were not observed in the sample (shadow species). This non-parametric approach provides an unbiased estimate of the relative frequency distribution of the species in the population, which differs very significantly from the sample distribution, particularly for the rare species. The approach leads to a new and ecologically meaningful estimator of the Rényi–Hill generalized species diversity measure, which includes species abundance, the Shannon–Weaver and Simpson's diversity measures, amongst others. The use of the estimator is illustrated on data from a biodiversity inventory of trees on a 3-ha forest sample plot in Sumatra.
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