Sample-size dependence of diversity indices and the determination of sufficient sample size in a high-diversity deep-sea environment

Diversity indices, although designed for comparative purposes, often cannot be used as such, due to their sample-size dependence. I t is argued here that this dependence is more pronounced in h~gh divers~ty than in low diversity assemblages and that indices more sensitive to rarer species require larger sample sizes to estimate diversity with reasonable precision than indices which put more weight on commoner species. This was tested for Hill's diversity numbers No to N, (Hill 1973) and some other commonly used diversity indices for a high-diversity nematode assemblage in the Mediterranean deep sea. Although diversity indices were introduced into the ecological literature more than 20 yr ago and have very often been criticized since, their use in applied ecological research, mainly in pollution impact studies, is still very popular ( e . g . Heip et al. 1988a). A fundamental drawback of many diversity indices is their sample-size dependence (Sanders 1968 and references therein), making comparison between studies difficult. Yet, the main purpose of quantifying diversity by a numerical index is to provide means for comparison between different communities. One way of avoiding incomparability of measurements resulting from different-sized samples was provided by the rarefaction method of Sanders (1968). In this method, one calculates the number of species expected from each sample if sampling size is standardized. Hurlbert (1971) showed that the rarefaction method generally overestimates the expected number of species present and h e introduced an exact computational formula for this index: the expected number of species in a sample with size n , drawn from a population of size N which had S species, is given by i' Inter-Research/Printed in F. R. Germany where Ni represents the number of individuals in the i th species in the full sample (Hurlbert 1971). This index was used by Heck et al. (1975) to estimate sufficient sample size for the calculation of the number of species in a sample. However, a mere species count, like ES (n), does not cover all information present in the community as it is not related to the way the individuals are divided among the species. Thus other diversity measures should be considered as well. Sample size dependence of diversity indices. Intuitively, one expects that not all diversity indices are equally influenced by sample size, and that also the type of community (with high or low diversity) plays a role. Let us consider the influence of sample size on Hill's diversity numbers (N,) of various orders (Hill 1973). Hill's diversity number of order a is given by: S Na = I C Pia I("l-al