Diversity of litter-dwelling beetles in the Ouachita Highlands of Arkansas, USA (Insecta: Coleoptera)

Both the magnitude and the urgency of the task of assessing global biodiversity require that we make the most of what we know through the use of estimation and extrapolation. Likewise, future biodiversity inventories need to be designed around the use of effective sampling and estimation procedures, especially for 'hyperdiverse' groups of terrestrial organisms, such as arthropods, nematodes, fungi, and microorganisms. The challenge of estimating patterns of species richness from samples can be separated into (i) the problem of estimating local species richness, and (ii) the problem of estimating the distinctness, or complementarity, of species assemblages. These concepts apply on a wide range of spatial, temporal, and functional scales. Local richness can be estimated by extrapolating species accumulation curves, fitting parametric distributions of relative abundance, or using non-parametric techniques based on the distribution of individuals among species or of species among samples. We present several of these methods and examine their effectiveness for an example data set. We present a simple measure of complementarity, with some biogeographic examples, and outline the difficult problem of estimating complementarity from samples. Finally, we discuss the importance of using 'reference' sites (or sub-sites) to assess the true richness and composition of species assemblages, to measure ecologically significant ratios between unrelated taxa, to measure taxon/sub-taxon (hierarchical) ratios, and to 'calibrate' standardized sampling methods. This information can then be applied to the rapid, approximate assessment of species richness and faunal or floral composition at 'comparative' sites.

A point estimator and its associated confidence interval for the size of a closed population are proposed under models that incorporate heterogeneity of capture probability. Real data sets provided in Edwards and Eberhardt (1967, Journal of Wildlife Management 31, 87-96) and Carothers (1973, Journal of Animal Ecology 42, 125-146) are used to illustrate this method and to compare it with other estimates. The performance of the proposed procedure is also investigated by means of Monte Carlo experiments. The method is especially useful when most of the captured individuals are caught once or twice in the sample, for which case the jackknife estimator usually does not work well. Numerical results also show that the proposed confidence interval performs satisfactorily in maintaining the nominal levels.