AUTHOR: Nicholas Gotelli, Department of Biology, University of Vermont, Burlington, USA

SUMMARY: rarefaction methods allow for rigorous quantification of many biodiversity patterns at the landscape scale.

Ecologists still struggle to quantify landscape patterns of species richness and evenness and alpha, beta, and gamma diversity. However, most diversity metrics are sample-size dependent and do not have a solid statistical footing (Magurran 2004). Diversity can be understood in terms of a rarefaction curve, which plots the number of individuals on the x axis and the number of species accumulated on the y-axis (Gotelli and Colwell 2001). Although these sampling curves have been in the literature for decades (Sanders 1968), only recently has a comprehensive framework of biodiversity based on rarefaction emerged (Olzewski 2004).

A useful measure of species evenness is Hurlbert's (1971) Probability of an Interspecific Encounter (PIE), which itself is the complement of Simpson's (1949) D. This index of evenness turns out to be the slope of the rarefaction curve measured at its base (Olzewski 2004). PIE is sample-size independent and measures an aspect of diversity that is distinct from total species richness (the asymptote of the rarefaction curve). Lande's (1996) partitioning of alpha and beta diversity can be realized by comparing PIE for an aggregated set of samples to the average PIE calculated for the individual samples. Differences between these two curves quantify beta diversity, the change in species composition among patches. The same strategy can be used to analyze species-area curves and diversity at the landscape scale, because patches of different area accumulate individuals and contribute to within and between patch species richness (Brewer and Williamson 1994).

Although rarefaction analysis requires data on abundances, the statistical framework has recently been extended to accommodate incidence-based presence-absence data (Colwell et al. 2004). Finally, a family of asymptotic estimators can be used to estimate total species richness (Colwell and Coddington 1994). Whereas rarefaction involves interpolation of data to smaller sample sizes, asymptotic estimators require extrapolation beyond the limits of the sampled data. For this reason, variances associated with asymptotic estimators may be large, but they are still the best approach for trying to estimate diversity in speciose taxa that cannot be sampled exhaustively (Longino et al. 2002).

The traditional measure of species richness is species density, which is the number of species per unit area (James and Wamer 1982). However, species density is actually the product of species richness (species number/number of individuals) and total density (number of individuals / unit area). Rarefaction allows one to decompose these elements and to understand the contribution of both species richness and total density to observed patterns of species density. Although ecologists have rarely paid attention to the distinction between species richness and species density, the difference between these two metrics is profound, and they may yield completely different answers for the same data set (McCabe and Gotelli 2000). Rarefaction and sampling curves provide landscape ecology with a more solid footing for quantifying diversity patterns at multiple spatial scales, and for understanding the effects of abundance and area on biodiversity measures.

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