Assessment of species diversity from species abundance distributions at different localities Steinar Engen, Bernt-Erik Sæther, Anne Sverdrup-Thygeson, Vidar Grøtan and Frode Ødegaard S. Engen, Centre for Conservation Biology, Dept of Mathematical Sciences, Norwegian Univ. of Science and Technology, NO7491 Trondheim, Norway.  B.-E. Sæther (bernt-erik.sather@bio.ntnu.no) and V. Grøtan, Centre for Conservation Biology, Dept of Biology, Norwegian Univ. of Science and Technology, NO7491 Trondheim, Norway.  A. Sverdrup-Thygeson and Frode Ødegaard, Norwegian Inst. for Nature Research, Tungasletta 2, NO7047 Trondheim, Norway. We show how the spatial structure of species diversity can be analyzed using the correlation between the log abundances of the species in the communities, assuming that two communities at different localities can be described by a bivariate lognormal species abundance distribution. A useful property of this approach is that the log abundances of the species at two localities can be considered as samples from a bivariate normal distribution defined by only five parameters. The variances and the correlation can be estimated by maximum likelihood methods even if there is no information about the sampling intensity and the number of unobserved species. This method also enables estimation of over-dispersion in the sampling relative to a Poisson distribution that allows sampling adjustment of the estimate of b-diversity. Furthermore, we also obtain a partitioning of species diversity into additive components of a-, b- and g-diversity. For instance, if the correlation between the log abundances of the species is close to one, the same species will be common and rare in the two communities and the b-diversity will be low. We illustrate this approach by analysing similarities of communities of rare and endangered species of oak-living beetles in south-eastern Norway. The number of recorded species was estimated to be only 48.1% of the total number of species actually present in these communities. The correlations among communities dropped rather quickly with distance with a scaling of order 200 km. This illustrates large spatial heterogeneity in species composition, which should be accounted for in the design of schemes of such series for assessing species diversity in these habitat-types. A proper assessment of species diversity in an area is important for examining many relevant questions in ecology as well as for development of management actions for conserving biodiversity. In many cases the data are based on single samples of species abundances from different sampling sites. The species diversity is then estimated by a comparison of the similarity in species composition, e.g. by the use of the some indices of community similarity (Magurran 2004, Legendre et al. 2005, Anderson et al. 2006) or by some information theoretic measures (Levins 1968, Ludovisi and Taticchi 2006). A central problem in such assessments of species diversity is to account for sampling. In general, the number of species recorded will be closely related to the sampling effort (Pielou 1975, Lande 1996), i.e. the number of species in a sample will increase with the number of individuals sampled. As a consequence, the number of species recorded and hence the similarity of the communities will be strongly influenced by variation in sampling intensity (Chao et al. 2005). Basically, two different approaches have been suggested to account for the effects of sampling on estimates of species diversity. One approach is to assess sample size-effect by using non- parametric techniques such as rarefaction (Mao and Colwell 2005, Crist and Veech 2006). A problem with this approach is that the procedures chosen for standardization of the data sets can give very different results, and it is not always clear which measure of the species diversity that is more appropriate (Gotelli and Colwell 2001). The other set of approaches for assessing species diversity is to use a parametric species abundance model (Golicher et al. 2006). A disadvantage of this approach is that the estimates of many parameters can be sensitive to the choice of commu- nity model (Palmer 1990, Baltana ´s 1992, Magurran 2004, Williamson and Gaston 2005). An important contribution to the study of species diversity was Whittaker’s (1970, 1972) partitioning of species diversity into components due to a-diversity within localities, g-diversity in the whole region and b-diversity which he defined as turnover of species among samples at different localities. This decomposition resulted in a large number of studies to estimate the relative contribution of these components to species diversity (McGill et al. 2007). In particular, b-diversity received huge attention because this component embeds many of the fundamental processes such as depletion of species numbers or homogenization of species composition across localities that affects species Oikos 000: 000000, 2008 doi: 10.1111/j.2008.0030-1299.16466.x, # The Authors. Journal compilation # Oikos 2008 Subject Editor: Nicholas Gotelli, Accepted 7 January 2008 Online Early (OE): 1-OE