Several stochastic models with environmental noise generate spatio-temporal Gaussian fields of log densities for the species in a community. Combinations of such models for many species often lead to lognormal species abundance distributions. In spatio-temporal analysis it is often realistic to assume that the same species are expected to occur at different times and/or locations because extinctions are rare events. Spatial and temporal β-diversity can then be analyzed by studying pairs of communities at different times or locations defined by a bivariate lognormal species abundance model in which a single correlation occurs. This correlation, which is a measure of similarity between two communities, can be estimated from samples even if the sampling intensities vary and are unknown, using the bivariate Poisson lognormal distribution. The estimators are approximately unbiased, although each specific correlation may be rather uncertain when the sampling effort is low with only a small fraction of the species represented in the samples. An important characteristic of this community correlation is that it relates to the classical Jaccard- or the Sørensen-indices of similarity based on the number of species present or absent in two communities. However, these indices calculated from samples of species in a community do not necessarily reflect similarity of the communities because the observed number of species depends strongly on the sampling intensities. Thus, we propose that our community correlation should be considered as an alternative to these indices when comparing similarity of communities. We illustrate the application of the correlation method by computing the similarity between temperate bird communities.