Community-level species' correlated distribution can be scale-independent and related to the evenness of abundance.

The spatial distribution of species is not random; instead, individuals tend to gather, resulting in a non-random pattern. Previous studies used the independent negative binomial distribution (NBD) to model the distributional aggregation of a single species, in which the independence of the distribution of individuals of a species in different quadrats had been assumed. This way of analyzing aggregation will result in the scale-dependent estimation of the aggregation or shape parameter. However, because non-random (and therefore non-independent) distribution of individuals of a species in a finite area can be caused by either correlated or clumped distribution of individuals of a species between neighboring sites, an alternative model would assume that the distribution of individuals of a species over different sampling areas is multinomial. Here, we showed that, by assuming that regional species abundance followed a NBD while using a multinomial distribution to assign individuals of species in different non-overlapped sampling quadrats that are from a partition of the entire region (quantifying positive correlation or synchrony), the estimation of the shape parameter in this probabilistic model, which is the negative multinomial distribution (NMD), was scale-invariant (i.e., the estimated shape parameter is identical across different partitions of the study region). Accordingly, the estimation of the shape parameter was related to regional species distribution alone. This implied that, the shape parameter at the community level, using the NMD model, reflected the evenness of interspecific abundance. As a comparison, if the distribution of individuals of a single species followed independent NBDs as studied previously, the shape parameter would measure the evenness of intraspecific abundance (quantifying single-species' distributional aggregation). Moreover, our study highlighted the necessity for adjusting the model for the effects of unsampled species when studying community-level distributional patterns. Collectively, as long as a target area is partitioned into non-overlapping quadrats (no matter how their sizes vary), the proposed NMD model in this study, along with the independent NBDs model, can be jointly formulated as a framework to reconcile the scale-dependent debate on the shape parameter, unifying the relationship between inter- or intraspecific abundance and distributional patterns.