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Aim: To derive null models for the expected number of species shared among multiple samples or habitat patches, allowing exploration of the geometric effects of subdivision on species diversity. Location: Global. Major taxa studied: Predominantly sessile organisms. Methods: The occurrence probability of a species in a subdivided area depends on its abundance and spatial pattern over a known habitat extent. The joint probability that two subareas share a species is the product of the probability of species occurrence in each subarea provided that the latter probability is independent. The sum of this probability over all species is the number of species the two subareas share, or zeta diversity of order 2. Generalizing from 2 to m subareas yields a null model for zeta diversity of order m. From zeta diversity, many metrics (e.g., beta and gamma diversity) for the m habitat patches can be calculated, revealing the effects of increasing habitat fragmentation. Results: The null models show the geometric effects of subdivision depend on patterns of spatial distribution of species within a landscape and evenness of species abundance distribution. For aggregated assemblages, increasing subdivision decreases shared species, increases beta diversity and results in higher total species richness in subdivided habitat than an equal contiguous area. Main conclusions: To correctly interpret diversity patterns in fragmented habitat the geometric effects of subdivision must be considered. Our models explain why fragmented habitat could have higher diversity than continuous habitat of equal area but predict a threshold patch‐size above which this will not occur (here c. 100 ha). Apparently positive diversity effects of subdivision, including more species in groups of small patches, are probable outcomes of spatial aggregation of assemblages. The shared species null models offer an analytical tool for exploring the geometric effects of subdivision on diversity while controlling for total habitat area. [ABSTRACT FROM AUTHOR]

We studied compositional turnover in communities of fleas and mites harboured by small mammals using zeta diversity metric (similarity between multiple communities) and asked whether the patterns of zeta diversity decline with an increase in the number of communities differ between taxa and hierarchical scales [infracommunities (parasite assemblages on individual hosts), component communities (parasite assemblages harboured by host populations), and compound communities (all parasite species in a locality)]. The average number of shared species declined with an increasing number of communities (zeta order). It attained zero at higher orders in infracommunities of both taxa with the shape of the zeta decline being best fitted by the negative exponential function, and the retention rate curves being modal. In contrast, zeta diversity values for compound communities of mites and fleas did not attain zero at higher zeta orders, and the form of the zeta decline was best fitted by the power-law function, whereas the retention rate curves were asymptotic. In component communities, the form of zeta decline was best fitted by either exponential or power-law function in dependence of whether communities were considered within a host across localities or across hosts within a locality and whether ubiquitous species were taken into account. Our main conclusions are that (a) the rules governing compositional turnover in parasite communities for the lowest and the highest hierarchical scales are taxon-invariant but scale-dependent and (b) species composition of infracommunities is mainly driven by stochastic assembly processed, whereas that of compound communities is mainly driven by niche-based processes. [ABSTRACT FROM AUTHOR]

The article presents a nonparametric lower bound for the number of species shared by multiple communities. Based on sample species abundance or replicated incidence records from each of the N communities, it derives a nonparametric approach to constructing a lower bound for the number of species shared by N communities. It also presents simulation results to examine the performance of the lower bounds.