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A useful method for characterizing biological numerous assemblages at regional scales is the species occupancy frequency distribution (SOFD). An SOFD shows the number or proportion of study sites each species occurred. Species that occur at only a few sites are termed satellite species, while species that occur at many sites are termed core species. This study is the first to document and assess SOFD patterns in aquatic macrophytes. It characterizes SOFD patterns of freshwater macrophyte assemblages in Finland at two spatial and two temporal scales. For this, I analyzed three published datasets on freshwater macrophyte distributions: two from studies conducted at a local scale and the third from large national surveys. One local study and the national study also included data on temporal variation in species occupancy frequencies. In the national study, the number of core and satellite species varied slightly between the older and the newer survey, respectively. Among the 113 waterbodies surveyed as part of the national study, the SOFD followed a unimodal satellite pattern. However, for the older dataset (from the 1930s), a bimodal symmetric pattern also fit the SOFD data well. At the local scale, I observed geographical variation in SOFD patterns. The dataset from southern Finland followed a unimodal satellite SOFD pattern; data from central Finland instead displayed a bimodal symmetric SOFD pattern, although they also fit equally well with a bimodal truncated pattern. Moreover, temporal patterns in central Finland seemed to demonstrate a shift from a bimodal symmetric to a bimodal asymmetric SOFD probably. Geographical variation in the SOFD pattern may be due to variation in the regional species pool. The temporal changes in SOFD pattern may be due to lake eutrophication and anthropogenic disturbance around waterbodies, which may increase number of macrophyte species., A useful method for characterizing biological numerous assemblages at regional scales is the species occupancy frequency distribution (SOFD). This study is the first to document and assess SOFD patterns in aquatic macrophytes. Geographical variation in the SOFD pattern may be due to variation in the regional species pool and the temporal changes in SOFD pattern may be due to lake eutrophication and anthropogenic disturbance around waterbodies, which may increase number of macrophyte species.

Aim Although species-occupancy distributions (SODs) and species-area relationships (SARs) arise from the two marginal sums of the same presence/absence matrices, the two biodiversity patterns are usually explored independently. Here, we aim to unify the two patterns for isolate-based data by constraining the SAR to conserve information from the SOD. Location Widespread. Methods Focusing on the power-model SAR, we first developed a constrained form that conserved the total number of occupancies from the SOD. Next, we developed an additive-constrained SAR that conserves the entire shape of the SOD within the power-model SAR function, using a single parameter (the slope of the endemics-area relationship). We then relate this additive-constrained SAR to multiple-sites similarity measures, based on a probabilistic view of Sorensen similarity. We extend the constrained and additive-constrained SAR framework to 23 published SAR functions. We compare the fit of the original and constrained forms of 12 SAR functions using 154 published data sets, covering various spatial scales, taxa and systems. Main conclusions In all 23 SAR functions, the constrained form had one parameter less than the original form. In all 154 data sets the model with the highest weight based on the corrected Akaike's information criteria (wAICc) had a constrained form. The constrained form received higher wAICc than the original form in 98.79% of valid pairwise cases, approaching the wAICc expected under identical log-likelihood. Our work suggests, both theoretically and empirically, that all SAR functions may have one unnecessary parameter, which can be excluded from the function without reduction in goodness-of-fit. The more parsimonious constrained forms are also easier to interpret as they reflect the probability of a randomly chosen occupancy to be found in an isolate. The additive-constrained SARs accounts for two complimentary turn-over components of occupancies: turnover between species and turnover between sites.

Patterns of species turnover may reflect the processes driving community dynamics across scales. While the majority of studies on species turnover have examined pairwise comparison metrics (e.g., the average Jaccard dissimilarity), it has been proposed that the species-area relationship (SAR) also offers insight into patterns of species turnover because these two patterns may be analytically linked. However, these previous links only apply in a special case where turnover is scale invariant, and we demonstrate across three different plant communities that over 90% of the pairwise turnover values are larger than expected based on scale-invariant predictions from the SAR. Furthermore, the degree of scale dependence in turnover was negatively related to the degree of variance in the occupancy frequency distribution (OFD). These findings suggest that species turnover diverges from scale invariance, and as such pairwise turnover and the slope of the SAR are not redundant. Furthermore, models developed to explain the OFD should be linked with those developed to explain species turnover to achieve a more unified understanding of community structure.

Species distributions are commonly measured as the number of sites, or geographic grid cells occupied. These data may then be used to model species distributions and to examine patterns in both intraspecific and interspecific distributions. Harte et al. (1999) used a model based on a bisection rule and assuming self-similarity in species distributions to do so. However, this approach has also been criticized for several reasons. Here we show that the self-similarity in species distributions breaks down according to a power relationship with spatial scales, and we therefore adopt a power-scaling assumption for modeling species occupancy distributions. The outcomes of models based on these two assumptions (self-similar and power-scaling) have not previously been compared. Based on Harte's bisection method and an occupancy probability transition model under these two assumptions (self-similar and power-scaling), we compared the scaling pattern of occupancy (also known as the area-of-occupancy) and the spatial distribution of species. The two assumptions of species distribution lead to a relatively similar interspecific occupancy frequency distribution pattern, although the spatial distribution of individual species and the scaling pattern of occupancy differ significantly. The bimodality in occupancy frequency distributions that is common in species communities, is confirmed to a result for certain mathematical and statistical properties of the probability distribution of occupancy. The results thus demonstrate that the use of the bisection method in combination with a power-scaling assumption is more appropriate for modeling species distributions than the use of a self-similarity assumption, particularly at fine scales.

Numerous hypotheses have been proposed to explain the shape of occupancy frequency distributions (distributions of the numbers of species occupying different numbers of areas). Artefactual effects include sampling characteristics, whereas biological mechanisms include organismal, niche-based and meta-population models. To date, there has been little testing of these models. In addition, although empirically derived occupancy distributions encompass an array of taxa and spatial scales, comparisons between them are often not possible because of differences in sampling protocol and method of construction. In this paper, the effects of sampling protocol (grain, sample number, extent, sampling coverage and intensity) on the shape of occupancy distributions are examined, and approaches for minimising artefactual effects recommended. Evidence for proposed biological determinants of the shape of occupancy distributions is then examined. Good support exists for some mechanisms (habitat and environmental heterogeneity), little for others (dispersal ability), while some hypotheses remain untested (landscape productivity, position in geographic range, range size frequency distributions), or are unlikely to be useful explanations for the shape of occupancy distributions 'species specificity and adaptation to habitat, extinction-colonization dynamics). The presence of a core (class containing species with the highest occupancy) mode in occupancy distributions is most likely to be associated with larger sample units, and small homogenous sampling areas positioned well within and towards the range centers of a sufficient proportion of the species in the assemblage. Satellite (class with species with the lowest occupancy) modes are associated with sampling large, heterogeneous areas that incorporate a large proportion of the assemblage range. However, satellite modes commonly also occur in the presence of a core mode, and rare species effects are likely to contribute to the presence of a satellite mode at most sampling scales. In most proposed hypotheses, spatial scale is an important determinant of the shape of the observed occupancy distribution. Because the attributes of the mechanisms associated with these hypotheses change with spatial scale, their predictions for the shape of occupancy distributions also change. To understand occupancy distributions and the mechanisms underlying them, a synthesis of pattern documentation and model testing across scales is thus needed. The development of null models, comparisons of occupancy distributions across spatial scales and taxa, documentation of the movement of individual species between occupancy classes with changes in spatial scale, as well as further testing of biological mechanisms are all necessary for an improved understanding of the distribution of species and assemblages within their geographic ranges.