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The positive relationship between spatial environmental heterogeneity and species diversity is a widely accepted concept, generally associated with niche limitation. However, niche limitation cannot account for negative heterogeneity-diversity relationships (HDR) revealed in several case studies. Here we explore how HDR varies at different spatial scales and provide novel theories for small-scale species co-existence that explain both positive and negative HDR. At large spatial scales of heterogeneity (e.g. landscape level), different communities co-exist, promoting large regional species pool size and resulting in positive HDR. At smaller scales within communities, species co-existence can be enhanced by increasing the number of different patches, as predicted by the niche limitation theory, or alternatively, restrained by heterogeneity. We conducted meta-regressions for experimental and observational HDR studies, and found that negative HDRs are significantly more common at smaller spatial scales. We propose three theories to account for niche limitation at small spatial scales. (1) Microfragmentation theory: with increasing spatial heterogeneity, large homogeneous patches lose area and become isolated, which in turn restrains the establishment of new plant individuals and populations, thus reducing species richness. (2) Heterogeneity confounded by mean: when heterogeneity occurs at spatial scales smaller than the size of individual plants, which forage through the patches, species diversity can be either positively or negatively affected by a change in the mean of an environmental factor. (3) Heterogeneity as a separate niche axis: the ability of species to tolerate heterogeneity at spatial scales smaller than plant size varies, affecting HDR. We conclude that processes other than niche limitation can affect the relationship between heterogeneity and diversity.

Summary Species absent from a community but with the potential to establish (dark diversity) are an important, yet rarely considered component of habitat‐specific species pools. Quantifying this component remains a challenge as dark diversity cannot be observed directly and must be estimated. Here, we empirically test whether species ecological requirements or species co‐occurrences provide accurate estimates of dark diversity. We used two spatially nested independent datasets, one comprising 3033 samples of coastal grassland vegetation from 4 m2 and 200 m2 plots from Scotland, UK, and another comprising 780 samples of forest vegetation plots from 30 m2 and 500 m2 plots from Switzerland. Dark diversity for each of the smaller scaled plots was estimated through investigating the degree of (i) similarity in ecological requirements (measured as Ellenberg values); and (ii) co‐occurrence likelihood. Estimates were validated using species from the larger spatial scales. Estimates were further validated using observations from all larger scale plots surrounding a focal assemblage within a 2 km (Scottish grassland) and 10 km (Swiss forest) radius. The co‐occurrence method was shown to be more accurate resulting in far fewer negative mismatches (i.e. species observed but not predicted), as well as higher proportions of observed and predicted species, relative to the Ellenberg method. Of the species observed in the large‐scale samples, 18% were estimated as part of the smaller scale dark diversity via the co‐occurrence approach relative to 8% for the Ellenberg method for both the Scottish and Swiss data, respectively. These values increased to 67% & 60% and 32% & 35%, respectively, across all observations within a 2 km (Scottish grasslands) and 10 km (Swiss forests) radius. The study demonstrates that dark diversity for a community can be successfully estimated using readily available data, through exploring species co‐occurrence patterns. This work substantiates that habitat‐specific species pools can be accurately quantified and should prove valuable for understanding underlying community processes and improving our knowledge of the mechanisms governing species co‐existence.

While an increasing number of indices for estimating the functional trait diversity of biological communities are being proposed, there is a growing demand by ecologists to clarify their actual implications and simplify index selection. Several key indices relate to mean trait dissimilarity between species within biological communities. Among them, the most widely used include (a) the mean species pairwise dissimilarity (MPD) and (b) the Rao quadratic entropy (and related indices). These indices are often regarded as redundant and promote the unsubstantiated yet widely held view that Rao is a form of MPD. Worryingly, existing R functions also do not always simplify the use and differentiation of these indices. In this paper, we show various distinctions between these two indices that warrant mathematical and biological consideration. We start by showing an existing form of MPD that considers species abundances and is different from Rao both mathematically and conceptually. We then show that the mathematical relationship between MPD and Rao can be presented simply as Rao = MPD × Simpson, where the Simpson diversity index is defined as 1 - dominance. We further show that this relationship is maintained for both species abundances and presence/absence. This evidence dismantles the paradigm that the Rao diversity is an abundance-weighted form of MPD and indicates that both indices can differ substantially at low species diversities. We discuss the different interpretations of trait diversity patterns in biological communities provided by Rao and MPD and then provide a simple R function, called "melodic," which avoids the unintended results that arise from existing mainstream functions.

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