Beta diversity (β) quantifies the dissimilarity between communities and is thus fundamental to biogeography and spatial ecology. However, multiple and conflicting hypotheses exist to explain how β varies with spatial scale (here grain within a constant extent). Some resolution on spatial scaling of β may help clarify long-standing debate about: (a) β itself and (b) the ecological community concept, because the clearest spatial size of an ecological community corresponds to the scale with maximal β. Here we test five alternative hypotheses for β spatial scaling by calculating β for four very different taxa (ants, birds, diatoms, and trees) at spatial grains ranging from one to one million km² in a constant spatial extent (contiguous USA). We also test repeatability for: (a) summer and winter bird β in six consecutive years; (b) trees through time (4 years, spaced 5 years apart). Specifically, we organize point data into hexagonal polygons, and then calculate mean pairwise β between each hexagon and its neighbors. We also calculate the deviation of β from two null models (assuming either spatial heterogeneity or homogeneity). For multiple reasons, β deviation based on spatial heterogeneity was preferable to that based on spatial homogeneity. For all taxa, β peaks at regional scales: trees ~300 km²; winter birds ~500 km²; summer birds ~2000 km²; ants ~2000 km²; diatoms ~11,000 km². Also, spatial scaling is consistent inter-annually (birds, trees) and sensitive to seasonality (birds). Results broadly support the regional community concept and, based on the variety of taxa evaluated here, similar patterns are likely across the tree of life. Local ecological and evolutionary forces scale up to form regional community patterns and results here support efforts to coordinate local conservation efforts in regions (e.g., corridors and networks) to best conserve biodiversity.

ants, beta deviation, beta diversity, birds, diatoms, ecological community concept, spatial grain, spatial scale, trees

Ecological communities are often defined as “multiple species living in a specified place and time” (e.g., Vellend 2010) and are an important focal point in ecology. This definition is purposefully flexible in its spatial scale (i.e., grain and extent; Wiens 1989) when referring to different study systems and taxa. However, it leaves hanging a question at the heart of critiques for ecology (McIntosh 1986; Wilson 1991; Lawton 1999; Ricklefs 2008; Roughgarden 2009; Vellend 2010): Are ecological communities natural entities (i.e., they exist as particular and discrete units) or mere abstract concepts of convenience?

The absence of a clear answer to the question above has been an obstacle for a century’s studies of biodiversity (McIntosh 1986) and continues to cause difficulty in biogeographical and ecological studies. Research on natural biodiversity has navigated around this obstacle by one of four paths. A common approach is to use an operational community definition (e.g., the first sentence above) to bear “as little conceptual baggage as possible, so that we can put the debate about their existence behind us” (Palmer and White 1994). Some disagree (e.g., Wilson 1994; Jax et al. 1998), leading to reliance instead on external proxies (i.e., not based on community patterns) such as geomorphology or habitat (e.g., Cadenasso et al. 2003; Fagan et al. 2003; Yarrow and Marin 2007). A third path is to focus instead on levels of organization that lie below (i.e., individual organisms or populations; Clark et al. 2011) or above (i.e., metacommunities; Leibold et al. 2004) the community level. Unfortunately, the fundamental problem remains for metacommunity ecology, which relies on local communities as basal units of study. Finally, Lawton (1999) and Ricklefs (2008) viewed the problem as one of scale, and Ricklefs (2008) argued that regional scales should be preferred to local scales in order to better address the full suite of selective conditions driving diversity. Here we work with spatial scale by varying resolution (i.e., grain) but holding spatial extent constant (Wiens 1989).

The lingering question and its decades of debate (summarized above) are relevant to effective conservation biogeography. Whereas conservation biology has steered toward single species (Simberloff 1988), conservation biogeography explicitly addresses multispecies biodiversity patterns (Whittaker et al. 2005; Richardson and Whittaker 2010), where clear patterns are required to best understand and address anthropogenic impacts. For example, spatial strategies such as coordinated corridors and networks among conserved sites (e.g., Rouget et al. 2006) may be most effective if targeted to scales best representing biodiversity patterns. If those scales of community biodiversity can be approximated well, then both lingering uncertainty on the ecological community concept, and the building blocks of conservation biogeography may be better resolved.

Here we assess the empirical spatial scale of communities by evaluating beta diversity (β), which represents the difference between two sets of species (Whittaker 1972; Tuomisto 2010; Anderson et al. 2011). We reasoned simply that maximal β indicates the clearest possible separation between neighboring communities, and so the corresponding spatial grain of this maximal β represents the optimal spatial scale of ecological communities. Our approach adopts long-standing logic from research on optimized spatial resolution in remote sensing (Woodcock and Strahler 1987), where an optimal grain size in a satellite image is needed to discern empirical objects without errors of omission expected at finer spatial grains and errors of commission expected at coarser spatial grains (Ming et al. 2011; Mutowo et al. 2023). The empirical “object” here is β among neighboring hexagonal grids (Fig. 1a), where fine spatial grains may sample only common species but coarse spatial grains may be overly inclusive and essentially blur existing pattern. The spatial grain with maximal β is then the optimized balance between errors of omission and commission and indicates the empirical size of a community, given that scale finds the clearest differences between adjacent communities.

Maximal β was free to occur at any spatial grain within the million-fold range evaluated here. Diversity patterns of the focal organisms make no assumptions based on external landscape or habitat features because those are not used in analyses. Likewise, diversity patterns do not require information or make assumptions based on population or metacommunity biology (e.g., dispersal distances, etc.). Additionally, our approach obtains a quantitative gradient showing maximal β and its associated variance across spatial grains; as such, it does not presume a priori thresholds or categories. To detect such pattern is a precursor for potential subsequent research to understand mechanisms underpinning the pattern; our research simply seeks to identify spatial grains at which that research may best reflect community patterns. We work with data for four very different taxa (ants, birds, diatoms, and trees) that help to consider potential generality of pattern but also require we treat the community concept here as assemblages (Fauth et al. 1996; Stroud et al. 2015).

We tread carefully with both β and spatial scale, which are entangled throughout relevant literature and require brief explanation here. Enough confusion has accrued about β for it to be described as “a concept gone awry” (Tuomisto 2010) with a “confusing array of concepts, measures and methods” (Anderson et al. 2011). For clarity, the general beta diversity concept is denoted here by β, but specific versions have subscripts. Here we use a β based on a multiplicative relationship (i.e., β = γ/α), where γ is overall diversity and α is local diversity (Tuomisto 2010; Xing and He 2021). An even more important decision for our purposes here is to use a deviation of β from randomized expectations (e.g., β_DEV). This matters because β is a function of both γ and α. Thus, β in neighborhoods of sites with different γ and/or α will inherently differ but can be adjusted to evaluate spatial patterns more fairly by calculating the difference from randomizations conducted with the same data. Initially, β_DEV was calculated using a spatially-homogeneous null (Kraft et al. 2011), but a recent version based on spatial heterogeneity (called β_NBD for its underlying negative binomial distribution) can represent clustered patterns more accurately across spatially-varying regions (Xing and He 2021). Here we use β_NBD as our main measure of β but also compare results to β_DEV and observed β (β_OBS), where more details on the three βs are below in Methods and evidence of this secondary consideration is presented in Suppl. material 1.

Spatial scale is important to ecology because both patterns (e.g., β) and processes have inherent scales (Wiens 1989; Barton et al. 2013; Zhang et al. 2015); to discern well the process-pattern linkage requires matching scales. Here we hold spatial extent constant as the contiguous USA (8.08 × 10⁶ km²) to evaluate the relationship between β and spatial grain (i.e., resolution) from 1.0 km² to 1 million km². At each spatial grain, we compare a central hexagonal grid to each of its immediate neighbors (Fig. 1a) to obtain a mean pairwise β for each grid. Thus, the focal scale of analysis (Whittaker et al. 2001) for β is the neighborhood, where neighborhoods are constrained (i.e., N < 6 adjacent grids with spatial size = central grid) for all β estimates at all spatial grain sizes, and pairwise comparisons of grid cells (i.e., β) avoids errors inherent in other methods (Marion et al. 2017).

Based on prior research, β is expected to depend on spatial grain in at least five different ways (Fig. 1b), where that variety appears related (in part) to the variety of β measures and spatial scales that have been studied. If maximal β occurs at small spatial grains (Fig. 1b1), then locally-scaled communities would be supported (Keil et al. 2012; Barton et al. 2013). Alternatively, β may progressively increase with spatial grain, reflecting sample size effects (Fig. 1b2; Zhang et al. 2015; Keil and Chase 2019; Xing and He 2021). Both trends may occur but represent studies conducted at different spatial scales, so β may first decrease and then increase to follow a V- or U-shaped curve across a wider range of spatial grains (Fig. 1b3). Alternatively, the regional community concept (Ricklefs 2008) would be supported if β exhibited hump-shaped peaks at an intermediate spatial grain (Fig. 1b4), which would also be consistent with patterns of an optimized spatial grain (expressed as local variance) in remote sensing (Woodcock and Strahler 1987; Ming et al. 2011; Mutowo et al. 2023). In that research, optimal spatial grain is often at intermediate sizes, though outcomes vary, depending on the image. Finally, it is possible that β exhibits no clear trend with spatial grain (Fig. 1b5; Lira‐Noriega et al. 2007).

Xing and He (2021) cautioned about potential effects of spatial scale on β and deviations of β from null models (β_DEV or β_NBD), and wrote “the same grain size and similar spatial extent are required when β or β-deviation is compared among different regions.” We paid heed, and vary only one potential effect (i.e., spatial scale) while holding the other two effects (extent and region of interest) constant while evaluating responding β and β deviations.

If spatial scale is composed of two axes (grain and extent), a third and related axis is represented by study scale, often measured as sample size (e.g., Jenkins 2011; Xing and He 2021). Study scale can affect observed β if larger areas include more samples that enable the detection of more species, as expressed in rarefaction of species-sample curves (Chao et al. 2014). We addressed study scale effects across spatial grains using both a priori and a posteriori approaches.

Beyond β scaling shape (Fig. 1b), differences in the details among taxa could inform long-standing questions of dispersal scaling of diversity among microbial and macroscopic organisms (Fontaneto 2011). Assuming similar general β spatial scaling shapes across taxa, we expected diatoms to exhibit smaller spatial grains for peak β than other taxa because: diatoms exist within hard ecotones (i.e., lake shores here); are sensitive to local water quality (Reid et al. 1995); and most species inhabit one or few lakes (USEPA 2009). In comparison, species of trees, ants and birds inhabit intergrading habitats, have aerial life stages, and/or inhabit substantial ranges. In combination with the general scaling of dispersal distances for actively dispersing organisms (Jenkins et al. 2007), we expected spatial scales of peak β_NBD would rank as diatoms < ants < trees < birds.

Ants, birds, diatoms, and trees all demonstrated peak β_NBD at intermediate spatial grains that were roughly consistent in shape (Fig. 2), despite wide differences in natural history and data properties (Table 1). As may be expected for ants, birds, and diatoms from Fig. 2, hump-shaped quadratic curves (i.e., peak β_NBD at intermediate spatial grains) more efficiently represented data than linear models that would have supported some other scaling hypotheses depicted in Fig. 1 (all AIC_C weights > 0.95). Moreover, curve coefficients supported hump-shaped curves rather than V- or U-shaped curves. Trees exhibited a second but highly variable peak β_NBD at greatest spatial grains, which made null models more plausible than linear or quadratic models. The impact of grains of 500,000 and 1 million km² on that analysis was demonstrated by omitting them from analyses; then hump-shaped patterns were confirmed (AIC_C weights > 0.95). The broadly consistent result across very different taxa and data sets were consistent with the regional community concept. Moreover, interannual or interseason variation (where possible; birds, trees) indicated remarkable consistency.

Within that broad pattern, values of peak β_NBD (Fig. 2) differed substantially among taxa, and our hypothesis about the rankings of β_NBD was incorrect. Peak mean β_NBD for ants was about 1,500 km² (Fig. 2a). Peak mean β_NBD values for birds were about ~ 2,000 km² in summer but substantially reduced to roughly 500 km² in winter (green and gray vertical arrows in Fig. 2b, respectively). Peak mean β_NBD values were greatest for diatoms (~11,000 km²; Fig. 2c), but for trees peak mean β_NBD values were consistently at about 300 km² through 4 evaluated years spanning 2 decades (Fig. 2d). Mean β_NBD for trees increased again at greatest spatial grains, but with wide confidence intervals (Fig. 2d), for reasons we explain below, and which led us to disregard the second peak. Tree mean β_NBD values at about 300 km² had very little within- or among-annual variation (95% confidence intervals are smaller than symbols in Fig. 2d). Thus, we ranked peak mean β_NBD among taxa as [trees < winter birds < ants ≈ summer birds < diatoms], rather different from our naive hypothesis (diatoms < ants < trees < birds).

We also evaluated variation of β_NBD as a function of spatial grain, where each central hexagon’s mean β_NBD contributed to a plotted distribution (note the “flipped” axes between Figs 2, 3). Essentially, wider confidence intervals around peak mean β_NBD (Fig. 2) were related to the number of hexagons contributing to a mean (e.g., only 14 at 1 million km² grain) and variation in mean β_NBD values (Fig. 3). Ants had substantial variation in β_NBD at any one spatial grain (Fig. 3a), where multimodal distributions of β_NBD were apparent at both smallest and greatest grains but unimodal and narrower distributions at peak β_NBD were most appropriate for a mean (Fig. 3a). Birds had remarkably narrow β_NBD distributions, so mean values in Fig. 2 represented patterns quite well regardless of season at spatial grains < 500,000 km² (Fig. 3b, c). Like ants, distributions for diatoms were multimodal at smallest and greatest grains but appropriate to a mean value at intermediate grains where peak values occurred (Fig. 3d). Distributions for trees supported the use of mean peak β_NBD values at smaller grains, but multimodal and wide variation at greater grains reduced validity of a mean to represent patterns (Fig. 3e). In all cases, spatial grains with peak β_NBD obtained data distributions most appropriately described by a mean and confidence intervals, whereas other spatial grains represented more problematic distributions. Thus, distributions of mean β_NBD (Fig. 3) validated inferences about peak mean β_NBD values at intermediate spatial grains across taxa analyzed here.

Deviation of β from a null model based on spatial homogeneity (β_DEV) increased with sample size as expected, but β_NBD did not. Instead, β_NBD consistently peaked at intermediate grain sizes that corresponded to intermediate numbers of samples, hexagons, species, and neighboring hexagonal grid cells. Based on results above (Figs 2, 3) and additional results summarized here (details are in Suppl. material 1), mean pairwise β_NBD was not a simple progressive function of sample size, which could confuse results; because bigger hexagons can include more observation locations. This detail is secondary to our main question here but is important to an alternative hypothesis that β simply scales with sample size (e.g., Fig. 1b) and because β has been historically calculated in multiple ways. Moreover, peak β_NBD occurred at different spatial scales among taxa despite having data assigned to identical base hexagonal maps at each grain size, indicating that the methods adopted did not cause roughly-similar patterns to emerge. In all, multiple lines of evidence demonstrated that sample size effects were not important contributors to patterns in spatial scaling of mean pairwise β_NBD. Also, β_NBD repeatedly represented a modest adjustment to β_OBS whereas β_DEV represented substantial changes relative to β_OBS.

Figure 2. 

Spatial scaling of beta diversity, calculated as deviation from a null expectation (β_NBD, 29) and potentially ranging 0–1. β_NBD scaling of (a) ants; (b) birds (summer = green; winter = grey, 2010–2015); (c) diatoms; and (d) trees (2002, 2007, 2012, and 2017). Arrows indicate spatial grains corresponding to approximate peak β_NBD. Note log scale for spatial grain. Public domain organism images.

Figure 3. 

Data distributions for beta diversity, calculated as deviation from a null expectation (β_NBD, Xing and He 2021) and potentially ranging 0–1. Normal data are best represented by means, and narrow variance generates narrow confidence intervals (see Fig. 2). (a) Ant β_NBD was most variable and multimodal at small and large spatial grains. Bird β_NBD in both (b) winter and (c) summer was relatively narrow overall but especially suited to means at peak β_NBD. (c) Similar to ants, diatoms were best represented by means at peak values. (d) Trees data were multimodal at greatest spatial grains. Note log scale for spatial grain.

Results here help address decades of confusion about beta diversity (β) and spatial scaling, and the conceptual reality and practical value of ecological communities (Whittaker 1972; McIntosh 1986; Wilson 1991; Lawton 1999; Ricklefs 2008; Roughgarden 2009; Tuomisto 2010; Vellend 2010; Anderson et al. 2011; Chave 2013). As such, it helps better resolve units of study and action for conservation biogeography (Whittaker et al. 2005). Work here was based on the premise that an entity is best measured by its own properties, and thus β (i.e., differences between communities) patterns can indicate a spatial scale that most clearly differentiates between neighboring communities. We obtained empirical gradients of β across spatial grains, which were free to form inherent shapes and where peak values represented spatial scales of the maximal differences between adjoining communities. Below we elaborate on lessons learned regarding β, ecological communities, interdisciplinary methods, and implications for conservation.

While β is a fundamental measure of ecological diversity patterns (Whittaker 1972), it has a long history of disputes spanning its concepts and metrics that largely coincided with debate on the veracity of ecological communities. Work to organize research on β (e.g., Tuomisto 2010; Anderson et al. 2011) made it more clearly understood, including the use of deviations from null expectations (β_DEV, Kraft et al. 2011) that led to the recent update based on spatial heterogeneity (β_NBD; Xing and He 2021) used here. We showed that β_NBD moderately adjusted observed β values (β_OBS) and did not introduce sample size effects, unlike β_DEV which greatly altered β_OBS and was subject to sample size effects. Thus, results here among very different taxa and data sources support the value of β_NBD (Xing and He 2021) for future research on β diversity.

Very different taxa (and data origins) obtained a remarkably consistent general shape for β spatial scaling here (and yes, differences existed in the details). If this general pattern holds among other taxa across the tree of life and different data sources, some generality is enticingly possible for the spatial scaling of biodiversity patterns and the regional community concept. Moreover, spatial scaling of β_NBD for birds and trees is inter-annually repeatable and (for birds) sensitive to seasonal conditions, suggesting stability of β_NBD spatial scaling. What processes might cause such general patterns? Much of our collective understanding of ecological processes is necessarily obtained at local scales much finer than those used here, related to historical and logistical limits on data collection.

We stress that results here do not disavow local-scale research, which is vital to understand mechanisms of biotic and abiotic interactions and provided data amassed here and then integrated into a variety of spatial units. However, results here support efforts to better understand how myriad local processes (i.e., abiotic and biotic interactions affecting individuals or demes) cascade up to cause regional patterns, and to compare those local processes to regional processes (Ricklefs and Schluter 1993; Ricklefs 2008; D’Amen et al. 2017). Also, we may infer that local and/or regional processes acting on individuals, demes, or a species must be general enough to translate to regional β diversity patterns detected here, consistent with Ricklefs’ (2008) regional community concept.

Results for birds and trees indicate spatial scaling of β_NBD is inter-annually repeatable and (for birds) sensitive to seasonal conditions. Given that birds and trees differ so greatly in life histories and mobility, this commonality suggests community assembly processes are a strong and common basis for β_NBD spatial scaling. Future work on the spatial scales of those processes, including effects of habitat heterogeneity, may help explain the regional scales observed here. Interestingly, ants and summer birds had roughly similar regional community scales, perhaps related to similar scales of factors that control distributions of birds and founding ant queens that establish colonies (Helms et al. 2016). Finally, differences in bird β_NBD scaling between summer and winter indicate that the approach here is sensitive to temporal conditions across substantial extent (contiguous US). Given this pattern, changes in β_NBD scaling over longer terms may represent effects of changing climate and/or land cover.

Results here also inform the dispersal scaling of communities, where potential long-range dispersal of microscopic organisms has long been debated as causing greater global taxonomic similarity than observed for macroscopic organisms (Fontaneto 2011). At first glance, spatial scaling of β_NBD for diatoms appeared to support long-range dispersal scaling of microbial diversity. However, community size of lake diatoms roughly matched the average sampled lake density (1071 sampled lakes / 8.08 × 10⁶ km² in the contiguous US = 1 lake / 1.3 × 10⁴ km²), and the majority (52%) of species were recorded in <3 lakes. Thus, diatom results here are consistent with a diatom community being bounded by one lake shore, on average. Spatial scaling of diatom β_NBD may actually represent the average dispersion of sampled discrete diatom habitats, in contrast to intergrading terrestrial habitats represented here for ants, birds, and trees. If so, other microbial communities (e.g., soils) sampled at greater spatial density may be evaluated with the approach here to further evaluate dispersal scaling of microbial community structure.

The community concept has been debated almost since its origin (McIntosh 1986; Wilson 1991; Lawton 1999; Ricklefs 2008; Roughgarden 2009). Ecology and biogeography have nonetheless progressed, often by ignoring this problem. At the same time, scale became widely recognized as fundamental to understand natural processes and patterns (Chave 2013), and β emerged (with its many versions; Tuomisto 2010, Anderson et al. 2011) as an important measure in ecology and biogeography. In that context, ecology has (in part) expanded toward biogeographical spatial scales (Lawton 1999; Leibold et al. 2004; Roughgarden 2009; Jenkins and Ricklefs 2011). Results here support this fusion by showing empirical differences between adjacent communities are most apparent at regional scales (i.e., hundreds to tens of thousands of km²), consistent with the regional community concept (Ricklefs 2008).

In that theme, a regional community has been interpreted as the scope of an entire metacommunity (Jenkins and Ricklefs 2011). Results here support that view and point to a way to identify the potential size of a regional community / metacommunity / regional source pool, whether for broad taxa (as done here) or more specific subsets (e.g., based on habitat use or traits). However, the same old problem (see Introduction) remains for the subsequent definition of local communities within a metacommunity. Relatively low β_NBD at fine scales here supports the argument of Ricklefs (2008) that local communities are one end of spatiotemporal continua, rather than empirically distinct entities. Much of metacommunity ecology may be wise to treat local communities as sample points rather than empirically bounded, discrete units. This view steers metacommunity ecology away from the frail local community concept and toward a species-centric approach (Ricklefs 2008; Jenkins 2011) that is conceptually consistent with hierarchy theory (Allen and Starr 1982). Alternatively, if one regards results here to indicate a single community is ~10³ km², then a metacommunity is vast – perhaps too vast for the metacommunity concept to be useful. We prefer the former view.

Long-standing work in remote sensing to optimize spatial resolution of images (e.g., Woodcock and Strahler 1987; Ming et al. 2011; Mutowo et al. 2023) provides lessons for how biogeography may improve understanding of spatiotemporal patterns. Modern biogeography relies heavily on spatially-distributed data in multiple ways, including rasterized representations like those used here. Both old (e.g., Woodcock and Strahler 1987) and new (e.g., Wylie et al. 2019) practical lessons from remote sensing and GIS can be fruitfully applied in biogeography. This may seem obvious, but the fact that optimized spatial resolution does not seem to have been applied to β justifies making the point here. Other biogeographical patterns may also exhibit similar peaked spatial scaling that may help reveal maximal signal amidst the noise to better represent natural patterns than making maps with tidy space filling or visual appeal. If so, various ecological and biogeographical concepts tested so far at widely varying spatial grains (and then debated) may gain better resolution.

Finally, our results bear fundamental implications for conservation biogeography in the Anthropocene because they indicate that regional scales are appropriate to conserve biodiversity (Whittaker et al. 2005). Thus, our results add importance to work toward corridors and networks among conserved sites (e.g., Rouget et al. 2006), and may help researchers reconsider the appropriate spatial grains to use when studying diversity responses to land use and climate change. For example, a study to evaluate diversity responses to changing land use and climate may obtain maximal resolution by using rasterized units of study that match peak β.

All data analyzed here were obtained from publicly-accessible sources, cited in References. Code central to calculate β in all forms here is provided by Xing and He (2021).

We thank the Cornell Lab of Ornithology, the GABI network, the USEPA, and the US Forest Service for making many data publicly-available; we hope results here help validate that work. We thank Drs. Franklin and Whittaker for helpful editorial suggestions, and we thank the Ying Family Fund for continuing support.