Research Article 
Corresponding author: David G. Jenkins ( david.jenkins@ucf.edu ) Academic editor: Janet Franklin
© 2024 Leo Ohyama, Juan D. BogotaGregory, David G. Jenkins.
This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Citation:
Ohyama L, BogotaGregory JD, Jenkins DG (2024) Peak beta diversity occurs at regional spatial grains. Frontiers of Biogeography 17: e132675. https://doi.org/10.21425/fob.17.132675

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 longstanding 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 km^{2} 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 km^{2}; winter birds ~500 km^{2}; summer birds ~2000 km^{2}; ants ~2000 km^{2}; diatoms ~11,000 km^{2}. Also, spatial scaling is consistent interannually (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.
Beta diversity peaked at substantial spatial scales for all taxa evaluated here (ants, birds, diatoms, trees), suggesting a general pattern.
The regional community concept advanced by Robert Ricklefs is supported empirically, in preference to four other hypotheses also tested.
Beta diversity calculations used a relatively new deviation from a spatially heterogeneous null, which modestly adjusted observed beta diversity.
Results support use of this newer beta deviation rather than the older beta deviation based on spatial homogeneity.
Given that ecological communities appear regional in scale, local biodiversity conservation work can best ensure success if it is regionally coordinated.
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.,
The absence of a clear answer to the question above has been an obstacle for a century’s studies of biodiversity (
The lingering question and its decades of debate (summarized above) are relevant to effective conservation biogeography. Whereas conservation biology has steered toward single species (
Here we assess the empirical spatial scale of communities by evaluating beta diversity (β), which represents the difference between two sets of species (
Maximal β was free to occur at any spatial grain within the millionfold 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 (
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” (
Spatial scale is important to ecology because both patterns (e.g., β) and processes have inherent scales (
Based on prior research, β is expected to depend on spatial grain in at least five different ways (Fig.
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.,
Beyond β scaling shape (Fig.
We obtained data for the contiguous USA for ants (
Data for trees (i.e., stems with diameter at breast height > 5 cm) were extracted from the US Forest Service’s Forest Inventory Analysis (FIA) data using the rFIA package in R (
Ants  Birds  Diatoms  Trees  

Number of species  699  1,560  1,957  403 
Number of samples  24,893  810,921  1,070  39,396 
Temporal range  2 centuries  2010–2015  2007  2002–2017* 
Data type  presence  Mean count per personhour  presence  presence 
Temporal analyses?  No  Yes; seasonal  No  Yes; annual 
Data Source 


USEPA ( 
USDA ( 
Each taxon was analyzed similarly using an iterative process summarized here, based on multiple R packages (
Hexagonal grids and their 1^{st}degree adjoining neighbors comprised a neighborhood (Fig.
(a) Beta diversity (β) was calculated for each central hexagon as the mean of its pairwise β with its adjoining neighbor hexagons. (b) Hypothetical shapes of beta diversity spatial scaling. As spatial grain increases, beta diversity may (1) decrease because diversity patterns are caused by local processes (e.g.,
By working with hexagonal grid cells and their neighbors, study size was standardized into the number of grids. We compared each grid cell to each of its adjoining neighbors, where hexagonal grids are constrained to have < 6 neighbors (thus controlling grid sample size across spatial grains). A tradeoff may still linger, where smaller grid cells contain too few samples for reliable diversity estimation (i.e., errors of omission) but very large grid cells are so inclusive as to blur actual patterns (i.e., errors of commission;
Data for birds and trees enabled comparisons within each data set (Table
We calculated three β versions using code from
${\beta}_{OBS}=1\frac{\overline{\alpha}}{\gamma}$ Eqn. 1
where α = mean number of species in a hexagon and γ = total number of species in the pair of hexagons being compared;
${\beta}_{DEV}=\frac{{\beta}_{OBS}{\beta}_{null}}{\sqrt{va{r}_{\Pi}\left({\beta}_{null}\right)}}$ Eqn. 2
where β_{NULL} is:
${\beta}_{NULL}=\frac{\mathrm{ln}\left(1p\left(1\frac{1}{M}\right)\right)}{\mathrm{ln}(1p)}\approx \frac{\mathrm{ln}\left(\frac{M}{1+\lambda M}\right)}{\mathrm{ln}(1/\lambda )}$ Eqn. 2a
and var_{Π} is the variance of β in the null model, M is the size of the metacommunity relative to the size of the local community (constrained here to <7), and p = e^{λ}, related to a logseries speciesabundance distribution and determined by N (total number of individuals) and S (total number of species; see
Spatial randomness (as in β_{NULL}) may apply in some cases, but spatial aggregation at all scales is well known (e.g.,
${\beta}_{NBD}=\frac{1}{\mathrm{ln}(1p)}\sum _{n=1}^{\infty}\frac{{p}^{n}}{n}{\left(1+\frac{n}{Mk}\right)}^{k}\approx \frac{\mathrm{ln}\left(\frac{M}{1+\lambda M}\right)+C(k,\lambda M)}{\mathrm{ln}(1/\lambda )}$ Eqn. 3a
where n is species abundance and k represents aggregation, with smaller values indicating more aggregated distributions. As above, note that the approximation uses only M and λ, plus a term C(k, λM) which itself can be approximated as:
$C(k,\lambda M)\approx \frac{\mathrm{ln}\left(\frac{1}{\lambda M}+1\right)}{1=(5.070.44\mathrm{ln}(\lambda M\left)\right)k}$ Eqn. 3b
We used β_{NBD} to evaluate alternative hypotheses (Fig.
We also evaluated potential sample size effects on β_{NBD} results, because β_{DEV} increases with greater sample size but such an effect was undescribed for β_{NBD} by
In summary, we controlled for scaling effects of spatial extent and sample size to evaluate potential β ~ spatial grain relationships. We then evaluated mean pairwise β (in several forms) among spatial hexagons across a millionfold range of sizes for four very different taxa (ants, birds, diatoms, and trees). Because data sets differed substantially in their sources, subject taxa, and features (Table
Ants, birds, diatoms, and trees all demonstrated peak β_{NBD} at intermediate spatial grains that were roughly consistent in shape (Fig.
Within that broad pattern, values of peak β_{NBD} (Fig.
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
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
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.
Data distributions for beta diversity, calculated as deviation from a null expectation (β_{NBD},
Results here help address decades of confusion about beta diversity (β) and spatial scaling, and the conceptual reality and practical value of ecological communities (
While β is a fundamental measure of ecological diversity patterns (
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 interannually 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 localscale 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 (
Results for birds and trees indicate spatial scaling of β_{NBD} is interannually 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 (
Results here also inform the dispersal scaling of communities, where potential longrange dispersal of microscopic organisms has long been debated as causing greater global taxonomic similarity than observed for macroscopic organisms (
The community concept has been debated almost since its origin (
In that theme, a regional community has been interpreted as the scope of an entire metacommunity (
Longstanding work in remote sensing to optimize spatial resolution of images (e.g.,
Finally, our results bear fundamental implications for conservation biogeography in the Anthropocene because they indicate that regional scales are appropriate to conserve biodiversity (
All data analyzed here were obtained from publiclyaccessible sources, cited in References. Code central to calculate β in all forms here is provided by
We thank the Cornell Lab of Ornithology, the GABI network, the USEPA, and the US Forest Service for making many data publiclyavailable; 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.