Power-law Species-area Relationships Research Articles

Fine-grain beta diversity in Palaearctic open vegetation: variability within and between biomes and vegetation types

Aims: To quantify how fine-grain (within-plot) beta diversity differs among biomes and vegetation types. Study area: Palaearctic biogeographic realm. Methods: We extracted 4,654 nested-plot series with at least four different grain sizes between 0.0001 m² and 1,024 m² from the GrassPlot database spanning broad geographic and ecological gradients. Next, we calculated the slope parameter (z-value) of the power-law species–area relationship (SAR) to use as a measure of multiplicative beta diversity. We did this separately for vascular plants, bryophytes and lichens and for the three groups combined (complete vegetation). We then tested whether z-values differed between biomes, ecological-physiognomic vegetation types at coarse and fine levels and phytosociological classes. Results: We found that z-values varied significantly among biomes and vegetation types. The explanatory power of area for species richness was highest for vascular plants, followed by complete vegetation, bryophytes and lichens. Within each species group, the explained variance increased with typological resolution. In vascular plants, adjusted R2 was 0.14 for biomes, but reached 0.50 for phytosociological classes. Among the biomes, mean z-values were particularly high in the Subtropics with winter rain (Mediterranean biome) and the Dry tropics and subtropics. Natural grasslands had higher z-values than secondary grasslands. Alpine and Mediterranean vegetation types had particularly high z-values whereas managed grasslands with benign soil and climate conditions and saline communities were characterised by particularly low z-values. Conclusions: In this study relating fine-grain beta diversity to typological units, we found distinct patterns. As we explain in a conceptual figure, these can be related to ultimate drivers, such as productivity, stress and disturbance, which can influence z-values via multiple pathways. The provided means, medians and quantiles of z-values for a wide range of typological entities provide benchmarks for local to continental studies, while calling for additional data from under-represented units. Syntaxonomic references: Mucina et al. (2016) for classes occurring in Europe; Ermakov (2012) for classes restricted to Asia. Abbreviations: ANOVA = analysis of variance; EDGG = Eurasian Dry Grassland Group; SAR = species-area relationship.

Fine‐grain beta diversity of Palaearctic grassland vegetation

AbstractQuestionsWhich environmental factors influence fine‐grain beta diversity of vegetation and do they vary among taxonomic groups?LocationPalaearctic biogeographic realm.MethodsWe extracted 4,654 nested‐plot series with at least four different grain sizes between 0.0001 m² and 1,024 m² from the GrassPlot database, covering a wide range of different grassland and other open habitat types. We derived extensive environmental and structural information for these series. For each series and four taxonomic groups (vascular plants, bryophytes, lichens, all), we calculated the slope parameter (z‐value) of the power law species–area relationship (SAR), as a beta diversity measure. We tested whether z‐values differed among taxonomic groups and with respect to biogeographic gradients (latitude, elevation, macroclimate), ecological (site) characteristics (several stress–productivity, disturbance and heterogeneity measures, including land use) and alpha diversity (c‐value of the power law SAR).ResultsMean z‐values were highest for lichens, intermediate for vascular plants and lowest for bryophytes. Bivariate regressions of z‐values against environmental variables had rather low predictive power (mean R² = 0.07 for vascular plants, less for other taxa). For vascular plants, the strongest predictors of z‐values were herb layer cover (negative), elevation (positive), rock and stone cover (positive) and the c‐value (U‐shaped). All tested metrics related to land use (fertilization, livestock grazing, mowing, burning, decrease in naturalness) led to a decrease in z‐values. Other predictors had little or no impact on z‐values. The patterns for bryophytes, lichens and all taxa combined were similar but weaker than those for vascular plants.ConclusionsWe conclude that productivity has negative and heterogeneity positive effects on z‐values, while the effect of disturbance varies depending on type and intensity. These patterns and the differences among taxonomic groups can be explained via the effects of these drivers on the mean occupancy of species, which is mathematically linked to beta diversity.

Comparing species–area relationships of native and exotic species

The species–area relationship (SAR) is one of the most general patterns in ecology. Recently, SARs have been employed as tools for comparing the ecology and biogeography of native and exotic species across spatial scales and exploring the influence of invasive species on native biodiversity. Here, we assess published studies to determine if SARs differ between native and exotic assemblages. We conducted a literature search to find studies that estimated the exponent (z) of the power-law SAR for native and exotic species across the same set of locales. We also compiled intercepts (c) of SARs where available. We used linear mixed models to test if z and c differed between native and exotic SARs and if this relationship differed across taxa. Our literature search produced 36 native-exotic pairs from 23 studies with which to compare the exponent of the power-law SAR. Further, SAR intercepts were available for 21 native-exotic pairs. Overall, exotic SAR exponents (z) did not differ from those of natives. However, this pattern did not hold across all taxonomic groups. Plant assemblages, which are best represented in our data (61% of total), mirrored the overall pattern showing no differences in exponents between native and exotic SARs. On the other hand, SAR exponents were greater for both native bird and animal assemblages. The intercepts (c) of native SARs were significantly greater than those of exotics for all taxa combined and for each individual taxonomic grouping. Our results suggest processes driving the increase in species richness with area are similar for native and exotic plant species, but not for animals. Expanding studies that compare SARs of native and exotic species to more taxonomic groups and different types of SARs (e.g., nested, contiguous, non-contiguous) will facilitate a better understanding of how native and exotic species richness scale with area.

Geographic changes in the Aegean Sea since the Last Glacial Maximum: Postulating biogeographic effects of sea-level rise on islands

In order to assess how the last sea level rise affected the Aegean archipelago, we quantified the magnitude and rate of geographic change for the Aegean islands during the last sea-level-rise episode (21kyrBP–present) with a spatially explicit geophysical model. An island-specific Area-Distance-Change (ADC) typology was constructed, with higher ADC values representing a higher degree of change. The highest fragmentation rates of the Aegean archipelago occurred in tandem with the largest rates of sea-level-rise occurring between 17kyr and 7kyr ago. Sea-level rise resulted in an area loss for the Aegean archipelago of approximately 70%. Spatiotemporal differences in sea-level changes across the Aegean Sea and irregular bathymetry produced a variety of island surface-area loss responses, with area losses ranging from 20% to >90% per island. In addition, sea-level rise led to increased island isolation, increasing distances of islands to continents to >200% for some islands. We discuss how rates of area contractions and distance increases may have affected biotas, their evolutionary history and genetics. Five testable hypotheses are proposed to guide future research. We hypothesize that islands with higher ADC-values will exhibit higher degrees of community hyper-saturation, more local extinctions, larger genetic bottlenecks, higher genetic diversity within species pools, more endemics and shared species on continental fragments and higher z-values of the power-law species-area relationship. The developed typology and the quantified geographic response to sea-level rise of continental islands, as in the Aegean Sea, present an ideal research framework to test biogeographic and evolutionary hypotheses assessing the role of rates of area and distance change affecting biota.

Diversity patterns of seasonal wetland plant communities mainly driven by rare terrestrial species

In cleared landscapes, wetlands can represent important reservoirs of native plant diversity, which include terrestrial species. Depending on study aims, non-wetland plants might be removed before analysis, affecting conclusions around biodiversity and community structure. We compared the native plant communities of seasonal wetlands in a predominately agricultural landscape as defined geographically (including all species) with that of the obligate wetland assemblage. We were primarily concerned with determining how this design decision affects ecological and conservation conclusions. We analysed a survey database containing >12,900 flora records from South Australia, developing a new area-based method to remove sampling bias to include only wetlands with a near-complete census. We modelled occupancy, species-area relationships, β-diversity and nestedness under our contrasting community definitions. Terrestrial species were 57.4 % of total richness. Removing these species reduced wetland α-diversity by 45 %, but did not affect the scaling of richness with area (power-law species-area relationship z = 0.21 ± 0.01). Occupancies for wetland plants were relatively uniform, but were heavily dominated by rare (satellite) species when terrestrial plants were included, and this also increased β-diversity. Nestedness for terrestrial species occupancies was marginally lower than predicted under null models, suggesting that rare species often do not co-occur with common species. An implication of these occupancy patterns is that twice as many wetlands (and 50 % more wetland area) would be needed to include every native species within at least one wetland compared with wetland-only species.

Patterns and drivers of phytodiversity in steppe grasslands of Central Podolia (Ukraine)

We asked: (i) Which environmental factors determine the level of α-diversity at several scales and β-diversity in steppic grasslands? (ii) How do the effects of environmental factors on α- and β-diversity vary between the different taxonomic groups (vascular plants, bryophytes, lichens)? We sampled nested-plot series ranging from 0.0001 to 100 m2 and additional 10-m2 plots, covering different vegetation types and management regimes in steppes and semi-natural dry grasslands of Central Podolia (Ukraine). We recorded all terricolous taxa and used topographic, soil, land-use and climatic variables as predictors. Richness-environment relationships at different scales and across taxonomic groups were assessed with multimodel inference. We also fitted power-law species-area relationships, using the exponent (z value) as a measure of β-diversity. In general, the richness values in the study region were intermediate compared to those known from similar grasslands throughout the Palaearctic, but for 1 cm2 we found seven species of vascular plants, a new world record. Heat index was the most important factor for vascular plants and bryophytes (negative relation), while lichen diversity depended mainly on stone and rock cover (positive). The explanatory power of climate-related variables increased with increasing grain size, while anthropogenic burning was the most important factor for richness patterns at the finest grain sizes (positive effect). The z values showed more variation at the finest grain sizes, but no significant differences in their mean between scales. The results highlight the importance of integrating scale into ecological analyses and nature conservation assessments in order to understand and manage biological diversity in steppe ecosystems.

Scale collapse and the emergence of the power law species–area relationship

AbstractAimThe recently proposed maximum entropy theory of ecology predicts that all nested species–area relationships (SARs) will collapse to a single, universal curve that exhibits a decreasing log–log slope with increasing scale, suggesting that the power law form of the SAR is invalid at any scale. In this analysis we test the generality of this scale collapse behaviour and determine the scale at which approximate power law behaviour of the SAR is predicted to occur.LocationGlobal.MethodsWe use common SAR models to recursively upscale SARs to (1) look for scale collapse of SARs built from different community assumptions and (2) identify the scale at which approximate power law SARs are recovered. We explore four SAR models in which species abundance distributions and the spatial aggregation of species vary within and across scales according to observed patterns.ResultsWe show that scale collapse is a property of nested SARs, not of maximum entropy theory, and that many types of SARs can exhibit scale‐collapsed curves that follow the general pattern of empirical communities. Moreover, we use the scale‐collapsed curves to show that power law behaviour is not predicted to occur at the scale of most SAR studies and that variation in species spatial aggregation or the scaling of species abundance distributions are needed to produce power law SARs at realistic scales.Main conclusionsOur findings show that power law behaviour of nested SARs is rare and that communities displaying approximate power law SARs may exhibit predictable characteristics within and across scale, such as interspecific variation in aggregation. Our findings regarding the general rarity of power law behaviour suggests that careful consideration of the curvature of a SAR and the scale of an ecological community are necessary before using power law SARs to predict biodiversity across scales.

Contrasting effects of habitat reduction, conversion and alteration on neutral and non neutral biological communities

While habitat transformation driven by human activities is the main driver of current biodiversity changes, there is still no framework to explore and forecast the effects of different types of habitat changes on the richness and composition of biological communities. To tackle this issue, we modeled the dynamics of a regional meta‐community, composed either of ecologically equivalent species (neutral model) or of generalist and specialist species (specialization model), and explored the impact of the overall reduction, patch conversion or alteration of an original habitat into one or several other habitats of different total carrying capacity on the community metrics at equilibrium. Our simulations reveal strong interactions between the community model considered (neutral or specialization model) and the type of habitat change. Under neutrality, the impact of habitat changes on richness can be approached by a power law species–individual relationship (SIR), which may at constant density be simplified into the widely used power law species–area relationship (SAR), independent of the type of change. However, in the presence of generalist and specialist species, we found that 1) while habitat reduction in area also leads to approximately power law SIRs and SARs, 2) patch conversion and alteration have more complex effects on regional species richness, and 3) habitat alteration elicits the functional homogenization of communities, involving a decrease of their average level of specialization.

Scale- and taxon-dependent biodiversity patterns of dry grassland vegetation in Transylvania

Patterns of biodiversity may vary across spatial scales and between taxonomic groups; therefore, specific studies are needed to provide insights into factors driving community structure. Semi-natural grasslands are among the most biodiverse ecosystems, providing a suitable model for examining key ecological mechanisms. We analysed dry grasslands in Transylvania (Romania), which harbor extraordinarily species-rich plant communities, including the global maxima for two small grain sizes. We sampled data of vascular plants, bryophytes, and lichens in both nested and separate plots. We used soil, topographic, climatic, and land-use variables as predictors. Species richness at seven grain sizes (0.0001–100m2) was modeled as a function of these predictors by generalized linear models, followed by multimodel inference over all possible variable combinations with AICc. We also fitted power-law species–area relationships (SARs), both across the full range and for each transition of two subsequent plot sizes, as they provide a way of assessing β-diversity (through z-values) and its dependence on environmental variables. We found large differences in factors between scales and taxonomic groups, which generally supports the hypothesis that niche-related variables are important at very fine scales, while heterogeneity and disturbance-associated parameters become influential at larger scales. We explained the differences among the responses of taxonomic groups by their ecology. The exponents of the power-law SARs (z) for total richness were higher than in most other European dry grasslands, demonstrating that β-diversity is also extraordinary here. Further, the z-values showed strong and unexpected scale dependence, peaking at 0.01–0.1m2, and exponentially decreasing above these grain sizes. In conclusion, our study highlights the strong scale dependence of diversity-environment relationships, both in the case of α- and β-diversity, while emphasizing the importance to study multiple taxonomic groups.

Species–fragmented area relationship

The species-area relationship (SAR) gives a quantitative description of the increasing number of species in a community with increasing area of habitat. In conservation, SARs have been used to predict the number of extinctions when the area of habitat is reduced. Such predictions are most needed for landscapes rather than for individual habitat fragments, but SAR-based predictions of extinctions for landscapes with highly fragmented habitat are likely to be biased because SAR assumes contiguous habitat. In reality, habitat loss is typically accompanied by habitat fragmentation. To quantify the effect of fragmentation in addition to the effect of habitat loss on the number of species, we extend the power-law SAR to the species-fragmented area relationship. This model unites the single-species metapopulation theory with the multispecies SAR for communities. We demonstrate with a realistic simulation model and with empirical data for forest-inhabiting subtropical birds that the species-fragmented area relationship gives a far superior prediction than SAR of the number of species in fragmented landscapes. The results demonstrate that for communities of species that are not well adapted to live in fragmented landscapes, the conventional SAR underestimates the number of extinctions for landscapes in which little habitat remains and it is highly fragmented.

Unraveling the drivers of community dissimilarity and species extinction in fragmented landscapes

Communities in fragmented landscapes are often assumed to be structured by species extinction due to habitat loss, which has led to extensive use of the species-area relationship (SAR) in fragmentation studies. However, the use of the SAR presupposes that habitat loss leads species to extinction but does not allow for extinction to be offset by colonization of disturbed-habitat specialists. Moreover, the use of SAR assumes that species richness is a good proxy of community changes in fragmented landscapes. Here, we assessed how communities dwelling in fragmented landscapes are influenced by habitat loss at multiple scales; then we estimated the ability of models ruled by SAR and by species turnover in successfully predicting changes in community composition, and asked whether species richness is indeed an informative community metric. To address these issues, we used a data set consisting of 140 bird species sampled in 65 patches, from six landscapes with different proportions of forest cover in the Atlantic Forest of Brazil. We compared empirical patterns against simulations of over 8 million communities structured by different magnitudes of the power-law SAR and with species-specific rules to assign species to sites. Empirical results showed that, while bird community composition was strongly influenced by habitat loss at the patch and landscape scale, species richness remained largely unaffected. Modeling results revealed that the compositional changes observed in the Atlantic Forest bird metacommunity were only matched by models with either unrealistic magnitudes of the SAR or by models ruled by species turnover, akin to what would be observed along natural gradients. We show that, in the presence of such compositional turnover, species richness is poorly correlated with species extinction, and z values of the SAR strongly underestimate the effects of habitat loss. We suggest that the observed compositional changes are driven by each species reaching its individual extinction threshold: either a threshold of forest cover for species that disappear with habitat loss, or of matrix cover for species that benefit from habitat loss.

Database Species-Area Relationships in Palaearctic Grasslands

The Database Species-Area Relationships in Palaearctic Grasslands (GIVD ID EU-00-003) is an initiative of the European Dry Grassland Group (EDGG) and primarily functions as repository for all data sampled during the EDGG Research Expeditions. During these expeditions two types of highly standardised sampling of dry grassland vegetation in the Palaearctic realm are carried out: (i) nested-plot sampling on squares of 0.0001, 0.001, 0.01, 0.1, 1, 10, and 100 m2; (ii) additional normal releves of 10-m2 plots. For all plot sizes, the terricolous vascular plants, bryophytes, and lichens are recorded that are superficially present (shoot presence). Additionally, for all 10-m2 plots species cover is estimated directly in percent and a wide range of topographic, soil, and land use parameters is determined. Five such expeditions have been carried out so far (2009: Transylvania, Romania; 2010: Central Podolia, Ukraine; 2011: NW Bulgaria; 2012a: Sicily, Italy; 2012b: N Greece). Additionally, the database contains similar nested-plot data from published and unpublished sources covering dry grasslands in Czech Republic, Estonia, Germany, the Netherlands, Russia, Sweden, Switzerland, and the United Kingdom. The vegetation classes Festuco-Brometea and Koelerio-Corynephoretea prevail, but there are also some data from Mediterranean grasslands. Presently, the database contains data from 402 nested-plot series plus 325 separate 10m2 plots. Data from future EDGG Expeditions will be added and we are open to add other nested-plot data from any type of grassland in the Palaearctic. This huge collection of nested-plot data is very valuable for the study of species-area relationships (SARs) in grasslands and how their function types and parameters (e.g. the z-values of the power-law SARs) depend on grassland type, region, and taxon considered. The 10-m2 plots from the EDGG Expeditions (from inside and outside the nested plots) are an important contribution to consistent large-scale classifications as they were sampled by using a uniform plot size, recording also non-vascular plants, and consistently determining a set of plot-based plot-based environmental variables. The dataset will be available to the scientific public based on individual arrangements.

SPECIES-AREA RELATIONSHIP FOR POWER-LAW SPECIES ABUNDANCE DISTRIBUTION

We studied the mathematical relations between species abundance distributions (SADs) and species-area relationships (SARs) and found that a power-law SAR can be generally derived from a power-law SAD without a special assumption such as the "canonical hypothesis". In the present analysis, an SAR-exponent is obtained as a function of an SAD-exponent for a finite number of species. We also studied the inverse problem, from SARs to SADs, and found that a power-SAD can be derived from a power-SAR under the condition that the functional form of the corresponding SAD is invariant for changes in the number of species. We also discuss general relationships among lognormal SADs, the broken-stick model (exponential SADs), linear SARs and logarithmic SARs. These results suggest the existence of a common mechanism for SADs and SARs, which could prove a useful tool for theoretical and experimental studies on biodiversity and species coexistence.

What causes geographical variation in the species-area relationships? A test from forests in China

Th e increase of species richness with sampling area and the decrease with latitude and altitude are two of the most frequently studied patterns in biogeography. However, few studies have simultaneously examined these two patterns to investigate how species – area relationships (SAR) vary with latitude and altitude. In this study, we explore the spatial patterns of SAR in forests in China by investigating numbers of species by life form group (trees, shrubs and herbs) in 32 nested plots from 12 mountains ranging from 18.7 ° N to 51.9 ° N in latitude and from 300 to 3150 m in altitude. Th e slopes of the power law SAR ( z -values) decreased with increasing latitude for all life forms except herbaceous plants, and also decreased with increasing altitude for all life forms but not for shrubs. Latitude and altitude, as well as their interactions, together explained 65.4, 61.8, 48.9 and 45.3% of the variation in z -values for overall species, trees, shrubs and herbaceous plants, respectively. In addition, actual evapotranspiration aff ected SAR signifi cantly, but this eff ect varied signifi cantly among life forms. We concluded that there are signifi cant geographical patterns of SAR for China ’ s forests, which is primarily controlled by energy availability.

Questioning Israel's Great Biodiversity—Relative to Whom? A Comment on Roll et al., 2009

Each evolutionary-independent province has its own mainland species area relationship (SPAR). When using the power law SPAR (S = cAz), separate mainland SPARs are parallel in a log-log space (similar z value), yet they differ in species density per unit area (c value). This implies that there are two main SPAR-based strategies to identify biodiversity hotspots. The first treats all mainland SPARs of all provinces as if they form one global SPAR. This is the strategy employed by Roll et al. (2009) when questioning Israel's high biodiversity. They concluded that Israel is not a global biodiversity hotspot. Their results may arise from the fact that Israel's province, the Palaearctic, is relatively poor. Therefore, countries from richer provinces, whose mainland SPAR lies above the Palaearctic SPAR, are identified as global hotspots. The second strategy is to construct different mainland SPARs for each province and identify the provincial hotspots. In this manuscript I ask whether Israel's biodiversity is high relative to other countries within its province. For six different taxa, I analyzed data for Palaearctic countries. For each taxon, I conducted a linear regression of species richness against the country's area, both log transformed. The studentized residuals were used to explore Israel's rank relative to all other Palaearctic countries. I found that Israel lies above the 95th percentile for reptiles and mammals and above the 90th percentile for birds. Therefore, within the Palaearctic province, Israel is indeed a biodiversity hotspot.

Effects of area, temperature and geometric constraints on elevational patterns of species richness: a case study in the Mountain Taibai, Qinling Mountains, China

Aims Recent studies have illustrated that area, climate and geometric constraints were the main determinants of elevational patterns of species richness; however, the relative importance of these factors is unknown because these factors co-vary with elevation. Based on these factors, the power law species-area relationship (SAR), the metabolic theory of ecology (MTE) and the mid-domain effect hypothesis (MDE) have been proposed to explain elevational patterns of species richness. Our objective is to compare the relative performance of SAR, MTE and MDE in shaping elevational patterns of species richness, using vegetation and climatic data from Mt. Qinling Mountains as a case study. Methods We used a database, Distribution of Plants in Mt. Taibai, composed of 2 132 plant species, to derive species richness values for different plant groups. A digital elevation model was used to calculate the area of each elevational band. Eighteen data loggers were set along south and north slopes and at different elevations to record air temperature. RangeModel software was applied to predict species richness of each elevational band, based on the MDE hypothesis. We then compared the explanatory strengths of SAR, MTE and MDE models and used variation partition and stepwise regression to assess their relative importance in shaping elevational patterns of species richness. Important findings Plant species richness followed a unimodal pattern; however, species richness of each plant group peaked at a different elevational band. As single predictors, SAR, MTE, and MDE explained 66.4%, 19.8% and 37.9% of the variation in species richness, respectively. Together they explained 84.6% of the variation. When

PACT in practice: comparative historical biogeographic patterns and species-area relationships of the Greater Antillean and Hawaiian Island terrestrial biotas

Aim To compare the evolutionary and ecological patterns of two extensively studied island biotas with differing geological histories (the Hawaiian Islands and the GreaterAntilles).We evaluated the results from PACT (phylogenetic analysis for comparing trees), an innovative approach that has been proposed to reveal general patterns of biotic expansion (between regions) and in situ (within a region) diversification, as well as species‐area relationships (SAR) and the taxon pulse dynamic. Location The Hawaiian Islands and Greater Antilles. Methods We used the PACT algorithm to construct general area cladograms and identified biotic expansion and in situ nodes. We analysed the power-law SAR and relative contribution of biotic expansion and in situ diversification events using power-law and linear regression analyses.

Biodiversity scales from plots to biomes with a universal species–area curve

Classic theory predicts species richness scales as the quarter-power of area, yet species-area relationships (SAR) vary widely depending on habitat, taxa, and scale range. Because power-law SAR are used to predict species loss under habitat loss, and to scale species richness from plots to biomes, insight into the wide variety of observed SAR and the conditions under which power-law behavior should be observed is needed. Here we derive from the maximum entropy principle, a new procedure for upscaling species richness data from small census plots to larger areas, and test empirically, using multiple data sets, the prediction that up to an overall scale displacement, nested SAR lie along a universal curve, with average abundance per species at each scale determining the local slope of the curve. Power-law behaviour only arises in the limit of increasing average abundance, and in that limit, the slope approaches zero, not (1/4). An extrapolation of tree species richness in the Western Ghats to biome scale (60,000 km(2)) using only census data at plot scale ((1/4) ha) is presented to illustrate the potential for applications of our theory.

Cost-effective conservation decisions are robust to uncertainty in the species–area relationship

Guilhaumon et al. (1) use an extensive dataset to determine the most appropriate functional form for species–area relationships (SARs) among terrestrial plants and vertebrates. Their discovery that the traditional power-law relationship is not the most appropriate model in the majority of ecoregions raises compelling macroecological questions. However, their subsequent conservation analyses are based on outdated hotspot methods (2), and the “significant concerns” they raise about the use of power-law SARs in conservation prioritization may therefore be premature.

Incipient criticality in ecological communities.

In ecology, there have been attempts to establish links between the relative species abundance (RSA), the fraction of species in a community with a given abundance, and a power-law form of the species area relationship (SAR), the dependence of species richness on sampling area. However the SAR and other patterns in ecology often do not exhibit power-law behavior over an appreciable range of scales. This raises the question whether a scaling framework can be applied when the system under analysis does not exhibit power-law behavior. Here, we derive a general finite-size scaling framework applicable to such systems that can be used to identify incipient critical behavior and links the scale dependence of the RSA and the SAR. We confirm the generality of our theory by using data from a serpentine grassland plot, which exhibits a power-law SAR, and the Barro Colorado Island plot in Panama, whose SAR shows deviations from power-law behavior at every scale. Our results demonstrate that scaling provides a model-independent framework for analyzing and unifying ecological data and that, despite the absence of power laws, ecosystems are poised in the vicinity of a critical point.