A hierarchical theory of macroecology


Correspondence: E-mail: sophia.passy@uta.edu


The relationships of local population density (N) with body size (M) and distribution (D) have been extensively studied because they reveal how ecological and historical factors structure species communities; however, a unifying model explaining their joint behaviour, has not been developed. Here, I propose a theory that explores these relationships hierarchically and predicts that: (1) at a metacommunity level, niche breadth, population density and regional distribution are all related and size-dependent and (2) at a community level, the exponents b and d of the relationships N ~ M  b and N ~ D  d are functions (f) of the environment and, consequently, species richness (S), allowing the following reformulation of the power laws: N ~ M  f(S) and N ~ D f(S) . Using this framework and continental data on stream environment, diatoms, invertebrates and fish, I address the following fundamental, but unresolved ecological questions: how do species partition their resources across environments, is energetic equivalence among them possible, are generalists more common than specialists, why are locally abundant species also regionally prevalent, and, do microbes have different biogeography than macroorganisms? The discovery that community scaling behaviour is environmentally constrained calls for better integration of macroecology and environmental science.


The scaling relationships of population density with body size and distribution have been the subjects of numerous and ongoing investigations (White et al. 2007; Borregaard & Rahbek 2010) because they provide insight into the ecological and historical factors that structure organismal communities and influence the patterns of resource utilisation, species turnover and regional biodiversity. The power function of population density (N) vs. body size (M, measured here as biovolume or weight), i.e. M  b (= scaling exponent), reflects how energy flows in communities of trophically similar species. In particular, invariance of exponent b around −0.75 implies energetic equivalence among populations of differently sized species (Damuth 1981; Enquist et al. 1998; Li 2002; Cermeño et al. 2006), whereas its variability indicates that the species taking disproportionately more of the shared resources differ in size across localities and regions (Brown & Maurer 1986; Blackburn & Gaston 1997; Cyr 2000; Schmid et al. 2000; McGill 2008; Passy 2008b). Although competition, habitat productivity and complexity, and phylogenetic relatedness have been implicated in the variability of exponent b (Brown & Maurer 1986; Nee et al. 1991; Cyr et al. 1997; Schmid et al. 2002; Russo et al. 2003), a general understanding of the physiological, ecological and environmental constraints on the density-body size relationship and the role of scale is lacking (Cyr 2000; White et al. 2007).

A relationship between population density (N) and distribution (D, measured here as occurrence and geographical range), i.e. D  d (= scaling exponent), showing that locally abundant species are also regionally common, was found decades ago (Hanski 1982) and extensively investigated across scales and organismal groups (Blackburn et al. 1997; Gaston et al. 2000; Blackburn et al. 2006; Zuckerberg et al. 2009; Webb et al. 2011); yet, its causes are still debated (Borregaard & Rahbek 2010). The arguments that species with wider resource breadths (Brown 1984) or adaptations to broadly distributed and locally abundant resources (Hanski et al. 1993) were more likely to attain both high local density and regional presence were put forth by the resource use and resource availability hypotheses respectively. Demographical responses to environmental gradients (Holt et al. 1997) and metapopulation processes of colonisation and extinction (Hanski 1982) were also considered responsible for producing positive abundance-distribution correlations.

The relationships of population density with body size and distribution are generally studied independently of one another, but see Brown & Maurer (1987), Gaston & Lawton (1988), Brown (1995), Blackburn & Gaston (2001) and Passy (2008b), and despite years of research, very little is known about their joint behaviour. Here, I address this deficiency and propose a hierarchical theory, which predicts existing, but group-specific relationships among body size, niche breadth, population density and distribution and an increasing role of the environment as these relationships are viewed from a metacommunity to a community perspective (Fig. 1). The metacommunity model is built on earlier work (Brown 1984; Gaston & Lawton 1988; Passy 2008b), but its conceptual framework is novel; the community model, on the other hand, allowing assessments of how the environment and biodiversity shape community scaling behaviour, is completely novel.

Figure 1.

The hierarchical theory. (a, c) Metacommunity model: body size and niche breadth control distribution directly and indirectly through maximum (max) population density; the positive relationship between max density and distribution reflects their equivalent response to common driving forces. (b, d) Community model: pathways of environmental and richness control of scaling exponents b and d. Richness correlates with body size, the size-dependent variables in (a, c), and the exponents b and d of their relationships, which should be correlated. The hierarchical model makes different predictions for organisms varying in size and dispersal mode. Arrows = causal links (only solid arrows are tested statistically), double-headed arrows = correlations, broken lines = concurrent responses, positive (+) and negative (−) relationships.

Abundance is measured here as maximum number of individuals per area or maximum proportion relative abundance across all collections at a metacommunity level (continental scale, Suppl. Figure S1a) and number of individuals per area or proportion relative abundance at a community level (stream reach scale, Suppl. Figure S1b). Distribution is defined in two ways – as regional occurrence and geographical range (Suppl. Figure S2). Population density and distribution have been expressed as both a predictor and a response of one another (Borregaard & Rahbek 2010). In this study, their relationship is considered scale-dependent – at a metacommunity level, maximum abundance is the predictor because it reflects the species' physiological ability to cope with the environment, grow in numbers and then successfully disperse. At a community level, local population density is the response because as a local property, it is governed by the regional factor, i.e. distribution.

The Hierarchical Theory

Metacommunity model

Metacommunities function over large scales, where the importance of the local environment is diminished. At this level, species abundance and distribution are constrained by species traits, including body size and niche breadth, which are products of evolutionary forces (Fig. 1a and c). The strong influence of body size on species properties is evident across scales and levels of biological organisation, i.e. on niche breadth (organismal level), local density (population level) and regional distribution (metapopulation level). Body size controls metabolic and growth rates (Peters 1983; Finkel 2001) and with this, population density and regional distribution (Gaston & Lawton 1988). Large species require more energy and typically maintain smaller populations, which produce fewer potential dispersers with a lower likelihood of reaching suitable habitats and expanding the overall distribution (Passy 2008b). However, a positive scaling of density with body size was also reported, but generally in macroorganisms, e.g. in some plants, fish, birds and mammals (Brown & Maurer 1986). In some marine invertebrates, the large body size is associated with a greater reproductive capacity, and consequently, with a higher density and distribution (Reaka et al. 2008).

Body size can also impact distribution by affecting dispersal (e.g. the distance an individual can travel), but as dispersal is not measured here, this pathway is depicted in the proposed conceptual model as a direct effect of size on distribution (Fig. 1a and c). It is further noted that depending on the mode of dispersal, the body size-distribution relationship may vary from negative to positive (Etienne & Olff 2004). Specifically, in passive dispersers, the large body size limits distribution (Fig. 1a), e.g. in algae it increases the sinking velocity, which explains why dispersal in stream diatoms scales inversely with cell size (Passy 2007b). In active dispersers, the body size-distribution relationship is often positive (Fig. 1c), as shown for some fish, birds and mammals, because it is associated with a greater colonisation success (Brown & Maurer 1987, 1989; Luiz et al. 2012).

Niche breadth, including tolerance to physical stress and extreme environments, is size-dependent across organismal groups. In microbes, small species sustain growth along disturbance and trophic gradients and have broad niches (Cattaneo et al. 1998; Passy & Larson 2011), whereas large species require high nutrient supply and low shear stress for biomass accumulation and have narrow niches (Pringle 1990; Passy 2007a). In animals, this pattern appears to be reversed – the large size is linked to resource- (Brown 1995), habitat- (Griffiths 2010) and environmental generalism (Luiz et al. 2012). Consistent with Brown's resource use hypothesis (Brown 1984), niche breadth is regarded here as a constraint on distribution, which has already been demonstrated in stream environments (Heino 2005; Heino & Soininen 2006). However, niche breadth also determines local population density because species with broad niches can maintain positive growth under stressful conditions, e.g. resource limitation (Passy & Larson 2011). According to the metacommunity model, body size and niche breadth control distribution directly and indirectly through population density. In small and passively dispersing organisms, abundance and distribution respond negatively to body size, but positively to niche breadth (Fig. 1a), whereas in larger and actively dispersing animals, they may be positive functions of both body size and niche breadth (Fig. 1c). The equivalent response of population density and distribution to common factors underlies their positive relationship.

Community model

The environment causes variability in exponents b and d through its influence on: (1) population density, i.e. species reach high densities in favourable conditions; (2) species richness, i.e. by controlling the number of available niches and (3) body size (Fig. 1b and d). Evidence for the paramount impact of the environment on both richness and body size is found in two well-documented and concurrent biogeographical patterns, namely the latitudinal diversity gradient or the pole-ward decline of species richness and Bergmann's rule or the pole-ward increase of body size. The latitudinal diversity gradient is nearly universal (Hillebrand 2004) and as Bergmann's rule is corroborated in the majority of vertebrates (Millien et al. 2006), we can expect in these communities low richness and large body sizes in high latitude environments of low temperature and productivity and vice versa, high richness and small body sizes in the warm productive low latitudes. This has been directly observed in Northwest Atlantic fish, reaching maximum mean length and lowest diversity at the highest latitude (Fisher et al. 2010). Furthermore, this study reported a strong negative response of mean length to species richness across Atlantic and Pacific fish communities. Relationships among environment, richness and body size are also found in communities that deviate from the classical latitudinal pattern and are not subject to Bergmann's rule. Species richness in the stream biofilm is governed by resource supply and follows the unique latitudinal distribution of resources (Passy 2010). The resource-driven richness increase in algae is not indiscriminate to body size either, but unlike the more complex organisms already discussed, it favours large sizes, as predicted by the benthic model of coexistence in three-dimensional communities (Passy 2008a).

In summary, the environmental constraints on species richness and body size will lead to a predictable variability of the size-dependent exponents b and d (Fig. 1b and d). In organisms with a positive richness-body size relationship, such as algae, richness will correlate positively with exponent b, but negatively with exponent d and so will environments that promote richness, e.g. resource supply. The two exponents will be negatively correlated, indicating that rich communities will have more biomass derived from large and rare species (Fig. 1b). Notably, body size in these species is predicted to have a negative effect on niche breadth, density and distribution, i.e. large species will tend to be specialists with low densities and narrow distributions (Fig. 1a). In organisms with a negative richness-body size relationship, expected among vertebrates with large sizes often associated with broad niches, high densities and large distributions (Fig. 1c), the opposite pattern will be observed – rich communities will have more biomass derived from small and rare species and exponents b and d will be positively correlated (Fig. 1d). In these communities, environmental conditions supporting high richness, e.g. productivity and temperature, will correlate negatively with both exponents. In other words, environmentally driven changes in species richness and body size will cause predictable, but group-specific changes in exponents b and d.

Material and Methods

The National Water-Quality Assessment (NAWQA) Program datasets

Data on environmental properties and community composition of stream diatoms, invertebrates and fish from most major watersheds and aquifers in the US are generated by the NAWQA Program of the US Geological Survey (see http://water.usgs.gov/nawqa/studyu.html). Field protocols are described in detail in http://pubs.usgs.gov/of/2002/ofr-02-150/pdf/ofr02-150.pdf. Individuals are identified to the lowest possible taxonomic category, which is generally species in the diatom and fish data, but genus and family in the invertebrate data.

Periphytic diatoms

There are 1400 algal samples with a total of 1237 diatom species, collected from richest-targeted habitats (RTH), which are the most intensively sampled and taxonomically diverse stream benthic habitats. Between 1993 and 2003, the USGS sampled 720 distinct stream localities in the US, spanning 24 latitudinal and 52 longitudinal degrees. Biovolume (μm3), either measured in the sample or calculated for the species, and population density (cells · cm−2) of all constituent species as well as the number of all species (i.e. richness) are recorded for each sample. The sample biovolume information is used in testing the community model, whereas species' average biovolume, in testing the metacommunity model. Additional data on each species include maximum population density across all 1400 samples, and distribution, measured as both occurrence in the 720 studied localities and geographical range (Suppl. Figure S2). Stream physico-chemical properties for the month of algal collection and watershed information on human population density, landscape, land use and soil composition are available for a subset of 1370 streams from 703 localities with 1227 species (Suppl. Table S1). This subset is used in testing the metacommunity model and assessing the environmental influence in the community model. The relationships between richness and exponents b and d in the community model are analysed with the whole dataset.

Benthic invertebrates

There are 3719 RTH samples with a total of 2078 invertebrate taxa, collected between 1993 and 2011 from 1866 stream localities, spanning 42 latitudinal and 87 longitudinal degrees. Information is available on species population density (individuals · m−2) and richness. For each taxon, the following are determined: (1) maximum population density across all 3719 samples and (2) distribution, measured as both occurrence in the 1866 studied localities and geographical range. Environmental information is available for a subset of 2104 samples across 636 streams with 1739 taxa. The subset is used as described for diatoms. The relationship between richness and exponent d in the community model is analysed with the whole dataset.


There are 2383 samples with a total of 559 fish species, collected between 1993 and 2010 from 1105 stream localities, spanning 42 latitudinal and 87 longitudinal degrees. Body weight (g) is measured, often multiple times within and across samples, for 515 species. The average weight for the genus (or on a few occasions, for the family) is assigned to the 44 species with no weight data. As some samples lack body weight data, the species' average body weight is used to test both the metacommunity and community models. Additional information on each species includes maximum proportion relative abundance, derived from the sample within the 2383 sample dataset where the species attained the greatest proportion, and distribution, measured as occurrence in the 1105 streams and geographical range. Species richness is calculated for all samples. A subset of 488 species from 1443 samples across 417 streams with environmental information is used as described for diatoms. The relationships among richness, exponent d and parameter b 2 (see below) in the community model are explored with the whole dataset.

Statistical analyses

Environmental description

Principal component analysis (PCA) of 32 environmental variables (Suppl. Table S1) and K-means clustering are performed to identify sites with environmentally common vs. rare conditions using SYSTAT 12.02 (SYSTAT Software, Inc., Chicago, IL, USA). These analyses are based on physico-chemical stream variables, averaged over the study period (1993–2003) for streams with multiple samplings, and watershed properties (soil, landscape and land use).

Measuring niche breadth

Niche breadth is calculated as the species' root mean square standard deviation across the first four axes of canonical correspondence analysis, CCA (the RMSTOL metric in CANOCO) (ter Braak & Smilauer 2002). The species dataset in CCA comprises the ln-transformed species densities or proportions, averaged across all samples taken from a locality. The environmental dataset in CCA encompasses the first six principal components (PC) of the aforementioned PCA, explaining 84% of the variability in the environmental data. Using PCs in CCA instead of raw environmental variables reduces the dimensionality and eliminates the collinearity in the predictor set.

Measuring environmental preference

Environmental preference is defined as the proportion of common to all sites (P) where a species occurs. The relationship between niche breadth (NB) and P is modelled with a Gaussian response curve (TableCurve 2D 5.01; SYSTAT Software, Inc., Chicago, IL, USA): NB aexp[−0.5(− b)2/c 2], where = amplitude or maximum niche breadth (NB max), = optimum or the proportion (P u ) yielding NB max and = horizontal spread, which can be defined as one standard deviation (SD) from the optimum (ter Braak & Looman 1995).

Regressions and structural equation modelling

Ordinary least squares (OLS) regressions and structural equation modelling at a metacommunity level are undertaken to assess the relationships among body size (M), NB, maximum local abundance (N max) and distribution (D). The implementation of OLS regressions is justified by the causality assumptions of the hierarchical theory, whereby the predictor is viewed as the cause of the response (Smith 2009). In fish, the parameters of the quadratic regression: b 0 + b 1ln b 2(ln M)2, where NB, ln N max or ln D, are used to calculate the body weight (M u ) associated with, respectively, the greatest NB, maximum abundance or distribution as follows: M u  −b 1 /(2b 2) (ter Braak & Looman 1995). Regressions are also performed at a community level for parameter estimation, i.e. the parameter b 2 of the quadratic abundance-weight relationship in fish and the slopes b and d of the ln-ln relationships of local population density/abundance (N) with M and D : ln b 0 + bln M and ln d 0 + dln D, where b 0 and d 0 are the respective intercepts. Parameter b 2 and slopes b and d are examined as functions of environmental variables and species richness by means of regression and variance partitioning. All analyses are carried out with SYSTAT 12.02.


Site and species group designation

Eutrophication, resulting from agriculture and urbanisation, is the major environmental gradient in US running waters, captured by the first axis of PCA of stream chemistry and watershed properties across 703 stream localities (Fig. 2, Suppl. Table S1). The first axis (PC1) accounts for 40% of the variance in the data and segregates streams with elevated nutrient levels and human impact (at the negative end of PC1) from the comparatively pristine streams with undeveloped and forested watersheds (at the positive end of PC1). The second axis explains substantially lower amount of variance in the data (15%) and isolates the Fe-rich streams with larger wetlands in the watersheds. K-means clustering using the first six principal components indicates that only PC1 contributes significantly to cluster discrimination (F-ratio = 1408.38), whereas the other five PCs have non-substantial contributions (F-ratios = 0.01 to 3.63). Consequently, only PC1 is retained in K-means clustering, which subdivides the localities into two distinct groups, i.e. large (= 495) and small (= 208), thus reflective of common and rare conditions respectively. Although both groups have overlapping geographical distributions, sites in the common group have significantly higher levels of human impact, nutrient supply and ionic strength than the more pristine sites in the rare group (Suppl. Table S1). Therefore, common conditions in US streams are eutrophic, while rare conditions are oligotrophic.

Figure 2.

Environment. Principal component analysis (PCA) of environmental variables, measured at local to watershed scale, including water chemistry, human population density, land cover and use, and soil properties, reveals two major gradients across US streams, namely eutrophication and iron enrichment (directions of increase are shown by bold arrows). Variables with comparatively strong correlations with the first two PCA axes are plotted on the ordination, but detailed information on all variables in the analysis is given in Suppl. Table S1. +N/+P = N/P fertilisation in agriculture, % Sand in soil, c = continentally common group (495 sites), r = continentally rare group (208 sites).

The proportion of common to all sites (P) where a species is detected is taken as an indicator of species' environmental preference with P close to 0 vs. 1, meaning that a species occurs exclusively in rare (pristine) vs. common (impacted) streams. Conversely, species detected in common conditions with statistically the same frequency as these conditions occur continentally, have no environmental preference. In the three organismal groups, species NB and P exhibit a comparatively strong Gaussian relationship (R 2  = 0.36 − 0.52, Suppl. Figure S3a), indicating that species occurring in common or rare conditions exclusively have the narrowest niches, whereas species with no environmental preference (intermediate P values), have the broadest niches. The latter species are defined as having P in the range of P u  ± 1SD. Species with P below or above this range have a preference for rare or common conditions respectively.

Metacommunity model

There are 1227 diatom species in this dataset with biovolume ranging between 7.41 and 1 069 835 μm3 – a span of nearly 6 orders of magnitude. The effects of the three predictors of species distribution are determined by linear and non-linear regressions. The relationship of distribution (occurrence) with maximum population density (N max) and NB is positive linear (R 2  = 0.57 and 0.55 respectively), while with biovolume it is monotonically declining (R 2  = 0.12) (Fig. 3a–c). When distribution is measured as ln geographical range (y), the response to N max is positive linear (= −0.85 + 0.67ln N max, R 2  = 0.32, < 0.00001), to NB, positive but saturating (= 0.32 + 0.84NB 0.5, R 2  = 0.92, < 0.00001 for both parameters), and to biovolume, it is negative linear (= 9.32 − 0.50ln M, R 2  = 0.07, < 0.00001). The similar behaviour of species occurrence and geographical range is due to their high correlation (R 2  = 0.96), indicating that the two metrics are good substitutes (Suppl. Figure S2a). Notably, occurrence shows stronger correlations with biovolume and density, whereas geographical range is nearly completely predicted by niche breadth. However, as occurrence displays a more gradual increase (Suppl. Figure S2a) and linear correlations with the predictors, most subsequent analyses are performed with this metric.

Figure 3.

Diatoms, testing the metacommunity model. Regressions of ln occurrence (D) against: (a) ln maximum population density (N max): ln = −2.12 + 0.41ln N max (< 0.000001); (b) ln biovolume (M): ln = 3.97 − 0.30ln M (< 0.000001) and (c) niche breadth ( NB ): ln = 0.08 + 0.03 NB (< 0.000001). (d) A structural equation model showing the paths with corresponding standardised regression coefficients and, in parentheses, coefficients of non-determination (1 − R 2) for each response variable (< 0.05 for all paths). A sample discrepancy function value of 3.35e −13 indicates an excellent model fit. E1–E3 = error terms. Number of species = 1227.

A structural equation model (SEM) testing the predictions of the metacommunity model (Fig. 1a), reveals that diatoms with the smallest biovolume also have the broadest niche, the highest maximum population density and the largest distribution (Fig. 3d). The SEM explains 8, 32 and 73% of the variance in niche breadth, maximum population density and occurrence respectively. Species with broad niches and no environmental preference have the greatest occurrence and geographical range and these differences are highly significant (Suppl. Figure S3b). From the diatoms with narrower niches, those with a preference for common conditions significantly exceed in occurrence and geographical range species with a preference for rare conditions (Suppl. Figure S3b).

Similar patterns emerge in the continental data on benthic invertebrate (1739 taxa) and fish (488 species) distributions. Like diatoms, both invertebrates and fish with the broadest niches display the largest distributions (both occurrence and geographical range) and the highest maximum abundance, measured either as individuals per m2 (invertebrates) or proportion relative abundance (fish) (Suppl. Figures S3c–d, S4 and S5). However, unlike diatoms, invertebrates and fish with a preference for rare vs. common conditions exhibit statistically equivalent distributions (both occurrence and geographical range). The invertebrate and fish SEMs account for 74 and 72% of the variance in distribution respectively. Fish weight is a significant predictor of niche breadth, maximum relative abundance and distribution (Suppl. Figures S5b and S6), but in the SEM, its influence on distribution is subsumed by the other two predictors (Suppl. Figure S5d). Unlike diatoms, fish body size is a quadratic determinant of all these variables, i.e. fish with the broadest niches, greatest relative abundance and widest distributions are of intermediate weights (Suppl. Figures S5b and S6), estimated at 62 g for maximum niche breadth, 41 g for maximum local abundance and 51 or 57 g for maximum distribution when measured as occurrence or geographical range respectively (the fish weight range is between 0.1 and 7229 g with an average of 135 g and a median of 8 g).

Community model

Regression parameters vs. species richness

Of the 1400 examined diatom samples, 35% show significant ln-ln relationships of population density with biovolume (slope b ≠ 0, average R 2  = 0.15), 52%, with occurrence (slope d ≠ 0, average R 2  = 0.17), and 21%, with both size and occurrence at < 0.1. The 490 significant slope b values are overwhelmingly negative with the exception of nine positive cases, whereas the 728 significant slope d values are positive with only 10 negative exceptions. The positive b and negative d slopes are outliers in all subsequent regressions and are removed together with nine other extreme b and one extreme d values. The relationships of slopes b and d with richness (S) are comparatively strong (R 2  = 0.39 − 0.68), highly significant (< 0.000001) and non-linear (Fig. 4a and b), allowing the following reformulation of the power functions: M −1/S and D −ln S respectively. The two slopes are negatively correlated (Pearson = −0.53, < 0.000001, = 296).

Figure 4.

Diatoms, testing the community model. The slopes of the regressions of ln population density vs. ln biovolume (slope b) (a) and ln population density vs. ln occurrence (slope d) (b) are treated as a response of diatom species richness and fit with non-linear models, given in the figures. № = number of communities.

Additional tests of the community model are performed with the invertebrate and fish datasets. In invertebrates, slope d is significant (< 0.1) in 2354 (63%) of the 3717 samples with richness ≥ 3 species (at least three species are required to estimate the two parameters of the linear equation) having an average R 2 of 0.18. The significant slope d values are negative in only 11 samples, identified as outliers and removed prior to regression. Slope d responds significantly to richness (< 0.000001), permitting the same reformulation of the power function in invertebrates as in diatoms: D −ln S (Suppl. Figure S7a).

In fish, the quadratic term (b 2) of the abundance-body weight relationship is significant in 287 (13%) of the 2194 communities with richness ≥ 4 species (at least four species are necessary to estimate the three parameters of the quadratic equation). Of these values, 189 (66%) are negative, while the rest are positive, describing a unimodal vs. a U-shaped response of relative abundance to weight respectively. Parameter b 2 is highly variable at low richness, but its regression estimate is positive, indicating that species at the ends of the size spectrum tend to reach the highest biomass in poor communities (Suppl. Figure S8a). Parameter b 2 decreases significantly with richness, becoming generally negative, which suggests that the most abundant fish in speciose communities are of intermediate body sizes. The fish relative abundance-distribution relationship is significant (< 0.1) in only 323 (14%) of the 2273 samples with  3 (average R 2  = 0.38). From the significant slope d values, 76 (24%) are negative. After the removal of eight extreme values, the best fit of slope d is generated by an inverse function of S (< 0.000001), translating into: D −1/S (Suppl. Figure S8b).

Regression parameters and species richness vs. environment

Although the measured environment provides direct information on resource supply only for diatoms, it captures many important niche characteristics of all three studied groups, e.g. temperature, pH, ionic strength and habitat (Suppl. Table S1), and its role is assessed, as defined in Fig. 1b and d. Step-wise multiple regressions of diatom slopes b and d, invertebrate slope d, and fish parameter b 2 and slope d against water chemistry and watershed properties select those variables that are the strongest predictors of richness as well. In diatoms, these variables include micronutrient concentration (Fe and Mn), per cent watershed covered by wetlands, surface water, forest and barren land and amount of N fertilisation in agriculture (Fig. 5). Notably, all selected environmental variables are directly or indirectly related to micro and macronutrient supply, e.g. wetland and surface water areas correlate positively, while soil silt content, negatively, with Fe concentration; N fertilisation in agriculture correlates positively, while forest cover, negatively, with all ions, Mn, nitrate and orthophosphate concentrations; and barren land correlates negatively with all ions. In general, environmental factors that are positively correlated with diatom slope b are also positively correlated with richness. On the contrary, positive predictors of slope d are negative determinants of diatom richness and vice versa. The covariance between richness and environment captures most of the variance in diatom slopes b and d, explained by the environment, whereas richness retains a substantial independent portion, as demonstrated by variance partitioning (Fig. 5).

Figure 5.

Diatoms, testing the community model. Relationships of (a) slope b and (b) slope d with the environment and local diatom richness. The variance of slopes b and d and the variance of diatom richness, explained by the environment are shown next to the solid grey arrows, whereas the variance of slopes b and d explained by richness, next to the solid black arrows. Pure environmental effect (next to the dotted grey arrows), pure richness effect (next to the dotted black arrows) and covariance effect of richness and environment (in the grey triangles) on slopes b and d are also given. ± = positive/negative correlation with slope b or d. Number of communities = 472 (a) and 717 (b).

In invertebrates, the environment explains 11% of the variance in slope d and 18% of the variance in richness (Suppl. Figure S7b), while richness contributes a comparatively small amount to the explained variance in slope d (5%). Watersheds subject to urbanisation and agriculture have invertebrate fauna with high values of slope d and low richness, while comparatively pristine watersheds with larger areas covered by forests and wetlands, exhibit lower values of slope d and high richness. Variance partitioning reveals that pure environment underlies the variability of slope d, whereas pure richness and the covariance effect are of a lesser importance.

In fish, the environment accounts for 38–39%, while richness explains 7–10% of the variance in parameter b 2 and slope d. The richness effect on both parameters is derived entirely from covariance with the environment (Suppl. Figure S9). Fish richness and slope d increase with temperature, ionic strength and human impact, while parameter b 2 shows the opposite response.


Metacommunity model

Two of the predictions of the metacommunity model (Fig. 1a and c) are fully confirmed in stream periphytic diatoms and fish, but partially in benthic invertebrates (due to the lack of body size data): (1) body size controls directly and/or indirectly species properties manifested from the organismal to the metapopulation level, including niche breadth, maximum local abundance and regional distribution; and (2) the strong positive relationship between abundance and distribution reflects their equivalent response to common determinants, namely body size and niche breadth. Across groups, species with the highest maximum abundance and regional prevalence possess the broadest niches; however, the influence of body size is group-specific. In diatoms, these species are small, whereas in fish, they are of intermediate body size within a very narrow range, i.e. between 41 and 62 g. Thus, the prediction for positive relationships of body size with niche breadth, abundance and distribution in macroorganisms (Fig. 1c) is not confirmed in fish. This divergence from the model expectation is attributed to the complex life history tradeoffs in fish, imposing constraints on extreme body sizes, i.e. small fish experience higher mortality and reproductive effort, while large fish reach maturity later (Gunderson 1997). Collectively, these limitations should give advantage to intermediate sizes, as seen not only here but also in fish from different areas of the marine environment, including the demersal zone and the coral reefs (Blackburn & Lawton 1994; Ackerman et al. 2004). A peak population density at intermediate threshold body size was also reported in birds and explained with the operation of energetic constraints below the threshold (i.e. increased energy requirements per unit mass) vs. energetic tradeoffs above it (i.e. energy controlled biomass-for-density tradeoff) (Brown & Maurer 1987). Evidently, the density-body size relationship in large macroorganisms is frequently unimodal, but further research is necessary to elucidate whether life history or energetic constraints or both are responsible for this pattern. Diatoms, on the other hand, conform to the model expectations – the small size is beneficial all around, promoting faster turnover rates, broader dispersal and greater disturbance resistance, all leading to high abundance and distribution. Similar inverse relationships of body size with abundance and distribution were found in herbivorous insects (Gaston & Lawton 1988), suggesting that this trend may persist among smaller organisms both protists and multicellular forms across aquatic and terrestrial environments, as predicted in Fig. 1a.

The metacommunity model sheds light on a long-standing controversy in ecology as to whether species characteristics, i.e. niche breadth (Brown 1984), or environmental properties, i.e. resource availability (Hanski et al. 1993), define the relationship of species abundance with distribution. Criticism of the resource use hypothesis points to unclarity as to why species with broader niches should exhibit greater local abundance and redundancy in comparison with the resource availability hypothesis, which explains the same patterns, but without invoking variability in niche breadth (Gaston et al. 1997). The present results disagree with this assessment of the resource use hypothesis. Across all major freshwater organismal groups, niche breadth is a dominant factor behind the variability in maximum abundance (R 2  = 0.27–0.40) and regional distribution, including occurrence and geographical range (R 2  = 0.55–0.92). On the contrary, habitat and resource availability appears to be of little consequence as species with a preference for common or rare conditions have highly significantly narrower distributions than species with no environmental preference (Suppl. Figure S3). In diatoms, species with a preference for common conditions exceed in distribution those with a preferential occurrence in the pristine, but rare habitats, whereas in invertebrates and fish, this trend disappears. Therefore, an adaptation for common environments is insufficient to confer a species broad distribution. Finally, body size underlies all relationships depicted in the metacommunity model (Fig. 3d; Figures S4c, S5d) – species with the widest niches, highest abundances and broadest distributions have optimised body sizes, i.e. small in diatoms, but intermediate in fish.

An earlier study on Finnish diatoms demonstrated that even though niche breadth was a significant predictor of regional distribution, it was secondary to niche position (a measure of how common species' habitat was) (Heino & Soininen 2006). Investigations on French riverine fish (Tales et al. 2004) and British breeding birds (Gregory & Gaston 2000) found that local density and distribution correlated with niche position, but not niche breadth. Although the use of different methods for measuring niche breadth and habitat commonness may have contributed to the divergent conclusions of these studies and the present work, the main cause is most likely the dissimilarity in taxonomic diversity and in the number and length of the underlying environmental gradients and with this, the ability to adequately measure species niche breadth. In particular, the Finnish diatom study was restricted to near pristine sites in the boreal region (Heino & Soininen 2006) and the fish study, to a small number of most common and native fish (29 species) across undisturbed, reference sites only (Tales et al. 2004). This investigation, on the other hand, is based on continental variability in climate, topography, nutrient supply and human impact as well as the occurrence of all members of a particular group, including native and introduced, common and uncommon. In the bird study (Gregory & Gaston 2000), resource variables were not explicitly incorporated, while the used descriptors, reflecting primarily land use, might have been incapable of capturing important niche properties. As recently shown, even substantial anthropogenic modifications of the terrestrial landscape, such as urbanisation, are not strong enough to generate commensurate community responses because remnant habitats are sufficient to maintain the bird community structure (Pautasso et al. 2011). In contrast, cultural eutrophication of aquatic ecosystems leads to pronounced alterations across communities (Smith & Schindler 2009), which can explain why invertebrates and fish conform to the hypothesised patterns even though their niche is defined here by habitat, but not resource variables.

The present findings also provide an answer to two fundamental, but still open questions in ecology, i.e. are resource generalists broadly distributed, while specialists, uncommon and does this pattern hold in microbial communities with theoretically unlimited dispersal (Finlay et al. 2002; Telford et al. 2006; Pither 2007; Bennett et al. 2010). As revealed here, the distribution of freshwater organisms scales strongly and positively with niche breadth, indicating that narrowing of the niche brings about a corresponding decline in distribution. Contrary to perceptions that body size diminution expands distribution, but only in larger bodied species, e.g. over 1–10 mm in length (Finlay 2002), I demonstrate that: (1) size matters even within microbial communities with small species having significantly greater distributions than large forms and (2) the influence of body size is not always linear, i.e. a decrease in body size beyond a certain optimum in fish is not beneficial for maintaining high abundance and distribution.

Community model

The community model (Fig. 1b and d) is confirmed in diatoms, but to a lesser extent in fish. The lack of body size data in invertebrates results in a partial support of the model. Richness determines the relationships of population density with body size and distribution, regardless of their shape, described by either power laws or quadratic functions. In diatoms, the environment constrains both richness and slopes b and d, but its effect on the two slopes is mostly indirect through richness. Pure environment in invertebrates and fish and environment-richness covariance in fish contribute to the explained variance in slope d and parameter b 2 (in fish), whereas richness is a weaker predictor compared to diatoms. This may be due to the fact that, unlike diatoms, invertebrates and fish encompass multiple trophic levels and habitat guilds. Richness, which gives the same weight to all taxa, regardless of their ecological differences, may underrepresent the true diversity of these communities and consequently, correlates less strongly with the scaling exponents and regression parameters. Therefore, further tests of the hierarchical theory at a functional level are necessary.

A pathway of watershed impact on stream diatom biodiversity through local control of nutrient concentrations has already been established (Passy 2010), but I show here that important community scaling relationships across freshwater groups are too part of this pathway. In diatoms, the negatively correlated slopes b and d become the flattest in productive species-rich streams with elevated nutrient concentrations due to cultural eutrophication or proximity to large and Fe-abundant wetlands. In contrast, the steepest b and d slopes are found in species-poor oligotrophic streams in undeveloped watersheds with extensive forest or barren land covers. Thus, rich communities have a greater proportion of their biomass derived from large and rare species, whereas the biomass of impoverished communities comes primarily from small and common species, as predicted (Fig. 1b). A community shift towards greater numbers of large diatoms with Fe and macronutrient enrichment is a well-documented phenomenon in many parts of the world's ocean (de Baar et al. 2005). Here, I report a similar transition across the continental stream network, evident in the positive correlations of slope b with Fe and N fertilisation. It has already been suggested that Fe controls diatom richness globally (Passy 2010) and now it becomes clear that diatom body size organisation is influenced by Fe across aquatic environments as well.

The predictable deviation of slope b from −0.75 (Fig. 4a), i.e. the condition necessary for energetic equivalence (Damuth 1981), allows estimation of the resource partitioning patterns among coexisting diatoms. Communities of about 15 species, clustered at the low end of the richness gradient, have slopes approaching −0.75. In communities of higher richness, which are the majority, large species acquire disproportionately more of the shared resources (> −0.75), whereas the opposite is true in the few communities of richness lower than 15. Previous studies on organisms, ranging from plants to mammals, demonstrated that large species monopolised greater resource amounts and attributed this to their lower energy requirements per unit biomass, tolerance to broader environmental gradients, greater mobility, weaker predation pressure and stronger aggression than small species (Brown & Maurer 1986; Pagel et al. 1991). As seen here, both small and large diatoms reach densities much higher than expected under the energetic equivalence rule, although it is much more common for large species to do so. However, most of the aforementioned reasons for this disparity are inapplicable to diatoms. The shift from small species' to large species' control of the energy flow across diatom communities is environmentally determined (Fig. 5a), which is expected under the benthic model (Passy 2008a) and the present community model (Fig. 1b). Large species are unable to grow well in oligotrophic environments (slope < −0.75), but their advantageous position in the overstory under high nutrient supply, affording unimpeded access to resources, results in substantial biomass accumulation (slope > −0.75). Conversely, small species persist across all environments due to their high tolerance to nutrient limitation and even though with reduced biomass when overgrown in eutrophic conditions, their density consistently exceeds this of large species (slope < 0). Thus, the energy distribution among differently sized diatoms is a function of environmental inputs, having an impact on reproduction, and biofilm three-dimensional spatial organisation, with an influence on both reproduction and competition.

A comparatively overlooked aspect of the density-body size relationship is that species not only consume resources but also contribute to community biomass, which is then used by higher trophic levels (Cohen et al. 2003). As established here, species of different size and distribution are responsible for biomass accrual in communities of contrasting biodiversity. Diatoms are major producers in streams and their body size organisation influences herbivore composition, e.g. invertebrate grazers preferentially ingest diatoms with sizes commensurate with their head width (Tall et al. 2006). This implies that rich diatom communities, with more equitable biomass distribution across the body size spectrum (i.e. flatter b slopes), provide food resources for a broader diversity of herbivores.

In invertebrates, the highest values of slope d are found in poor communities, which unlike diatoms, are located in impacted habitats. In contrast, pristine forested watersheds are inhabited by rich invertebrate fauna exhibiting lower values of slope d, consistent with the model prediction for a negative richness–slope d relationship (Fig. 1b). Agriculture and/or urbanisation are associated with: (1) deforestation and subsequent stream bank erosion, elevated stream turbidity and siltation and decreased leaf litter inputs; (2) an increased area of impervious surfaces, affecting the intensity of urban runoffs and (3) benthic habitat loss and homogenisation, all with negative consequences for invertebrate community richness (Allan 2004; Walsh et al. 2007; Bêche & Statzner 2009; Death & Collier 2010). Here, we see that these stream alterations are also correlated with significant density reductions in regionally rare invertebrates, evident in the significant increase in slope d (Suppl. Figure S7b). Diatom local richness, on the other hand, is not as sensitive to the aforementioned habitat modifications (Passy & Blanchet 2007), but responds positively to nutrient enrichment, which explains why diatoms and invertebrates display contrasting patterns along the anthropogenic impact gradient.

In fish, temperature and land use have strong effects on richness as well as parameter b 2 and slope d. Consistent with previous observations (Oberdorff et al. 1995; Knouft & Page 2011), streams of higher temperature, found at lower elevations, have greater richness. As these streams are often located in human-modified watersheds, fish richness also responds positively to agriculture, which too has been previously reported (Strayer et al. 2003). On the contrary, shrublands occur in watersheds of higher elevation and lower temperature and they are a negative predictor of fish richness. The comparatively limited dispersal of fish and their strong response to stochastic flow disturbance (Grossman et al. 1998) are probably the reasons why parameter b 2 and slope d are generally non-significant. Their greater variability at low richness suggests that species-poor fish communities are more susceptible to environmental stochasticity and thus more unpredictable. In comparison, fish parameter b 2 and slope d are highly significant in the metacommunity, where they are derived from the continental metapopulations, transcending the local environmental vagaries. Diatom and invertebrate communities, on the other hand, even though subjected to the same environmental fluctuations as fish, display generally significant scaling exponents, varying predictably along the richness- and habitat gradients. There are multiple reasons why diatom and invertebrate patterns persist at a community level despite local disturbance, including shorter generation times (allowing proliferation between major flow events), adaptations for withstanding drag (e.g. substrate attachment and growth on sheltered surfaces), benefit from the higher supply of resources in faster currents and comparatively unlimited dispersal, facilitated by small sizes and large local population densities, providing a continuous supply of colonists. In the cases where fish parameter b 2 and slope d are significant, they exhibit opposite responses along the richness gradient. Thus, in species-poor communities, found in non-impacted watersheds of low temperature, rare fish of generally extreme body sizes maintain high densities. Conversely, common fish of intermediate body size predominate in speciose communities, inhabiting streams of high temperature and human disturbance. This discrepancy with the model prediction for a negative richness–slope d relationship across all groups (Fig. 1b and d) is due to the already discussed erratic behaviour of species-poor fish communities, where slope d is frequently negative, driving the relationship with richness in a positive direction. These results reveal a tendency of rare species of both invertebrates and fish to maintain greater density in the vanishing pristine streams, which may be a contributing factor to the unprecedentedly high extinction rates in freshwater fauna (Ricciardi & Rasmussen 1999).

As shown here, the response of population density to body size and distribution cannot be described by an invariant power law, but by a wide variety of power laws or quadratic models with scaling exponents or coefficients dependent on the environment and richness. Consistent with other field observations (Cyr 2000; Knouft 2002), energetic equivalence in the trophically homogenous diatoms is inconceivable, whereas in fish, encompassing different consumer guilds, it is improbable, given the distinct quadratic abundance-average body weight relationship at the level of the whole community. The combination of two factors is most likely responsible for this departure from energetic equivalence: (1) size is coupled with niche breadth – broad niches are associated with small sizes in diatoms, but intermediate sizes in fish and (2) environmental variability in streams is substantial, e.g. resource supply ranges from extreme natural limitation to extreme anthropogenic enrichment and flow disturbance, from intermittent to continuous. Therefore, species of different size will produce biomass along the wide resource and disturbance gradients, giving rise to environmentally constrained abundance-body size and abundance-distribution relationships. Considering that other important power laws too depend on the environment, e.g. the home range-body size (Haskell et al. 2002), ecologists should broaden their search for environmental causes of community scaling behaviour.

The novel mathematical formulation of the abundance-distribution relationship, i.e. D −ln S , has profound implications for conservation planning, which is faced with the difficult challenges of selecting the right targets of conservation action and managing their landscape requirements (Schwenk & Donovan 2011). The new power function, showing that as community richness increases so does the abundance of rare species, is confirmed in both diatoms and invertebrates. If a similar richness dependence of the abundance-distribution relationship is found in communities of threatened species, changes in environmental protection and species conservation policies may ensue. Specifically, broad community-based conservation efforts to promote biodiversity will be adequate for increasing the abundance, and with this, the chance of survival of rare and potentially endangered species.

In conclusion, the present hierarchical theory explains the variability of the relationships among body size, abundance and distribution in the major organismal groups in streams from a metacommunity to a community level. It elucidates that the driving mechanisms differ along this hierarchy with evolutionarily constrained species traits, e.g. body size and niche breadth, giving way to environmental forces, e.g. resource supply, temperature and human impact. These findings emphasise the necessity for better integration of macroecology and environmental science.


I thank Jim Brown, Brian Enquist, Jordi Bascompte and three anonymous referees for their insight, encouragement and many constructive suggestions for improvement. I am grateful to all researchers, involved in the NAWQA Program for generating the comprehensive and high quality data used here. This research was supported by the Norman Hackerman Advanced Research Program under Grant No. 003656-0054-2009.