Climatological data for the 27 sites were obtained from the eMAST/ANUClimate data set (www.emast.org.au), which extends from 1970 to 2012 with 1 km spatial resolution across the entire continent. Mean annual precipitation (MAP) over this period at the sampling sites ranged from 154 to 1726 mm and mean annual temperature (MAT) from 14.1 to 27.6∘. The moisture index (MI =P/Eq, where P is mean annual precipitation and Eq is equilibrium evapotranspiration, calculated with the STASH program: Gallego-Sala et al., 2012) varied from 0.07 to 0.82. The mean incident flux of photosynthetically active radiation (PAR) during daylight hours, expressed as photosynthetic photon flux density (µmol m-2 s-1), was also calculated using STASH. This incident flux (at the top of the canopy) was averaged through the canopy using Beer's law, as follows. First leaf area index (L) was estimated from a remotely sensed (MODIS NBAR-derived using MOD43A4: http://remote-sensing.nci.org.au/u39/public/html/modis/fractionalcover-clw) fractional cover of photosynthetic vegetation (fv) at 1 km resolution at each site, from data assembled by the TERN AusCover facility (Guerschman et al., 2009): L≈-(1/k)ln(1-fv), where k=0.5. Then absorbed PAR per unit leaf area (IL) was calculated as IL≈I0(1-e-kL)/L≈I0kfv/ln⁡1/(1-fv), where I0 is the incident PAR above the canopy. This calculation yields IL≈I0 for sparse vegetation (L<1), but IL becomes progressively smaller than I0 as foliage density increases, reflecting the fact that the irradiance experienced by the average species is much lower in, say, a closed woodland than in an open shrubland, even if the PAR incident at the top of canopy is the same. In dense vegetation IL will underestimate the PAR exposure of canopy dominants and overestimate the PAR exposure of understorey species. However, the use of a canopy average in this way was a necessary approximation (because we did not have quantitative information about the canopy position of each species) and considered preferable to using I0, which will systematically overestimate PAR exposure for most species in a dense community.

Mature outer-canopy leaves of each species were sampled during the growing season using the AusPlots methodology (White et al., 2012). (Note that in denser vegetation many species sampled are in the understorey, so their “outer-canopy” leaves are still shaded by the overstorey. Many species thus receive considerably reduced sunlight compared to the overstorey, implying that the canopy-average irradiance IL is more suitable than the top-of-canopy value I0 as a community measure of irradiance.) In total, the 27 selected sites included 442 unique species, of which 37 were C4 plants (not analysed further here). LMA was measured on the archived leaf samples by scanning and weighing the leaves. Subsamples (a mixture of material from at least two replicates) were analysed for C and N contents and bulk δ13C at the Stable Isotope Core Laboratory of Washington State University, USA. Narea was calculated from N content and LMA. Carbon isotope discrimination (Δ) values were derived from the reported δ13C values using the standard formula Δ=(δair-δplant)/(1+δplant), where δair is the carbon isotope composition of air and δplant is the carbon isotope composition of the plant material. Because of the different diffusion rates and biochemical rates of carboxylation between 13CO2 and 12CO2, Δ can be used to estimate the ci:ca ratio as ci:ca≈(a+Δ)/(b-a), where the recommended standard values are a=4.4 ‰ and b= 27 ‰ (e.g. Cernusak et al. 2013).

Values of Vcmax were predicted based on the co-ordination hypothesis, by equating the carboxylation- and electron transport-limited rates of photosynthesis and, as a simplifying assumption, treating the electron transport-limited rate as proportional to absorbed PAR (i.e. ignoring the saturation of the electron transport rate at high irradiances). These assumptions lead to the following estimate: Vcmax≈φ0IL(ci+K)/(ci+2Γ*), where φ0 is the intrinsic quantum efficiency of photosynthesis (0.093: Long et al., 1993), ci is the leaf-internal concentration of CO2, K is the effective Michaelis–Menten coefficient of Rubisco, and Γ* is the photorespiratory compensation point. Values of both these quantities and their activation energies (governing their temperature responses) are based on the empirical in vivo determinations by Bernacchi et al. (2001) widely used in photosynthesis research. Both K and Γ* were evaluated at standard atmospheric pressure and oxygen concentration, and site MAT. Predicted values of Vcmax were adjusted to 25∘, because the amount of N allocated to Rubisco and other enzymes involved in carboxylation should be proportional to Vcmax at a standard temperature, not at the growth temperature.

All statistics were performed in R3.1.3 (R Core Team, 2015). Linear regressions were fitted using the lm function, partial residual plots were generated using the visreg package, and the relative contributions of different predictors were quantified using the Lindeman et al. (1980) method as implemented in the relaimpo package. In a first, exploratory statistical analysis, a linear model was fitted for ln Narea with ci:ca, MAT, ln IL, ln LMA, and the factor “N-fixer” as predictors. The regression slopes of ln Narea against ci:ca, MAT and ln IL can all be independently predicted from the co-ordination hypothesis by differentiation of Eq. (5) (see Appendix A; note that these formulae explicitly predict the slopes for ln Narea). These predicted values were compared with the fitted values and their 95 % confidence limits in order to assess support for the co-ordination hypothesis.

In a second analysis, community-mean values were calculated as simple averages across the species in each plot, omitting the factor “N-fixer”. A linear model was fitted to the community means of ln Narea as a function of ci:ca, MAT, ln IL, and ln LMA to assess the predictability of leaf N at the community level.

In a third analysis, Narea was modelled as a linear combination of the predictors Rubisco N, Nrubisco (derived from predicted Vcmax at 25∘), and structural N, Nstructure (derived from LMA using the empirical relationship Nstructure=10-2.67 LMA0.99, in g m-2: Yusuke Onoda,personal communication 2015), including “N-fixer” as a factor and allowing interactions of the predictors with this factor.

Trait gradients were generated for ln LMA, ln Narea, and ci:ca following the analysis method of Ackerly and Cornwell (2007), again using simple averages across species to estimate community means. In this analysis species trait values were plotted against site-mean trait values. By definition, the regression of the species trait values against site-mean trait values has a slope of unity. For a perfectly plastic trait, regression of trait variation within species against the site-mean trait values would also yield a slope of unity. The common within-species slope that this approach provides is a measure of the fraction of trait variation due to phenotypic plasticity and/or genotypic variability. Its one-complement measures the fraction due to species turnover. Natural log transformation was applied to LMA and Narea because of their large variance and skewed distributions, but not to ci:ca, because of its small variance and approximately normal distribution.

Significant partial relationships were found for ln Narea vs. ci:ca, MAT, and ln IL (Table 1, Fig. 2). The relationship was negative for ci:ca, as expected, because lower ci:ca implies that a greater photosynthetic capacity is required to achieve a given assimilation rate (or equivalently: a stronger CO2 drawdown is enabled by a higher Vcmax). The relationship was also negative for MAT, as expected, because there is an inverse relationship between temperature and the quantity of leaf proteins required to support a given value of Vcmax. The relationship was positive for ln IL (PAR), as expected, because the higher the irradiance, the greater the carboxylation capacity required for co-limitation with the rate of electron transport.

Theoretical slopes for these relationships (derived in Appendix A) are compared with the fitted slopes in Table 1. For ln Narea vs. ln IL, the theoretical slope is unity. The fitted slope of 0.874 (95 % confidence limits: 0.685, 1.063) was statistically indistinguishable from unity. (A slope significantly greater than unity was found for ln Narea vs. ln I0, i.e. top-of-canopy PAR, as expected, as this measure underestimates the change in mean canopy PAR along the gradient from sparse, high-PAR to dense, lower-PAR communities.) For ln Narea vs. ci:ca, the fitted slope of -0.611 (-1.107, -0.115) was fortuitously close to the theoretical slope of -0.615, although the value was only weakly constrained for these data. For ln Narea vs. MAT, the theoretical slope was obtained by subtracting the “kinetic” slope of ln Vcmax vs. temperature (from the activation energy of carboxylation as given by Bernacchi et al., 2001) from the shallow positive slope implied by Eq. (5). The kinetic effect was dominant and results in an overall predicted negative slope of -0.048. The fitted slope of -0.047 (-0.060, -0.034) was indistinguishable from this theoretical slope, indicating acclimation to temperature by diminished allocation of N to metabolic functions at higher temperature, offsetting the increased reaction rate predicted by the Arrhenius equation. However, this slope was shallower than would be predicted by the Arrhenius equation alone, reflecting the reduced quantum efficiency of assimilation (a higher Vcmax is required to support a given assimilation rate) at higher temperatures.

The proportion of leaf N allocated to Rubisco has generally been found to decline, while the total N allocated to cell walls increases with increasing LMA (Hikosaka and Shigeno, 2009). Figure 2 shows a strong positive partial relationship between ln Narea and LMA. N-fixers had generally higher Narea than non-N-fixers (Fig. 2e: p<0.001). The predictors together explained 55 % of the variation in leaf N across species and sites.

Fully 82 % of the variation in the community-mean value of ln Narea could be explained by the combination of community-mean LMA and environmental variables. Significant partial relationships of community-mean ln Narea with MAT, ln IL, and ln LMA (Table 2) were consistent with the results obtained at species level. The fitted slopes of ln Narea against ln IL and MAT were again indistinguishable from the theoretical values, albeit with wide error bounds due to the much smaller sample size (27 as opposed to 405). The community-level partial relationship between ln Narea and ci:ca showed a negative slope as predicted, although this relationship was barely significant (p≈0.1) due to the small sample size.

Highly significant (p< 0.001) positive relationships were found between Narea and the predicted Rubisco-N content per unit leaf area (Nrubisco), and the predicted cell-wall N content per unit leaf area (Nstructure) (Fig. 3). A priori we would expect the regression coefficient for Nstructure to be close to unity, and that for Nrubisco to be about 6 to 20 (if Rubisco constitutes about 5 to 15 % of total leaf protein: Evans, 1989; Evans and Seemann, 1989; Onoda et al., 2004). The fitted slopes of 1.2 (p< 0.001; 95 % confidence limits: 1.0, 1.4) and 9.5 (p< 0.001; 7.6, 11.5) in Table 3 respectively were consistent with these expectations.

There was no significant main effect of the factor “N-fixer” and no significant interaction between Nrubisco and the factor “N-fixer”. The co-ordination hypothesis predicts that the metabolic component of Narea should be environmentally optimized and therefore independent of N supply. This could not be tested without direct measurements of Vcmax or Nrubisco, which were precluded by the design of this study. However, N-fixers showed a steeper relationship between Narea and Nstructure. This was manifested as a significant interaction between the factor “N-fixer” and Nstructure (p< 0.01). This model, in which Narea was decomposed into a metabolic component predicted by the co-ordination hypothesis and a structural component proportional to LMA, explained 52 % of the variance in Narea across species and sites. The relative importance of variations in the metabolic and structural components was determined to be 39 and 61 % respectively, showing inter alia the importance of variation in LMA in determining leaf N content.

In total, 243 C3 species were sampled at two or more sites. These species allowed calculation of a common slope, being an estimate of trait plasticity sensu lato (that is, phenotypic plasticity or genetic adaptation or both) across species (Fig. 4), for the traits ci:ca, ln LMA, and ln Narea. Contrasting results were obtained for the three traits. It appeared that ci:ca is perfectly plastic, with a common (within-species) slope indistinguishable from unity. The common slope of Narea was close to 0.5, indicating approximately equal contributions of plasticity and species turnover to the total variation. In the case of LMA, however, there was significant heterogeneity (p< 0.05) among the within-species slopes, with Marsdenia viridiflora showing a significantly steeper slope than the other species. After excluding this species, the common slope for LMA was also close to 0.5. A positive common slope indicates the ability of species to adapt their leaf morphology to environment. The positive common slope found for Narea is consistent with this trait's nature as a combination of metabolic and structural components; its similarity to the slope for LMA is consistent with the importance of variations in structural N in determining total N.

The variety of environments provided in this study by the long transcontinental transect, and the number of species sampled, allowed us to statistically separate the effects of ci:ca, irradiance, temperature, and LMA on Narea. The relationships with ci:ca, irradiance, and temperature were in the directions and magnitudes predicted by the co-ordination hypothesis. The relationship with site mean irradiance had a slope as predicted by the co-ordination hypothesis (i.e. close to 1), but a strong relationship, with a steeper slope as expected, was found when top-of-canopy irradiance was used instead of the canopy mean – indicating that both spatial variations and within-canopy shading were contributing to the relationship with site mean irradiance. We performed an additional regression using leaf nitrogen content per unit mass (Nmass) which showed, as expected, identical fitted coefficients for all predictors except LMA (Appendix B). However, because of the regression coefficient of ln Narea with respect to ln LMA < 1, the regression coefficient of ln Nmass with respect to ln LMA < 0, i.e. Nmass, declines with increasing LMA – as has been widely reported. We also tried a regression of Nmass on the same set of predictors but without the inclusion of LMA; this yielded a much poorer fit and is not shown.

High Narea in plants from arid environments has been described often, and has traditionally been explained as a consequence of high N supply in environments with low rainfall (reducing leaching losses) and restricted plant cover (reducing total vegetation N demand) (e.g. Field and Mooney, 1986). This explanation would imply that plants in wetter environments have lower (and suboptimal) Narea due to low availability of N. However, the negative relationship commonly found between ci:ca and Narea supports an alternative, adaptive (plant-centred) explanation. The least-cost hypothesis (Wright et al., 2003; Prentice et al., 2014) predicts lower ci:ca in drier environments. This is because the drier the atmosphere, the greater the flux of water required to support a given rate of assimilation, which in turn shifts the balance of costs and benefits towards investment in photosynthetic capacity (Vcmax) and away from water transport capacity. When ci:ca is lower, the co-ordination hypothesis predicts that a higher Vcmax (and therefore higher Narea) will be optimal, in order for the leaves to fully utilize the available light. The co-ordination hypothesis also predicts a further increase in Narea with increasing aridity due to reduced cloudiness and reduced shading by competitors, both factors tending to increase IL (and both apparently contributing to the fitted relationship of Narea with IL). Thus the co-ordination hypothesis could account for independent positive effects of site irradiance and aridity on Narea, as previously reported by Wright et al. (2005). The fitted relationship of Narea with temperature, PAR, and ci:ca is consistent with our theoretical prediction, which implicitly includes all of these effects.

Despite the large within-site variation in LMA found at all points along the aridity gradient, there is a significant tendency for LMA to increase with aridity, perhaps because of the resistance to dehydration conferred by stiffer leaves (Niinemets, 2001; Wright and Westoby, 2002; Harrison et al., 2010) and/or the need for leaves to avoid overheating under transient conditions of high radiation load and low transpiration rates combined with low wind speed (Leigh et al., 2012). This increase in LMA is inevitably accompanied by an increasing structural N component.

Thus, several distinct aspects of plant allocation tend to increase Narea along gradients of increasing dryness. The predicted response of Nrubisco to temperature is a result of opposing effects: the declining efficiency of photosynthesis with increasing temperature (due to the temperature dependencies of K and Γ*) is offset by the increased catalytic capacity of Rubisco at higher temperatures. The latter effect is predicted to be stronger, implying reduced Narea with increasing temperature, as observed.

Predicted Nrubisco and Nstructure together explained more than half of the variation in total Narea across species and sites. Our approach to predicting these two quantities invokes a simplified formula, Eq. (5), which is based on the co-ordination hypothesis for Nrubisco, assuming proportionality with Rubisco capacity, and assumes a simple proportionality with LMA for Nstructure. Our finding of highly significant multiple regression coefficients for both variables indicates that the prediction obtained when taking both into account is more accurate than could be obtained from either variable alone. Osnas et al. (2013), analysing a large global leaf-trait data set and applying a novel method to determine the extent to which different traits are area- vs. mass-proportional, found leaf N to be an intermediate case. This is to be expected if leaf N is, as our results suggest, a composite of an area-proportional (Nrubisco) and a mass-proportional (Nstructure) component. The two predictors (Rubisco capacity and LMA) are not fully independent, because leaves with higher photosynthetic capacity tend to have higher LMA for structural reasons. But such leaves must have increased structural N as well. By showing independently significant regression coefficients for modelled Nrubisco and LMA, the multiple regression results establish that successful prediction of Narea requires consideration of both components, and that each has an independent effect, irrespective of their correlation (r2= 0.28 in this data set). Osnas et al. (2013) also fitted various statistical models for the relationships among leaf traits. Their “model LN” for ln Narea vs. ln LMA yielded a slope of 0.38 (95 % confidence interval 0.36 to 0.40). This value, based on a global data set, can be compared directly with – and is indistinguishable from – our fitted partial regression coefficient of ln Narea vs. ln LMA, which is 0.42 (0.34 to 0.49) (Table 1).

In reality, however, leaf N does not consist exclusively of Rubisco and cell-wall constituents. Leaf N includes multiple additional components, including other photosynthetic proteins, proteins of the light-harvesting complexes and electron transport chains, cytosolic proteins, ribosomes and mitochondria, nucleic acids (which account for about 10–15 % of leaf N: Chapin III and Kedrowski, 1983), and N-based defensive compounds. It is possible that the higher N found for N-fixers resides in N-based osmolytes (Erskine et al., 1996) or defence compounds (Gutschick, 1981). Nonetheless, our simplifications suggest that Narea – especially at the community level, which is key for large-scale modelling – is, to first order, inherently predictable from leaf morphology and the physical environment. A corollary is that limitation in N supply may act primarily by changing plant allocation patterns (reducing allocation to light capture by leaves while increasing allocation to N uptake by roots), rather than by altering leaf stoichiometry.

By testing for acclimation along spatial gradients, the design of our study did not allow phenotypic plasticity to be distinguished from genetic adaptation. Phenotypic plasticity is the ability of a genotype to alter its expressed trait values in response to environmental conditions (Bradshaw, 1965; Sultan, 2000). A part of the observed variation in trait values within species could be due to shifts in the occurrence and frequency of different genotypes, producing different preferred trait values. Thus, when we refer to traits as “plastic”, this should be understood in a broad sense to allow the possibility of a genetic component of the observed adaptive differentiation within species. Seasonal acclimation within individual plants can provide more direct evidence for phenotypic plasticity (Togashi et al., 2017), whereas in this study we disregard possible seasonal variations and instead relate trait variations to the mean annual environment. However, by sampling all of the species present at each site and including measurements on species at multiple sites, we could distinguish between the contribution of plasticity sensu lato (phenotypic plasticity and/or genetic adaptation) vs. species turnover, i.e. the progressive replacement of species with different mean trait values, to spatial variation in the community-mean values of a given trait. We found that δ13C was perfectly plastic, perhaps not surprisingly, as variations in ci:ca are under stomatal control. In contrast, LMA and Narea showed approximately equal contributions from plasticity and species turnover.

There has been a surge of interest in schemes to predict continuous trait variation in DGVMs (e.g. Scheiter et al., 2013; Fyllas et al., 2014; van Bodegom et al., 2014; Ali et al., 2015; Fisher et al., 2015; Meng et al., 2015; Sakschewski et al., 2015). Some trait-based modelling approaches have relied on empirical information on trait–trait and trait–environment covariation, but others (e.g. Scheiter et al., 2013) have aimed to represent the adaptive nature of trait variation explicitly. Our focus has been on testing an explicit adaptive hypothesis for the controls of one key trait, Narea, which in addition to a structural component (necessarily linked to LMA) includes an important metabolic component, reflecting the leaf-level investment in photosynthetic proteins. All models that attempt to represent the coupling between C and N cycles in terrestrial ecosystems require a method to calculate leaf N content, given other environmental and plant characteristics. Some models prescribe fixed values of Vcmax (per plant functional type), but this approach does not take account of the observed variation in Vcmax with environmental conditions. Models that assume proportionality between Vcmax and Narea neglect the important variation in leaf structural N. We have shown that Narea is predictable, to a degree that is useful for modelling, when both metabolic and structural components are taken into account. Our prediction is based on LMA, ci:ca, and a theoretically predicted value of Vcmax based on the co-ordination hypothesis – for which there is strong independent evidence (e.g. Maire et al., 2012). The partial responses of Narea to ci:ca, irradiance, and temperature are consistent with predictions of the co-ordination hypothesis, and the inclusion of predicted Vcmax adds significantly and substantially to the predictive power of LMA and ci:ca alone. As both LMA (Wright et al., 2005) and ci:ca (Prentice et al., 2014) show relationships with environment, our results suggest a possible route towards a general adaptive scheme for the prediction of major leaf traits in DGVMs, which would be an improvement on models that assume a one-to-one relationship between photosynthetic capacity and Narea (see e.g. Adams et al., 2016, who showed that there is considerable variation in Narea among N-fixers that is unrelated to photosynthetic capacity). Our results also suggest some priorities for trait data collection and analysis: to test the predicted controls of Narea over a wider range of environments, and to test the predicted environmental controls of Vcmax directly in the field.

Our application of trait gradient analysis also points out a way towards process-based treatments of functional trait diversity in next-generation models. It is increasingly accepted that models could, and should, sample “species” from continuous gradients of traits rather than fix the traits associated with discrete PFTs. A hybrid approach to modelling Narea based on the present analysis would consider Narea explicitly as the sum of metabolic and structural components. The metabolic component would be treated as plastic and subject to environmental optimization (in space and time), consistent with the least-cost and co-ordination hypotheses. The structural component would be tied to LMA, which is a key variable of the “leaf economics spectrum” (Wright et al., 2004), strongly expressed both within and between environments and therefore requiring a broad range of values to be assigned to model “species”.

Finally, we note that if our results can be corroborated more widely, this would point to the need for a shift in the way N “limitation” is treated – both in models and in analyses of field data. In studies of the relationship between Vcmax and leaf N, for example, it is conventional to plot N on the x axis and Vcmax on the y axis, and it is then often stated that the positive relationship found shows that variation in leaf N “causes” variation in Vcmax. But all that is shown on the graph is a correlation, and our “plant-centred” interpretation is the opposite of the conventional one: that is, Vcmax is adaptively matched (acclimated) to environmental conditions, and the metabolic component of leaf N is a consequence of this acclimation. Low N availability would then result in reduced allocation of C (and N) to leaves, and increased allocation below ground – which is also an adaptive response, but at the whole-plant rather than the leaf level.