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Keywords:

  • Aridity;
  • nitrogen;
  • optimality;
  • photosynthesis;
  • plant functional traits;
  • stable isotopes;
  • stomatal conductance;
  • temperature;
  • transpiration;
  • viscosity

Abstract

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Theoretical analysis
  6. Empirical results
  7. Discussion
  8. Acknowledgements
  9. Statement of authorship
  10. References
  11. Supporting Information

A novel framework is presented for the analysis of ecophysiological field measurements and modelling. The hypothesis ‘leaves minimise the summed unit costs of transpiration and carboxylation’ predicts leaf-internal/ambient CO2 ratios (ci/ca) and slopes of maximum carboxylation rate (Vcmax) or leaf nitrogen (Narea) vs. stomatal conductance. Analysis of data on woody species from contrasting climates (cold-hot, dry-wet) yielded steeper slopes and lower mean ci/ca ratios at the dry or cold sites than at the wet or hot sites. High atmospheric vapour pressure deficit implies low ci/ca in dry climates. High water viscosity (more costly transport) and low photorespiration (less costly photosynthesis) imply low ci/ca in cold climates. Observed site-mean ci/ca shifts are predicted quantitatively for temperature contrasts (by photorespiration plus viscosity effects) and approximately for aridity contrasts. The theory explains the dependency of ci/ca ratios on temperature and vapour pressure deficit, and observed relationships of leaf δ13C and Narea to aridity.


Introduction

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Theoretical analysis
  6. Empirical results
  7. Discussion
  8. Acknowledgements
  9. Statement of authorship
  10. References
  11. Supporting Information

Optimisation by natural selection is a powerful concept for generating testable hypotheses about organismal traits and their relationships to the environment (Givnish 1986; Mäkelä et al. 2002). We explore the consequences of a simple optimality criterion that provides a unifying explanation for the following observations on plants, all strongly supported in the literature:

  • The relative conservatism of the ratio between leaf-internal (ci) and ambient (ca) mole fractions of CO2 (Wong et al. 1979; Ehleringer & Cerling 1995). The ratio tends to vary by only about ± 30% (rates of gas exchange can vary through two orders of magnitude), and to be constant under variation of ca, light and nutrient supply. This conservatism signifies tight regulation of the balance between carbon gain and water loss. We introduce the symbol χ = ci/ca to simplify the notation later on.
  • The decline of χ with vapour pressure deficit (D). Previously assigned various mathematical forms (Leuning 1990; Oren et al. 1999; Medlyn et al. 2011), this decline is well described by χ = ξ/(ξ + √D) where ξ is a parameter related to the ‘carbon cost of water’ (Medlyn et al. 2011). Medlyn et al. (2011) refer to this parameter as g1.
  • The tendency demonstrated in many transect studies for the stable carbon isotope signature (δ13C) in the leaves of C3 plants – a proxy for time-averaged values of χ – to become less negative, indicating lower χ, with increasing aridity (Stewart et al. 1995; Miller et al. 2001; Zheng & Shangguan 2007; Prentice et al. 2011).
  • The tendency of leaf N per unit area (Narea) in all plants to increase from wet to dry climates (Wright et al. 2003, 2005), implying that Narea increases as χ declines (Prentice et al. 2011).

A general microeconomic optimisation criterion concerns investments in two or more resources required to manufacture a product. Here, the product is photosynthate, and the resources are the photosynthetic apparatus (with costs assumed proportional to Rubisco carboxylation capacity, Vcmax, at a standard temperature, and approximately proportional to Narea) and the transpiration pathway (with costs assumed proportional to the maximal transpiration rate, E). Wright et al. (2003) proposed the existence of an optimum rate of investment in transpiration and photosynthetic capacity, dependent on the ratio of their costs, which would achieve a given rate of net assimilation at least total cost. This analogy requires that the resources are substitutable, e.g. that plants can compensate for high water costs in dry climates by keeping stomata relatively closed while increasing investment in photosynthetic capacity, maintaining a given level of carbon assimilation at reduced ci. Wright et al. (2001) noted that this form of resource substitution constitutes a widespread, previously overlooked mechanism of drought tolerance in plants.

Wright et al. (2003) considered carbon assimilation as proportional to the product of two inputs, conceptualised as water and nitrogen. We extend their reasoning to make quantitative predictions of trade-offs between photosynthetic and water-transport parameters from the standard model of C3 photosynthesis (Farquhar et al. 1980) combined with plant water-relations theory. We use a graphical approach analogous to Wright et al. (2003) to analyse field data on photosynthesis, stomatal conductance and leaf traits from species in contrasting climates.

Cowan & Farquhar (1977) introduced an optimisation hypothesis for stomatal behaviour. Their hypothesis is equivalent to maximising (A − λE) where A is net carbon assimilation and λ is an ‘exchange rate’ between carbon and water. Biochemical properties of leaves, and hydraulic properties of stems, were assumed fixed over the time scale of interest (principally the diurnal cycle), although λ could vary more slowly. The general solution to this optimisation is complex (Arneth et al. 2002; Konrad et al. 2008; Katul et al. 2010); tractable approximations have been proposed (Katul et al. 2010; Medlyn et al. 2011). However, as noted in a pioneering analysis by Givnish (1986), the Cowan-Farquhar optimality hypothesis is incomplete because it does not account for the (competing) costs of maintaining both water flow and photosynthetic capacity. Following Wright et al. (2003), we propose an optimal balance of investments in both functions. Remarkably, we predict a relationship between χ and D mathematically identical to that of Medlyn et al. (2011). But its single parameter (here called ξ) has a subtly different interpretation, based on the relative costs of maintaining a transpiration pathway capable of delivering water at a rate E, and leaf proteins capable of delivering photosynthate at a rate Vcmax. These costs can be expressed in terms of traits, and are expected to vary across environments. We examine how relationships among Vcmax, Narea and gs vary across environments, and provide a coherent, quantitative interpretation of these variations.

Materials and methods

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Theoretical analysis
  6. Empirical results
  7. Discussion
  8. Acknowledgements
  9. Statement of authorship
  10. References
  11. Supporting Information

Data

Data were field measurements on all abundant woody dicots (trees if present, and shrubs) at four sites in eastern Australia (Table 1). Latitude ranges from 18°S to 42°S; mean annual temperatures (MAT) from 10.4 and 22.6 °C; longitude over 5° (coastal to interior) and mean annual precipitation (MAP) from 396 to 1133 mm. The sites were paired as follows. A ‘cold’ high-latitude site in Tasmania was contrasted with a ‘hot’ low-latitude site in Queensland. The Queensland site has higher rainfall but similar climatic moisture index MI = P/Eq, where P is MAP and Eq is equilibrium evapotranspiration (calculated as in Gallego-Sala et al. 2010. See Appendix S1 for definitions of hydroclimatic variables). At intermediate latitudes, in New South Wales, a ‘wet’ coastal site was contrasted with a ‘dry’ inland site. These sites have intermediate temperature (MAT 17 to 18°C) between the cold and hot sites; but the wet site has a much higher MI, and the dry site a much lower MI, than either the cold or the hot site.

Table 1. Site locations and climates: mean annual precipitation (MAP); mean annual temperature (MAT); and moisture index (MI), Cramer-Prentice α, equilibrium evapotranspiration (Eq) and incident photosynthetically active radiation during the growing season (PAR0) all based on annual mean climate values and calculated as in Gallego-Sala et al. (2010). Primary data (monthly means of precipitation, temperature and incident shortwave radiation) were obtained from ANU climatologies at 0.05˚ resolution (M. Hutchinson, personal communication 2012) for 1970–2010
SitesLocationMAP (mm)MAT(◦ C)MIαEq (mm)PAR0 (mol m−2)
‘cold’42.387˚S54010.40.680.727999484
147.048˚E
‘hot’18.295˚S106621.60.700.64151513869
145.492˚E
‘wet’33.680˚S113317.31.000.92113811604
151.148˚E
‘dry’32.976˚S39617.90.310.36128911487
146.156E

Net photosynthesis (Asat) and stomatal conductance (gs) were measured simultaneously in the field at saturating light intensity (800 to 1500 μmol m−1 s−1, depending on the ambient light intensity) and temperatures close to ambient, using either a LiCor 6400 (Tasmania, Queensland) or a CIRAS-1 PP (New South Wales) infra-red gas analysis system. Measurements were made on freshly cut, sun-exposed branches. Fieldwork was scheduled so that ambient temperatures were similar regardless of site. CO2 concentration, vapour pressure deficit and measurement temperatures were held within narrow ranges (388–402 ppm, 1.8–2.1 kPa, 23.0–27.0 °C). Four to seven replicate measurements per species were made, on different individuals. Leaf samples were analysed for specific leaf area (SLA), N by mass (converted to Narea using SLA) and δ13C. Carboxylation capacity at 25 °C (Vcmax[25]) was calculated using the Farquhar et al. (1980) model, assuming that Asat is Rubisco-limited (Kattge et al. 2009) and applying the temperature dependency of Vcmax from Bernacchi et al. (2003, 2009). Day respiration was estimated by Rd = 0.01 Vcmax. Vcmax[25] is expected to be more closely related to nitrogen investment than Vcmax at ambient temperature, but the differences were slight because measurement temperatures were close (within ± 2°) to 25 °C.

MI (Table 1) is used as an (inverse) index of general climatic aridity. Note that lower P and/or higher Eq both imply increasing limitation on ecosystem-level evapotranspiration, Ea, which in turn is a principal driver of D on large spatial and temporal scales (McNaughton & Jarvis 1991; Raupach 2000). An alternative measure of climatic aridity is the Cramer-Prentice α (Table 1), a standardised estimate of Ea/Eq (Gallego-Sala et al. 2010). α is related to MI by the Budyko framework for water vs. energy controls of catchment water balance (Wang et al. 2012). For quantitative analysis of aridity effects on χ, we use ΔΕ = Eq − Ea = Eq (1 − α) as a proxy for the long-term effective value of D. Appendix S1 explains the rationale for our choice of hydroclimatic variables, and the relationships among them.

Graphical and statistical analyses

All species sampled were included except two C4 species (Atriplex stipitata and Triodia scariosa) and two species of Exocarpus (E. aphyllus and E. cupressiformis). The latter are leafless, with photosynthetic stems, and were extreme outliers in the relationship between Vcmax[25] and Narea. The analysis included 14 species from the cold site, 17 from the hot site, and 35 each from the wet and the dry site (Table 2). Twenty-six species were classified as N-fixers based on available information. This category consists mainly of Fabaceae but also includes two actinorhizal Allocasuarina species and one cycad (Macrozamia communis), which has a cyanobacterial symbiont.

Table 2. Species analysed
SitesGenus_speciesFamilyNitrogen-fixing species
‘Cold’Acacia dealbataMimosaceaeYes
Aotus ericoidesFabaceaeYes
Banksia marginataProteaceaeNo
Bossiaea cinereaFabaceaeYes
Cassinia aculeataAsteraceaeNo
Daviesia latifoliaFabaceaeYes
Epacris impressaEpacridaceaeNo
Eucalyptus paucifloraMyrtaceaeNo
Eucalyptus rubidaMyrtaceaeNo
Eucalyptus tenuiramisMyrtaceaeNo
Leucopogon ericoidesEpacridaceaeNo
Leucopogon virgatusEpacridaceaeNo
Persoonia juniperinaProteaceaeNo
Pultenaea juniperinaFabaceaeYes
‘Hot’Acacia flavescensMimosaceaeYes
Acacia leptostachyaMimosaceaeYes
Allocasuarina torulosaCasuarinaceaeYes
Bursaria incanaPittosporaceaeNo
Corymbia citriodoraMyrtaceaeNo
Corymbia intermediaMyrtaceaeNo
Corymbia trachyphloiaMyrtaceaeNo
Eucalyptus portuensisMyrtaceaeNo
Gastrolobium grandiflorumFabaceaeYes
Grevillea glaucaProteaceaeNo
Grevillea parallelaProteaceaeNo
Lophostemon suaveolensMyrtaceaeNo
Persoonia falcataProteaceaeNo
Petalostigma pubescensPicrodendraceaeNo
Planchonia careyaLecythidaceaeNo
Pogonolobus reticulatusRubiaceaeNo
Xylomelum scottianumProteaceaeNo
‘Wet’Acacia floribundaFabaceaeYes
Astrotricha floccosaAraliaceaeNo
Correa reflexaRutaceaeNo
Dodonaea triquetraSapindaceaeNo
Eucalyptus paniculataMyrtaceaeNo
Eucalyptus umbraMyrtaceaeNo
Lasiopetalum ferrugineumMalvaceaeNo
Leptospermum polygalifoliumMyrtaceaeNo
Lomatia silaifoliaProteaceaeNo
Macrozamia communisZamiaceaeYes
Persoonia linearisProteaceaeNo
Pomaderris ferrugineaRhamnaceaeNo
Pultenaea daphnoidesFabaceaeYes
Pultenaea flexilisFabaceaeYes
Syncarpia glomuliferaMyrtaceaeNo
Synoum glandulosumMeliaceaeNo
Xylomelum pyriformeProteaceaeNo
Allocasuarina spCasuarinaceaeYes
Acacia suaveolensFabaceaeYes
Banksia marginataProteaceaeNo
Boronia ledifoliaRutaceaeNo
Corymbia gummiferaMyrtaceaeNo
Eriostemon australasiusRutaceaeNo
Eucalyptus haemostomaMyrtaceaeNo
Gompholobium glabratumFabaceaeYes
SitesGenus_speciesFamilyNitrogen-fixing species
  1. Two C4 species (Atriplex stipitata and Triodia scariosa) and two species of Exocarpus (E. aphyllus and E. cupressiformis) were excluded from the analysis.

‘Wet’Grevillea buxifoliaProteaceaeNo
Grevillea speciosaProteaceaeNo
Hakea dactyloidesProteaceaeNo
Hakea teretifoliaProteaceaeNo
Hibbertia bracteataDilleniaceaeNo
Lambertia formosaProteaceaeNo
Leptospermum trinerviumMyrtaceaeNo
Persoonia levisProteaceaeNo
Phyllota phylicoidesFabaceaeYes
Pimelea linifoliaThymelaeaceaeNo
‘Dry’Acacia doratoxylonFabaceaeYes
Acacia oswaldiiFabaceaeYes
Callitris glaucophyllaCupressaceaeNo
Dodonaea viscosa ssp angustissimaSapindaceaeNo
Dodonaea viscosa ssp cuneataSapindaceaeNo
Dodonaea viscosa ssp spatulataSapindaceaeNo
Eremophila mitchelliMyoporaceaeNo
Eucalyptus intertextaMyrtaceaeNo
Geijera parvifloraRutaceaeNo
Hakea tephrospermaProteaceaeNo
Pimelea microcephalaThymelaeaceaeNo
Senna artemisioides var 1lftFabaceaeYes
Senna artemisioides var 3lftFabaceaeYes
Solanum ferocissiumSolanaceaeNo
Spartothamnella puberulaLamiaceaeNo
Acacia colletioidesFabaceaeYes
Acacia havilandiorumFabaceaeYes
Acacia wilhelmianaFabaceaeYes
Bertya cunninghamiiEuphorbiaceaeNo
Beyeria opacaEuphorbiaceaeNo
Brachychiton populneusMalvaceaeNo
Cassinia laevisAsteraceaeNo
Eremophila desertiMyoporaceaeNo
Eremophila glabraMyoporaceaeNo
Eucalyptus dumosaMyrtaceaeNo
Eucalyptus socialisMyrtaceaeNo
Eutaxia microphyllaFabaceaeYes
Grevillea anethifoliaProteaceaeNo
Melaleuca uncinataMyrtaceaeNo
Micromyrtus sessilisMyrtaceaeNo
Olearia decurrensAsteraceaeNo
Olearia pimelioidesAsteraceaeNo
Philotheca difformisRutaceaeNo
Santalum acuminatumSantalaceaeNo
Bossiaea walkeriFabaceaeYes

Relationships examined (within and across sites) were Vcmax[25] vs. Narea, Vcmax and Narea vs. gs, the normalised values Vcmax/Asat and Narea/Asat vs. gs/Asat (the rationale for these comparisons is described below), δ13C vs. χ, Narea vs. δ13C, and Narea and δ13C vs. MI. All gs values are given as conductances to CO2. Statistical analyses were carried out using SMATR, which fits standardised major axis slopes – suitable when the choice of the ‘x’ or ‘y’ variable is not predetermined (Warton et al. 2006). Non-significant intercepts were set to zero.

Hypothesis and approach

We hypothesised that plants minimise Cost = a.E/A + b.Vcmax/A where a is the (carbon) cost of maintaining the transpiration stream required to support assimilation at a rate A under normal daytime conditions, and b is the cost of maintaining photosynthetic proteins at the level required to support assimilation at the same rate. Vcmax, E and A here are molar flux densities (mol CO2 or H2O per unit leaf area and time). Note that whereas both E and A can vary rapidly (minutes), Cost expresses the maintenance requirements for the capacities for maximum rates of transpiration and photosynthesis. These vary much less rapidly (weeks to months).

Previous analyses have often focused on predicting gs, but it is conceptually simpler to predict χ. The two are related by Fick's law, gs = (A/ca)/(1 − χ). a.E/A and b.Vcmax/A represent the ‘unit costs’ of transpiration and carboxylation respectively. They respond in opposite ways to a change in χ, leading as we will show to the existence of a minimum in Cost that depends on the relative magnitudes of a and b.

Theoretical analysis

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Theoretical analysis
  6. Empirical results
  7. Discussion
  8. Acknowledgements
  9. Statement of authorship
  10. References
  11. Supporting Information

Principles

A value of χ that satisfies the optimisation criterion (χo) must satisfy the following:

  • display math(1)

Given that E = 1.6gsD and A = gsca(1 − χ), and assuming that A >> Rd (day respiration) and ci >> Γ* (the photorespiratory compensation point), it is shown below that the optimum is obtained for χ = χo where

  • display math(2)

and ξ = √(bK/1.6a), where K is the Michaelis–Menten coefficient for Rubisco-limited photosynthesis at a pO2 of 21 kPa.

By applying Fick's law to both transpiration and assimilation, we obtain

  • display math(3)

and from Farquhar et al. (1980) for Rubisco-limited photosynthesis,

  • display math(4)

The derivatives are

  • display math(5)

and

  • display math(6)

Therefore, if eqn (1) holds then

  • display math(7)

which on re-arrangement yields eqn (2). The turning point is a minimum, as both second derivatives are positive.

This simple derivation, to our knowledge, has not been published before. Relaxing the assumption that ci >> Γ* yields a small correction to eqn (2):

  • display math(8)

where ξ = √[b(K + Γ*)/1.6a]. This solution should be more accurate than eqn (2) at low ci . For simplicity, however, we use eqn (2) henceforward.

The interpretation of costs

Various predictions follow from eqn (2) by equating the cost of photosynthesis with the respiration required to maintain carboxylation capacity, and the cost of transpiration with the respiration required to maintain the transpiration pathway, over a timeframe of months to years and potentially including more and less favourable periods for growth. For simplicity we consider only these maintenance costs. We do not consider root costs, assumed to be common to both functions.

We can then express b as the ratio of total (24-h) leaf maintenance respiration to Vcmax. This is probably a relatively conservative quantity (Reich et al. 1998) but it will be several times larger than the ratio Rd/Vcmax measured during daytime, because mitochondrial respiration continues in the dark, and is partly inhibited in the light.

We can also relate the carbon cost of transpiration to E. Neglecting capacitance and gravitational effects, E equals the rate of flow of water through the stem according to Darcy's law (Whitehead 1998):

  • display math(9)

where vH is the Huber value (the ratio of sapwood area to the leaf area it supplies), ΔΨ (Pa) the typical daytime water potential difference between the soil and the leaf, ks (m2) sapwood permeability (a wood property independent of the properties of water: see Reid et al. 2005 for definitions), ρw (mol m−3) the density of water, η (Pa s) the viscosity of water, and h (m) the mean path length (approximately the mean foliage height). The Huber value enters here because Darcy's law describes total water flow through a stem of given area, whereas transpiration is expressed as the water flow per unit leaf area. The leaf-specific maintenance respiration cost of the sapwood, assuming a paraboloid stem, is

  • display math(10)

where rs is the sapwood specific respiration rate (s−1) and ρs (mol m−3) sapwood density. The maintenance cost of sapwood per unit transpiration is given by the following:

  • display math(11)

This expression does not allow for the effect of the tapering of xylem elements, which would result in ks decreasing with height and potentially reduce the dependence of a on height from quadratic to linear: see Becker et al. (2000), McCulloh et al. (2003, 2009).

Key implications of the theory

Equation (2) describes a dependence of χo on aridity through D. Other things being equal, a drier atmosphere implies a lower χo – because high D increases water flow through the plant, with no benefit in carbon gain. At very high D some plants show a decline in water flow, but this is necessarily accompanied by a further reduction in χ. Thus, we predict that χ should increase with MI, if temperature is held constant. (Temperature effects are considered below.) Equation (10) further suggests how plants in dry environments might counter this direct effect of aridity by lowering a, thereby increasing ξ. These include reduced height, and maintaining a constant ΔΨ even at low soil water potential; both of which can be considered adaptations to drought.

Equations (2) and (10) also imply responses of ξ to temperature. K in eqn (2) increases steeply with temperature (Bernacchi et al. 2009), from 196 ppm at 10 °C to 1094 ppm at 30 °C. Other things being equal, this effect should lead to increased χo at higher temperature. Among the terms contributing to a, it is unlikely that the specific respiration rate of sapwood (rs) over the growing season would be greater in a warmer environment, because of the ubiquitous thermal acclimation of basal respiration rates (Atkin & Tjoelker 2003). The term in eqn (10) expected to change most steeply with temperature is the viscosity of water (η) (Roderick & Berry 2001), 1.31 mPa s at 10 °C but only 0.798 mPa s at 30 °C. This response should increase ξ, and thereby increase χo, with increasing temperature. Thus, the temperature dependencies of both K and η lead to the prediction that χ should increase with temperature, if MI is held constant.

Graphical representations of data

Using Narea as an index of investment in photosynthetic capacity and gs for water transport, Wright et al. (2003) observed that isopleths of A in Narea-gs space would be hyperbolas; and that for any pair of cost values for water and N, the least-cost investment strategy would be where the tangent to the curve has a slope equal to the ratio of these costs. This prediction was supported by field measurements from sites differing in aridity. Within a site, different species showed widely ranging values of Narea and gs that nevertheless fell around a line corresponding to proportionality. The slope of this line was greater in drier sites, as expected when investment in water becomes more costly relative to investment in N.

The analogous representation in the Farquhar et al. (1980) model framework is in Vcmax-gs space. Using the eqn for Rubisco-limited photosynthesis together with Fick's law, it can be shown that the constant of proportionality between Vcmax and gs is a function only of χ, ca and K; and that for any given value of K, if both Vcmax and gs are normalised by A (hereafter V and G), then the relationship between them collapses to a single hyperbola (see Appendix S2). The optimality theory above predicts steeper slopes of Vcmax with respect to gs, and higher values of V (with correspondingly lower values of G) as the costs of transpiration increase relative to those of photosynthesis.

Sensitivity coefficients

Sensitivity coefficients (S) for χo with respect to different variables can be obtained by differentiation of eqn (2). Sensitivity coefficients represent the ratio of fractional change in one variable (here χo) to fractional change in another variable (x): = (x/χo) ∂χo/∂x. For an increment Δx with respect to a reference value x, the increment Δχo with respect to the corresponding reference value χo can be approximated by

  • display math(12)

The sensitivity coefficients are −(1 − χo)/2 for a and D, and (1 − χo)/2 for b and K. This approach makes it possible to predict effects of relative changes in factors affecting any of the terms influencing χo , without knowing their absolute values.

Empirical results

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Theoretical analysis
  6. Empirical results
  7. Discussion
  8. Acknowledgements
  9. Statement of authorship
  10. References
  11. Supporting Information

Approximate proportionality between Vcmax[25] and Narea can be seen in Fig. 1. The relationship across all sites is weaker than in some studies (e.g. Kattge et al. 2009) because the data include species from a wider range of environments. Niinemets et al. (2009) showed a comparable scatter. In pairwise comparisons, the slope of the Vcmax-Narea relationship at the dry site is shallower (P < 0.05) than the slopes at all of the other sites. Thus, more N is required to support a given Vcmax at the dry site. The slope at the hot site is also shallower (P < 0.05) than the slope at the cold site. Other pairwise differences are non-significant.

image

Figure 1. Relationships between carboxylation capacity at 25 °C (Vcmax[25]) and nitrogen per unit leaf area (Narea), colour-coded by sites: cold = blue, hot = red, wet = green, dry = brown. N-fixing species are identified by crosses.

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Some N-fixing species have exceptionally high Narea for a given Vcmax, but others do not. The overall slope (across all sites) for N-fixers is slightly greater than that for non-N-fixers (P < 0.05), but the data do not suggest a general pattern of ‘luxury consumption’ or storage of N by N-fixers.

Within each site, species also show approximate proportionality between Vcmax and gs, but the slopes vary between sites. The cold site shows a steeper slope than the warm site (Fig. 2a: P < 0.01), and the dry site shows a steeper slope than the wet site (Fig. 2b: P < 0.01). There was no significant difference between the slopes of the cold and the dry site, or the hot and the wet site. These findings agree with our predictions that χ should increase towards both warmer and wetter climates. Results obtained using Vcmax[25] instead of Vcmax were closely similar and all the statistical statements applying to the one variable also apply to the other.

image

Figure 2. Relationships between carboxylation capacity (Vcmax) and stomatal conductance to CO2 (gs) in (a) cold vs. hot sites and (b) wet vs. dry sites; (c), (d) corresponding relationships between nitrogen per unit leaf area (Narea) and gs. Colours are as in Fig. 1. N-fixing species are identified by crosses.

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The plots for Narea vs. gs (Fig. 2c, d) show a similar pattern of differences between sites to the plots for Vcmax vs. gs, with one anomaly: the Narea-gs slopes between the dry and wet sites differ about threefold, while the Vcmax-gs slopes differ only about twofold. In pairwise comparisons, the pattern of differences is the same for Narea as for Vcmax, except that the Narea-gs relationship is shallower (P < 0.05) at the dry site than at the cold site. This difference is to be expected, given the lower ratio of to Vcmax to Narea at the dry site (Fig. 1).

The same data after normalisation by A collapse on to a single hyperbola (Fig. 3). Equation (Appendix S2.2) is exact – the scatter is due to small variations in measurement temperatures affecting K. This curve is analogous to the equiproduction functions in Wright et al. (2003). Different positions along the curve correspond to different χ values, or equivalently, different combinations of Vcmax and gs that yield the same assimilation rate. The species-mean values for each site are separated as our hypothesis predicts. The cold and dry sites both have higher mean values of Vcmax/A, and lower mean values of gs/A, than the other two sites. The same contrasts are shown in the measured χ values (Fig. 3, inset). On average, species at the dry and cold sites have lower χ than species at the wet and hot sites.

image

Figure 3. Demonstration of the ‘unit production’ function, which represents a trade-off between carboxylation capacity (V = Vcmax/A) and transpiration (G = gs/A). Colours as Fig. 1. Large squares denote values of V and G averaged over all species within each of the four sites. The inset shows box-and-whisker plots (mean, upper and lower quartiles, and minimum and maximum values) for the measured ci/ca values, similarly averaged over all species within each of the sites.

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To compare these differences with predictions of the change in χo between sites we applied eqn (11), summing the estimated effects of increments above and below the mid-point of temperature (for the cold-hot comparison) or ΔΕ (for the dry-wet comparison) (Appendix S3). Moving from the wet site to the dry site yielded Δχo ≈ −0.186. The observed difference between mean χ values is −0.155. This is only 17% less than the prediction, but the difference is significant (P < 0.002), suggesting that some mitigation mechanism (e.g. lower stature) may be allowing plants at the dry site to maintain more open stomata than they could otherwise.

For the cold-hot comparison, moving from the hot site to the cold site yielded Δχo ≈ −0.112 from the temperature effect on K, and −0.034 from the temperature effect on η. In other words, the predicted effect of temperature on χ due to Rubisco kinetics is three times larger than the effect of viscosity. However, neither effect alone is sufficient to explain the observed difference between mean χ values (−0.154). The predicted effect via K is significantly (P < 0.05) smaller than this observed difference. However, the sum of predicted effects via K and η combined (−0.146) is statistically indistinguishable from the observed difference.

Our hypothesis further predicts that δ13C (because of its relation to time-averaged χ) and Narea (because of its relation to Vcmax[25]) should covary, and each should be related to temperature and water availability. Fig. 4a, b show relationships of δ13C to χ, and Narea to δ13C, in the complete data set. The slope for Narea vs. δ13C is slightly steeper (P < 0.05) for N-fixers. The slope for δ13C vs. χ is indistinguishable between N-fixers and non-N-fixers. Both Narea and δ13C values at each site show systematic shifts, in the expected direction, with MI (Figs 4c, d). Narea shows a slightly steeper increase (P < 0.01) with MI in N-fixers, while the response of δ13C is indistinguishable between N-fixers and non-N-fixers.

image

Figure 4. Relationships between (a) δ13C and ci/ca, (b) Narea and δ13C, (c) δ13C and (d) Narea on the climatic moisture index (MI). Separate regressions are shown for N-fixing species (grey) and others (black).

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Multiple regressions using mean annual precipitation and temperature as predictors of Narea and δ13C showed significant additional effects of temperature (P < 0.001: data not shown). However, in multiple regressions using MI and mean annual temperature as predictors, Narea showed no significant additional effect of temperature, while δ13C showed a barely significant additional effects of temperature (P < 0.05). These findings suggest that MI adequately captures the response of Narea and the major part of the response of δ13C to climate, including both temperature and water availability effects.

Discussion

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Theoretical analysis
  6. Empirical results
  7. Discussion
  8. Acknowledgements
  9. Statement of authorship
  10. References
  11. Supporting Information

The predictability of environmental trends in leaf traits

The optimality hypothesis presented here provides a unifying explanation for the relative constancy of χ under a range of conditions, its quantitative variation with temperature and water availability, and the emergent responses of Narea and δ13C to climate.

Our theoretical analysis and empirical results support the prediction of Wright et al. (2003) that high Vcmax and Narea in arid environments represent an adaptation to drought. Large investment in photosynthetic capacity allows a given assimilation rate to be maintained with lower stomatal conductance and reduced water loss. Reduced χ towards dry environments is predicted by eqn (2). The observed reduction in mean χ across species is slightly smaller than predicted, suggesting involvement of plant-level mechanisms that could lower the cost of transpiration as described by eqn (10).

The data also support our prediction of reduced χ in cold climates. The dependence of χ on K follows from the expression for ξ in eqn (2). Equation (10) also predicts an increase in a due to the greater viscosity of colder water. The predicted enzymatic effect is about threefold larger than the viscosity effect, but both are needed to explain the data.

It might have been expected that the increase in temperature from the cold to the hot site would be accompanied by increased D. But the two sites have similar MI values, and the change in χ is opposite to what would be predicted from increased D. From eqn (2), increased D with temperature should cause a reduction in χ from the cold to the hot site. We observe an increase.

A ‘trade-off’ or ‘complementarity’ between the marginal nitrogen and water use efficiencies of photosynthesis (∂A/∂N, approximately proportional to ∂A/∂Vcmax, and ∂A/∂E) is inevitable even for an individual plant over a short period, because of their opposite responses to χ (Field 1983; Farquhar et al. 2002). Palmroth et al. (2013) demonstrated this trade-off for Pinus taeda leaves grown under ambient and elevated ca. They showed that leaves have higher efficiencies at high ca, but that for each value of ca they are disposed along a gradient characterised by a negative relationship between marginal nitrogen and water use efficiencies. Our analyses further show that the preferred χ values shift in a predictable way along this gradient.

The proportionality between Vcmax and Narea is not constant. In particular, more N is apparently required to support a given level of Vcmax in the dry climate. Prentice et al. (2011) found that the increase of Narea with aridity along the North East China Transect was steeper than expected given only the modest observed increase in PAR (photosynthetically active radiation) along the transect, and observed changes in δ13C. A requirement for extra N could arise due to greater investment in structural N in the thicker (low SLA) leaves characteristic of arid sites, and/or to reduced mesophyll conductance (Niinemets et al. 1998) under drought conditions (Zhou et al. 2013). Low mesophyll conductance would mean that the standard gas-exchange measurement of Vcmax yields an underestimate of Rubisco activity. We do not have data to distinguish these possibilities. However, our finding of elevated Vcmax with disproportionately elevated N in the dry environment is consistent with the idea that wild plants compensate for the decline in apparent Vcmax – shown in drying experiments (Manzoni et al. 2011; Zhou et al. 2013) – by further increasing their investment in leaf N.

Optimisation criteria

Medlyn et al. (2011) showed that the Cowan-Farquhar optimality criterion is well approximated for electron transport-limited photosynthesis by eqn (2), but with ξ = √(3Γ*/1.6λ). Equation (2) is independent of ca. The same criterion applied to Rubisco-limited photosynthesis (Katul et al. 2010) yields a related function, including the same dependence on √D (apparently a robust prediction from different approaches), but with an additional dependence on ca (Medlyn et al. 2013). Our approach provides an alternative derivation of the formula of Medlyn et al. (2011), extending its applicability to Rubisco-limited photosynthesis.

It cannot be assumed a priori that any plant- or leaf-level property is optimised, not least because the optimisation criterion is unknown. Alternative criteria could be supposed to be consistent with maximising reproductive fitness. However, our results show that the hypothesis proposed by Wright et al. (2003) can be applied in a standard ecophysiological modelling framework, yielding a robust, consistent and quantitative biological interpretation of a range of observed trait relationships.

Towards a comprehensive approach to trait data analysis and vegetation modelling

The present generation of large-scale vegetation models treats ecophysiological properties of plants simplistically (Prentice & Cowling 2013). Models neglect the diversity of trait combinations that co-exist (Wright et al. 2004; Maire et al. 2012). For example, values of Vcmax are usually imputed to a plant functional type (PFT), as a single value or a single-valued function of environmental variables (Haxeltine & Prentice 1996). A new theoretical framework is needed to assimilate into models the information now available on the variation, interrelationships and environmental dependencies of plant traits. Our hypothesis provides an essential element, by predicting environmental influences on the covariation of gs and Vcmax. It provides a way to link the key model variables Vcmax, Narea and χ, and suggests analyses to investigate whether the relationships among them vary as predicted with wood hydraulic properties and environmental variables.

The value of χ predicted by eqn (2) is independent of actual values of Vcmax or gs. However, Vcmax and the Huber value (vH) are necessarily linked (Katul et al. 2003) due to the steady-state flow constraint, eqn (8). It seems likely that different species range along a spectrum from low carboxylation capacity and small Huber values (and/or poorly conductive sapwood), to high carboxylation capacity and large Huber values (and/or highly conductive sapwood), while always satisfying the optimisation criterion. This idea is supported by large variation among species in Huber values, and in xylem hydraulic properties (Gleason et al. 2012). Large, co-ordinated variations in Vcmax, gs and A are seen within sites (Fig. 2) and may represent a spectrum of plant hydraulics, which could be modelled as continuous variation within PFTs.

Acknowledgements

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Theoretical analysis
  6. Empirical results
  7. Discussion
  8. Acknowledgements
  9. Statement of authorship
  10. References
  11. Supporting Information

The idea for this article was developed at a Working Group of the Australian Research Council (ARC) Vegetation Function Network. We thank Remko Duursma, Dan Falster, Belinda Medlyn and Mark Westoby for subsequent discussions, and Peter Reich for providing the stable isotope measurements for the New South Wales species. Remko Duursma and Belinda Medlyn provided detailed comments. The research is supported by an ARC Discovery grant (‘Next-generation vegetation model based on functional traits’) to ICP and IJW. VM is partly supported by this grant and partly by Macquarie University funding to IJW. ND is supported by an international Macquarie Research Excellence scholarship awarded to ICP. SG is supported by an ARC Australian Laureate Fellowship awarded to Mark Westoby. IJW is supported by an ARC Future Fellowship.

Statement of authorship

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Theoretical analysis
  6. Empirical results
  7. Discussion
  8. Acknowledgements
  9. Statement of authorship
  10. References
  11. Supporting Information

ICP developed the theoretical analysis and wrote the first draft; ND carried out the graphical and statistical analyses; SMG and IJW provided field and laboratory measurements; all authors contributed to the interpretation of the results and the final manuscript.

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  5. Theoretical analysis
  6. Empirical results
  7. Discussion
  8. Acknowledgements
  9. Statement of authorship
  10. References
  11. Supporting Information
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Supporting Information

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Theoretical analysis
  6. Empirical results
  7. Discussion
  8. Acknowledgements
  9. Statement of authorship
  10. References
  11. Supporting Information
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ele12211-sup-0001-AppendixS1.docxWord document23K 
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