Ecology Letters, (2014) 17: 82–91 doi: 10.1111/ele.12211 LETTER Balancing the costs of carbon gain and water transport: testing a new theoretical framework for functional ecology

Abstract I. Colin Prentice,1,2* Ning Dong,1 A novel framework is presented for the analysis of ecophysiological field measurements and mod- Sean M. Gleason,1 Vincent Maire1 elling. The hypothesis ‘ minimise the summed unit costs of and carboxylation’ and Ian J. Wright1 predicts -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 from con- 1Department of Biological Sciences, trasting climates (cold-hot, dry-wet) yielded steeper slopes and lower mean ci/ca ratios at the dry Macquarie University, North Ryde, or cold sites than at the wet or hot sites. High atmospheric vapour pressure deficit implies low ci/ NSW, 2109, ca in dry climates. High water viscosity (more costly transport) and low photorespiration (less 2AXA Chair of Biosphere and costly ) imply low ci/ca in cold climates. Observed site-mean ci/ca shifts are pre- Climate Impacts, Department of Life dicted quantitatively for temperature contrasts (by photorespiration plus viscosity effects) and Sciences and Grantham Institute for approximately for aridity contrasts. The theory explains the dependency of c /c ratios on temper- Climate Change, Imperial College, i a d13 Silwood Park, Ascot, SL5 7PY, UK ature and vapour pressure deficit, and observed relationships of leaf C and Narea to aridity.

*Correspondence: Keywords E-mail: [email protected] Aridity, nitrogen, optimality, photosynthesis, plant functional traits, stable isotopes, stomatal con- ductance, temperature, transpiration, viscosity.

Ecology Letters (2014) 17: 82–91

2005), implying that N increases as v declines (Prentice INTRODUCTION area et al. 2011). Optimisation by natural selection is a powerful concept for gen- A general microeconomic optimisation criterion concerns erating testable hypotheses about organismal traits and their investments in two or more resources required to manufacture relationships to the environment (Givnish 1986; Makel€ a€ et al. a product. Here, the product is photosynthate, and the 2002). We explore the consequences of a simple optimality crite- resources are the photosynthetic apparatus (with costs rion that provides a unifying explanation for the following assumed proportional to Rubisco carboxylation capacity, observations on , all strongly supported in the literature: Vcmax, at a standard temperature, and approximately propor- • The relative conservatism of the ratio between leaf-inter- tional to Narea) and the transpiration pathway (with costs nal (ci) and ambient (ca) mole fractions of CO2 (Wong et al. assumed proportional to the maximal transpiration rate, E). 1979; Ehleringer & Cerling 1995). The ratio tends to vary by Wright et al. (2003) proposed the existence of an optimum rate only about 30% (rates of gas exchange can vary through of investment in transpiration and photosynthetic capacity, two orders of magnitude), and to be constant under variation dependent on the ratio of their costs, which would achieve a of ca, light and nutrient supply. This conservatism signifies given rate of net assimilation at least total cost. This analogy tight regulation of the balance between carbon gain and water requires that the resources are substitutable, e.g. that plants loss. We introduce the symbol v = ci/ca to simplify the can compensate for high water costs in dry climates by keeping notation later on. stomata relatively closed while increasing investment in photo- • The decline of v with vapour pressure deficit (D). Previ- synthetic capacity, maintaining a given level of carbon assimi- ously assigned various mathematical forms (Leuning 1990; lation at reduced ci. Wright et al. (2001) noted that this form Oren et al. 1999; Medlyn et al. 2011), this decline is well of resource substitution constitutes a widespread, previously described by v = ξ/(ξ + √D) where ξ is a parameter related overlooked mechanism of drought tolerance in plants. to the ‘carbon cost of water’ (Medlyn et al. 2011). Medlyn Wright et al. (2003) considered carbon assimilation as pro- et al. (2011) refer to this parameter as g1. portional to the product of two inputs, conceptualised as • The tendency demonstrated in many transect studies for water and nitrogen. We extend their reasoning to make quan- 13 the stable carbon isotope signature (d C) in the leaves of C3 titative predictions of trade-offs between photosynthetic and plants – a proxy for time-averaged values of v – to become water-transport parameters from the standard model of C3 less negative, indicating lower v, with increasing aridity photosynthesis (Farquhar et al. 1980) combined with plant (Stewart et al. 1995; Miller et al. 2001; Zheng & Shangguan water-relations theory. We use a graphical approach analo- 2007; Prentice et al. 2011). gous to Wright et al. (2003) to analyse field data on photosyn- • The tendency of leaf N per unit area (Narea) in all plants thesis, stomatal conductance and leaf traits from species in to increase from wet to dry climates (Wright et al. 2003, contrasting climates.

© 2013 John Wiley & Sons Ltd/CNRS Letter Balancing costs of C gain and H2O transport 83

Cowan & Farquhar (1977) introduced an optimisation ate temperature (MAT 17 to 18°C) between the cold and hot hypothesis for stomatal behaviour. Their hypothesis is equiva- sites; but the wet site has a much higher MI, and the dry site lent to maximising (A kE) where A is net carbon assimila- a much lower MI, than either the cold or the hot site. tion and k is an ‘exchange rate’ between carbon and water. Net photosynthesis (Asat) and stomatal conductance (gs) were Biochemical properties of leaves, and hydraulic properties of measured simultaneously in the field at saturating light intensity stems, were assumed fixed over the time scale of interest (prin- (800 to 1500 lmol m1 s1, depending on the ambient light cipally the diurnal cycle), although k could vary more slowly. intensity) and temperatures close to ambient, using either a The general solution to this optimisation is complex (Arneth LiCor 6400 (, Queensland) or a CIRAS-1 PP (New et al. 2002; Konrad et al. 2008; Katul et al. 2010); tractable South Wales) infra-red gas analysis system. Measurements were approximations have been proposed (Katul et al. 2010; Med- made on freshly cut, sun-exposed branches. Fieldwork was lyn et al. 2011). However, as noted in a pioneering analysis by scheduled so that ambient temperatures were similar regardless Givnish (1986), the Cowan-Farquhar optimality hypothesis is of site. CO2 concentration, vapour pressure deficit and measure- incomplete because it does not account for the (competing) ment temperatures were held within narrow ranges (388– costs of maintaining both water flow and photosynthetic 402 ppm, 1.8–2.1 kPa, 23.0–27.0 °C). Four to seven replicate capacity. Following Wright et al. (2003), we propose an opti- measurements per species were made, on different individuals. mal balance of investments in both functions. Remarkably, Leaf samples were analysed for specific leaf area (SLA), N by 13 we predict a relationship between v and D mathematically mass (converted to Narea using SLA) and d C. Carboxylation identical to that of Medlyn et al. (2011). But its single param- capacity at 25 °C(Vcmax[25]) was calculated using the Farquhar eter (here called ξ) has a subtly different interpretation, based et al. (1980) model, assuming that Asat is Rubisco-limited on the relative costs of maintaining a transpiration pathway (Kattge et al. 2009) and applying the temperature dependency capable of delivering water at a rate E, and leaf proteins capa- of Vcmax from Bernacchi et al. (2003, 2009). Day respiration ble of delivering photosynthate at a rate Vcmax. These costs was estimated by Rd = 0.01 Vcmax. Vcmax[25] is expected to be can be expressed in terms of traits, and are expected to vary more closely related to nitrogen investment than Vcmax at ambi- across environments. We examine how relationships among ent temperature, but the differences were slight because mea- Vcmax, Narea and gs vary across environments, and provide a surement temperatures were close (within 2°)to25°C. coherent, quantitative interpretation of these variations. 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 evapotranspira- MATERIALS AND METHODS tion, Ea, which in turn is a principal driver of D on large spatial and temporal scales (McNaughton & Jarvis 1991; Data Raupach 2000). An alternative measure of climatic aridity is Data were field measurements on all abundant woody dicots the Cramer-Prentice a (Table 1), a standardised estimate of (trees if present, and shrubs) at four sites in eastern Australia Ea/Eq (Gallego-Sala et al. 2010). a is related to MI by the (Table 1). Latitude ranges from 18°Sto42°S; mean annual Budyko framework for water vs. energy controls of catchment temperatures (MAT) from 10.4 and 22.6 °C; longitude over 5° water balance (Wang et al. 2012). For quantitative analysis of (coastal to interior) and mean annual precipitation (MAP) aridity effects on v, we use DΕ = Eq Ea =Eq (1 a)asa from 396 to 1133 mm. The sites were paired as follows. A proxy for the long-term effective value of D. Appendix S1 ‘cold’ high-latitude site in Tasmania was contrasted with a explains the rationale for our choice of hydroclimatic vari- ‘hot’ low-latitude site in Queensland. The Queensland site has ables, and the relationships among them. higher rainfall but similar climatic moisture index MI = P/Eq, where P is MAP and E is equilibrium evapotranspiration q Graphical and statistical analyses (calculated as in Gallego-Sala et al. 2010. See Appendix S1 for definitions of hydroclimatic variables). At intermediate All species sampled were included except two C4 species latitudes, in New South Wales, a ‘wet’ coastal site was (Atriplex stipitata and Triodia scariosa) and two species of contrasted with a ‘dry’ inland site. These sites have intermedi- Exocarpus (E. aphyllus and E. cupressiformis). The latter are

Table 1 Site locations and climates: mean annual precipitation (MAP); mean annual temperature (MAT); and moisture index (MI), Cramer-Prentice a, 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

2 Sites Location MAP (mm) MAT(◦ C) MI a Eq (mm) PAR0 (mol m )

‘cold’ 42.387˚S 540 10.4 0.68 0.72 799 9484 147.048˚E ‘hot’ 18.295˚S 1066 21.6 0.70 0.64 1515 13869 145.492˚E ‘wet’ 33.680˚S 1133 17.3 1.00 0.92 1138 11604 151.148˚E ‘dry’ 32.976˚S 396 17.9 0.31 0.36 1289 11487 146.156E

© 2013 John Wiley & Sons Ltd/CNRS 84 I. C. Prentice et al. Letter leafless, with photosynthetic stems, and were extreme outliers E=A ¼ 1:6ðD=caÞ=ð1 vÞð3Þ in the relationship between Vcmax[25] and Narea. The analysis included 14 species from the cold site, 17 from the hot site, and from Farquhar et al. (1980) for Rubisco-limited photo- and 35 each from the wet and the dry site (Table 2). Twenty- synthesis, six species were classified as N-fixers based on available = ¼ð þ = Þ= ð Þ information. This category consists mainly of but Vcmax A v K ca v 4 also includes two actinorhizal Allocasuarina species and one The derivatives are cycad (Macrozamia communis), which has a cyanobacterial 2 symbiont. @ðE=AÞ=@v ¼ 1:6ðD=caÞ=ð1 vÞ ð5Þ Relationships examined (within and across sites) were and Vcmax[25] vs. Narea, Vcmax and Narea vs. gs, the normalised values @ðV =AÞ=@v ¼K=v2c : ð6Þ Vcmax/Asat and Narea/Asat vs. gs/Asat (the rationale for these com- cmax a 13 13 parisons is described below), d C vs. v, Narea vs. d C, and Narea 13 Therefore, if eqn (1) holds then and d C vs. MI. All gs values are given as conductances to 2 2 CO2. Statistical analyses were carried out using SMATR, which 1:6ðaD=caÞ=ð1 vÞ ¼ bK=v ca ð7Þ fits standardised major axis slopes – suitable when the choice of the ‘x’ or ‘y’ variable is not predetermined (Warton et al. 2006). which on re-arrangement yields eqn (2). The turning point is a Non-significant intercepts were set to zero. minimum, as both second derivatives are positive. This simple derivation, to our knowledge, has not been pub- lished before. Relaxing the assumption that ci >> Γ* yields a Hypothesis and approach small correction to eqn (2): We hypothesised that plants minimise Cost = a.E/A + p ¼ C= þð C= Þ =ð þ ÞðÞ b.Vcmax/A where a is the (carbon) cost of maintaining the vo ca 1 ca n n D 8 transpiration stream required to support assimilation at a rate ξ = √ + Γ* A under normal daytime conditions, and b is the cost of main- where [b(K )/1.6a]. This solution should be more taining photosynthetic proteins at the level required to sup- accurate than eqn (2) at low ci . For simplicity, however, we use eqn (2) henceforward. port 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 (min- The interpretation of costs utes), Cost expresses the maintenance requirements for the capacities for maximum rates of transpiration and photosyn- Various predictions follow from eqn (2) by equating the cost thesis. These vary much less rapidly (weeks to months). of photosynthesis with the respiration required to maintain carboxylation capacity, and the cost of transpiration with the Previous analyses have often focused on predicting gs, but it is conceptually simpler to predict v. The two are related by respiration required to maintain the transpiration pathway, over a timeframe of months to years and potentially Fick’s law, gs = (A/ca)/(1 v). a.E/A and b.Vcmax/A represent the ‘unit costs’ of transpiration and carboxylation respectively. including more and less favourable periods for growth. For They respond in opposite ways to a change in v, leading as simplicity we consider only these maintenance costs. We do we will show to the existence of a minimum in Cost that not consider root costs, assumed to be common to both depends on the relative magnitudes of a and b. functions. We can then express b as the ratio of total (24-h) leaf main- tenance respiration to Vcmax. This is probably a relatively con- THEORETICAL ANALYSIS servative quantity (Reich et al. 1998) but it will be several times larger than the ratio Rd/Vcmax measured during daytime, Principles because mitochondrial respiration continues in the dark, and is partly inhibited in the light. A value of v that satisfies the optimisation criterion (vo) must satisfy the following: We can also relate the carbon cost of transpiration to E. Neglecting capacitance and gravitational effects, E equals the a:@ðE=AÞ=@v þ b:ðVcmax=AÞ=@v ¼ 0 ð1Þ rate of flow of water through the stem according to Darcy’s law (Whitehead 1998): Given that E = 1.6gsD and A = gsca(1 v), and assuming that A >> R (day respiration) and c >> Γ* (the photorespi- d i E ¼ m :DWk q =gh ð9Þ ratory compensation point), it is shown below that the H s w optimum is obtained for v = vo where where v is the Huber value (the ratio of sapwood area to the p H ¼ =ð þ ÞðÞ leaf area it supplies), DΨ (Pa) the typical daytime water vo n n D 2 2 potential difference between the soil and the leaf, ks (m ) and ξ = √(bK/1.6a), where K is the Michaelis–Menten coeffi- sapwood permeability (a wood property independent of the cient for Rubisco-limited photosynthesis at a pO2 of 21 kPa. properties of water: see Reid et al. 2005 for definitions), qw By applying Fick’s law to both transpiration and assimila- (mol m 3) the density of water, g (Pa s) the viscosity of water, tion, we obtain and h (m) the mean path length (approximately the mean

© 2013 John Wiley & Sons Ltd/CNRS Letter Balancing costs of C gain and H2O transport 85

Table 2 Species analysed Table 2 (continued)

Nitrogen- Nitrogen- Sites Genus_species Family fixing species Sites Genus_species Family fixing species

‘Cold’ dealbata Mimosaceae Yes ‘Wet’ buxifolia No Aotus ericoides Fabaceae Yes Proteaceae No marginata Proteaceae No dactyloides Proteaceae No cinerea Fabaceae Yes Proteaceae No Cassinia aculeata Asteraceae No Hibbertia bracteata Dilleniaceae No latifolia Fabaceae Yes formosa Proteaceae No Epacris impressa Epacridaceae No trinervium No pauciflora Myrtaceae No levis Proteaceae No Eucalyptus rubida Myrtaceae No Phyllota phylicoides Fabaceae Yes Eucalyptus tenuiramis Myrtaceae No Pimelea linifolia Thymelaeaceae No Leucopogon ericoides Epacridaceae No ‘Dry’ Acacia doratoxylon Fabaceae Yes Leucopogon virgatus Epacridaceae No Acacia oswaldii Fabaceae Yes Proteaceae No Callitris glaucophylla Cupressaceae No juniperina Fabaceae Yes Dodonaea viscosa ssp angustissima Sapindaceae No ‘Hot’ Acacia flavescens Mimosaceae Yes Dodonaea viscosa ssp cuneata Sapindaceae No Acacia leptostachya Mimosaceae Yes Dodonaea viscosa ssp spatulata Sapindaceae No Allocasuarina torulosa Casuarinaceae Yes Eremophila mitchelli Myoporaceae No Bursaria incana Pittosporaceae No Eucalyptus intertexta Myrtaceae No Corymbia citriodora Myrtaceae No Geijera parviflora Rutaceae No Corymbia intermedia Myrtaceae No Proteaceae No Corymbia trachyphloia Myrtaceae No Pimelea microcephala Thymelaeaceae No Eucalyptus portuensis Myrtaceae No Senna artemisioides var 1lft Fabaceae Yes Gastrolobium Fabaceae Yes Senna artemisioides var 3lft Fabaceae Yes grandiflorum Solanum ferocissium Solanaceae No Proteaceae No Spartothamnella puberula Lamiaceae No Proteaceae No Acacia colletioides Fabaceae Yes Lophostemon Myrtaceae No Acacia havilandiorum Fabaceae Yes suaveolens Acacia wilhelmiana Fabaceae Yes Proteaceae No Bertya cunninghamii Euphorbiaceae No Petalostigma pubescens Picrodendraceae No Beyeria opaca Euphorbiaceae No Lecythidaceae No Brachychiton populneus Malvaceae No Pogonolobus reticulatus Rubiaceae No Cassinia laevis Asteraceae No scottianum Proteaceae No Eremophila deserti Myoporaceae No ‘Wet’ Acacia floribunda Fabaceae Yes Eremophila glabra Myoporaceae No Astrotricha floccosa Araliaceae No Eucalyptus dumosa Myrtaceae No Correa reflexa Rutaceae No Eucalyptus socialis Myrtaceae No Dodonaea triquetra Sapindaceae No Eutaxia microphylla Fabaceae Yes Eucalyptus paniculata Myrtaceae No Proteaceae No Eucalyptus umbra Myrtaceae No Melaleuca uncinata Myrtaceae No Lasiopetalum Malvaceae No Micromyrtus sessilis Myrtaceae No ferrugineum Olearia decurrens Asteraceae No Leptospermum Myrtaceae No Olearia pimelioides Asteraceae No polygalifolium Philotheca difformis Rutaceae No silaifolia Proteaceae No Santalum acuminatum Santalaceae No Macrozamia communis Zamiaceae Yes Bossiaea walkeri Fabaceae Yes Proteaceae No Two C species (Atriplex stipitata and Triodia scariosa) and two species of Pomaderris ferruginea Rhamnaceae No 4 Exocarpus (E. aphyllus and E. cupressiformis) were excluded from the Pultenaea daphnoides Fabaceae Yes analysis. Pultenaea flexilis Fabaceae Yes Syncarpia glomulifera Myrtaceae No Synoum glandulosum Meliaceae No Proteaceae No foliage height). The Huber value enters here because Darcy’s Allocasuarina sp Casuarinaceae Yes law describes total water flow through a stem of given area, Acacia suaveolens Fabaceae Yes whereas transpiration is expressed as the water flow per unit Proteaceae No leaf area. The leaf-specific maintenance respiration cost of the Boronia ledifolia Rutaceae No Corymbia gummifera Myrtaceae No sapwood, assuming a paraboloid stem, is Eriostemon australasius Rutaceae No ¼ = ð Þ Eucalyptus haemostoma Myrtaceae No Rs mH:rshqs 2 10 Gompholobium Fabaceae Yes 1 glabratum where rs is the sapwood specific respiration rate (s ) and qs (mol m3) sapwood density. The maintenance cost of sap- wood per unit transpiration is given by the following:

© 2013 John Wiley & Sons Ltd/CNRS 86 I. C. Prentice et al. Letter

g is a function only of v, c and K; and that for any given ¼ = ¼ 2 = DW ð Þ s a a Rs E rsh qsg 2 ksqw 11 value of K, if both Vcmax and gs are normalised by A (hereafter This expression does not allow for the effect of the tapering V and G), then the relationship between them collapses to a single hyperbola (see Appendix S2). The optimality theory of xylem elements, which would result in ks decreasing with height and potentially reduce the dependence of a on height above predicts steeper slopes of Vcmax with respect to gs, and from quadratic to linear: see Becker et al. (2000), McCulloh higher values of V (with correspondingly lower values of G)as et al. (2003, 2009). the costs of transpiration increase relative to those of photo- synthesis.

Key implications of the theory Sensitivity coefficients Equation (2) describes a dependence of vo on aridity through D. Other things being equal, a drier atmosphere implies a Sensitivity coefficients (S) for vo with respect to different vari- ables can be obtained by differentiation of eqn (2). Sensitivity lower vo – because high D increases water flow through the plant, with no benefit in carbon gain. At very high D some coefficients represent the ratio of fractional change in one var- plants show a decline in water flow, but this is necessarily iable (here vo) to fractional change in another variable (x): = o o D accompanied by a further reduction in v. Thus, we predict S (x/vo) vo/ x. For an increment x with respect to a D that v should increase with MI, if temperature is held constant. reference value x, the increment vo with respect to the corre- (Temperature effects are considered below.) Equation (11) fur- sponding reference value vo can be approximated by ther suggests how plants in dry environments might counter D ð = ÞD ð Þ vo S vo x x 12 this direct effect of aridity by lowering a, thereby increasing ξ. These include reduced height, and maintaining a constant DΨ The sensitivity coefficients are (1 vo)/2 for a and D, and even at low soil water potential; both of which can be consid- (1 vo)/2 for b and K. This approach makes it possible to ered adaptations to drought. predict effects of relative changes in factors affecting any of Equations (2) and (11) also imply responses of ξ to tempera- the terms influencing vo , without knowing their absolute ture. K in eqn (2) increases steeply with temperature (Bernacchi values. 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 vo EMPIRICAL RESULTS at higher temperature. Among the terms contributing to a,itis Approximate proportionality between V [25] and N can unlikely that the specific respiration rate of sapwood (rs) over cmax area the growing season would be greater in a warmer environment, be seen in Fig. 1. The relationship across all sites is weaker because of the ubiquitous thermal acclimation of basal respira- than in some studies (e.g. Kattge et al. 2009) because the data tion rates (Atkin & Tjoelker 2003). The term in eqn (11) include species from a wider range of environments. Niine- expected to change most steeply with temperature is the viscos- mets et al. (2009) showed a comparable scatter. In pairwise ity of water (g) (Roderick & Berry 2001), 1.31 mPa s at 10 °C comparisons, the slope of the Vcmax-Narea relationship at the but only 0.798 mPa s at 30 °C. This response should increase ξ, 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 V and thereby increase vo, with increasing temperature. Thus, the cmax temperature dependencies of both K and g lead to the predic- at the dry site. The slope at the hot site is also shallower tion that v should increase with temperature, if MI is held (P < 0.05) than the slope at the cold site. Other pairwise constant. differences are non-significant. Some N-fixing species have exceptionally high Narea for a given Vcmax, but others do not. The overall slope (across all Graphical representations of data sites) for N-fixers is slightly greater than that for non-N-fixers < Using Narea as an index of investment in photosynthetic capac- (P 0.05), but the data do not suggest a general pattern of ity and gs for water transport, Wright et al. (2003) observed ‘luxury consumption’ or storage of N by N-fixers. that isopleths of A in Narea-gs space would be hyperbolas; and Within each site, species also show approximate proportion- that for any pair of cost values for water and N, the least-cost ality between Vcmax and gs, but the slopes vary between sites. investment strategy would be where the tangent to the curve The cold site shows a steeper slope than the warm site has a slope equal to the ratio of these costs. This prediction (Fig. 2a: P < 0.01), and the dry site shows a steeper slope was supported by field measurements from sites differing in than the wet site (Fig. 2b: P < 0.01). There was no significant aridity. Within a site, different species showed widely ranging difference between the slopes of the cold and the dry site, or values of Narea and gs that nevertheless fell around a line corre- the hot and the wet site. These findings agree with our predic- sponding to proportionality. The slope of this line was greater tions that v should increase towards both warmer and wetter in drier sites, as expected when investment in water becomes climates. Results obtained using Vcmax[25] instead of Vcmax more costly relative to investment in N. were closely similar and all the statistical statements applying The analogous representation in the Farquhar et al. (1980) to the one variable also apply to the other. model framework is in Vcmax-gs space. Using the eqn for Rubi- The plots for Narea vs. gs (Fig. 2c, d) show a similar pattern sco-limited photosynthesis together with Fick’s law, it can be of differences between sites to the plots for Vcmax vs. gs, with shown that the constant of proportionality between Vcmax and one anomaly: the Narea-gs slopes between the dry and wet sites

© 2013 John Wiley & Sons Ltd/CNRS Letter Balancing costs of C gain and H2O transport 87

N−fixer The same data after normalisation by A collapse on to a sin- Non N−fixer gle hyperbola (Fig. 3). Equation (Appendix S2.2) is exact – the 150 Cold

) Hot scatter is due to small variations in measurement temperatures 1

– Wet

s Dry affecting K. This curve is analogous to the equiproduction func- 2 – tions in Wright et al. (2003). Different positions along the curve m 2 correspond to different v values, or equivalently, different com- 100 binations 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 [25] (µmol CO 50 the other two sites. The same contrasts are shown in the mea- cmax

V sured v values (Fig. 3, inset). On average, species at the dry and cold sites have lower v than species at the wet and hot sites. To compare these differences with predictions of the change 0 1234567 in vo between sites we applied eqn (12), summing the esti- –2 Narea (g m ) mated effects of increments above and below the mid-point of temperature (for the cold-hot comparison) or DΕ (for the dry-

Fig. 1 Relationships between carboxylation capacity at 25 °C(Vcmax[25]) wet comparison) (Appendix S3). Moving from the wet site to = and nitrogen per unit leaf area (Narea), colour-coded by sites: cold blue, the dry site yielded Dvo 0.186. The observed difference hot = red, wet = green, dry = brown. N-fixing species are identified by between mean v values is 0.155. This is only 17% less than crosses. the prediction, but the difference is significant (P < 0.002), suggesting that some mitigation mechanism (e.g. lower stat- ure) may be allowing plants at the dry site to maintain more differ about threefold, while the Vcmax-gs slopes differ only open stomata than they could otherwise. about twofold. In pairwise comparisons, the pattern of differ- For the cold-hot comparison, moving from the hot site to ences is the same for Narea as for Vcmax, except that the Narea- the cold site yielded Dvo 0.112 from the temperature effect gs relationship is shallower (P < 0.05) at the dry site than at on K, and 0.034 from the temperature effect on g. In other the cold site. This difference is to be expected, given the lower words, the predicted effect of temperature on v due to Rubi- ratio of to Vcmax to Narea at the dry site (Fig. 1). sco kinetics is three times larger than the effect of viscosity.

(a) (b) )

1 150

– y = 1131x Y = 1041x s

2 y = 487x Y = 460x – m 2 100

(µmol CO 50 N−fixer N−fixer Non N−fixer Non N−fixer

cmax Cold Wet V Hot Dry 0 (c) (d)

6 y = 31x y = 44x )

2 y = 14x y = 15x –

4 (g m area N 2

0 0.05 0.1 0.15 0.2 0.25 0.3 0.05 0.1 0.15 0.2 0.25 0.3 –2 –1 gs (mol CO2 m s )

Fig. 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.

© 2013 John Wiley & Sons Ltd/CNRS 88 I. C. Prentice et al. Letter

However, neither effect alone is sufficient to explain the 0.8 observed difference between mean v values (0.154). The pre- 25 dicted effect via K is significantly (P < 0.05) smaller than this 0.6 observed difference. However, the sum of predicted effects via ratio a 20 0.4 K and g combined (0.146) is statistically indistinguishable : C i from the observed difference. C 0.2 Our hypothesis further predicts that d13C (because of its 15 V 0.0 relation to time-averaged v) and N (because of its relation cold hot wet dry area sites to Vcmax[25]) should covary, and each should be related to 10 temperature and water availability. Fig. 4a, b show relation- 13 13 ships of d Ctov, and Narea to d C, in the complete data 13 5 set. The slope for Narea vs. d C is slightly steeper (P < 0.05) for N-fixers. The slope for d13C vs. v is indistinguishable 13 between N-fixers and non-N-fixers. Both Narea and d C val- 0 0.01 0.02 0.03 0.04 0.05 ues at each site show systematic shifts, in the expected direc- G tion, with MI (Figs 4c, d). Narea shows a slightly steeper increase (P < 0.01) with MI in N-fixers, while the response of Fig. 3 Demonstration of the ‘unit production’ function, which d13C is indistinguishable between N-fixers and non-N-fixers. represents a trade-off between carboxylation capacity (V=Vcmax/A) Multiple regressions using mean annual precipitation and and transpiration (G = gs/A). Colours as Fig. 1. Large squares 13 temperature as predictors of Narea and d C showed signifi- 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 cant additional effects of temperature (P 0.001: data not and lower quartiles, and minimum and maximum values) for the shown). However, in multiple regressions using MI and measured ci/ca values, similarly averaged over all species within each of mean annual temperature as predictors, Narea showed no the sites. significant additional effect of temperature, while d13C

−24 8 2 (a) R = 0.30 , P < 0.001 (b) R2 = 0.18 , P < 0.05

−26 6 ) 2 – (g m

13C −28 4 δ area N

−30 2

R2 = 0.15 , P < 0.001 R2 = 0.18 , P < 0.05 0 0 0.2 0.4 0.6 0.8 −30 −28 −26 −24 Ci : Ca δ13C

−24 8 2 (c) (d) R = 0.59 , P < 0.001 R2 = 0.39 , P < 0.001

−26 6 ) 2 –

13C −28 4 δ (g m area N −30 2

R 2 = 0.43 , P < 0.001 R 2 = 0.47 , P < 0.001 0 0 0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1 MI MI

13 13 13 Fig. 4 Relationships between (a) d C and ci/ca, (b) Narea and d C, (c) d C and (d) Narea on the climatic moisture index (MI). Separate regressions are shown for N-fixing species (grey) and others (black).

© 2013 John Wiley & Sons Ltd/CNRS Letter Balancing costs of C gain and H2O transport 89 showed a barely significant additional effects of temperature arid sites, and/or to reduced mesophyll conductance (Niinemets (P < 0.05). These findings suggest that MI adequately cap- et al. 1998) under drought conditions (Zhou et al. 2013). Low tures the response of Narea and the major part of the mesophyll conductance would mean that the standard gas- 13 response of d C to climate, including both temperature and exchange measurement of Vcmax yields an underestimate of Ru- water availability effects. bisco activity. We do not have data to distinguish these possi- bilities. However, our finding of elevated Vcmax with disproportionately elevated N in the dry environment is consis- DISCUSSION tent with the idea that wild plants compensate for the decline in apparent V – shown in drying experiments (Manzoni et al. The predictability of environmental trends in leaf traits cmax 2011; Zhou et al. 2013) – by further increasing their investment The optimality hypothesis presented here provides a unifying in leaf N. explanation for the relative constancy of v under a range of conditions, its quantitative variation with temperature and Optimisation criteria water availability, and the emergent responses of Narea and d13C to climate. Medlyn et al. (2011) showed that the Cowan-Farquhar opti- Our theoretical analysis and empirical results support the mality criterion is well approximated for electron transport- prediction of Wright et al. (2003) that high Vcmax and Narea in limited photosynthesis by eqn (2), but with ξ = √(3Γ*/1.6k). arid environments represent an adaptation to drought. Large Equation (2) is independent of ca. The same criterion applied investment in photosynthetic capacity allows a given assimila- to Rubisco-limited photosynthesis (Katul et al. 2010) yields a tion rate to be maintained with lower stomatal conductance related function, including the same dependence on √D and reduced water loss. Reduced v towards dry environments (apparently a robust prediction from different approaches), is predicted by eqn (2). The observed reduction in mean v but with an additional dependence on ca (Medlyn et al. 2013). across species is slightly smaller than predicted, suggesting Our approach provides an alternative derivation of the for- involvement of plant-level mechanisms that could lower the mula of Medlyn et al. (2011), extending its applicability to cost of transpiration as described by eqn (11). Rubisco-limited photosynthesis. The data also support our prediction of reduced v in cold It cannot be assumed a priori that any plant- or leaf-level climates. The dependence of v on K follows from the expres- property is optimised, not least because the optimisation crite- sion for ξ in eqn (2). Equation (11) also predicts an increase rion is unknown. Alternative criteria could be supposed to be in a due to the greater viscosity of colder water. The predicted consistent with maximising reproductive fitness. However, our enzymatic effect is about threefold larger than the viscosity results show that the hypothesis proposed by Wright et al. effect, but both are needed to explain the data. (2003) can be applied in a standard ecophysiological modelling It might have been expected that the increase in temperature framework, yielding a robust, consistent and quantitative bio- from the cold to the hot site would be accompanied by logical interpretation of a range of observed trait relationships. increased D. But the two sites have similar MI values, and the change in v is opposite to what would be predicted from Towards a comprehensive approach to trait data analysis and increased D. From eqn (2), increased D with temperature vegetation modelling should cause a reduction in v from the cold to the hot site. We observe an increase. The present generation of large-scale vegetation models treats A ‘trade-off’ or ‘complementarity’ between the marginal ecophysiological properties of plants simplistically (Prentice & nitrogen and water use efficiencies of photosynthesis (oA/oN, Cowling 2013). Models neglect the diversity of trait combina- approximately proportional to oA/oVcmax, and oA/oE) is inevi- tions that co-exist (Wright et al. 2004; Maire et al. 2012). For table even for an individual plant over a short period, because example, values of Vcmax are usually imputed to a plant func- of their opposite responses to v (Field 1983; Farquhar et al. tional type (PFT), as a single value or a single-valued function 2002). Palmroth et al. (2013) demonstrated this trade-off for of environmental variables (Haxeltine & Prentice 1996). A Pinus taeda leaves grown under ambient and elevated ca. They new theoretical framework is needed to assimilate into models showed that leaves have higher efficiencies at high ca, but that the information now available on the variation, interrelation- for each value of ca they are disposed along a gradient charac- ships and environmental dependencies of plant traits. Our terised by a negative relationship between marginal nitrogen hypothesis provides an essential element, by predicting envi- and water use efficiencies. Our analyses further show that the ronmental influences on the covariation of gs and Vcmax.It preferred v values shift in a predictable way along this gradient. provides a way to link the key model variables Vcmax, Narea The proportionality between Vcmax and Narea is not constant. and v, and suggests analyses to investigate whether the rela- In particular, more N is apparently required to support a given tionships among them vary as predicted with wood hydraulic level of Vcmax in the dry climate. Prentice et al. (2011) found properties and environmental variables. that the increase of Narea with aridity along the North East The value of v predicted by eqn (2) is independent of actual China Transect was steeper than expected given only the mod- values of Vcmax or gs. However, Vcmax and the Huber value est observed increase in PAR (photosynthetically active radia- (vH) are necessarily linked (Katul et al. 2003) due to the tion) along the transect, and observed changes in d13C. A steady-state flow constraint, eqn (9). It seems likely that dif- requirement for extra N could arise due to greater investment ferent species range along a spectrum from low carboxylation in structural N in the thicker (low SLA) leaves characteristic of capacity and small Huber values (and/or poorly conductive

© 2013 John Wiley & Sons Ltd/CNRS 90 I. C. Prentice et al. Letter sapwood), to high carboxylation capacity and large Huber Farquhar, G.D., Caemmerer, S. & Berry, J.A. (1980). A biochemical values (and/or highly conductive sapwood), while always satis- model of photosynthetic CO2 assimilation in leaves of C3 species. – fying the optimisation criterion. This idea is supported by Planta, 149, 78 90. Farquhar, G.D., Buckley, T.N. & Miller, J.M. (2002). Optimal stomatal large variation among species in Huber values, and in xylem control in relation to leaf area and nitrogen content. Silva Fenn., 36, hydraulic properties (Gleason et al. 2012). Large, co-ordinated 625–637. variations in Vcmax, gs and A are seen within sites (Fig. 2) and Field, C. (1983). Allocating leaf nitrogen for the maximization of carbon may represent a spectrum of plant hydraulics, which could be gain: Leaf age as a control on the allocation program. Oecologia, 56, modelled as continuous variation within PFTs. 341–347. Gallego-Sala, A., Clark, J., House, J., Orr, H., Prentice, I., Smith, P. et al. (2010). Bioclimatic envelope model of climate change impacts on ACKNOWLEDGEMENTS blanket peatland distribution in Great Britain. Clim. Res., 45, 151–162. Givnish, T.J. (1986). On the Economy of Plant Form and Function. The idea for this article was developed at a Working Group Cambridge University Press, Cambridge, UK, p. 736. of the Australian Research Council (ARC) Vegetation Func- Gleason, S.M., Butler, D.W., Zieminska, K., Waryszak, P. & Westoby, tion Network. We thank Remko Duursma, Dan Falster, Be- M. (2012). Stem xylem conductivity is key to plant water balance linda Medlyn and Mark Westoby for subsequent discussions, across Australian angiosperm species. Funct. Ecol., 26, 343–352. and Peter Reich for providing the stable isotope measure- Haxeltine, A. & Prentice, I.C. (1996). A general model for the light use – ments for the New South Wales species. Remko Duursma efficiency of primary production. Funct. Ecol., 10, 551 561. Kattge, J., Knorr, W., Raddatz, T. & Wirth, C. (2009). Quantifying and Belinda Medlyn provided detailed comments. The photosynthetic capacity and nitrogen use efficiency for earth system research is supported by an ARC Discovery grant (‘Next- models. Glob. Change Biol., 15, 976–991. generation vegetation model based on functional traits’) to Katul, G.G., Leuning, R. & Oren, R. (2003). Relationship between plant ICP and IJW. VM is partly supported by this grant and hydraulic and biochemical properties derived from a steady-state partly by Macquarie University funding to IJW. ND is sup- coupled water and carbon transport model. Plant, Cell Environ., 26, – ported by an international Macquarie Research Excellence 339 350. Katul, G., Manzoni, S., Palmroth, S. & Oren, R. (2010). A stomatal scholarship awarded to ICP. SG is supported by an ARC optimization theory to describe the effects of atmospheric CO2 on leaf Australian Laureate Fellowship awarded to Mark Westoby. photosynthesis and transpiration. Ann. Bot., 105, 431–442. IJW is supported by an ARC Future Fellowship. Konrad, W., Roth-Nebelsick, A. & Grein, M.J. (2008). Modelling of

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