Plant, Cell and Environment

(2002)

25,

1167–1179

© 2002 Blackwell Publishing Ltd

1167

Blackwell Science, LtdOxford, UKPCEPlant, Cell and Environment0016-8025Blackwell Science Ltd 200225891Temperature response of photosynthetic parameters – reviewB. E. Medlyn

et al

.10.1046/j.0016-8025.2002.00891.xOriginal Article11671179BEES SGML

Correspondence: Belinda E. Medlyn, School of Biological, Earthand Environmental Science, University of New South Wales, UNSWSydney 2052, Australia. Fax:

+

61 (0)29385 1558; e-mail: B.Medlyn@unsw.edu.au

Temperature response of parameters of a biochemically based model of photosynthesis. II. A review of experimental data

B. E. MEDLYN

1,2

, E. DREYER

3

, D. ELLSWORTH

4

, M. FORSTREUTER

5

, P. C. HARLEY

6

, M. U. F. KIRSCHBAUM

7

, X. LE ROUX

8,9

,

P. MONTPIED

3

, J. STRASSEMEYER

5

, A. WALCROFT

8,10

, K. WANG

11

& D. LOUSTAU

1

1

INRA Pierroton, Laboratoire d'Ecophysiologie et Nutrition, 33611 Gazinet Cedex, France,

2

School of Biological, Earth and Environmental Science, University of NSW, Sydney 2052, Australia,

3

UMR INRA UHP, Ecologie et Ecophysiologie Forestières, 54280 Champenoux, France,

4

School of Natural Resources and Environment, University of Michigan, Ann Arbor, MI 48109, USA,

5

Institut für Ökologie, Technische Universität Berlin, Königin-Luise-Str.22, D-100 Berlin 33, Germany,

6

Atmospheric Chemistry Division, NCAR, Boulder, CO 80307–3000, USA,

7

CSIRO Forestry and Forest Products, PO Box E4008, Kingston ACT 2604, Australia,

8

UMR PIAF (INRA/University Blaise Pascal), 234 avenue du Brezet, 63039 Clermont Ferrand, France,

9

UMR 5557 Ecologie Microbienne, 43 bd du 11 novembre 1918, 69622 Villeurbanne, France,

10

Manaaki Whenua – Landcare Research, Private Bag 11 052, Palmerston North, New Zealand and

11

Faculty of Forestry, University of Joensuu, PO Box 111, Joensuu, Finland

ABSTRACT

The temperature dependence of C

3

photosynthesis isknown to vary with growth environment and with species.In an attempt to quantify this variability, a commonly usedbiochemically based photosynthesis model was parameter-ized from 19 gas exchange studies on tree and crop species.The parameter values obtained described the shape andamplitude of the temperature responses of the maximumrate of Rubisco activity (

V

cmax

) and the potential rate ofelectron transport (

J

max

). Original data sets were used forthis review, as it is shown that derived values of

V

cmax

and itstemperature response depend strongly on assumptionsmade in derivation. Values of

J

max

and

V

cmax

at 25

°°°°

C variedconsiderably among species but were strongly correlated,with an average

J

max

:

V

cmax

ratio of 1·67. Two species grownin cold climates, however, had lower ratios. In all studies,the

J

max

:

V

cmax

ratio declined strongly with measurementtemperature. The relative temperature responses of

J

max

and

V

cmax

were relatively constant among tree species. Acti-vation energies averaged 50 kJ mol

−−−−

1

for

J

max

and 65 kJmol

−−−−

1

for

V

cmax

, and for most species temperature optimaaveraged 33

°°°°

C for

J

max

and 40

°°°°

C for

V

cmax

. However, thecold climate tree species had low temperature optima forboth

J

max

(

19

°°°°

C) and

V

cmax

(29

°°°°

C), suggesting acclimationof both processes to growth temperature. Crop species hadsomewhat different temperature responses, with higheractivation energies for both

J

max

and

V

cmax

, implying nar-rower peaks in the temperature response for these species.The results thus suggest that both growth environment and

plant type can influence the photosynthetic response totemperature. Based on these results, several suggestions aremade to improve modelling of temperature responses.

Key-words

: electron transport; model parameters;photosynthesis; ribulose-1,5-

bis

phosphate carboxylase-oxygenase; ribulose-1,5-

bis

phosphate regeneration; tem-perature acclimation.

INTRODUCTION

Many of the models used to study effects of global changeon plant function and growth incorporate the Farquhar, vonCaemmerer & Berry (1980) model of C

3

photosynthesis(e.g. Cramer

et al

. 2001). This model is particularly useful inthis context because it represents mechanistically theeffects of elevated atmospheric [CO

2

], a major factor in glo-bal change, on photosynthesis. The model has two majorparameters, the potential rate of electron transport (

J

max

)and the maximum rate of ribulose-1,5-

bis

phosphate car-boxylase-oxygenase (Rubisco) activity (

V

cmax

). There is nowa large database of values of

J

max

and

V

cmax

(Wullschleger1993) and the effects of elevated [CO

2

] on these parameters(Medlyn

et al

. 1999). The model also has the potential toaccurately represent the effects of elevated temperature, asecond major factor in global change that directly affectsplant growth. However, as many modellers are aware, thereis a dearth of information regarding the temperatureresponses of

J

max

and

V

cmax

(Leuning 1997).We know that these temperature responses are likely to

vary, because the temperature response of photosynthesisitself varies with genotype and environmental conditions,and may acclimate to changes in growth temperature(Slatyer & Morrow 1977; Berry & Björkman 1980). To date,however, there has been a fairly limited number of studies

1168

B. E. Medlyn

et al.

© 2002 Blackwell Publishing Ltd,

Plant, Cell and Environment

,

25

, 1167–1179

examining temperature responses in the context of the Far-quhar model (Leuning 1997). The limited amount of infor-mation available can result in possibly inappropriateparameter choices. The database of temperature responsesof model parameters has the potential to expand in the nearfuture, given recent improvements in temperature controlin commercially available gas exchange systems. However,there is a second obstacle to identifying variation in theseresponses between species, which is that parameter valuesobtained from data can differ according to the method usedto derive them, as is shown below. Direct comparison ofparameter values between different studies can thereforebe misleading. Wullschleger (1993) solved this problemwhen compiling a database of

J

max

and

V

cmax

by deriving allparameter values himself directly from

A

–

C

i

curves, thusensuring consistency between parameters.

The aim of this study was to improve modelling of pho-tosynthetic temperature responses by compiling and com-paring existing information on the temperature response ofthe parameters of the Farquhar

et al

. (1980) model of pho-tosynthesis. Few studies have compared variation of theseparameters among species, so a broad understanding oftemperature responses and their relationship to speciescharacteristics and growth environment is lacking. Weadopted the approach of Wullschleger (1993), using consis-tent methods to derive model parameters from the originaldata sets. Some 19 data sets were obtained. In order to drawsome generalizations from these data sets, we attemptedto link variation in the parameters between data sets toecological factors such as functional type and growthenvironment.

METHODS

Data

Estimates of the parameters

J

max

and

V

cmax

may beobtained in several ways including gas exchange (Kirsch-baum & Farquhar 1984; Harley, Tenhunen & Lange 1986),

in vitro

methods (Badger & Collatz 1977; Armond,Schreiber & Björkman 1978) or chlorophyll fluorescence(Niinemets, Oja & Kull 1999). In order to ensure thatresponses were comparable, we chose only to include gasexchange data. In this method, values of

J

max

and

V

cmax

areobtained from the response of photosynthesis under highlight (

A

) to intercellular CO

2

(

C

i

). A family of

A

–

C

i

curvesat different temperatures will thus give the temperatureresponse of the two parameters

J

max

and

V

cmax

. Obtainingsuch a family of curves is very time-consuming and henceseveral authors have attempted to estimate the tempera-ture responses of

J

max

and

V

cmax

using reduced data sets(e.g. Hikosaka, Murakami & Hirose 1999; Wohlfahrt

et al

.1999). We attempted to include some of these studies here,but we found that such shortcuts considerably reduced theaccuracy of the parameter values, and therefore decidedagainst their inclusion.

We required the original

A

–

C

i

curves from each study,for reasons illustrated below. However, in two cases the

original data were no longer available (Kirschbaum & Far-quhar 1984; Harley

et al

. 1992). Temperature responsesfrom these two studies have been extensively used in mod-elling, so we thought it important to include them in thecomparison. Therefore, in these two cases, typical

A

–

C

i

curves were reconstructed from reported parameter valuesand the model was re-fitted to these curves. Statisticalinformation on parameters obtained in this way is neces-sarily missing. Details of all data sets used are given inTable 1.

In most cases, temperature responses were obtained byapplying temperature control to leaves for the duration ofthe gas exchange measurements. In contrast, in the exper-iments carried out by Dreyer

et al

. (2001) and Robakowski,Montpied & Dreyer (2002) (Table 1), temperature changeswere applied to the whole seedlings for the night precedingthe measurements. This procedure could potentially havemodified the temperature response, as there is evidencethat the thermal properties of photosystem II (PSII) and ofelectron transport may begin to acclimate after even a fewhours at a given temperature (e.g. Havaux 1993). Theresults presented below, however, do not appear to indicateany difference between the experiments carried out by thisgroup and other experiments.

Model

Overview of the Farquhar et al. (1980) model of photosynthesis

Farquhar

et al

. (1980) proposed that net leaf photosynthe-sis,

A

n

, could be modelled as the minimum of two limitingrates:

(1)

A

c

is the rate of photosynthesis when Rubisco activity islimiting and

A

j

the rate when ribulose-1,5-

bis

phosphate(RuBP)-regeneration is limiting.

R

d

is the rate of mitochon-drial respiration. Rubisco-limited photosynthesis is givenby:

(2)

where

V

cmax

is the maximum rate of Rubisco activity,

C

i

and

O

i

are the intercellular concentrations of CO

2

and O

2

,respectively,

K

c

and

K

o

are the Michaelis–Menten coeffi-cients of Rubisco activity for CO

2

and O

2

, respectively, andΓ* is the CO2 compensation point in the absence of mito-chondrial respiration. This formulation of the modelassumes that the cell-wall conductance, the conductancebetween the intercellular space and the site of carboxyla-tion, is negligible. Some authors have argued that this con-ductance is significant and may vary with leaf temperature(e.g. Makino, Nakano & Mae 1994). For most species con-sidered here, we did not have access to appropriate data toevaluate the cell-wall conductance and hence were obligedto use the form of the model given above.

A A A Rn c j d= ( ) -min ,

AV C

C KOK

ccmax i

i ci

0

=-( )

+ +ÊË

ˆ¯

ÈÎÍ

˘˚̇

G *

1

Temperature response of photosynthetic parameters – review 1169

© 2002 Blackwell Publishing Ltd, Plant, Cell and Environment, 25, 1167–1179

Tab

le1.

Det

ails

of

expe

rim

enta

l dat

a se

ts u

sed

Spec

ies

Com

mon

nam

eA

utho

rM

easu

rem

ent

TP

lant

sPo

ints

Gro

wth

TG

row

th c

ondi

tion

sA

ge o

f pl

ants

Not

es

Cro

psG

lyci

ne m

axSo

ybea

nH

arle

y, W

eber

&

Gat

es(1

985)

20,2

5,30

,35,

403

4825

GH

– T

seed

lings

O2

vari

ed a

lso

Gos

sypi

um h

irsu

tum

Cot

ton

Har

ley

et a

l. (1

992)

18,2

6,29

,35

229

GH

– T

seed

lings

Raw

dat

aun

avai

labl

e

Dec

iduo

us t

rees

Ace

r ps

eudo

plat

anus

Syca

mor

eD

reye

r et

al.

(200

1)10

,18,

25,3

2,36

,40

528

16N

(Fr

ance

)se

edlin

gsB

etul

a pe

ndul

aSi

lver

bir

chW

ang

(unp

ub.)

5,10

,22,

26,3

24

2014

OT

C (

Finl

and)

seed

lings

Bet

ula

pend

ula

Silv

er b

irch

Dre

yer

et a

l. (2

001)

10,1

8,25

,32,

405

2517

N (

Fran

ce)

seed

lings

Fagu

s sy

lvat

ica

Com

mon

bee

chD

reye

r et

al.

(200

1)10

,18,

25,3

2,40

525

17N

(Fr

ance

)se

edlin

gsFa

gus

sylv

atic

aC

omm

on b

eech

Stra

ssem

eyer

& F

orst

reut

er(1

997)

19,2

3,26

,30,

357

2820

ME

(G

erm

any)

seed

lings

Fra

xinu

s ex

cels

ior

Ash

Dre

yer

et a

l. (2

001)

10,1

8,25

,32,

36,4

05

3016

N (

Fran

ce)

seed

lings

Jugl

ans

regi

aW

alnu

tD

reye

r et

al.

(200

1)10

,18,

25,3

2,40

525

17N

(Fr

ance

)se

edlin

gsP

runu

s pe

rsic

aP

each

Wal

crof

t et

al.

(200

2)10

,20,

25,3

2,37

519

19G

H (

Fran

ce)

2ye

arQ

uerc

us p

etra

eaSe

ssile

oak

Dre

yer

et a

l. (2

001)

10,1

8,25

,32,

36,4

05

2516

N (

Fran

ce)

seed

lings

Que

rcus

rob

urE

nglis

h oa

kD

reye

r et

al.

(200

1)10

,18,

25,3

2,36

,40

530

16N

(Fr

ance

)se

edlin

gsQ

uerc

us r

obur

Eng

lish

oak

Stra

ssem

eyer

& F

orst

reut

er(u

npub

.)15

,21,

26,3

0,36

829

20M

E (

Ger

man

y)se

edlin

gs

Eve

rgre

en t

rees

Abi

es a

lba

Silv

er fi

rR

obak

owsk

i et

al.

(200

2)10

,18,

26,3

2,36

,40

528

25N

(Fr

ance

)se

edlin

gsE

ucal

yptu

s pa

ucifl

ora

Snow

gum

Kir

schb

aum

& F

arqu

har

(198

4)15

–35

120

GH

– T

seed

lings

Raw

dat

aun

avai

labl

eP

inus

pin

aste

rM

arit

ime

pine

Med

lyn

et a

l. (2

002)

15,2

0,25

,30,

356

2724

field

(Fr

ance

)30

year

Loc

al p

rove

nanc

e,A

ugus

tP

inus

rad

iata

Rad

iata

pin

eW

alcr

oft

et a

l. (1

997)

8,15

,20,

25,3

03

1424

GH

(N

Z)

seed

lings

Two

fert

iliza

tion

trea

tmen

tsP

inus

syl

vest

ris

Scot

s pi

neW

ang,

Kel

lom

aki

&L

aiti

nen

(199

6)6,

11,2

1,26

,31

418

14O

TC

(Fi

nlan

d)20

–25

year

Pin

us t

aeda

Lob

lolly

pin

eE

llsw

orth

& K

limas

(sub

mit

ted)

15,2

8,35

514

24FA

CE

(N

. Car

olin

a)12

year

June

and

Aug

ust

com

bine

d

Poin

ts is

the

tot

al n

umbe

r of

dat

a po

ints

use

d. G

row

th T

is t

he m

ean

tem

pera

ture

in t

he m

onth

pre

cedi

ng t

he m

easu

rem

ents

. Gro

wth

con

diti

ons:

GH

, gre

enho

use;

GH

– T

, tem

pera

ture

-co

ntro

lled

gree

nhou

se; N

, nur

sery

; OT

C, o

pen-

top

cham

ber

(con

trol

tre

atm

ent)

; ME

, min

i-ec

osys

tem

(co

ntro

l tre

atm

ent)

; FA

CE

, fre

e-ai

r C

O2

exch

ange

(co

ntro

l rin

g).

1170 B. E. Medlyn et al.

© 2002 Blackwell Publishing Ltd, Plant, Cell and Environment, 25, 1167–1179

The rate of photosynthesis when RuBP regeneration islimiting is given by:

(3)

where J is the rate of electron transport. J is related toincident photosynthetically active photon flux density, Q,by:

(4)

where Jmax is the potential rate of electron transport, θ is thecurvature of the light response curve and α is the quantumyield of electron transport. The value of α was fixed at0·3 mol electrons mol−1 photon, based on an average C3 pho-tosynthetic quantum yield of 0·093 and a leaf absorptanceof 0·8 (Long, Postl & Bolharnordenkampf 1993). The valueof θ was taken to be 0·90. These parameter values have onlya slight effect on the estimated value of Jmax.

The key parameters of the model, which vary amongspecies, are Jmax and Vcmax. It is the temperature depen-dences of these parameters that we set out to examine. Inaddition, it is known that the parameters Kc, Ko and Γ*vary with temperature. These parameters, by contrast, arethought to be intrinsic properties of the Rubisco enzymeand are generally assumed constant among species, therebyminimizing the number of parameters to be fitted (Harleyet al. 1986).

T-dependence of Kc, Ko, and Γ*

The in-vivo temperature dependence of the Michaelis–Menten coefficients of Rubisco, Kc (µmol mol−1) and Ko

(mmol mol−1), was recently measured in transgenic tobaccoover the temperature range 10–40 °C (Bernacchi et al. 2001)and the following relationships obtained:

(5)

(6)

Tk denotes leaf temperature in K and R is the universal gasconstant (8·314 J mol−1 K−1). Previous parameterizations ofthe photosynthesis model have been based on in vitrodeterminations of these functions, carried out by Badger &Collatz (1977) and Jordan & Ogren (1984), which are givenhere for comparison. Badger & Collatz (1977) determinedcarboxylase and oxygenase activities over the temperaturerange 5–35 °C of Rubisco purified from leaves of Atriplexglabriscula. They obtained the following relations (as givenin Farquhar et al. 1980):

(7)

(8)

(9)

AJ C

Cj

i

i= Ê

ˈ¯ ¥

-( )+( )4 2

GG

**

q a aJ Q J J QJ2 0- +( ) + =max max

KTRT

ck

k= ◊

-( )( )

ÈÎÍ

˘˚̇

404 979430 298

298exp

KTRT

ok

k= ◊

-( )( )

ÈÎÍ

˘˚̇

278 436380 298

298exp

KTRT

Tck

kC=

-( )( )

ÈÎÍ

˘˚̇

> ∞( )46059 536 298

29815exp

=-( )

( )ÈÎÍ

˘˚̇

< ∞( )920109 700 298

29815exp

TRT

Tk

kC

KTRT

ok

k=

-( )( )

ÈÎÍ

˘˚̇

33035 948 298

298exp

Jordan & Ogren (1984), working with Rubisco purifiedfrom spinach over the temperature range 5–40 °C, obtainedthe following relationships (equations derived by Harley &Baldocchi 1995):

(10)

(11)

Figure 1a illustrates the temperature dependence of theeffective Michaelis–Menten coefficient for CO2,Km = Kc(1 + Oi/Ko), at an intercellular O2 concentration of210 mmol mol−1, using each of these three sets of equations.

Similarly, the temperature dependence of the CO2 com-pensation point, Γ* (µmol mol−1), was estimated by Bernac-chi et al. (2001) to be:

(12)

Alternative expressions of the temperature dependence ofthe CO2 compensation point, Γ*, are generally based onthe work of either Badger and colleagues (Badger &Andrews 1974, Badger & Collatz 1977), Jordan & Ogren(1984) or Brooks & Farquhar (1985). These three alterna-tive temperature dependences are illustrated in Fig. 1b. TheCO2 compensation point is related to Kc and Ko and to themaximum oxygenation activity of Rubisco, Vomax(Farquharet al. 1980):

(13)

Badger & Andrews (1974) observed that the ratio Vomax/Vcmax = 0·21, independent of temperature, allowing the tem-perature dependence of Γ* to be determined from that ofKc and Ko. Jordan & Ogren (1984) studied the CO2 speci-ficity factor τ = KcVomax/(KoVcmax) of Rubisco purified fromspinach and obtained (equation derived by Harley et al.1992):

(14)

Brooks & Farquhar (1985) estimated the CO2 compensa-tion point of spinach in vivo using a gas-exchange techniqueand obtained the following relation, valid over the range15–30 °C:

(15)

They report that this relationship closely resembles thatobtained by Jordan & Ogren (1984).

We explored the significance of the differences betweenthese alternative formulations when fitting the parametersJmax and Vcmax. We found that the parameter Jmax was onlyvery slightly sensitive to the formulation of either Km or Γ*(not shown). However, the parameter Vcmax was highly sen-sitive to the formulation of Km chosen (Fig. 1c). The ratio ofJmax: Vcmax was thus also highly sensitive to Km (Fig. 1d). Thissensitivity is the reason why we considered it necessary to

KTRT

ck

k= ◊

-( )( )

ÈÎÍ

˘˚̇

274 680 500 298

298exp

KTRT

ok

k= ◊

-( )( )

ÈÎÍ

˘˚̇

419 814 500 298

298exp

G * exp= ◊-( )

( )ÈÎÍ

˘˚̇

42 7537 830 298

298TRTk

k

G * =( )K V O

Vc omax i

o cmax2K

t = ◊ --( )

( )ÈÎÍ

˘˚̇

2 32129 000 298

298exp

TRTk

k

G * = ◊ + ◊ -( ) + ◊ -( )42 7 1 68 298 0 0012 298 2T Tk k

Temperature response of photosynthetic parameters – review 1171

© 2002 Blackwell Publishing Ltd, Plant, Cell and Environment, 25, 1167–1179

use a consistent method to derive all parameters in a con-sistent fashion from original A–Ci curves before comparingthe temperature responses.

In the current work, we chose to use the temperaturefunctions obtained by Bernacchi et al. (2001), because thesefunctions were measured in vivo, without disturbance ofthe leaf, and are hence more likely to reflect accuratelyactivity within the leaf. When using the temperature depen-dences of Jmax and Vcmax presented below, it is important toalso use the Bernacchi et al. (2001) temperature depen-dences for Kc, Ko and Γ*, because of the sensitivity of themodel to these functions illustrated in Fig. 1.

T-dependence of Jmax and Vcmax

On reviewing the literature, it is daunting to observe thenumber of alternative functions that have been used tomodel the temperature dependences of Jmax and Vcmax (com-pare, for example, Harley et al. 1986; Long 1991; Harley etal. 1992; Harley & Baldocchi 1995; Lloyd et al. 1995). How-ever, all these equations are actually just alternative expres-sions of two basic functions. The first is the Arrheniusfunction:

(16)

which has parameters k25 (the value at 25 °C) and Ea (theexponential rate of rise of the function). The second is apeaked function (Johnson, Eyring & Williams 1942), whichis essentially the Arrhenius equation (Eqn 16) modified bya term that describes how conformational changes in theenzyme at higher temperatures start to negate the on-goingbenefits that would otherwise come from further increasingtemperature. This equation can be written in two equivalentforms:

(17)

(18)

f T kE T

RTk

a k

k( ) =

-( )( )

ÈÎÍ

˘˚̇25

298298

exp

f T kE T

RT

S H

RT S H

T R

ka k

k

d

k d

k

( ) =-( )

( )ÈÎÍ

˘˚̇

+-Ê

ˈ¯

+-Ê

ˈ¯

25298

298

1298

298

1exp

exp

exp

D

D

or k opt

da k opt

k opt

d ad k opt

k opt

f T kH

H T TT RT

H HH T T

T RT

( ) =

-( )ÊËÁ

ˆ¯̃

- - -( )ÊËÁ

ˆ¯̃

ÊËÁ

ˆ¯̃

exp

exp1

Figure 1. (a) Alternative forms for the response of Km = Kc(1 + Oi/Ko) to leaf temperature. (b) Alternative forms for the response of Γ* to leaf temperature. (c) Response of Vcmax to leaf temperature obtained by fitting a sample data set using alternative forms for Km. (d) Response of ratio Jmax : Vcmax to leaf temperature obtained by fitting a sample data set using alternative forms for Km. Key: Solid line: data from Badger & Collatz (1977). Dotted line: data from Jordan & Ogren (1984). Dashed line: data from Bernacchi et al. (2001).

G

1172 B. E. Medlyn et al.

© 2002 Blackwell Publishing Ltd, Plant, Cell and Environment, 25, 1167–1179

The first form has parameters k25, Ha, Hd and DS, whereasthe second form has parameters kopt, Ha, Hd and Topt. Ha andHd are the same between the two forms, whereas DS andTopt are related by:

(19)

The parameters can be interpreted as follows: k25 and kopt

are the values of Jmax or Vcmax at temperatures 25 °C andTopt, respectively; Ha gives the rate of exponential increaseof the function below the optimum (and is analogous toparameter Ea in the Arrhenius function); Hd describes therate of decrease of the function above the optimum; andTopt is the optimum temperature. DS is known as an entropyfactor but is not readily interpreted.

Model fitting

The first step in fitting the model was to obtain a value ofJmax and Vcmax for each individual A–Ci curve. This stepwas carried out by fitting Eqns 1, 2, 3 and 4 to each curveusing the non-linear regression routine with Gaussianalgorithm in SAS (SAS Institute Inc., Cary, NC, USA).The parameter Rd was also fitted but was not used further,because this parameter was found to be poorly estimatedby the model.

Temperature response parameters were then obtained byfitting Eqns 16, 17 and 18 to response curves of Jmax and Vcmax

to leaf temperature, using SigmaPlot (SPSS Inc. Chicago, IL,USA). It was assumed that Jmax and Vcmax at a given tem-perature could vary between leaves (according to factorssuch as leaf nitrogen per unit area) but that relative tem-perature responses of the parameters would be constant.This assumption was incorporated in the model by intro-ducing dummy variables li to represent each leaf and putting:

(20)

in Eqns 16, 17 and 18 (Kleinbaum et al. 1998). Here, li = 1 forleaf i and 0 otherwise, and ki is the value of k25 or kopt forleaf i. Reported values of the parameters k25 and kopt aremean and standard deviation of values of ki.

The Arrhenius model is a subset of the peaked model(compare Eqns 16 and 17). Therefore, an F-test was used todetermine whether the peaked model gave a significantlybetter fit to data than the Arrhenius model (Kleinbaum etal. 1998). As others have found, the four-parameter peakedmodel was often over-parameterized, i.e. there was insuffi-cient data to determine all parameters (Harley et al. 1992;Dreyer et al. 2001). Hence, this model was also fitted underthe assumption that Hd = 200 kJ mol−1, and an F-test used todetermine whether Hd was significantly different from thisvalue.

Implied temperature response of photosynthesis

We wanted to identify the implications for photosynthesisof differences in the temperature responses of model

TH

S RH

H H

optd

a

d a

=-

-( )ÈÎÍ

˘˚̇

D ln

k l ki ii= Â

parameters. To do so, Eqns 1, 2, 3 and 4 were used to cal-culate a typical temperature response of net photosynthesisfrom the derived parameter values. This calculation wasmade by assuming standard ambient environmental condi-tions for light-saturated photosynthesis: an atmospheric[CO2] concentration of 350 µmol mol−1, a constant Ci : Ca

ratio of 0·7, and a value for J of 0·9Jmax. Leaf respiration wasmodelled for all species using a base rate of 0·01 Vcmax anda Q10 of 2.

RESULTS

Temperature response of Vcmax

Fitted parameters of the temperature response of Vcmax aregiven in Table 2. In most cases, the peaked function (Eqn17) with Hd fixed at 200 kJ mol−1 gave a significantly betterfit to the data than the Arrhenius function (Eqn 16). In nocase, however, did relaxing the constraint on Hd signifi-cantly improve the fit to the data. Species for which nopeak in the temperature response of Vcmax was discerniblewere Fraxinus excelsior, Prunus persica, Pinus taeda andPinus radiata. Note, however, that measurements on P.radiata did not go above 30 °C (Table 1), and that peak val-ues close to 40 °C (maximal measurement temperature)are statistically difficult to estimate (e.g. for F. excelsior); inall cases a peak may well occur above the highest measure-ment temperature.

Values of k25, the maximum rate of Rubisco activity at25 °C, varied across data sets by a factor of three. Some ofthis variation is probably caused by variations in leaf nitro-gen content between data sets. Values were highest for cropspecies, but were comparable for coniferous and deciduousspecies. Note that all rates are expressed on a one-sided leafarea basis.

The activation energy Ha was generally in the range 60–80 kJ mol−1, implying a similarity in the temperatureresponses of Vcmax across data sets. Two data sets had valuesof Ha slightly below this range (F. excelsior and fertilized P.radiata) whereas another two had values of Ha consider-ably above this range (Gossypium hirsutum and Juglansregia).

The optimum temperature for Vcmax, Topt, was undeter-mined for those experiments where the peaked functionwas not a significantly better fit than the Arrhenius func-tion. Among the other experiments, Topt was generally inthe range 35–41 °C, with no clear pattern in the variation,with two exceptions. Betula pendula and Pinus sylvestris,grown in Finland, experienced the lowest growing temper-atures and showed significantly lower values of Topt (27–29 °C).

The variability in the temperature response of Vcmax isillustrated in Fig. 2a, which shows the temperatureresponses normalized to 1 at 25 °C. Most of the tempera-ture responses lie between the two curves shown forJuglans regia and Acer pseudoplatanus. The exceptions arecotton, Gossypium hirsutum, which has a much steeperVcmax–T response owing to its high value of Ha, and the

Temperature response of photosynthetic parameters – review 1173

© 2002 Blackwell Publishing Ltd, Plant, Cell and Environment, 25, 1167–1179

Tab

le2.

Par

amet

ers

of t

he t

empe

ratu

re r

espo

nse

of V

cmax

Spec

ies

Arr

heni

us m

odel

Pea

ked

mod

el

k 25

(µm

olm

−2s−1

)E

a (k

Jm

ol−1

)r2

k 25

(µm

olm

−2s−1

)k o

pt (

µmol

m−2

s−1)

Ha

(kJ

mol

−1)

Hd

(kJ

mol

−1)

Top

t (°C

)r2

P

Cro

psG

lyci

ne m

ax97

·76

(9·1

5)54

·08

(3·8

6)0·

8793

·89

(8·3

4)27

7·50

(24

·66)

69·5

0 (2

4·37

)20

0·00

41·8

9 (9

·92)

0·88

0·05

Gos

sypi

um h

irsu

tum

91·4

893

·59

(4·5

0)1·

0090

·22

399·

2611

6·38

200·

0040

·60

1·00

Dec

iduo

us t

rees

Ace

r ps

eudo

plat

anus

72·9

6 (8

·66)

33·9

2 (7

·19)

0·66

78·1

6 (1

1·01

)13

6·28

(19

·20)

75·8

8 (2

3·93

)20

0·00

34·9

5 (1

·21)

0·86

0·00

Bet

ula

pend

ula

OT

C85

·07

(3·6

5)37

·19

(4·9

8)0·

8710

1·90

(3·

85)

114·

82 (

4·34

)63

·75

(11·

44)

200·

0029

·28

(0·5

9)0·

970·

00B

etul

a pe

ndul

a G

H68

·85

(14·

19)

50·6

0 (3

·86)

0·94

69·0

9 (1

4·72

)17

7·31

(37

·78)

77·0

2 (1

8·76

)20

0·00

39·2

0 (3

·76)

0·97

0·00

Fagu

s sy

lvat

ica

GH

60·9

5 (5

·48)

41·3

8 (4

·31)

0·89

63·8

3 (5

·17)

133·

13 (

10·7

8)72

·36

(15·

34)

200·

0037

·36

(0·8

7)0·

970·

00Fa

gus

sylv

atic

a M

E27

·21

(3·4

1)46

·81

(3·5

3)0·

9227

·51

(2·9

3)49

·25

(5·2

4)65

·40

(19

·48)

200·

0036

·16

(3·6

3)0·

950·

00F

raxi

nus

exce

lsio

r77

·97

(9·6

5)50

·61

(3·6

0)0·

9378

·43

(9·6

0)23

5·89

(28

·88)

54·5

8 (1

3·11

)20

0·00

45·5

2 (3

6·87

)0·

930·

47Ju

glan

s re

gia

62·1

0 (1

0·24

)43

·98

(6·2

1)0·

8363

·98

(10·

62)

146·

39 (

24·3

0)10

4·58

(23

·56)

200·

0036

·05

(0·4

5)0·

970·

00P

runu

s pe

rsic

a65

·50

(3·8

8)73

·74

(3·2

8)0·

9966

·16

(3·9

1)46

4·59

(27

·49)

75·1

4 (2

3·38

)20

0·00

50·8

6 (3

96·9

9)0·

991·

00Q

uerc

us p

etra

ea79

·50

(8·5

5)56

·28

(2·7

9)0·

9879

·11

(8·1

0)24

4·53

(25

·04)

67·7

2 (9

·40)

200·

0042

·77

(6·9

6)0·

990·

01Q

uerc

us r

obur

GH

89·9

9 (1

1·98

)55

·50

(3·4

5)0·

9689

·71

(11·

92)

295·

01 (

39·1

9)61

·77

(13·

57)

200·

0044

·87

(25·

44)

0·96

0·26

Que

rcus

rob

ur M

E40

·83

(12·

28)

46·2

6 (3

·11)

0·97

42·3

2 (1

3·42

)84

·97

(26·

94)

57·5

9 (1

2·22

)20

0·00

38·7

6 (1

0·69

)0·

970·

06

Eve

rgre

en t

rees

Abi

es a

lba

41·6

4 (5

·15)

35·1

6 (3

·97)

0·86

43·5

0 (5

·33)

78·1

1 (9

·56)

60·0

2 (9

·88)

200·

0036

·81

(0·6

5)0·

950·

00E

ucal

yptu

s pa

ucifl

ora

87·7

351

·56

(2·0

9)0·

9990

·42

175·

8160

·79

(4·9

3)20

0·00

37·8

3 (3

·54)

1·00

Pin

us p

inas

ter

89·9

8 (5

·01)

62·2

2 (2

·76)

0·99

92·4

2 (4

·65)

213·

30 (

10·7

7)74

·16

(11·

17)

200·

0038

·34

(7·3

6)0·

990·

01P

inus

rad

iata

fer

t.97

·01

(4·4

6)49

·07

(3·7

3)0·

9699

·15

(4·7

1)17

4·33

(8·

33)

51·3

2 (1

9·21

)20

0·00

37·7

4 (1

52·0

4)0·

960·

77P

inus

rad

iata

unf

ert.

83·5

7 (1

7·5)

61·3

1 (3

·71)

0·98

85·8

6 (1

7·7)

171·

59 (

35·8

1)64

·78

(21·

32)

200·

0037

·68

(125

·99)

0·98

0·69

Pin

us s

ylve

stri

s53

·99

(7·2

2)35

·53

(5·9

3)0·

8167

·33

(9·7

2)70

·75

(10·

21)

69·8

3 (1

2·56

)20

0·00

27·5

6 (0

·61)

0·96

0·00

Pin

us t

aeda

57·0

5 (9

·33)

60·8

8 (3

·68)

0·98

57·6

6 (9

·43)

340·

45 (

55·6

3)61

·21

(304

·11)

200·

0053

·30

(470

33)

0·98

1·00

Val

ues

of k

25 a

nd k

opt a

re e

xpre

ssed

on

a on

e-si

ded

leaf

are

a ba

sis.

Stan

dard

dev

iati

ons

of k

25 a

nd k

opt,

and

stan

dard

err

ors

of o

ther

par

amet

ers,

are

give

n in

par

enth

eses

. P, p

roba

bilit

y th

at

the

peak

ed m

odel

is n

ot a

sig

nific

antl

y be

tter

fit

to t

he d

ata

than

the

Arr

heni

us m

odel

. OT

C, o

pen

top

cham

ber

expe

rim

ent;

GH

, gre

enho

use

expe

rim

ent;

ME

, min

i-ec

osys

tem

exp

erim

ent.

1174 B. E. Medlyn et al.

© 2002 Blackwell Publishing Ltd, Plant, Cell and Environment, 25, 1167–1179

Finnish plants, B. pendula and P. sylvestris, which have amuch lower optimal temperature for Vcmax.

Temperature response of Jmax

The peaked function (Eqn 17) described the temperatureresponse of Jmax significantly better than the Arrheniusfunction (Eqn 16) for all experiments other than P. radiataand P. taeda. Parameters for the peaked function are givenin Table 3.

Values of the activation energy Ha were in general high-est for crop species (80–90 kJ mol−1), intermediate fordeciduous species (40–60 kJ mol−1) and lowest for conifer-ous species (30–40 kJ mol−1). The major exceptions to thispattern were again the cold-climate trees from Finland, B.pendula and P. sylvestris, which both had high values of Ha,and F. excelsior. Values of Hd were significantly less than200 kJ mol−1 for these three species and for soybean.

The optimal temperature for Jmax is generally in therange 30–38 °C, with no clear pattern among species, withthe exception again of the Finnish plants. Betula pendulaand P. sylvestris had much lower optimal temperatures forJmax of about 20 °C.

The variability in the temperature response of Jmax isillustrated in Fig. 2b. The two Finnish species have similarresponses, with low optimal temperatures. The other coni-fers have responses resembling that of P. pinaster, with a

relatively low slope owing to low values of Ha. Deciduoustree responses generally lie between those of F. excelsiorand F. sylvatica. Crop species responses are steeper again,as illustrated by the G. hirsutum response.

Ratio of Jmax : Vcmax

Figure 3 shows the relationship between values of Jmax andVcmax at 25 °C. Most of the data points fall close to a straightline with a slope of 1·67. The major exceptions to this pat-tern are soybean, with a ratio of 2·4, and the two Finnishplants, which both have ratios of about 1. For each experi-ment, a linear function was fitted to the relationshipbetween the Jmax : Vcmax ratio and leaf temperature. Therewas a significant negative slope in all cases, ranging from −0·045 to −0·08, highlighting the difference in activationenergies for Jmax and Vcmax.

Implications for the temperature response of light-saturated photosynthesis

The temperature response of photosynthesis was modelledfor each data set, under the assumption of a constant Ci : Ca

ratio. From the resulting curves, the optimal temperaturefor photosynthesis and its rate of increase over the range15–30 °C were calculated, and these are plotted in Figs 4and 5 against growth temperature. Figure 4 illustrates that

Figure 2. Sample responses of (a) Vcmax and (b) Jmax to leaf temperature. Values are normalized to 1 at 25 °C.

Temperature response of photosynthetic parameters – review 1175

© 2002 Blackwell Publishing Ltd, Plant, Cell and Environment, 25, 1167–1179

for the majority of broadleaf and coniferous trees, the opti-mal temperature for photosynthesis varies between 23 and30 °C and is largely unrelated to growth temperature. How-ever, the trees grown in cold conditions in Finland hadconsiderably lower optimal temperatures. The optimal tem-peratures for the two crop species, which were grown inwarm conditions, were comparable to the highest optimaltemperatures obtained for the tree species. The rate of

increase of photosynthesis between 15 and 30 °C was alsosimilar for most plants in the survey, ranging from 1·2 to 1·6(Fig. 5). The exceptions were the Finnish trees, again, forwhich photosynthesis actually decreased over this temper-ature range, and walnut (J. regia) and cotton (G. hirsutum),which had particularly high rates of increase. From Figs 4and 5 we can identify three broad classes of implied photo-synthetic temperature response (Fig. 6). Most plants had

Table 3. Parameters of the temperature response of Jmax

Species k25(µmol m−2 s−1) kopt(µmol m−2 s−1) Ha(kJ mol−1) Hd(kJ mol−1) Topt(°C) r2

CropsGlycine max 217·88 (2·89) 328·57 (4·35) 88·82 (36·57) 113·77 (10·78) 38·17 (2·33) 0·89Gossypium hirsutum 131·82 221·57 77·17 200 34·44 1·00

Deciduous treesAcer pseudoplatanus 142·23 (12·37) 173·90 (15·12) 44·14 (10·02) 200 31·96 (1·16) 0·82Betula pendula OTC 111·89 (1·48) 128·45 (1·70) 108·45 (18·29) 156·84 (12·60) 19·20 (0·70) 0·96Betula pendula GH 116·33 (13·21) 169·66 (19·27) 42·83 (4·09) 200 35·77 (0·41) 0·98Fagus sylvatica GH 97·91 (12·31) 173·18 (18·20) 48·09 (7·86) 200 35·24 (0·78) 0·95Fagus sylvatica ME 44·83 (7·50) 51·89 (8·68) 43·36 (12·37) 200 30·78 (0·65) 0·94Fraxinus excelsior 147·03 (18·51) 170·10 (21·42) 91·20 (15·20) 131·89 (7·58) 31·38 (0·62) 0·95Juglans regia 103·81 (16·75) 165·86 (26·76) 56·30 (8·59) 200 35·53 (0·60) 0·97Prunus persica 106·27 (7·83) 154·81 (11·41) 42·04 (8·73) 200 35·87 (1·56) 0·95Quercus petraea 144·01 (12·02) 220·75 (18·43) 42·14 (2·99) 200 36·89 (0·34) 0·99Quercus robur GH 139·59 (23·98) 212·90 (36·57) 36·92 (7·19) 200 37·91 (1·29) 0·92Quercus robur ME 66·03 (20·18) 80·75 (24·68) 35·87 (13·52) 200 32·86 (1·19) 0·89

Evergreen treesAbies alba 95·49 (5·73) 128·15 (7·69) 50·82 (8·20) 200 33·20 (0·78) 0·90Eucalyptus pauciflora 141·94 175·13 43·79 200 32·19Pinus pinaster 154·74 (10·80) 220·91 (15·40) 34·83 (9·24) 200 36·87 (9·34) 0·97Pinus radiata fert. 175·43 (14·29) 189·66 (15·46) 43·18 (12·41) 200 29·01 (2·76) 0·95Pinus radiata unfert. 136·57 (17·66) 145·99 (18·85) 44·14 (16·60) 200 28·63 (3·21) 0·92Pinus sylvestris 70·77 (2·65) 78·36 (2·93) 100·28 (17·76) 147·92 (10·28) 19·89 (0·73) 0·96Pinus taeda 98·54 (14·09) 155·76 (22·26) 37·87 (394·31) 200 38·48 (1213) 0·95

Values of k25 and kopt are expressed on a one-sided leaf area basis. Standard deviations of k25 and kopt, and standard errors of other parameters, are given in parentheses. OTC, open top chamber experiment; GH, greenhouse experiment; ME, mini-ecosystem experiment.

Figure 3. Relationship between Jmax and Vcmax at 25 °C. Filled symbols: crop species; open symbols: broadleaf species; crosses: coniferous species. Fitted regression line has slope of 1·67.

1176 B. E. Medlyn et al.

© 2002 Blackwell Publishing Ltd, Plant, Cell and Environment, 25, 1167–1179

fairly similar responses, falling between those of A. pseudo-platanus and Q. petraea. The two Finnish trees, B. pendulaand P. sylvestris, had distinctly different responses, withmuch lower optimal temperatures. Finally, cotton (and to alesser extent J. regia) differed in having a much steeperresponse curve.

DISCUSSION

The aim of this review was to investigate variability in thetemperature responses of the model parameters Jmax andVcmax, with a view to improving parameter choice whenmodelling photosynthetic processes. The major factorsthought to affect these responses are growth temperature

and genotype or species (Berry & Björkman 1980). It hasalso been suggested that nutrition (Martindale & Leegood1997) and light availability (Niinemets et al. 1999) may playa role.

We found that the temperature responses of Jmax andVcmax obtained in gas exchange experiments were quite sim-ilar across many of the species included in the review(Tables 2 and 3), a promising finding as it potentially sim-plifies parameter choice. Parameter values obtained byalternative means (in vitro, chlorophyll fluorescence) areincluded for comparison in Table 4, and generally fallwithin the range of values reported in Tables 2 and 3.Responses of coniferous and broadleaf trees were broadlysimilar, with only a slight trend for lower Ha of Jmax in coni-fers. However, the responses of the two crop species, par-

Figure 4. Modelled optimal temperature of light-saturated net photosynthesis plotted against mean temperature in month prior to measurements. Filled symbols: crop species; open symbols: broadleaf species; crosses: coniferous species.

Figure 5. Modelled ratio of light-saturated net photosynthesis at 30 °C to that at 15 °C, plotted against mean temperature in month prior to measurements. Filled symbols: crop species; open symbols: broadleaf species; crosses: coniferous species.

Temperature response of photosynthetic parameters – review 1177

© 2002 Blackwell Publishing Ltd, Plant, Cell and Environment, 25, 1167–1179

ticularly cotton, differed from tree species in severalaspects including activation energies of both Jmax and Vcmax

and the ratio of Jmax : Vcmax at 25 °C, suggesting that alterna-tive parameter sets are required for modelling these twoplant types. This result needs to be clarified by expansion ofthe database on herbaceous species and crops, however.

It is not possible to draw inferences about acclimation ofphotosynthesis to growing conditions from such a diverseset of studies, because several alternative explanations arepossible for any observed differences, such as differences inexperimental protocol or genotypic differences. Neverthe-less some interesting comparisons can be made which canserve as a preliminary basis for generalizations about tem-perature responses in different environments.

For example, we can compare studies on the same spe-cies growing in different environmental conditions. BothFagus sylvatica and Quercus robur were the subject of twodifferent studies, one with seedlings growing individually in

pots and one with seedlings growing densely in mini-eco-systems. Low foliar nitrogen in the mini-ecosystem studiesled to low values of k25 for both Jmax and Vcmax. The relativetemperature response of Vcmax was unchanged, but Topt ofJmax was lower in the mini-ecosystem experiment. Thisresult parallels that of Niinemets et al. (1999) who foundthat the temperature optimum of Jmax was positively corre-lated with light availability and suggested that the correla-tion was a result of photosynthetic acclimation tomicroclimate.

There was generally a poor relationship between param-eter values and growth temperature, with the clear excep-tion of the lowest-temperature-grown plants, B. pendulaand P. sylvestris, which had distinctly different temperatureresponses compared to plants of the same genus grown intemperate climates. The low-temperature-grown plants hadlow optimal temperatures for both Jmax and Vcmax, and lowJmax : Vcmax ratios. Although not completely comparable, a

Figure 6. Sample responses of modelled leaf photosynthesis to leaf temperature. Values are normalized to 1 at 25 °C.

Parametervalues Material Authors

VcmaxEa58·52 Atriplex glabriscula,

purified RubiscoBadger & Collatz (1977)1

65·33 transgenic Nicotiana tabacum Bernacchi et al. (2001)2

JmaxHa Hd Topt65·01 179·2 33·7 Populus tremula, intact leaves Niinemets et al. (1999)3

54·97 325·5 40·3 Tilia cordata, intact leaves Niinemets et al. (1999)3

37 220 31 barley chloroplasts Nolan & Smillie (1976)1

1in vitro; 2in vivo measurements with transgenic low-Rubisco plants; 3chlorophyll fluorescence.

Table 4. Comparable parameter values obtained by other methods

1178 B. E. Medlyn et al.

© 2002 Blackwell Publishing Ltd, Plant, Cell and Environment, 25, 1167–1179

study on alpine grasses growing in low temperature envi-ronments (Wohlfahrt et al. 1999) does not show such dra-matic differences in the temperature optima of Jmax andVcmax. Further research is required to clearly establish theeffects of growth in a cold climate on the temperatureresponses of Jmax and Vcmax. No data were available for trop-ical species; it would be interesting to see how optimal tem-peratures for such species compare with those reportedhere.

Another key requirement for future research high-lighted by this study is the need for more information onthe temperature dependence of Kc and Ko, the Michaelis–Menten coefficients for Rubisco activity. We have illus-trated the fact that values of Vcmax derived from gasexchange data depend strongly on the assumed values of Kc

and Ko and hence are not readily comparable between stud-ies. In the absence of a clear resolution of the temperaturedependence of these parameters, it is important, particu-larly when modelling, to ensure that parameter sets areconsistent (Medlyn et al. 1999).

It should be noted that photosynthetic rates are deter-mined not only by biochemical processes, but also by sto-matal conductance to CO2. In this study we have omitted toconsider the effects on photosynthesis of possible acclima-tion of stomatal conductance to temperature. (Figs 4–6were constructed assuming a constant Ci : Ca ratio.) In thecompanion paper (Medlyn, Loustau & Delzon 2002), weshowed that changes in stomatal conductance could con-tribute considerably to photosynthetic temperature accli-mation. A similar result was found by Ferrar, Slatyer &Vranjic (1989) for Eucalyptus species and Ellsworth (2000)for Pinus taeda. Berry & Björkman (1980) suggested sto-matal acclimation to temperature was uncommon but alsonoted that information on this topic was scarce. Even with-out acclimation, photosynthetic rates at ambient CO2 con-centration at optimum temperature, and the temperature ofoptimum photosynthesis itself, can be strongly affected bystomatal responses to temperature and water vapour pres-sure deficits (Kirschbaum & Farquhar 1984). Hence, evenwith identical photosynthetic parameters, leaves can havedifferent photosynthetic rates under ambient conditionsdue to different stomatal conductances caused by internal(e.g. water stress) or external (e.g. water vapour pressuredeficits) factors. It has also been suggested that changes inthe temperature response of cell-wall conductance may bea factor in temperature acclimation (Makino et al. 1994).We were unable to evaluate this possibility owing to lack ofdata.

CONCLUSION

The primary aim of this review of the temperatureresponses of model parameters Jmax and Vcmax was to high-light variability in these responses among species andgrowth environments in order to improve parameter choicewhen modelling temperature effects on photosynthesis andgrowth. In general, it was found that parameters for crop

species, temperate trees, and boreal trees, fell into three dis-tinct groups (see Tables 2 and 3), suggesting that modellersshould use a set of parameters from the appropriate group.The limited data analysed here also revealed differences inphotosynthetic temperature response parameters amonggrowth environments, suggesting that equations should bechosen, where possible, to be appropriate for given radia-tion and temperature conditions. However, to better modeltemperature responses, a greater understanding of thefunctional significance of differences among broad planttypes and growth environments is needed, which willrequire more careful experimental comparisons of within-versus among-species variation in temperature responseparameters.

ACKNOWLEDGMENTS

B.M. acknowledges financial support from the French Insti-tut National de la Recherche Agronomique and the Aus-tralian Research Council. D.E. was supported by fundsfrom the US Department of Energy, Office of Biologicaland Environmental Research under the Forest-Atmo-sphere Carbon Transfer and Storage (FACTS) project. Wethank Georg Wohlfahrt for helpful discussion and MichaelBattaglia for insightful comments on the manuscript.

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Received 8 November 2001; received in revised form 28 March 2002;accepted for publication 2 April 2002