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Supporting Information for Evaluating the kinetic basis of plant growth from organs to ecosystems

Authors:
NewPhytologistSupportingInformation
Articletitle:Evaluatingthekineticbasisofplantgrowthfromorganstoecosystems
Authors:SeanT.Michaletz(michaletz@email.arizona.edu)
Articleacceptancedate:18December2017
ThefollowingSupportingInformationisavailableforthisarticle:
Fig.S1Atypicaltemperatureresponsecurveforabiologicalrate.
Fig.S2ModifiedArrheniusplotsofSharpeSchoolfieldmodelfits(withEhasafreeparameter)
tophotosynthesistemperatureresponsedata.
Fig.S3ModifiedArrheniusplotsofSharpeSchoolfieldmodelfits(withEhasafixedparameter)
tophotosynthesistemperatureresponsedata.
Fig.S4Treegrowthratesacrossabroadairtemperaturegradient.
Fig.S5Distributionsofintraspecificoptimaltemperaturesforphotosynthesis,estimatedfrom
Eqn(2)withEhasafreeparameter.
Fig.S6Distributionsofintraspecificoptimaltemperaturesforphotosynthesis,estimatedfrom
Eqn(2)withEhasafixedparameter.
TableS1Listoftaxa,numberofcurvespertaxon,andprimarysourcesforphotosynthesis
temperatureresponsedatausedinanalyses.
TableS2Listofgrowthvariables,temperaturevariables,samplesizes,andprimarysourcesfor
growthanalyses.
MethodsS1Descriptionofdataandmethodsusedforanalyses.
NotesS1RcodeforfittingtheSharpeSchoolfieldmodel(TPCfitting_stm.R).

Fig.S1Atypicaltemperatureresponsecurveforabiologicalrate.Ingeneral,biologicalratesB
increasewithtemperatureTtoamaximumvalueB
opt
atanoptimaltemperatureT
opt
,andthen
decreasewithtemperatureabovethisoptimum.TheeffectiveactivationenergyEandthe
enzymeinactivationparameterE
h
(bothnonlinearinthisspace)influencetheincreasingand
decreasingportionsofthecurve,respectively,asformalizedinEqn(2).Datapointsarenet
photosynthesis(µmolm
2
s
1
)ofJuniperusmonosperma(Michaletzetal.,2016b),andsolidline
isafittedSharpeSchoolfieldmodel(Eqn(2)).

Fig.S2ModifiedArrheniusplotsofSharpeSchoolfieldmodel(Eqn(2))fits(withE
h
asafree
parameter)tophotosynthesistemperatureresponsedatafor(a)anindividualJuniperus
monospermaleafcluster(E=0.22eV,quasir
2
=0.996)and(b)119leavesfrom32species(E=
0.03to3.06eV,quasir
2
=0.672to1.000).RelationshipsarepresentedasmodifiedArrhenius
plotsthatlinearizeassimilationratesrelativetoleaftemperature1/kT,yieldingalinearslopeof
Eonthedecreasingportionofthecurve.DatausedinanalysesaredescribedinTableS1.
Fig.S3ModifiedArrheniusplotsofSharpeSchoolfieldmodel(Eqn(2))fits(withE
h
asafixed
parameter)tophotosynthesistemperatureresponsedatafor(a)anindividualJuniperus
monospermaleafcluster(E=0.24eV,quasir
2
=0.993)and(b)119leavesfrom32species(E=
1.98x10
8
to2.07eV,quasir
2
=0.146to0.999).Relationshipsarepresentedasmodified
Arrheniusplotsthatlinearizeassimilationratesrelativetoleaftemperature1/kT,yieldinga
linearslopeof‐Eonthedecreasingportionofthecurve.Datausedinanalysesaredescribedin
TableS1.

Fig.S4Treegrowthratesacrossabroadairtemperaturegradient(N=210).DatafromFig.2b
replottedwithwithinsitemeasurementstreatedasindependentsamplesratherthansite
means.ThesamegeneralresultsareobservedhereandinFig.2b.Treegrowthratewas
invariantwithairtemperature(P=0.373,r2=0.004).ThefittedE=0.09has95%CI=‐0.11to
0.28thatexcludehypothesizedvaluesof0.32eV(Allenetal.,2005)and0.65eVforrespiration
(Gilloolyetal.,2001).ThisisamodifiedArrheniusplotthatlinearizestherelationshipbetween
growthandtemperaturetoyieldaslopeEthatisequalinmagnitudebutoppositeindirection
totheactivationenergyE(Eqns(1)and(S1)).Temperatureisquantifiedas1/kT(eV1),wherek
(8.617x105eVK1)isBoltzmann’sconstantandT(K)isairtemperature.Treegrowthratesare
expressedasmassadjustedrates,3/4 /
1
EkT
BM B e

.Thisrelationshipisobtainedvia
rearrangementof3/4 /
1
EkT
BBMe
,whichisinturnobtainedbyunpackingthenormalization
constantB0inEqn(1)torevealtheinfluenceofbiomassM,whereB1isabiomassindependent
normalizationconstant.DatafromEnquistetal.(2007).

Fig.S5Distributionsofintraspecificoptimaltemperaturesforphotosynthesis,estimatedfrom
Eqn(2)withEhasafreeparameter.Optimaltemperaturesforphotosynthesisvarysubstantially
withinandamongspecies,reflectingacclimationandlocaladaptationofphotosynthetictraits
tositeaveragedleafoperatingtemperatures.Themeanoptimaltemperatureacrossall
samplesis25.66˚C.Thickblacklinescorrespondtomedians,lowerandupperhinges
correspondtofirstandthirdquartiles,respectively,lowerandupperwhiskerscorrespondto
smallestandlargestvaluesthatdonotexceed1.5timestheinterquartilerangeofthehinges,
respectively,andpointscorrespondtooutliersbeyondtheendofthewhiskers.
Fig.S6Distributionsofintraspecificoptimaltemperaturesforphotosynthesis,estimatedfrom
Eqn(2)withEhasafixedparameter.Optimaltemperaturesforphotosynthesisvary
substantiallywithinandamongspecies,reflectingacclimationandlocaladaptationof
photosynthetictraitstositeaveragedleafoperatingtemperatures.Themeanoptimal
temperatureacrossallsamplesis26.21˚C.Thickblacklinescorrespondtomedians,lowerand
upperhingescorrespondtofirstandthirdquartiles,respectively,lowerandupperwhiskers
correspondtosmallestandlargestvaluesthatdonotexceed1.5timestheinterquartilerange
ofthehinges,respectively,andpointscorrespondtooutliersbeyondtheendofthewhiskers.
TableS1Listoftaxa,numberofcurvespertaxon,andprimarysourcesforphotosynthesis
temperatureresponsedatausedinanalyses
TaxonNumberofcurvesPrimarysource
Acersaccharum1Gundersonetal.(2000)
Artemisiatridentata5Michaletzetal.(2016b)
Atriplexdioica1Sageetal.(2011)
Atriplexglabriuscula1Osmondetal.(1980)
Balsamorhizasagittata2Michaletzetal.(2015)
Carexduriuscula3Monsonetal.(1983)
Carexhelleri1Sageetal.(2011)
Chamerionangustifolium3Michaletzetal.(2016b)
Delphiniumbarbeyi1Michaletzetal.(2016b)
Helianthusannuus1Pauletal.(1990)
Helianthusmollis1Zhouetal.(2007)
Juniperusmonosperma31Michaletzetal.(2016b)
Larixdecidua4Tranquillinietal.(1986)
Larreadivaricata7Mooneyetal.(1978)
Ligusticumporteri4Michaletzetal.(2016b)
Piceaengelmannii1Huxmanetal.(2003)
Piceamariana3Way&Sage(2008a)(2008b)
Pinuscontorta1Huxmanetal.(2003)
Pinusedulis21Michaletzetal.(2016b)
Pinussylvestris1Wangetal.(1996)
Plantagolanceolata4Atkinetal.(2006)
Potentillagracilis3Michaletzetal.(2016b)
Prosopisvelutina6BarronGaffordetal.(2012)
Solanumlycopersicum2Yamorietal.(2010)
Solanumtuberosum2Yamorietal.(2010)
Valerianaoccidentalis3Michaletzetal.(2016b)
Veratrumcalifornicum6Michaletzetal.(2016b)

TableS2Listofgrowthvariables,temperaturevariables,samplesizes,andprimarysourcesfor
growthanalyses
Levelof
organization
Growthvariable
Temperature
variable
Sample
size
Primarysource
OrganRootmeristemcelldoubling
rate(h1)
Celltemperature
(˚C)
60Körner(2003a)

IndividualMassadjustedindividual
treegrowthrate(kg1/4mo1)
Growingseason
airtemperature
(˚C)
210Enquistetal.(2007)

EcosystemAdjustednetprimary
production(kgm2mo1)
Growingseason
airtemperature
(˚C)
138Michaletzetal.(2014;2016a)

MethodsS1Descriptionofdataandmethodsusedforanalyses.
PhotosynthesistemperatureresponsedataandSharpeSchoolfieldfittingprocedures
PhotosynthesistemperatureresponsecurveswereobtainedfromMichaletzetal.
(2016b).Allcurveswereunimodal(e.g.seeFig.S1)andcomprisedatameasuredinColorado
andNewMexico,aswellascompiledfromtheliterature.Furtherdetailsonmeasurement
methodologiesareavailableintheprimarysources.Atotalof184curvesfrom32specieswere
available.Taxa,numberofcurvespertaxa,andprimarysourcesaresummarizedinTableS1.
ThesetemperatureresponsedatawereusedtoestimateactivationenergiesEfornet
photosynthesis.
VariousapproachescanbeusedtoestimateactivationenergiesEfromunimodal
temperatureresponsedata.Forexample,theBoltzmannArrheniusmodel(Eqn(1))canbefit
separatelytotheincreasinganddecreasingportionsofthecurve,yieldingseparateestimates
ofEforeachportion(Knies&Kingsolver,2010;Delletal.,2011).However,suchestimatescan
bestronglybiasedbythetemperaturerangesusedtodefinetheincreasinganddecreasing
portionsofthecurve(Knies&Kingsolver,2010;Pawaretal.,2016).Thus,inthispaper,
activationenergiesEfornetphotosynthesiswereestimatedusingSharpeSchoolfieldmodelfits
(Sharpe&DeMichele,1977;Schoolfieldetal.,1981).Thisapproachcanhelpreducebiasand
variationinestimatesofEascomparedwiththeBoltzmannArrheniusapproachdescribed
above(Pawaretal.,2016).Followingrecentmethodology,Eqn(2)wasfittocurvesforwhich
photosynthesiswasmeasuredataminimumoffivetemperaturesspanningarangeofatleast5
˚C(Delletal.,2011;Pawaretal.,2016),yieldingatotalof119fittedcurvesfrom27species
(FigsS2,S3).FittingwasaccomplishedusingLevenbergMarquardtnonlinearregressionwith
Gaussianrandomstartingvalues,followedbyAICcmodelselectionfrom100fitsforeachcurve.
ModelfittingwasconductedinthestatisticalsoftwareRusingamodifiedversionofcode
providedbyTonyDell,SamraatPawar,andSofiaSal(seeNotesS1).
Eqn(2)hasbeensuggestedtobeoverparameterizedforsomephotosynthesisdatasets
thatarerelativelylimitedinthenumberofobservationsorrangeoftemperatures(Harleyetal.,
1992;Dreyeretal.,2001;Medlynetal.,2002).Thus,IalsoconductedasecondsetofSharpe
SchoolfieldmodelfitsusingafixedvalueofEh=200kJmol1=2.073eV.Thisvaluehasbeen
usedinmanypreviousstudies(Farquharetal.,1980;Medlynetal.,2002;Slot&Winter,2017;
Stinzianoetal.,Inpress),andoriginatesfromdataforJmaxinHordeumvulgare(Nolan&Smillie,
1976).However,estimatesofEhforJmaxareavailableforothertaxa(Dreyeretal.,2001;
Leuning,2002;Warren&Dreyer,2006;Galmésetal.,2015),andtheseestimatesshowthatof
Ehvariesmorethan8foldacrosstaxa(Dreyeretal.,2001).Itisthusunclearhowappropriateit
istoapplyasinglefixedvalueofEhforJmaxfromasinglespeciestonetphotosynthesisdatafor
diversetaxa(asinTableS1).Additionally,thedatausedherewereallunimodalwitharelatively
largenumberofobservationsandrangeoftemperatures(e.g.FigsS1S3).Itmaybeforthese
reasonsthattheSharpeSchoolfieldmodelprovidedvastlybetterfitstodata(TableS1)whenEh
wastakenasafreeparameter(quasir2=0.672to1.000)ratherthanafixedparameter(quasir2
=0.146to0.999).
PerhapsabetteralternativetoafixedEhistouseafreeEhandrejectfittedcurvesbased
onstandarderrorsofestimatesforeachparameter(cf.Pawaretal.,2016).Nonetheless,
evaluationofSharpeSchoolfieldfittingproceduresisbeyondthescopeofthispaper,andthe
abovetwoapproachesarepresentedinordertohighlightthesensitivityofEtoSharpe
Schoolfieldfittingprocedures.
PlantgrowthdataandBoltzmannArrheniusfittingprocedures
Plantgrowthdatawerecompiledandanalyzedforthreelevelsofbiological
organization:organs,individuals,andecosystems.Rootorgangrowthdata(Fig.2a)were
obtainedfromFigure3ofKörner(2003b),whichisacompilationofdatafromapproximately50
primarysources.Dataaredivisionratesofrootmeristemcells.Forlandplants,rootmeristem
cellsprovideoneofthemostaccurateandresolvedmeasuresofinsitugrowthrates,forthree
reasons.First,ratesofcelldivisionaretightlycoupledtoratesofcelldifferentiation,whenmost
biomassgrowthoccurs(Körner,2003a;Körner,2012).Second,rootoperativetemperaturesare
inthermalequilibriumwithsoil,sotheyarerelativelystraightforwardtocontrolandquantify
(unlikeabovegroundorgans;Michaletzetal.,2015;Michaletzetal.,2016b).Third,cellsizeis
essentiallyconstant,whicheliminatesconfoundingeffectsofbiomass.Datawereextracted
fromFigure3usingthesoftwareDataThiefIIIv1.7.Dataweregivenascelldoublingtimes(h),
whichwerecalculatedasthestatisticalmeansacrossallcellswithinameristematicregion.The
inverseofcelldoublingtimeswasusedtocalculatethecellgrowthrates(h1)thatwereusedin
Fig.2a.
Individualgrowthdata(Fig.2b)wereobtainedfromEnquistetal.(2007).Datacomprise
massadjustedtreegrowthratesthatcontrolforvariationintreesizeandgrowingseason
length(moyr1),whichisneededtoproperlyevaluatetemperatureeffectsonplantmetabolic
kinetics(Michaletzetal.,Inpress).Growthratescorrespondtototal(above‐plusbelowground)
biomassgrowth.Massadjustedrates3/4
B
M(kg1/4mo1)aregivenby3/4 /
1
EkT
BM B e

(Brown
&Sibly,2012;Whiteetal.,2012),whereB(kgmo1)istheseasonalgrowthrate(Michaletzet
al.,Inpress),M(kg)isthetotaltreebiomass,andthe3/4scalingexponentisbasedon
extensiveempiricalandtheoreticalsupport(Brown&Sibly,2012).Sincemultiplegrowthrate
datawereavailableforsomesitesinthisdataset,theyweretakenasthemean±1standard
errorinFig.2b(althoughthesamegeneralresultswereobtainedwhentheseweretreatedas
independentsamples;Fig.S4).Airtemperaturedataarebasedonmonthlyaverageair
temperaturesduringthegrowingseason(includingdayandnight).Growingseasonair
temperatureisthemonthlyaverageairtemperatureduringthegrowingseasonmonths
(includingdayandnight).Datawerecalculatedfromsitelatitudeandlongitudeandagridded
globalclimatedataset(Newetal.,2002).Thisdatasetinterpolatesweatherstationdata,so
thesetemperaturescorrespondtoweatherstationstandardsandnotplantoperative
temperatures.Growingseasonmonthswereestimatedfromairtemperature,precipitation,
andpotentialevapotranspirationdataasdescribedinKerkhoffetal.(2005).
Ecosystemproductiondata(Fig.2c)wereobtainedfromMichaletzetal.(2016a),which
isasubsetofdatacompiledbyMichaletzetal.(2014).Dataaremonthlynetprimary
production(NPP;kgm2mo1)ratescalculatedoverthegrowingseason(moyr1).Fig.2cisa
partialregressionplotthatshowsthecorrectrelationship(slopeandvariance)betweennet
primaryproductionandtemperaturewhilecontrollingfortheinfluenceofbiomass,age,and
precipitation.Inthisanalysis,samplesfromthesamelatitudeandlongitudethatshare
temperatureandprecipitationdataallhaveuniquedataforageand/orstandbiomass,andare
thustreatedasindependentsamples.Airtemperaturedataarebasedonmonthlyaverageair
temperaturesduringthegrowingseason(includingdayandnight).Growingseasonair
temperatureisthemonthlyaverageairtemperatureduringthegrowingseasonmonths
(includingdayandnight).Datawerecalculatedfromsitelatitudeandlongitudeandagridded
globalclimatedataset(Newetal.,2002).Thisdatasetinterpolatesweatherstationdata,so
thesetemperaturescorrespondtostandardweatherstationmeasurementsandnotplant
operativetemperatures.Growingseasonmonthswereestimatedfromairtemperature,
precipitation,andpotentialevapotranspirationdataasdescribedinMichaletzetal.(2014).
Sinceorgan,individual,andecosystemlevelgrowthdatacorrespondtotemperatures
belowthoseoptimalforplantmetabolism(FigsS5,S6;Delletal.,2011;Slot&Winter,2017),
activationenergiesEwereestimatedusingBoltzmannArrheniusmodelfits.Specifically,Eqn(1)
waslogetransformedtogivethegrowthrateBas

0
1
ln lnBBE
kT

 (S1)
whereB0isanormalizationconstantthatimplicitlyincludeseffectsofothervariablesnot
consideredhere,kistheBoltzmannconstant(8.617x105eVK1),andE(eV)isaneffective
activationenergythatcharacterizesthetemperaturedependenceoftherateunder
consideration.Notethathere,theunitsofBandB0willvarydependingonthegrowthrate
underconsideration(h1forcells,kg1/4mo1forindividuals,andkgm2mo1forecosystems).
Theselogescaledgrowthdatawerethenregressedovertemperature1/kT,toproduce
modifiedArrheniusplots(Fig.2)withaslopeEthatisequalinmagnitudebutoppositein
directiontotheactivationenergyE.
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