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NewPhytologistSupportingInformation
Articletitle:Evaluatingthekineticbasisofplantgrowthfromorganstoecosystems
Authors:SeanT.Michaletz(michaletz@email.arizona.edu)
Articleacceptancedate:18December2017
ThefollowingSupportingInformationisavailableforthisarticle:
Fig.S1Atypicaltemperatureresponsecurveforabiologicalrate.
Fig.S2ModifiedArrheniusplotsofSharpe‐Schoolfieldmodelfits(withEhasafreeparameter)
tophotosynthesistemperatureresponsedata.
Fig.S3ModifiedArrheniusplotsofSharpe‐Schoolfieldmodelfits(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.
NotesS1RcodeforfittingtheSharpe‐Schoolfieldmodel(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
isafittedSharpe‐Schoolfieldmodel(Eqn(2)).
Fig.S2ModifiedArrheniusplotsofSharpe‐Schoolfieldmodel(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.S3ModifiedArrheniusplotsofSharpe‐Schoolfieldmodel(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
replottedwithwithin‐sitemeasurementstreatedasindependentsamplesratherthansite
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
growthandtemperaturetoyieldaslope–Ethatisequalinmagnitudebutoppositeindirection
totheactivationenergyE(Eqns(1)and(S1)).Temperatureisquantifiedas1/kT(eV‐1),wherek
(8.617x10‐5eVK‐1)isBoltzmann’sconstantandT(K)isairtemperature.Treegrowthratesare
expressedasmass‐adjustedrates,3/4 /
1
EkT
BM B e
.Thisrelationshipisobtainedvia
rearrangementof3/4 /
1
EkT
BBMe
,whichisinturnobtainedbyunpackingthenormalization
constantB0inEqn(1)torevealtheinfluenceofbiomassM,whereB1isabiomass‐independent
normalizationconstant.DatafromEnquistetal.(2007).
Fig.S5Distributionsofintraspecificoptimaltemperaturesforphotosynthesis,estimatedfrom
Eqn(2)withEhasafreeparameter.Optimaltemperaturesforphotosynthesisvarysubstantially
withinandamongspecies,reflectingacclimationandlocaladaptationofphotosynthetictraits
tosite‐averagedleafoperatingtemperatures.Themeanoptimaltemperatureacrossall
samplesis25.66˚C.Thickblacklinescorrespondtomedians,lowerandupperhinges
correspondtofirstandthirdquartiles,respectively,lowerandupperwhiskerscorrespondto
smallestandlargestvaluesthatdonotexceed1.5timestheinterquartilerangeofthehinges,
respectively,andpointscorrespondtooutliersbeyondtheendofthewhiskers.
Fig.S6Distributionsofintraspecificoptimaltemperaturesforphotosynthesis,estimatedfrom
Eqn(2)withEhasafixedparameter.Optimaltemperaturesforphotosynthesisvary
substantiallywithinandamongspecies,reflectingacclimationandlocaladaptationof
photosynthetictraitstosite‐averagedleafoperatingtemperatures.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)
Prosopisvelutina6Barron‐Gaffordetal.(2012)
Solanumlycopersicum2Yamorietal.(2010)
Solanumtuberosum2Yamorietal.(2010)
Valerianaoccidentalis3Michaletzetal.(2016b)
Veratrumcalifornicum6Michaletzetal.(2016b)
TableS2Listofgrowthvariables,temperaturevariables,samplesizes,andprimarysourcesfor
growthanalyses
Levelof
organization
Growthvariable
Temperature
variable
Sample
size
Primarysource
OrganRootmeristemcelldoubling
rate(h‐1)
Celltemperature
(˚C)
60Körner(2003a)
IndividualMass‐adjustedindividual
treegrowthrate(kg1/4mo‐1)
Growingseason
airtemperature
(˚C)
210Enquistetal.(2007)
EcosystemAdjustednetprimary
production(kgm‐2mo‐1)
Growingseason
airtemperature
(˚C)
138Michaletzetal.(2014;2016a)
MethodsS1Descriptionofdataandmethodsusedforanalyses.
PhotosynthesistemperatureresponsedataandSharpe‐Schoolfieldfittingprocedures
PhotosynthesistemperatureresponsecurveswereobtainedfromMichaletzetal.
(2016b).Allcurveswereunimodal(e.g.seeFig.S1)andcomprisedatameasuredinColorado
andNewMexico,aswellascompiledfromtheliterature.Furtherdetailsonmeasurement
methodologiesareavailableintheprimarysources.Atotalof184curvesfrom32specieswere
available.Taxa,numberofcurvespertaxa,andprimarysourcesaresummarizedinTableS1.
ThesetemperatureresponsedatawereusedtoestimateactivationenergiesEfornet
photosynthesis.
VariousapproachescanbeusedtoestimateactivationenergiesEfromunimodal
temperatureresponsedata.Forexample,theBoltzmann‐Arrheniusmodel(Eqn(1))canbefit
separatelytotheincreasinganddecreasingportionsofthecurve,yieldingseparateestimates
ofEforeachportion(Knies&Kingsolver,2010;Delletal.,2011).However,suchestimatescan
bestronglybiasedbythetemperaturerangesusedtodefinetheincreasinganddecreasing
portionsofthecurve(Knies&Kingsolver,2010;Pawaretal.,2016).Thus,inthispaper,
activationenergiesEfornetphotosynthesiswereestimatedusingSharpe‐Schoolfieldmodelfits
(Sharpe&DeMichele,1977;Schoolfieldetal.,1981).Thisapproachcanhelpreducebiasand
variationinestimatesofEascomparedwiththeBoltzmann‐Arrheniusapproachdescribed
above(Pawaretal.,2016).Followingrecentmethodology,Eqn(2)wasfittocurvesforwhich
photosynthesiswasmeasuredataminimumoffivetemperaturesspanningarangeofatleast5
˚C(Delletal.,2011;Pawaretal.,2016),yieldingatotalof119fittedcurvesfrom27species
(FigsS2,S3).FittingwasaccomplishedusingLevenberg‐Marquardtnonlinearregressionwith
Gaussianrandomstartingvalues,followedbyAICcmodelselectionfrom100fitsforeachcurve.
ModelfittingwasconductedinthestatisticalsoftwareRusingamodifiedversionofcode
providedbyTonyDell,SamraatPawar,andSofiaSal(seeNotesS1).
Eqn(2)hasbeensuggestedtobeover‐parameterizedforsomephotosynthesisdatasets
thatarerelativelylimitedinthenumberofobservationsorrangeoftemperatures(Harleyetal.,
1992;Dreyeretal.,2001;Medlynetal.,2002).Thus,IalsoconductedasecondsetofSharpe‐
SchoolfieldmodelfitsusingafixedvalueofEh=200kJmol‐1=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
Ehvariesmorethan8‐foldacrosstaxa(Dreyeretal.,2001).Itisthusunclearhowappropriateit
istoapplyasinglefixedvalueofEhforJmaxfromasinglespeciestonetphotosynthesisdatafor
diversetaxa(asinTableS1).Additionally,thedatausedherewereallunimodalwitharelatively
largenumberofobservationsandrangeoftemperatures(e.g.FigsS1‐S3).Itmaybeforthese
reasonsthattheSharpe‐Schoolfieldmodelprovidedvastlybetterfitstodata(TableS1)whenEh
wastakenasafreeparameter(quasir2=0.672to1.000)ratherthanafixedparameter(quasir2
=0.146to0.999).
PerhapsabetteralternativetoafixedEhistouseafreeEhandrejectfittedcurvesbased
onstandarderrorsofestimatesforeachparameter(cf.Pawaretal.,2016).Nonetheless,
evaluationofSharpe‐Schoolfieldfittingproceduresisbeyondthescopeofthispaper,andthe
abovetwoapproachesarepresentedinordertohighlightthesensitivityofEtoSharpe‐
Schoolfieldfittingprocedures.
PlantgrowthdataandBoltzmann‐Arrheniusfittingprocedures
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(h‐1)thatwereusedin
Fig.2a.
Individualgrowthdata(Fig.2b)wereobtainedfromEnquistetal.(2007).Datacomprise
mass‐adjustedtreegrowthratesthatcontrolforvariationintreesizeandgrowingseason
length(moyr‐1),whichisneededtoproperlyevaluatetemperatureeffectsonplantmetabolic
kinetics(Michaletzetal.,Inpress).Growthratescorrespondtototal(above‐plusbelowground)
biomassgrowth.Mass‐adjustedrates3/4
B
M(kg1/4mo‐1)aregivenby3/4 /
1
EkT
BM B e
(Brown
&Sibly,2012;Whiteetal.,2012),whereB(kgmo‐1)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;kgm‐2mo‐1)ratescalculatedoverthegrowingseason(moyr‐1).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,andecosystem‐levelgrowthdatacorrespondtotemperatures
belowthoseoptimalforplantmetabolism(FigsS5,S6;Delletal.,2011;Slot&Winter,2017),
activationenergiesEwereestimatedusingBoltzmann‐Arrheniusmodelfits.Specifically,Eqn(1)
wasloge‐transformedtogivethegrowthrateBas
0
1
ln lnBBE
kT
(S1)
whereB0isanormalizationconstantthatimplicitlyincludeseffectsofothervariablesnot
consideredhere,kistheBoltzmannconstant(8.617x10‐5eVK‐1),andE(eV)isaneffective
activationenergythatcharacterizesthetemperature‐dependenceoftherateunder
consideration.Notethathere,theunitsofBandB0willvarydependingonthegrowthrate
underconsideration(h‐1forcells,kg1/4mo‐1forindividuals,andkgm‐2mo‐1forecosystems).
Theseloge‐scaledgrowthdatawerethenregressedovertemperature1/kT,toproduce
modifiedArrheniusplots(Fig.2)withaslope–Ethatisequalinmagnitudebutoppositein
directiontotheactivationenergyE.
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