4.1Controloftreesizeongrowth

Ourresultshighlighttheinteractionbetweenfunctionaltraitsandsize,asshowninFigs.7and8.Ontheonehand,canopy/sizeandSWA/HWAchangewithsize;andtheotherhand,theycanfutheraffectthegrowthrateandmaximumbiomassoftrees,whichhighlightsthesize-drivengrowthmechanism.Infact,treesizeactsinorganismdesignandfunction(Gibertetal.,2016).Insomeexperiments,sizehasagreatereffectonage-relateddeclinesinrelativegrowthandnetassimilationratesthancellularsenescence(Mencuccinietal.,2005).Environmentalfactors,suchastemperatureandprecipitation,canalsoaffectproductionindirectlythroughvariationinplantsize(Michaletzetal.,2014),suggestingsize-dependenttreegrowthshouldbequitecommoninnature.Mathematically,growthcanbeformulatedasaseriesofspontaneousiterationcyclicequationswithaninitialinputofsomestartingbiomassM0,M0f(M0)+M0f(f(M0)+M0)+f(M0)+M0…→Mmax,causingthebiomassM0toapproachMmax.Achievingbalancebetweenphotosynthesisandrespirationstopstheiterationmapping.Atleasttwotypesofunimodalcurvesareassociatedwiththiscontrol(i.e.,Eqs.1and2).

4.2CauseofAbiesfabricascadinggrowth

Wefoundthatthemostcommoncascadinggrowthtypesareβandγ(datanotfullyshown)(e.g.,Fig.4c).Modularproliferationandgradualphysiologicaladaptationprovideamoremoderateandconservativegrowthstrategytomitigatetheriskofdrasticchange.Inthisprocess,Canopy/sizeandSWA/HWAreflecttherelativenumberrelationshipbetweenphotosyntheticandrespirationmodulesandthechangedofplantcompounds,respectively,whichdeterminesthebalanceofphotosynthesisandrespiration.Thus,Canopy/size×HWA/SWA,physiologically,arecloselyrelatedtocM/mr(∝Mamax)(linearpartinFig.8d).ItshouldbenotedthattheeffectofCanopy/size×HWA/SWAoncM/mrmayweakenduetotheshadingandwearofleavesinthecanopyofverylargetrees(nonlinearpartinFig.8d).Treesmayoffsetthislossbyadjustingotherfunctionaltraits.Overall,astreesgrow,thehighercanopy/sizeandlowerSWA/HWAcanresultinahigherratioofresourceuptaketorespiratoryexpenditure,whichisthemainreasonfortheincreaseinthescaleoftheunimodalcurve.Canopygrowthhasgeneticandenvironmentallimitations.Exceptforspecies-specific,shootramificationpatterns,syllepticandprolepticgrowthortheratiooflongandshortshootsshowcleardependenceonlightquantityorquality(KullandTulva,2000).Speciesthatattainlargesizesmayinterceptmorelight,sothatcanopy/sizeshouldincreasewithtreeheight.However,increasedheight-relatedhydraulicconstraints(Ryanetal.,2006)stimulateaslowersapwood-to-heartwoodtransitionrate(McDowelletal.,2002),resultinginalowerSWA/HWA.Thesechangesmaybethemainmechanismtoformthelargerunimodalcurve.Ofcourse,thelimitsofcanopy/sizeandSWA/HWAmeanthatthereisanupperlimittothescaleoftheunimodalcurve.Ifthischangeisnotregular,theremaynotbeaunimodaltrend,asshowninFigs.3dand7d.SincethisstudyisonlyforAbiesfabridistributedinsameregion,someimportantmoduletraits,suchasleafandwoodeconomics,donotshowsignificantdifferences.Nevertheless,someresultsarestillpredictable.Forexample,higherwooddensitynotonlyincreasegr,butalsomaydecreasemrbecausecertainplantcompoundsrequirelittleornomaintenance(e.g.ligninandCellulose)(Johnson1990;VanIersel2003).Fromtheviewofresult,adecreaseinmr/grwillincreasethekurtosisofthegrowthcurve(Fig.1),whichisconsistwiththeviewsofHéraultetal(2011).Thechangeofbisalsoanimportantreasonforcascadinggrowth.Inourmodel,bisthekeytocontrolthetransitionofgrowthtrajectoryfromGompertztologisticpatterns.Mathematically,theGompertzandlogisticpatternsrequirethemetabolicscalingexponentoftrees<1(alsoneed>0)and=1(i.e.,Mbwhereb=0.75or=1).Inpractice,thediametergrowthofoldtreesmaycontinuelongaftertheheightgrowthhasslowed(Phillipsetal.,2008a),whichmeanstreebiomassisproportionaltobothtreediameterandleafarea.Duetoleafarea∝respirationrate∝Mb(Wangetal.,2015),theninthelaterperiodofgrowth,bmayindeedequalto1.Undertheeffectofcompetition,thelogisticgrowthpatternismoresuitabletodescribetreegrowth(rightsideoftheverticalsolidlineinFig.3).

4.3Implicationsoflargertreegrowth

ManyinvestigationshaveaimedtoidentifythesourcesofinterannualvariationinNPP,andfocusedonenvironmentalconditionsthataffectgrowthratetobetterpredictcarbonsourcesand/orsinksofthecommunity.However,estimatesofthecarbonsequestrationcapacityofindividualsorthecommunitythroughshort-termmeasurementsofthegrowthratesorNPParenotconclusive.Ontheonehand,thegrowthoflargetreeshasstronggrowthplasticity;andotherhandtreesizeheterogeneityalsocomplicatesthecarbonsequestrationofcommunity.Ifthemaximumandaveragegrowthincrementsoftreesstillhaveaclearpattern(Fig.3a),individualsizedistributionseemstobethekeyfactorforcarbonsequestration.Ourresultsalsoshowthatthelargestunimodalgrowthtrajectoryisincompleteforstudyoftreeswiththelargesttimespan(>390years)(Fig.3a).Wespeculatedthelargestindividualsmayhavediedbeforeachievinggrowthbalanceduetodisturbanceor/andcompetition(Shuetal.,2019).Theseexternalfactorsmaybeparticularlyimportantforcarbonsequestrationinoldforests,becausetheycanpromotetheformationofstabletreesizeheterogeneityandthecontinuousentryofcarbonintothesoil.Infact,U-shapedsize-mortalitytrendsarecommoninnaturaloldforests(e.g.,Lorimeretal.,2001Fosteretal.,2014,CoomesandAllen,2015;Pilletetal.,2017).