Scaling of angiosperm xylem structure with safety and efficiency

13 Pages·2006·0.16 MB·English

Tree Physiology26, 689–701
© 2006 Heron Publishing—Victoria, Canada
Scaling of angiosperm xylem structure with safety and efficiency
1,3 1 1 2
UWE G.HACKE, JOHN S. SPERRY, JAMES K. WHEELER and LAURA CASTRO
1 Department of Biology, University of Utah, Salt Lake City, UT 84112, USA
2 UnidaddeAnatomía,FisiologíayGenéticaForestal,EscuelaTécnicaSuperior deIngenierosde Montes,UniversidadPolitécnicade Madrid,
CiudadUniversitarias/n, 28040 Madrid, Spain
3 Corresponding author ([email protected])
Received June 9, 2005; accepted September 28, 2005; published online March 1, 2006
Summary We tested the hypothesis that greater cavitation thatisundersignificantnegativepressure.Theconduitsmust
resistancecorrelateswithlesstotalinter-vesselpitareaperves- protectthisstreamagainstrupturebycavitation—theabrupt
sel(thepitareahypothesis)andevaluatedatrade-offbetween transitionfrommetastableliquidtogasphase(Zimmermann
cavitation safety and transport efficiency. Fourteen species 1983).Atthesametimethatthexylemmustbesafefromcavi-
of diverse growth form (vine, ring- and diffuse-porous tree, tation,itmusthaveasufficientlylowresistancetowaterflow
shrub)andfamilyaffinitywereaddedtopublisheddatapre-
to minimize the transpiration-induced drop in negative pres-
dominatelyfromtheRosaceae(29speciestotal).Twotypesof
sure. Most plants regulate their canopy xylem pressures
vulnerability-to-cavitation curves were found. Ring-porous
through adjustments in stomatal conductance and leaf area
treesandvinesshowedanabruptdropinhydraulicconductiv-
(MeinzerandGrantz1990,Hackeetal.2000,Hubbardetal.
itywithincreasingnegativepressure,whereashydrauliccon-
2001). Consequently, the lower the transport resistance, the
ductivityindiffuse-porousspeciesgenerallydecreasedgradu-
more water can flow to the canopy under a given pressure
ally. The ring-porous type curve was not an artifact of the
gradient,andthegreaterthecapacityforcarbonuptake.The
centrifugemethodbecauseitwasobtainedalsowiththeair-in-
lowerthexylemresistivityisonacross-sectionalareabasis,
jectiontechnique.Asafetyversusefficiencytrade-offwasevi-
dentwhencurveswerecomparedacrossspecies:foragiven the greater thephotosyntheticprofit per xylem investment.
pressure, there was a limited range of optimal vulnerability Thispaperfocusesonisolatingthestructuralrequirements
curves.Thepitareahypothesiswassupportedbyastrongrela- for safety on the one hand, and transport efficiency on the
tionship(r2=0.77)betweenincreasingcavitationresistance other.Thisallowsustoidentifymechanismsthatmaylimitthe
anddiminishingpitmembraneareapervessel(A ).SmallA simultaneousoptimizationofsafetyandtransportefficiency.
P P
wasassociatedwithsmallvesselsurfaceareaandhencenarrow Thispotentialtrade-offisdifferentfromthexylemsafetyver-
vessel diameter (D) and short vessel length (L)—consistent susxyleminvestmentconflictanalyzedpreviously(Hackeet
withanincreaseinvesselflowresistancewithcavitationresis- al.2001a,2004).Inthosestudies,increasingsafetyfromcavi-
tance.Thistrade-offwasamplifiedatthetissuelevelbyanin- tationcorrespondedwithincreasedinvestmentinconduitwall
crease in xylem/vessel area ratio with cavitation resistance. volumeperconduitvolumeaspredictedtowithstandimplo-
Ring-porousspeciesweremoreefficientthandiffuse-porous sion by greater negative pressure. This translated to a mini-
species on a vessel basis but not on a xylem basis owing mum wood density required to reinforce conduit walls—a
to higher xylem/vessel area ratios in ring-porous anatomy. constructioncostthatincreasedwiththecapacitytowithstand
Across four orders of magnitude, lumen and end-wall resis- negativepressure.Therelatedconflict,whichisthefocusof
tivities maintained a relatively tight proportionality with a thispaper,iswhetherincreasedcavitationsafetyrequiresde-
near-optimalmeanof56%ofthetotalvesselresistivityresid- creased hydraulic efficiency.
ing in the end-wall. This was consistent with an underlying Asafetyversusefficiencytrade-offhaslongbeenproposed
scalingofLtoD3/2acrossspecies.Pitflowresistancedidnot (ZimmermannandBrown1977,Carlquist1988),buttheevi-
increasewithcavitationsafety,suggestingthatcavitationpres- denceisambiguous(Tyreeetal.1994,Choatetal.2005).If
sure was not related to mean pit membrane porosity. thereisatrade-off,plantswithmorenegativecavitationpres-
sure might show an increase in the resistivity of their func-
Keywords: hydraulic conductivity, trade-offs, vulnerability
tionalxylemandadecreaseinvesselsize.Thisisseeninsome
curves, water transport, wood structure, xylem anatomy, xy-
datasets(Martinez-Vilaltaetal.2002),buttherelationshipcan
lem cavitation.
bestatisticallyweak(Tyreeetal.1994,PockmanandSperry
2000).Otherdatasetsshownorelationshipatall(Hackeand
Sperry 2001,Jacobsenet al. 2005).
Introduction
Addingtotheambiguityisthatthemechanismofcavitation
The xylem conduit network supplies a transpiration stream bywaterstressisnotlinkedinanyself-evidentwaytovessel
690 HACKE, SPERRY, WHEELER AND CASTRO
size(diameterandlength),whichhasastronginfluenceonxy- encesthelargestporepervessel(Hargraveetal.1994,Choatet
lemflowresistance.Thereisconsiderableevidencethatcavi- al.2005).Ourprevioussurveyshowedastronginverserela-
tation is caused by air being drawn into water-filled xylem tionshipbetweenincreasingtotalpitmembraneareapervessel
conduitsbynegativepressureandthatthemostimportantsites anddecreasingsafetyfromcavitation.Thegreaterthepitarea
of this air-seeding are the inter-conduit pits (Crombie et al. inthevessel,thelargerthemaximumporesizeforthevessel
1985, Sperry and Tyree 1988, 1990, Jarbeau et al. 1995). (Wheeleretal.2005).Thisconclusionsuggeststhereisanele-
Thesepitsconnectadjacentconduitstoallowwaterflowand mentofprobabilityinthesafetyofavesselfromcavitation.
theyalsoactassafetyvalvestoblockthespreadofgasfrom Addingmorepitstoavesselcompromisesitssafetyfromcavi-
embolized conduits. In inter-vessel membranes, the pit is tationbecausethemorepitsthereare,bychancethegreater
sealedagainstairentrybycapillaryforcesatthenarrowpores willbethesinglelargestporediameterinthevessel.Theaver-
ofthepitmembrane.Excessivelynegativepressureduringwa- ageporosityofthepitmembranesandtheirresistanceonan
terstress,however,canpullairacrossthepitvalvesandcause area basis, however, would not necessarily change. This pit
cavitation in adjacent water-filled conduits. It is unclear areahypothesisprovidesabasisforasafetyversusefficiency
whether the pit properties that dictate safety from cavitation trade-offbecausealimitationonvesselpitareacanalsolimit
alsoconstrainvessellengthanddiameter,andthustheoverall vessel size and flow resistance (Wheeler et al. 2005).
resistivity of the conduit network. TheresultsofWheeleretal.(2005)werefrom16species,
Inanattempttounravelthelinkbetweenpitfunctionand 11ofwhichweremembersoftheRosaceae(Table2).Theem-
xylem flow resistance, we have previously modeled the air- phasisontheRosaceaewasintendedtominimizequalitative
seeding and hydraulic properties of pits (Hacke et al. 2004, differencesinpitmembranestructureacrosslineages,andso
SperryandHacke2004).Amajorassumptionofthemodelas tomaximizetheprobabilityofdetectingsafety-relatedvaria-
appliedtohomogeneouspitmembranesofangiospermvessels tion in pit properties. However, this sampling prevented the
(todistinguishfromthetorus-margoorganizationingymno- widestpossiblevariationinvesselsizesandcavitationresis-
sperms),wasthatmeanporosityofthecellulosicmeshofthe tance.Furthermore,nofamilybiaswasdetectedintheresults,
pit membrane covaried with the maximum pore size of the suggesting the observed trends may cut across phylogenetic
membraneandthatallpitmembranesinavesselwereidenti- groups.
cal.Themaximummembraneporesizeinavesseliscritical Thepresentpaperadds14speciestothedatasetofWheeler
becausetherelativelyweakcapillaryforcesatthisporesetthe etal.(2005),thenewspecieswerechosenforextremesofves-
air-seedingpressurefortheentirevessel.Thebiggerthismax- selsizeandcavitationpressuretomoreeffectivelydetermine
imumpore,themorevulnerableisthevesseltocavitationby scaling relationships between the structure and function of
capillaryfailure(assumingthemembranedoesnotair-seedby vessels(Table1).Familyaffinitieswerediverse,butwiththe
rupture or extensive plastic yielding). According to our as- exceptionoftwospecies,theywerefamilieswithoutvestured
sumptions,avesselcouldachievegreatersafetyfromair-seed- pitting.Vesturescouldmodifysomestructure–functionrela-
ingonlybyhavingadenserpitmembranemeshwithreduced tionships(Choatetal.2004)andasystematiccomparisonwas
meanporosity.Thiswouldresultinastrongtrade-offbetween outsidethescopeofthisproject.Thespecieswerechosento
increasingsafetyfromair-seeding(setbyadeclineinmaxi- representlargevesselsof ring-porous trees(sixspecies)and
mum membrane pore size) and increasing flow resistance vines (one species) at one extreme, and narrower vessels of
throughapit(determinedbydecliningmeanporosityofthepit diffuse-porous treesandshrubs(sevenspecies)on theother.
membrane).Werefertothisasthepitresistancehypothesisfor The goalswere (1) to determine if the inclusionof more di-
a safety versus efficiency conflict at the pit level. versevesselsizesandsafetiesconfirmedthepitareahypothe-
Recentestimatesofpitmembraneresistancedonotsupport sis over the pit resistance hypothesis; (2) to evaluate the
this hypothesis.Instead of a strong increasein pit resistance implications of the hypothesis for a safety versus efficiency
(onamembraneareabasis)withincreasingsafetyfromcavita- trade-off;and(3)toexploretheramificationsofthering-po-
tion,therewasnorelationship(Wheeleretal.2005).Further- rousversusdiffuse-porousvesselorganizationswithrespectto
more, measured resistances were considerably greater than the safety versus efficiency conflict.
modelpredictions,indicatinganaveragemembraneporosity
farsmallerthanmodeled.Theseresultsagreewithsomeex-
Materials and methods
perimentalresultssuggestinganaveragemembraneporesize
muchsmallerthanthesizepredictedtoair-seedatthecavita- Our methods were nearly identical to those described by
tionpressure(Choatetal.2003,butseeJarbeauetal.1995). Wheeler et al. (2005) and only a brief summary is provided
The data of Wheeler et al. (2005) suggest that average pore hereexceptfordescriptionsuniquetothe14speciesaddedto
size,thoughvariable,doesnotcorrelatewellwiththelargest the existing data set.
membraneporepervesselthatlimitssafetyfromair-seeding.
Plant material
Thisresultleavesopenthequestionofwhatfeaturesofpitand
vessel structure influence the largest membrane pore per Studied plants (Table 1) represented different xylem types
vessel. (diffuse-porousandring-porous),growthforms(trees,shrubs
Apossibleanswertothisquestionisthatitisthetotalnum- andvines),ecosystems(fromtheabundantmoistureinNorth
ber,orcollectivemembranearea,ofpitsinavesselthatinflu- Carolina to the aridity of the American Southwest) and leaf
TREE PHYSIOLOGY VOLUME 26, 2006
SCALING OF XYLEM WITH SAFETY AND EFFICIENCY 691
Table1.Studyspecies,theirfiguresymbolsandmeasurementsnotshowninfigures.Thefirstfivespeciesarering-porousandaredesignatedby
asteriskeddoublecapitalsymbols.Measurementsrepresentthemeanvesselsize.Contactfractionisthefractionofvesselsurfaceareacontacting
anothervessel.Pit-fieldfractionisthefractionofinter-vesselcontactoccupiedbypitmembranes.Theproductofthesetwofractionsgivesthepit
fraction(F ),thetotalpitareapervesselsurfacearea.Lengthfractionistheportionofvessellengthoverlappingothervessels.TheratioL′/L=F
P L
is the length between end walls (L′) per vessel length (L). Grand means from a minimum of six stems per species ±SE.
Species Figure symbol Contact fraction Pit-field fraction Length fraction L′/L=F
L
Carya glabra(P. Mill.) Sweet (Juglandaceae) CG* 0.07 ±0.010 0.55 ±0.044 0.17 ±0.020 0.91 ±0.010
Fraxinus pennsylvanicaMarsh. (Oleaceae) FP* 0.11 ±0.009 0.55 ±0.019 0.26 ±0.022 0.87 ±0.011
Morus albaL. (Moraceae) MA* 0.08 ±0.013 0.61 ±0.014 0.19 ±0.022 0.91 ±0.011
QuercusgambeliiNutt.(Fagaceae) QG* 0.05 ±0.019 0.30 ±0.018 0.13 ±0.019 0.94 ±0.010
Quercus prinusL.(Fagaceae) QP* 0.05 ±0.014 0.39 ±0.020 0.17 ±0.019 0.91 ±0.009
Rhus trilobataNutt. (Anacardiaceae) RT* 0.17 ±0.015 0.52 ±0.031 0.53 ±0.026 0.74 ±0.013
AcergrandidentatumNutt. (Aceraceae) Acg 0.30 ±0.015 0.69 ±0.016 0.50 ±0.021 0.75 ±0.011
Arctostaphylos patulaE.L. Greene (Ericaceae) Arp 0.10 ±0.004 0.37 ±0.020 0.21 ±0.023 0.90 ±0.011
CeanothuscrassifoliusTorrey (Rhamnaceae) Cec 0.10 ±0.008 0.43 ±0.025 0.18 ±0.011 0.91 ±0.005
CeanothusvelutinusDougl. ex Hook. (Rhamnaceae) Cev 0.19 ±0.005 0.58 ±0.033 0.33 ±0.011 0.83 ±0.005
Larrea tridentata(Sessé&Moc. ex DC.) Coville Lat 0.01 ±0.001 0.40 ±0.019 0.03 ±0.003 0.99 ±0.002
(Zygophyllaceae)
Oxydendronarboreum(L.) D.C. (Ericaceae) Oxa 0.08 ±0.006 0.30 ±0.016 0.17 ±0.013 0.91 ±0.007
Paxistimamyrsinites(Pursh)Raf. (Celastraceae) Pam 0.13 ±0.005 0.41 ±0.023 0.21 ±0.006 0.89 ±0.003
Pueraria montana(Lour.)Merr. (Fabaceae) Pum 0.16 ±0.025 0.71 ±0.010 0.38 ±0.043 0.81 ±0.021
phenologies(evergreensincluded:Paxistimamyrsinites,Cer- duringtransport.AdditionalspeciesfromthestudyofWheeler
cocarpus ledifolius, Ceanothus velutinus, Larrea tridentata et al. (2005) are listed in Table 2.
andArctostaphylospatula).StemsofCaryaglabra,Quercus
prinus, Oxydendron arboreum and the introduced vine Cavitation pressure
Puerariamontana(Kudzu),werecollectednearTryon,North Vulnerability curves documenting the decrease in hydraulic
Carolina in the Appalachian mountain foothills. Ceanothus conductivitywithnegativepressureweremeasuredonatleast
crassifolius was collected from chaparral near Pepperdine six stems per species by the centrifuge method (Alder et al.
UniversityinMalibu,California.Fromthesedistantsites,the 1997) as in the previous study (Wheeler et al. 2005). Stems
materialwaswrappedinplasticbagsandshippedbyovernight were flushed with measuring solution (20 mM KCl) under
expresstoourlaboratoryinSaltLakeCity,Utah.Stemsofthe 100 kPa entry pressure to reverse native embolism before
remainingspecieswerecollectedwithinafewhoursdriveof curve determination. The hydraulic head used to measure
thelaboratoryandweresimilarlyprotectedfromdesiccation theconductivitywastypicallyabout4kPaindiffuse-porous
stemsand1–2kPainstemswithlargevessels.Alowpressure
headinlargeandlong-vesseledspecieswasessentialtoavoid
instant refilling of embolized vessels cut open at both ends.
Table2.SpeciesfromWheeleretal.(2005)andfiguresymbols.The Betweenconductivitymeasurements,stemswerecentrifuged
first 11 species are members of the Rosaceae. toprogressivelymorenegativepressureinacustom-designed
centrifugerotor.Vulnerabilitycurvesshowingthedropincon-
Species Figure symbol ductivitywithnegativepressurewereplottedforallsixstems
of a species and the collective species curve was fit with a
Amelanchier alnifoliaM.Roemer Aa
Weibullfunction:
A.utahensisKoehne Au
CercocarpusledifoliusTorr. & Gray Cl
C. montanusRaf. Cm K/K =e−(P/b)^c (1)
max
Holodiscusdumosus(Hook.) Heller Hd
Physocarpusmalvaceus(Greene)Kuntze Pm
whereK/K isconductivityrelativetothemaximuminthe
Purshiatridentata(Pursh) D.C. Pt max
absenceofanyreversibleembolism,Pistheabsolutevalueof
RosanutkanaC.Presl. Rn
thenegativepressure,bisacurvefittingparameterthatcorre-
RubusleucodermisTorr. & Gray Rl
R. parviflorusNutt. Rp spondstoPatK/Kmax=0.63andcisacurve-fittingparameter
SorbusscopulinaGreene Ss influencing the slope of the vulnerability curve. Table 3 de-
Acer negundoL. (Aceraceae) An fines major variables.
Salix exiguaNutt. (Salicaceae) Se Somespeciesforwhichstemsolderthanoneyearhadtobe
SambucusceruleaRaf. (Adoxaceae) Sc
used(becauseoflengthlimitationsofcurrent-yeargrowth)ex-
Vitis viniferaL. (Vitaceae) Vv
hibited the cavitation fatigue phenomenon (Hacke et al.
TREE PHYSIOLOGY ONLINE at http://heronpublishing.com
692 HACKE, SPERRY, WHEELER AND CASTRO
Table 3. Major variables with definition and units. Variables represent values for mean vessel size.
Symbol Definition Units
A Total inter-vessel pit membrane surface area of vessel mm2
P
A Total internal surface area of vessel mm2
V
D Diameter corresponding to mean vesselR µm
L
F R /R ratio –
L W
F L′/Lratio –
L
F Pit fraction =A /A –
P P V
K,K Xylem conductivity, maximum conductivity mm4MPa–1s–1
max
K Xylem cross-sectional area conductivity m2MPa–1s–1
Xa
K MaximumK fornon-embolizedxylem m2MPa–1s–1
Xa-max Xa
L Vessel length cm
L′ Length between vessel end-walls m
R Vessel resistivity MPas mm–4
C
R Vessel lumen resistivity MPas mm–4
L
R Vessel end-wall resistivity MPas mm–4
W
R Vessel cross-sectional area resistivity MPasm–2
Ca
R Xylem cross-sectional area resistivity = 1/K MPasm–2
Xa Xa
r Resistance of one vessel end-wall MPas mm–3
W
r Pit membrane area resistance MPasm–1
P
2001b). These species had high native embolism values and measured in between exposing the stem in the chamber to
included ring-porous trees and some diffuse-porous species stepwiseincreasesinairpressures(10minperpressure).Vul-
fromdrought-pronehabitats.Thefatiguephenomenonisthe nerabilitycurvesdevelopedbythismethodshowthedropin
reductionincavitationpressureinolderxylemasaresultof conductivityasafunctionoftheairpressureandgivethepres-
previouscavitationbydrought(Hackeetal.2001b),freezing surerangerequiredtopushtheairintothexylem(Cochardet
(J.S.SperryandL.Castrounpublisheddata;S.D.Davis,Pep- al.1992,SperryandSaliendra1994).Theair-injectioncurves
perdine University, Malibu, USA, personal communication) should be equal and opposite to the centrifuge curves if air-
and perhaps age itself (Sperry et al. 1991). The symptom of seedingisthemaincavitationmechanism.Thistestwasdone
cavitationfatigueishighlyvulnerablexylemlocalizedtoolder for P. montana, R. trilobata, Q. gambelii and Quercus tur-
growth rings. Dye perfusions show that this older xylem is binella(the latter species was not part of the extended study).
embolizedinthenativeconditionandwhenrefilledbyflush- Allcomparisonsofcavitationpressureandxylemstructure
ingbecomesre-embolizedatverymodestnegativepressures weremadebetweenthespecies’meanvalueforeachparame-
(e.g.,–0.5MPa)inthelaboratory.Toavoidbiasingestimates ter.Forthisreason,itwasnecessarytorepresentthespecies’
ofthecavitationpressureofthefunctionallymostimportant vulnerability curve with a single cavitation pressure. In the
current-yearxylembyincludingtheolderfatiguedxylem,the past, we have used either the pressure required to reduce
K ofthesespecieswasscaledtoKat–0.5MParatherthan K/K to0.5(P ),orthemeancavitationpressure(e.g.,Lin-
max max 50
the K after flushing (A. patula, C. glabra, Fraxinus penn- tonetal.1998).Thelattertreatsthevulnerabilitycurveasacu-
sylvanica, Paxistima myrsinites, Physocarpus malvaceaus, mulativedistributionofKwithpressureandisthemeanofthat
Purshia tridentata and Rosa nutkana). In Larrea tridentata, distribution.Forspecieswithnearlysymmetricalsigmoidalor
theK wasscaledtoKat–1.5MPabecauseeventhefatigued linearvulnerabilitycurves,P andmeancavitationpressure
max 50
xylemwasrelativelyresistanttocavitationinthisextremely areverysimilar.However,inthisstudy,large-vesseledspecies
drought-adapted species. typicallyhadasymmetricalvulnerabilitycurvescharacterized
Vulnerability curves of vines and ring-porous trees where by an initial abrupt drop in conductivity with pressure fol-
we could avoid the fatigue artifact by using current-year lowed by a tail where conductivity dropped more gradually
growth(Quercusgambelii,Q.prinus,P.montana,Morusalba (Figures1and2).Tobetterrepresentthecavitationpressure
andRhustrilobata)alsotendedtohaveasignificantamountof acrosscurvesofallshapes,weusedthemeancavitationpres-
nativeembolismandhighlyvulnerablevessels(e.g.,Figures1 sureforallspecies,includingthosepreviouslyrepresentedby
and2)—thoughlesssothanwasthecasewitholderstems.We theirP50(Wheeler et al. 2005).
did not scale these curves as described above because they
Xylem-area hydraulic resistivity
were based solely on current-year xylem.
Inasubsetoflarge-vesseledandfatigue-pronespecies,we The hydraulic resistivity (pressure gradient per flow rate) of
compared the centrifuge method with the air-injection tech- thesapwoodofallspecieswasmeasuredandexpressedrela-
niqueasacheckonthecentrifugemethodforlarge-vesseled tivetothesapwoodarea(R ).TheR correspondsto1/K ,
Xa Xa max
species. Stems about 25 cm in length were sealed in a dou- butisexpressedonafunctionalxylemareabasis.Weswitch
ble-ended pressure chamber and the hydraulic conductivity betweenconductivitiesandresistivitiesbecausethelatterare
TREE PHYSIOLOGY VOLUME 26, 2006
SCALING OF XYLEM WITH SAFETY AND EFFICIENCY 693
additive in series and this facilitates the separation of vessel havebeendescribedindetail(Sperryetal.2005,Wheeleretal.
functionintoitscomponents(e.g.,Equation2).TheR hadto 2005). Vessel length distributions are strongly short-skewed
Xa
bedeterminedforsegmentslongerthanthelongestvesselsto andthemeanLusedtorepresentasegmentcorrespondedto
include the influence of end-wall resistance. In most dif- the mean of the log-transformed vessel length distribution.
fuse-porousstems,R couldbedirectlymeasuredinstemseg-
Xa
Partitioning xylem resistivity into lumen and end-wall
mentsthatwerelongerthanthelongestvessels(Wheeleretal.
components
2005). In these cases, six stems per species were measured.
After the hydraulic measurements were completed, 0.05% Ourpurposewastoisolatethecontributionofend-wallandlu-
safranindyewassiphonedthroughthesegments(instems> men structure to the resistivity of intact vessels.To estimate
1 year old) to mark the functional xylem. The area of func- thesecontributions,weassumedasinpreviouswork(Wheeler
tionalxylematthemiddleofthestemsegmentwasmeasured etal.2005)that,onaverage,lumenandend-wallcomponents
withalightmicroscopeandimageanalysissoftware.Resistiv- werearrangedinseriesinthexylemnetwork.Ifallthevessels
itywasmultipliedbythisstainedareatoobtainR foreach ofastemarerepresentedbyanequalnumberofaverage-sized
Xa
stem. and average-resistance vessels,mean intact vessel resistivity
In long-vesseled species (P. montana, F. pennsylvanica, (R ) is the sum of the mean lumen (R ) and end-wall (R )
C L W
C.glabra,M.alba,R.trilobataandthetwoQuercusspecies), resistivities:
vesselsweretoolongfordirectmeasurementsofR .Instead,
Xa
weusedtheshorteningtechniquetodetermineR (Sperryet R = R +R (2)
Xa C L W
al.2005).Tensegmentsperspecieswereselected,andthere-
sistivity measured at segment lengths of 15, 5.1, 1.8 and WeestimatedR bymultiplyingR bymeanvesseldensity,
C Xa
0.6 cm. In all species, R decreased significantly with de- andR wasestimatedfrom vesseldiametersandthe Hagen-
Xa L
creasingsegmentlengthandasthepercentageofopenvessels Poiseuilleequation. TheR was determined by subtraction.
W
withoutendwallsincreased(Sperryetal.2005).Theportion
PartitioningR into end-wall resistance and pit area
ofopenvesselswasknownfromvessellengthmeasurements W
resistance
(seebelow).Theinterceptoftheresistivityversuspercentage
ofopenvesselsrelationship(at0cmsegmentlengthand100% BasedonthesameanalysispresentedinWheeleretal.(2005),
openvessels)gaveanestimateoftheresistivityofthevessel webrokedownthemeanend-wallresistivityR intothemean
W
lumens.Sperryetal.(2005)observedthatthisinterceptdidnot resistanceof asingleend-wall(r ) basedontheassumption
w
differstatisticallyfromlumenresistivity(R )calculatedfrom thatR (aresistivity)istheaverageend-wallresistanceperav-
L W
measurements of vessel diameter and the Hagen-Poiseuille erage length between successive end-walls in series (L′):
equation,andthiswasalsofoundinourstudyspecies.Forcon-
sistencyacrossspecies,weusedtheHagen-PoiseuilleR esti- R =r /L′ (3)
L W W
mate for all species (see next section). The other end of the
regressionline,theresistivityat0%openvessels,gaveoures- whereL′wascalculatedasmeanvessellength(L)minusthe
timate ofR for the xylem with fully intact vessels. meanlengthofoneofitstwoend-walls(Figure1inWheeleret
Xa
al.2005).WeestimatedL′accordingtoWheeleretal.(2005),
Vessel diameter,Hagen-Poiseuillelumen resistivity and using the same stems measured forRXa.
vessel density End-wallresistanceisafunctionofthenumberofpitsinthe
end-wallandtheirindividualresistancestoflow.Toestimate
After completion of the R measurements, a subset of the
Xa theresistanceofapitonitsmembraneareabasis(r ),weas-
same stems was used to measure vessel diameters, Hagen- P
sumed that all pits of an end-wall were in parallel, so that:
Poiseuille lumen resistivity (R ) and vessel densities. These
L
parametersweremeasuredontransversesectionsasdescribed
r =r /(A /2) (4)
byWheeleretal.(2005).Forthediffuse-porousspecies,allsix W P P
R stemsweremeasuredandforspeciesrequiringthestem-
Xa whereA istotalareaofinter-vesselpits,whichisdividedby2
shorteningmethod,fourofthe10stemswererandomlycho- p
toobtainthepitareainoneofthetwovesselend-walls.This
sen. Hagen-Poiseuille lumen resistivity was calculated for
continuestheassumptionthatallinter-vesselpitsarebetween
each vessel at the same temperature (and sap viscosity) at
endwalls.Totheextentthattheremaybetruelateralpitting
whichR wasmeasuredexperimentally.Becauseourpurpose
Xa between vessels (that is, two vessels meeting only at mid-
wastorelatevesselstructuretoresistivity,werepresentedthe
lengthandseparating),theend-wallpitareaisoverestimated,
meandiameter(D)asthediametercorrespondingtothemean
and hence ourr values will be overestimates.
R for each stem. P
L TheA wasestimatedasthesurfaceareaoftheaverageves-
P
sel(A =πDL)multipliedbythemeanfractionofthevessel
V
Vessel length
surfaceareaoccupiedbyinter-vesselpits(thepitfraction,F ).
P
Vessellengths(L)weremeasuredonaseparatesetofamini- TheF wastheproductoftheaveragevesselcontactfraction
P
mumoffivestemsperspecies,butfromthesamebatchand andpit-fieldfraction,wherethecontactfractionisthefraction
ageasthatusedforthehydraulicmeasurements.Themethods ofthevesselsurfaceareaincontactwithadjacentvesselsand
TREE PHYSIOLOGY ONLINE at http://heronpublishing.com
694 HACKE, SPERRY, WHEELER AND CASTRO
thepit-fieldfractionisthefractionoftheinter-vesselcontact
areaoccupiedbypits.Thesefractionsweremeasuredaccord-
ing to Wheeler et al. (2005) on the same stems measured
forR .
Xa
Summary equation forR and LversusD scaling
Ca
Tosummarizehowvesselstructureinfluencesvesselresistiv-
ity,wecombinedtheessentialparametersdescribedaboveinto
asinglesummaryequationforaspecies’meanvessel-areare-
sistivity(R =R ×meanlumencross-sectionalarea).This
Ca C
equation is derived in the appendix of Wheeler et al. (2005,
Equation A8) and modified slightly here:
R =6.06(π/A )4/5η3/5(F r /F )2/5(F2/5+F–3/5) (5)
Ca P P P L
Figure1.Vulnerabilitycurvesforselectedspeciesshowingthede-
clineinxylemconductivitypersapwoodarea(K )withnegativexy-
whereF=R /R ,andisusedforsimplicityinsteadoftheF = Xa
L W W lempressure.Opensymbols((cid:1)and(cid:2))arering-porousspeciesand
RW/RC fraction used in Wheeler et al. (2005, Equation A8). solidsymbols((cid:3),(cid:4)and(cid:5))arediffuse-porousspecies.Valuesare
TheFLterm=L′/L.AsummaryequationforLandDscaling means ±SE,n= 6 stems per species.
was similarly obtained:
 Fr 1/2 obtainedbytheair-injectionmethod(Figure2).Thetwometh-
L =0.125 P  (D)3/2 (6)
 ηF F ods were statistically identical at all pressures in the two
P L
QuercusspeciesandatthreeoffivepressuresinR.trilobata.
Inthelatterspecies,thecentrifugemethodtendedtoproduce
Equation6wasderivedfromEquationsA7andA9inWheeler
greater loss of conductivity for the same pressure than the
etal.(2005;noteerrorintheF termoftheirEquationA9:it
W
air-injection method,but the shapeof the curve wassimilar,
should beF /(1 – F )).
W W
withanabruptconductivitylossatmodestpressure.Although
Error propagation the stems for the centrifuge method were shorter (14.2 cm)
thanfortheair-injectionmethod(22cmminimum)andhada
Weusedstandardprocedures(BernardandEpp1995)toprop-
greaterportionofopenvesselsrunningthroughthestem(e.g.,
agatestandarderrorsfromparameterswhosevariationwasdi-
15versus5.4%inQ.gambeliiand3versus0.4%inR.trilo-
rectly determined from individual stem measurements (e.g.,
batabasedonvessellengthdistributions),thisdidnotappear
R , vessel density, R , R , R , L, D, F, length fraction, pit-
Xa C L W
toinfluencethecurves.ThedataforspeciesinFigure2were
field fraction and contact fraction) to parameters calculated
fromspeciesmeanswhereerrorshadtobecombined(A ,A , obtained from different populations, stem ages and season
P V
F ,F ,r andr ).Forthesevenspecieswherethestemshort- than for the main survey.
P L P W
ening method was used, the standard error of R was esti- InthevineP.montana,thecurvesobtainedbythecentrifuge
Xa
mated from the regression of R versus percentage of open methodwerequitevariableandgenerallyshowedgreatervul-
Xa
vessels for pooled data of all stems per species. nerabilitythanthoseobtainedbytheair-injectionmethod,al-
though the basic curve shape was similar (data not shown).
Thevariabilitywasattributedtotheextremelylongandwide
Results vessels in this vine, 35% of which were estimated to run
through the 14.2 cm segments required for the centrifuge
Vulnerability curves and the safetyversusefficiency
method. Open vessels may not have been the problem, but
relationship
rather the problem may have been that the vessels were so
Two types of vulnerability curves were observed (Figure 1). wide(meanD=150µm)thattheyemptiedbygravityifthe
Thesixring-porousspeciesandthevine,P.montana,tended stemsegmentwastiltedtothevertical.Toavoidthedifficulty
tohaverelativelyhighmaximumK fornon-embolizedxy- ofhandlingthismaterial(thecentrifugemethodrequiresmov-
Xa
lem(K ),butanabruptdeclineinK withpressure(Fig- ing and manipulating the stem multiple times), we used the
Xa-max Xa
ure1,Q.prinusandM.albacurves).Thesevendiffuse-porous air-injection curve for this species. For all other species the
species(anddiffuse-porousspeciesfromWheeleretal.2005) centrifuge method was used.
tendedtohavealowerK butgenerallyretainedK more ForthespeciesinFigure1,thehighertheK (theyinter-
Xa-max Xa Xa-max
effectively with pressure (Figure 1, Acer grandidentatum, cept),thesteeperthelossofconductivityatmodestpressure
Acer negundo and C. crassifolius curves; A. negundo data (theslope)and,ingeneral,thelowerthepressurerequiredto
fromSperryetal.2005).TheabruptdropinK observedin eliminateconductivity(thexintercept).Thisisconsistentwith
Xa
thering-poroustypeofcurvewasnotanartifactofthecentri- a trade-off between safety and conducting efficiency: for a
fugemethod,becausethesamepatternwasseeninthecurves givenpressure,thereisalimitedrangeofvulnerabilitycurves
TREE PHYSIOLOGY VOLUME 26, 2006
SCALING OF XYLEM WITH SAFETY AND EFFICIENCY 695
thebestcurveisforA.grandidentatumdespiteitsbeingabout
35% embolized at this pressure. Ceanothus crassifolius at
–3MPais hardlyembolizedat all, yet has the lowerK .
Xa
Scaling of safetyversusefficiency parameters across species
Representingtheslopeofthevulnerabilitycurvebythemean
cavitationpressure,asafetyversusefficiencyrelationshipwas
evidentacrossall29species(includingthe15fromWheeleret
al.2005,Table2)withmorenegativemeancavitationpressure
correspondingtohigherxylemarearesistivity(R =1/K ;
Xa Xa-max
Figure3A).Thus,thetrendseeninFigure1extendsacrossall
speciesinthedataset.Thetwovinespecieswithsomeofthe
widestandlongestvessels(Pum,Vv;Figure4)hadthelowest
R and among the least negative cavitation pressure (Fig-
Xa
ure 3A). The ring-porous specieshad similar or even higher
R forthesamecavitationpressureasthediffuse-porousspe-
Xa
cies(Figure3A,asteriskedsymbols,dashedline),despitetheir
tendencytohavewiderandlongervessels(Figure4,dashed
lines).Thering-porousspeciesalsotendedtoclustertowards
the vulnerable end of the cavitation pressure range (Fig-
ure 3A).
TheR isafunctionoftheR andthetotalcross-sectional
Xa Ca
areaofthexylemoccupiedbyvessels:R =R ×xylem/ves-
Xa Ca
selarearatio.TheR alsoincreasedwithcavitationpressure
Ca
(Figure3B,r2=0.60forallspecies),butmoreweaklythanthe
R scaling(Figure3A,r2forallspecies=0.86).Thiswasbe-
Xa
causering-porousspecieshadlowerR forthesamepressure
Ca
thantheotherspecies(Figure3B,dashedline),consistentwith
theirtendencytohavelargervesselsatthesamepressure(Fig-
ure4,dashedlines).DespitetheirlowerR ,thering-porous
Ca
speciesdidnothaveareducedR becausetheirxylem/vessel
Xa
arearatio wasmuchhigher for thesamepressurethanother
species(Figure3C,dashedline).Thelowvesselareainring-
porousspeciescancelledouttheeffectoftheirlowerR atthe
Ca
tissuelevel,yieldingcomparableorhigherR asdiffuse-po-
Xa
rous species.
Allspeciesconsidered,theefficiencyversussafetytrade-off
at the sapwood R level was much more severe than at the
Xa
conduitR level.TheR increased13-foldfromacavitation
Ca Xa
Figure2.Vulnerabilitycurvesofthreering-porousspeciesshowing pressureof–0.58to–8.1MPa,versusa4.5-foldincreasein
percentagelossofconductivityversuspressure.Thecurvescompare
R .ThesteeperincreaseinR wasowedtoastrongincrease
thecentrifuge((cid:4))andair-injection((cid:2))methodsforeachspecies.As- Ca Xa
in the xylem/vessel area ratio with cavitation pressure (Fig-
terisksindicatesignificantlydifferentmeans.Valuesaremeans±SE
forn=3(air-injection)andn=10(centrifuge)methods.Themethods ure3C).Thisinturnresultedfromadecreaseinvesseldiame-
comparisonforQ.gambeliiwasfromadifferentpopulationandtime ter with more negative cavitation pressure (Figure 4, r2 =
of year than the data for the anatomy–vulnerability survey. 0.71), which was more important than a weak tendency for
vessel density to increase (r2= 0.25; data not shown).
TheincreaseinR withsafetywasnearlyequallydivided
Ca
that provide optimal (maximum) K . Notably, this optimal between the R and R components (Figure 5). On average,
Xa L W
curvecanbeassociatedwithaveryhighnativeembolism.For 56%ofthevesselresistivitywasintheend-wallsand44%in
example,atapressureof–0.8MPa,the“best”vulnerability thelumen.MeanF=R /R was0.85±0.078.Thisratiodid
L W
curvewiththehighestK at–0.8MPaisforM.alba,although not differ between ring-porous and diffuse-porous species
Xa
atthispressure,thisspecieswouldbeabout50%embolized.In measuredforthispaper,orbetweentheWheeleretal.(2005)
contrast,thethreediffuse-porousspeciesat–0.8MPawould data and the species added in this study.
belessthan10%embolized,yetstillhavealowerK because In contradiction to the pit resistance hypothesis modeled
Xa
theirK (intercept)valuesweresomuchlower.Thispat- previously (Figure 6, circles; Sperry and Hacke 2004), the
Xa-max
ternismaintainedatlowerpressures.Forexample,at–3MPa, pooleddatasetshowednoincreaseinr withmorenegative
P
TREE PHYSIOLOGY ONLINE at http://heronpublishing.com
696 HACKE, SPERRY, WHEELER AND CASTRO
Figure4.Scalingofvesseldiameter(D)andlength(L)withmeancav-
itation pressure (shown as absolute value for log scaling). Dashed
linesandasteriskeddouble-capitalsymbolsidentifyring-porousspe-
cies.Standarderroraveraged12%ofmeanLand6%ofmeanD.Spe-
cies symbols are given in Tables 1 and 2.
erroraveraged33%ofr .Thishighpercentagewasaresultof
P
the propagation of error through multiple calculations.
In confirmation of the pit area hypothesis, the addition of
datafor14speciesofdiversevesselsizeandsafetyreinforced
thestronginverserelationshipbetweentotalA andmeancavi-
P
tationpressureacrossallspecieswithnocleardistinctionbe-
tweenring-anddiffuse-poroustypes(Figure7A,r2=0.77).
Totalvesselsurfacearea(A )alsoscaledwithincreasingmean
V
cavitation pressure, though much more weakly (Figure 7A,
r2= 0.47)becauseofvariationinthefractionofvesselsurface
thatwaspitted(thepitfraction,F =A /A ,Figure7B).Forex-
P P V
ample,thering-porousspeciestendedtohavehigherA forthe
V
same cavitation pressure than diffuse-porous species (Fig-
ure7A,asteriskedsymbols,dashedline)becausethering-po-
rousF tendedtobelowforthesamepressurecomparedwith
P
F of many diffuse-porous species (Figure 7B, dashed line).
P
Figure3.Safetyversusefficiencytrade-offacrossthe29-speciesdata
set. Speciessymbolsare given in Tables1 and 2. Dashed lineand
asterisked double-capitalsymbolsidentifyring-porousspecies. For
clarity,errorbarsonspeciesmeansarenotshown.(A)Xylemareare-
sistivity(R )versusmeancavitationpressure.Solidlineisregression
Xa
throughcompletedataset.Standarderroraveraged7%ofR .(B)
Xa
Vessel area resistivity (R ) versus mean cavitationpressure. Solid
Ca
lineisregressionforcompletedataset.Standarderroraveraged13%
ofR .(C)Xylem/vesselcross-sectionalarearatio.Dashedlineisre-
Ca
gressionforring-porousspecies,solidlineisseparateregressionfor
diffuse-porous species and vines. Standard error averaged 9% of
means.
cavitationpressure(Figure6,speciessymbols).Instead,there
wasaweaklysignificant(r2=0.17)oppositetrend.Measured
r wasalsosubstantiallygreaterthanmodeled(Figure6).The
P Figure5.Scalingofvesselend-wallresistivity(R )withvessellumen
29-species data set showed large variation in r , but it was W
P resisitivity(R ).Dashedlineis1:1.MeanR /R =Fratiowas0.85±
L L W
unrelated to safety from cavitation or to functional group 0.078.Standarderroraveraged13%ofmeanR and19%ofmean
L
(ring-porous versus diffuse-porous). The estimated standard R . Species symbols are given in Tables 1 and 2.
W
TREE PHYSIOLOGY VOLUME 26, 2006
SCALING OF XYLEM WITH SAFETY AND EFFICIENCY 697
Figure6.Pitarearesistance(r )versuscavitationpressure.Modeled
P
valuesfromSperryandHacke(2004)shownasopencircles.Standard
erroraveraged33%ofthemeanformeasuredvalues.Speciessym-
bols are given in Tables 1 and 2.
TheF averaged6.3±0.9%(range:0.4–21%)acrossthe
P
full data set. Whereas the Rosaceae-dominated data set of
Wheeler et al. (2005) showed a significant drop in F with
P
meancavitationpressure,additionofanother14specieselimi-
nated this trend. In the full data set, F did not vary signifi-
P
cantlywithsafetyfromcavitation(Figure7B).Thevariation
in F was primarily in the contact fraction rather than the
P Figure7.(A)Pitmembrane(A )andvessel(A )surfaceareasversus
P V
pit-field fraction (Table 1).
meancavitationpressure(shownasabsolutevalueforlog-scaling).
TheAP,besidesbeinghypotheticallyresponsibleforsetting Dashedlinehighlightsring-porousspeciesinAVplot.Standarderror
cavitation pressure, was also the dominant influence on the averaged19%ofA and14%ofA .(B)Pitfraction(F =A /A )ver-
P V P P V
variation in RCa compared with the other parameters in the susmeancavitationpressure.MeanFPwas6.3±0.9%.Dashedline
highlightsring-porousspecies.Standarderroraveraged13%ofmean.
summaryEquation5(Figure8).TheR changed165-foldfor
Ca Species symbols are given in Tables 1 and 2.
the observed 593-fold range in A (Figure 8, A curve). The
P P
nextmostimportantdeterminantsofR werer andF ,caus-
Ca P P
ingonlya5-foldchangeinR fortheir53-foldvariation(Fig-
Ca sidesDinEquation6(F,r ,F andF )didnotvarysystemati-
ure 8,r andF curves). P L P
P P callywithD,LscaledwithDtothe3/2poweracrossthewide
TheF=R /R fractionhadalimitedrange(0.85±0.078,
L W rangeoflengthsanddiametersinthedataset(Figure9,r2=
range 0.26–1.98; Figure 5) and a comparatively minor
0.63).
1.4-foldeffectonR acrossitsrange(Figure8,solidFcurve).
Ca
AsEquation5indicates,thereisanoptimalFthatminimizes
R whichisemphasizedgraphicallybytheshort-dashedex-
Ca
Discussion
tensionoftheFcurveinFigure8.TheobservedFrangekept
R nearthisoptimum.TheF =L′/Lfractionvariedlittlein Weobtainedevidenceforasignificantsafetyversusefficiency
Ca L
thedataset(Table1)andhadatrivial1.1-foldinfluenceonR trade-offinxylemhydraulicfunction(Figures1and3).This
Ca
(data not shown). trade-off,togetherwitharequirementforgreaterconstruction
Overall,thevariationinA explained72%ofthevariationin cost in cavitation-resistant xylem (Hacke et al. 2001a), may
P
R (datanotshown).BecauseA isalsolinkedtocavitation explainwhyangiospermxylemisusuallynotmoreresistant
Ca P
pressure(Figure7A),itprovidesabasisforthesafetyversus thanrequiredbythenormalnegativepressurerangeaspecies
efficiencytrade-off(Figures1and3):lowA mayberequired experiences.Thedatareinforcedthepitareahypothesiswhile
P
for more negative cavitation pressure, and it also results in contradicting the pit resistance hypothesis as an explana-
greater xylem resistivity. The effect of A on resistivity was tion for this trade-off. Increasing safety from cavitation was
P
throughitslinktovesselsurfacearea,A (Figure7A),which strongly associated with decreasing pit area per vessel (Fig-
V
resultedfromthelimitedrangeofF (Figure7B).TheA in ure 7A, r2 = 0.77), but not with increasing pit area resis-
P V
turnwasrelatedtovesselDandLandtheirrespectivedeclines tance(Figure6).Meanpitmembraneporosityapparentlydoes
with increasingly negative cavitation pressure (Figure 4). not correlate with cavitation pressure as previously modeled
As Equation 6 indicates, L versus D scaling is a complex (SperryandHacke2004).Ifair-seedingoccursatthelargest
functionofseveralvariables.However,becausethetermsbe- membrane pore per vessel, this limiting pore may be quite
TREE PHYSIOLOGY ONLINE at http://heronpublishing.com
698 HACKE, SPERRY, WHEELER AND CASTRO
pervesselandhenceitssusceptibilitytoair-seeding.Alimited
pitareaalsolimitsthevesselsurfacearea(Figure7A)which
translatesintoalimitonvesseldiameterandlength(Figure4)
and hence its resistivity (Figure 3B).
Intheory,itisnotnecessaryforpitareatolimitvesselsur-
faceareaifthefractionofthevesselwallthatispitted(thepit
fraction,F )canbecomeinfinitelysmall.Ifthatwerepossible,
P
asmallpitareaforsafetycouldresideinalargeandwideves-
selforefficiency.Accordingly,acorollaryofthepitareahy-
pothesis is that F should be small. This was generally the
P
case,withameanF of6.3±0.9%(Figure7B),withfourspe-
P
cies below 2% (Figure 7B). However, none were below the
0.4% extreme for L. tridentata. In the Rosaceae-dominated
datasetof Wheeleretal.(2005), there wasasignificantde-
creaseinF withsafetyfromcavitation,whichwouldhelpto
P
minimize the loss of conducting efficiency. However, this
Figure 8. Sensitivity of vessel area resistivity (R ) to changes in
Ca seeminglyadaptivetrendwasnotsupportedbytheinclusion
Equation5variables(A ,F,r andF )relativetotheirmeanvalues.
P P P ofmorediversespecies.Oneimportantdisadvantageofalow
VariableF inEquation5isnotshownbecauseithasminimalimpor-
L
pitfractionisamorerigidlyaxialflowpathwithlessability
tance. Each parameter curve shows the R calculated from Equa-
Ca
tion 5 for the full range of that parameter with the other variables forwatertoflowlaterallytocircumventwoundsortoprovide
constantattheirmeanvalues.ThedottedcurveforFextendsbeyond flexibility in distribution of resources from root to crown
theactualFrangeinthedataset(solidportionofcurve)toemphasize sections (Orianset al. 2004).
thatthereisanoptimalFthatminimizesRCa.Abbreviations:AP=to- Variationinthesafetyversusefficiencytrade-offatthexy-
tal inter-vessel pit membrane surface area of vessel; F = lumen to
lemtissuelevel(Figure3A)resultedfromavarietyofsources,
end-wallresistivityratio;r =pitmembranearearesistance;F =pit
P P beginningwithvariationintheproposedcause-and-effectre-
fraction;andF =lengthbetweenvesselend-walltovessellengthra-
L
tio. lationshipbetweenpitareapervesselandthecavitationpres-
sure(Figure7A).Althoughthisrelationshipwasstrong(r2=
0.77),therewasstillconsiderablevariationthatmaybemore
rare. Some support for this comes from observations of pit thanjustmeasurementerror.Amongspecies,thosewithmore
membraneswheremostofthemembraneporesaretoosmall pitareapervesselforthesamemaximumporesize(e.g.,CG,
toobserve,andporesofair-seedingsizearerelativelyfewand QGinFigure7A)havethepotentialtobemoreefficientwith
far-between (Sperry andTyree1988,Sano2004). the same safety from cavitation. There was also variation in
Thepitareahypothesisexplainstheobservedsafetyversus other aspects of vessel structure that may not be causally
efficiencytrade-off(Figure3)asfollows.Toachieveagiven linkedtocavitationsafety,ofwhichr andF weremostcon-
P P
safetyfromcavitation,thepitareapervesselmustbelimited, sequentialforresistivityatthevessellevel(Figure8).Scaling
becausethislimitsthemeansizeofthelargestmembranepore tothetissuelevel,thevariationinthexylem/vesselarearatio
(Figure3C)createsfurtherflexibilityintheR versussafety
Xa
relationship. With all of these intermediate steps between
safetyandefficiency,itfollowsthatthetrade-offwillbestatis-
ticallynoisyandnonexistentinmorelimiteddatasets(Hacke
and Sperry 2001,Jacobsenet al. 2005).
Ourr estimatesshowedtremendousvariation,from39to
P
2040MPasm–1(Figure6).Doubtless,someofthisvariation
resultedfromtheimpreciseandindirectmethodusedtoesti-
mate r , with standard errors averaging 33% of the mean
P
value.Pitresistancesofthismagnitudeshouldbeover99%de-
termined by the pit membrane (versus aperture resistance),
corresponding to a prevailing membrane pore diameter be-
tween3and8nm(Wheeleretal.2005).Thisporesizeissimi-
lartotheaveragesizerangeestimatedexperimentallyinsome
plants (Shane et al. 2000, Choat et al. 2003, 2004) lending
somecredencetoourestimates,althoughsimilarexperiments
ontwochaparralspeciesfoundlargerporesizes(Jarbeauetal.
1995).
Figure9.Scalingofvessellength(L)withdiameter(D).Slopeofthe
log–logplotwas1.48asindicatedfromEquation6whentheother
Scaling of vesselresistivitiesand dimensions
equationparametersdonotvarywithD.Speciessymbolsaregivenin
Tables 1 and 2. TherelativelytightscalingbetweenR andR componentsof
L W
TREE PHYSIOLOGY VOLUME 26, 2006