Transport efficiency through uniformity: Organization of veins and stomata in angiosperm leaves

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Transport efficiency through uniformity:
Organization of veins and stomata in
angiosperm leaves
ARTICLE in NEW PHYTOLOGIST · JULY 2015
Impact Factor: 7.67 · DOI: 10.1111/nph.13577 · Source: PubMed
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Research
Transport efficiency through uniformity: organization of veins
and stomata in angiosperm leaves
LuciaFiorin1,TimothyJ.Brodribb2andTommasoAnfodillo1
1DepartmentofTerritorioeSistemiAgro-Forestali(TeSAF),Universit(cid:1)adegliStudidiPadova,Vialedell’Universit(cid:1)a16,I-35020,Legnaro(PD),Italy;2SchoolofPlantScience,Universityof
Tasmania,PrivateBag55,Hobart,TAS7001,Australia
Summary
Authorforcorrespondence: (cid:1) Leaves of vascular plants use specific tissues to irrigate the lamina (veins) and to regulate
TimothyJ.Brodribb water loss (stomata), to approach homeostasis in leaf hydration during photosynthesis. As
Tel:[phone]
bothtissuescomewithattendantcosts,itwouldbeexpectedthatthesynthesisandspacing
Email:[email protected]
ofleafveinsandstomatashouldbecoordinatedinawaythatmaximizesbenefittotheplant.
Received:30March2015 (cid:1) Weproposeaninnovativegeoprocessingmethodbasedonimageeditingandageographic
Accepted:22June2015
informationsystemtostudythequantitativerelationshipsbetweenveinandstomatalspatial
patternsonleavescollectedfrom31angiospermspeciesfromdifferentbiomes.
NewPhytologist(2015) (cid:1) Thenumberofstomatawithineachareolewaslinearlyrelatedtothelengthofthelooping
doi:10.1111/nph.13577 veincontour.Asaconsequenceofthepresenceoffree-endingveinlets,theminimummean
distance of stomata from the nearest veins was invariant with areole size in most of the
species,andspecieswithsmallerdistancescarriedahigherdensityofstomata.
Keywords: angiosperms,free-ending
veinlets,geographicinformationsystem (cid:1) Uniformity of spatial patterning was consistent within leaves and species. Our results
(GIS),leafhydraulics,stomata,veinnetwork. demonstratetheexistenceofanoptimalspatialorganizationofveinsandstomata,andsug-
gest their interplay as a key feature for achieving a constant mesophyll hydraulic resistance
throughouttheleaf.
& Woodward, 2003; Kikuzawa etal., 2008; Baraloto etal.,
Introduction
2010; Kr€ober etal., 2012; Sack etal., 2012).
One of the principal limitations to photosynthesis in terrestrial Homogeneityinwaterdeliveryisachievedinangiospermsbya
plants is the need for continuous replenishment of water tran- highly reticulated structure of widened (tapered) conduits
spired through the stomata. Morphotypes producing a denser (Coomes etal., 2008; Beerling & Franks, 2010; Petit &
and more efficient irrigation system in the leaves were favoured Anfodillo, 2013), hierarchically organized (McKown etal.,
bynaturalselection,because thisallowed themtoachieve higher 2010),andincludingupto2mcm(cid:3)2ofminorveinlength(Sack
photosynthetic rates (Brodribb & Feild, 2010; Brodribb etal., etal., 2012), often terminating in free-ending veinlets (FEVs)
2010).Thisevolutionaryprocessappearstoculminateinthepro- (Sack&Scoffoni,2013).
duction of high-density reticulate vein networks in the leaves of The most remarkable and general characteristic of angiosperm
floweringplants(Brodribbetal.,2007;Boyceetal.,2009),allow- vein architecture is redundancy, where two nodes of the network
ingefficientandhomogenousdeliveryofwateracrosstheleafsur- are connected by more than one edge, producing loops usually
face(Roth-Nebelsick,2001;Zwienieckietal.,2002). referred to as ‘areoles’ in leaves (Roth-Nebelsick, 2001). Different
While axial water transport through roots and stems is effi- models have been developed to reproduce angiosperm vein net-
ciently achieved by basipetally widening nonliving pipes works (Price & Enquist, 2007; Corson, 2010; Mileyko etal.,
(xylem) (Anfodillo etal., 2006), in the leaf the transpiration 2012),redundancybeingexplainedasprovidinganincreaseinsys-
stream must move between the xylem and living mesophyll tis- temresiliencetodamage(Katiforietal.,2010)orasanadaptation
sues. As a result, the leaf has a disproportionately large to fluctuations in loads (Peak etal., 2004; Corson, 2010). These
hydraulic resistance, accounting for c. 30% of the total modelsfocusontheareolatedpatternproducedbyveins,approxi-
hydraulic resistance of the plant to water transport (Cochard mating thenetworkas ahoneycomb lattice structureof hexagons,
etal., 2004; Sack & Holbrook, 2006). Thus, the last few tens or squares and triangles (Price etal., 2012), while simple areoles
of microns of a hydraulic path that is typically tens of metres havebeenmodelledasregularpolygons(Blonderetal.,2011).
long has a large impact on the transport capacity and photosyn- Reducing the length of the hydraulic pathway from vein ter-
thetic performance of the whole plant (Enquist, 2003; minitothesitesofevaporationappearstobetheprincipalmeans
Kikuzawa etal., 2008; McMurtrie & Dewar, 2011; Edwards by which plant species achieve higher leaf hydraulic efficiency,
etal., 2014), and even on global biogeography (Hetherington and the most obvious means by which this is achieved is by
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increasingthedensityofvenation(Sack&Frole,2006;Brodribb species were selected to cover a range of different environments
etal.,2007). (tropical, alpine, Mediterranean and temperate), venation archi-
Adaptationtoimproveleafhydraulicconductancebyramifica- tecture (for a classification of vein architecture per species, see
tion of the vein network must attract costs in terms of material Supporting Information Table S1), and habits (trees, lianas,
investment and displacement of photosynthetic volume (Chapin grassesandshrubs;Table1).
etal.,2002).Such atrade-offwouldimply thatmaximum econ- Leaves were assumed to be anatomically acclimated to their
omy in terms of net carbon uptake should occur only if plants microenvironment (i.e. sun and shade leaves; Carins Murphy
coordinate the production of veins with tissues responsible for etal., 2012), so three to five single mature leaves without visible
photosynthetic gas exchange (Brodribb etal., 2007, 2013; damage were collected from a deliberately random position in
McKownetal.,2010).Highstomataldensityisaprerequisitefor thecrownofeachspecies.
achieving the high epidermal conductance to CO required for Inviewoftheunfeasibilityofmappingfeaturesonawholeleaf
2
rapid photosynthesis (Franks & Beerling, 2009), but, unless a surface,fourormoresamplingareasofc.30–40mm2wereiden-
highstomataldensityismatchedbyahighveindensity,stomata tified along first- and second-order vein directions on each leaf
will be forced to remain partially closed (Dow & Bergmann, (i.e.neartheleafbase,inthecentralregionandnearthetipalong
2014).Evidenceforsuchcoordinationhasbeendemonstratedin theleafstem,andinthecentralpositionnearthemargin;Fig.1).
terms of the densities of vein tissue and stomata on leaves The margin itself of the leaves was avoided, as some species had
(Brodribb & Jordan, 2011; Carins Murphy etal., 2012, 2014; revolute margins associated with mechanical strengthening
Zhangetal.,2012). (Niklas, 1999) which were thus not completely representative of
Ofcourse,homogeneity inwaterdeliverybytheveinnetwork the whole leaf vein architecture. Small cuts using a razor were
is only effective if water loss from the leaf surface is similarly madeontheleafsurfacetodemarcatesamplingareasduringfur-
homogeneous. In general, this is assumed to be the case theroperations.
(Croxdale, 2000), with stomatal spacing rules thought to guard
against clustering ofpores, undernonstressfulgrowth conditions
Imagecreationanddigitization
(Gan etal., 2010). Stomatal clustering in Arabidopsis mutants
has been shownto produce inefficient stomatal functionandgas For the sake of simplicity, only the abaxial side of the leaf was
exchange(Dowetal.,2013). investigated, as our focus was on the relative spatial distribution
Thus, spatial relationships between veins and stomata are of stomata and veins and not on total conductance measure-
demonstrated to have the potential to greatly influence the effi- ments. Only afew specieswere amphistomaticspecies (Bambusa
ciencyofgasexchangerelativetocarboninvestment(Brodribb& sp. and Sorghum bicolour), and in these cases only stomata from
Jordan, 2011). An optimal use of resources requires veins and onesidewereanalysed.
stomatatobehomogenouslydistributedintheleaf,andthatthe A stomatal impression was taken for each sample with trans-
densitiesofthesetwotissuesshouldremaincoordinated. parent nail varnish on adhesive tape on an area of c. 1cm2,
Itisassumedthatveinsandstomatafollowdiscrete,butcoor- including the sampling area. A clearing and staining protocol
dinated, developmental pathways, that culminate in an optimal based on that of P(cid:3)erez-Harguindeguy etal. (2013) was then fol-
irrigation of the leaf surface, but this assumption has never been lowed for the same areas in order to make all small veins
specifically tested. Recent studies have shown how coordinated detectable. All the pieces of the same leaf were put in a plastic
plasticityinveinandstomataldensitiesallowsliquidandvapour embeddingcassettelabelledwithaleafidentificationcodefortis-
conductances to remain linked during acclimation to sun and sue processing. Chlorophyll was partially extracted using a 50%
shade (Carins Murphy etal., 2012), but the spatial relationships solution of ethanol in water, followed by digestion in a weak
betweenveinsandstomataarealwaysassumed. solution of 5% NaOH (w/v) in order to erode nonvein tissues.
Here, we used a new geospatial approach to examine the Digestion was arrested by rinsing in a 10% solution of
mutual arrangement of stomata and veins in the leaves of 31 CH COOH (w/v), and then leaf pieces were bleached in 50%
3
angiospermspeciesinorder totestwhether assumptionsofopti- common house bleach (w/v) solution. A 2% solution of
malspacingofveinsandstomataareobservedinadiversesample Safranin-O (Sigma) in ethanol was used in order to stain lignin-
ofspeciesincludingmonocotanddicotnetworkarchitectures.In rich tissues. Stained samples were then temporarily mounted on
particular, we focused on the role of FEVs in maintaining uni- glassslides.
form water supply to stomata, using simple models of network The best four samples on one leaf per species were chosen for
geometrytoassessthebeneficialimpactofveinletpresenceupon furtheroperations.Stomatalimpressionsandstainedtissueswere
thehomogeneityinvein–stomatalspacing. photographed using a Nikon DS-L1 digital camera mounted on
a Nikon Eclipse 80i light microscope (Nikon Corporation Ltd,
Tokyo, Japan). In order to keep file size as small as possible, the
MaterialsandMethods
lowest magnification needed to clearly detect both physiological
featureswasadopted.
Datasetandsampling
Partial microscope images were merged with the help of a
Angiosperm leaves from 31 species and 16 orders were used in commercialgraphiceditor(PhotoshopCS4;AdobeSystemsInc.)
this study. The sample group was phylogenetically diverse and in order to acquire complete representations of stomatal
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Table1 Speciesdatasetandmeasuredfeatures
Analysed
Collecting Major leafsurface
Code Species Family Origin Habit place groups (mm2) Areoles Stomata
AC AcercampestreL. Sapindacee EU,SWAsia,NAfrica T BG D 58.52 55 2240
AN AcernegundoL. Sapindacee USA T BG D 42.46 60 7725
AP AcerpseudoplatanusL. Sapindacee Mediterraneanregion, T BG D 18.65 183 2496
Caucaso,Turkey
AT AmborellatrichopodaBaill. Amborellacee NewCaledonia S TAS D 117.16 94 18740
AU ArbutusunedoL. Ericaceae Mediterraneanregion S BG D 21.61 58 2047
BB Bambusasp. Poaceae China T CG M 11.58 969 1866
BH BerberishookeriL. Berberidacee Nepal,Bhutan,India S BG D 13.04 85 5552
BP BetulapendulaRoth Betulacee EU,SWAsia,Caucasus S FI D 34.98 535 6334
BD BuddlejadavidiiFranch. Scrophulariacee NativeofChina,Japan S CG D 37.22 255 6338
CB CarpinusbetulusL. Betulacee WAsia,EU T LA D 34.86 485 4412
CS CastaneasativaMill. Fagacee EU,Asia T FI D 47.07 382 5292
CE CercissiliquastrumL. Fabacee SEurope,WAsia T CG D 14.51 125 1801
CU CoccolobauviferaL. Polygonaceae Caribbean T FC D 55.51 355 9867
CA CorylusavellanaL. Betulaceae EU,WAsia T LA D 45.31 275 4240
CR CrataegusazarolusL. Rosaceae Mediterraneanregion T CG D 13.45 181 1143
FS FagussylvaticaL. Fagacee EU T FI D 62.4 517 8012
FE FraxinusexcelsiorL. Oleaceae EU,SWAsia T FI D 140.84 150 3679
FO FraxinusornusL. Oleaceae EUSWAsia T BG D 66 589 10750
HH HederahelixL. Araliaceae EU,WAsia L CG D 12.61 12 1912
OE OleaeuropaeaL. Oleaceae Africa,Arabia,SEAsia T FS D 206.5 337 8524
subsp.Africana(Mill.)
QC QuercuscerrisL. Fagacee EU,Anatolia T LA D 61.14 598 23295
QR QuercusroburL. Fagaceae EU,Anatolia,NAfrica T LA D 27.68 405 6378
QU QuercusrubraL. Fagaceae NAmerica T CG D 75.91 279 8358
RA RuscusaculeatusL. Asparagaceae EU S FI M 31.07 30 1270
SA SalixapenninaA.K. Salicaceae Italy T BG D 9.59 39 1953
Skvortsov
SN SambucusnigraL. Adoxaceae EU S LA D 97.64 293 5769
SM SmilaxasperaL. Smilacaceae CentralAfrica, L BG M 220.86 181 5335
Mediterraneanregion,
tropicalAsia
SH SorghumhalepenseL.D Poacee G CG M 100.04 311 2862
TC TamuscommunisL. Dioscoreaceae EU,NAfrica,WAsia L FI M 19.39 52 1384
TI TiliacordataMill. Malvaceae EU,WAsia T CG D 62.79 475 5928
UG UlmusglabraHuds. Ulmaceae EU,NEAsia T FI D 33.26 277 10014
Habit:T,tree;S,shrub;G,grass;L,liana.Collectingplace:BG,BotanicalgardenofUniversityofPadua,Padua;Italy;LA,TeSAFDepartmentArboretum,
UniversityofPadua;TAS,greenhouseofPlantScienceDepartment,UniversityofTasmania,Australia;FI,field(Italy);FC,field(CostaRica);FS,field(South
Africa);CG,commongarden(NorthernItaly,mesicconditionintemperateclimate);majorgroups:D,dicots;M,monocots.
distribution and vein pattern. The portion of image correspond- superposition. After superposition, the domain contour was
ingtoveinswasfurtherextractedfromtheclearerbackgroundby tracedalongtheoutermarginofveinsinordertoavoidintroduc-
settingathresholdvalueofgrey,andseparatelysaved. ingartificiallyshapedareoles,wherebothstomataandveinswere
Image content digitization was central in this work. Data for clearlydetectableandundamaged.Thisoperationresultedindif-
the mutual spatial arrangement of stomata and veins were ferentfinalsamplesizesamongspecies(seeFig.S1).
obtained by applying a georeferencing framework (ARCGIS Within the domain, images were then digitized (i.e. trans-
10.00;ESRIInc.,Redlands,CA,USA)tothevectorialrepresen- formed from pictures or rasters into vectorial representations) in
tation of leaf features. Using this method, c. 103 stomata and c. separate layers, each one containing only one class of primitive
102 areoles in each sample were analysed in a semi-automated entities(points,lines,andpolygons).Theveinlayerandtheare-
fashion(Table1). olelayerwereautomaticallygeneratedbytakingadvantageofthe
A detailed representation of stomata and vein pattern on the staining process that enhanced veins relative to the background,
same surface was obtained by superimposing each aggregated thus permitting easy reclassification of pixels into vein and non-
imageofveinsoverthecorrespondingaggregatedimageofstom- vein. The vein outlines were further converted into polygon fea-
ata with the georeferencing tool ARCVIEW (ESRI Inc.). Some tures (areole layer) or line features (vein contour layer). The
clearlyrecognizablecontrolpointswereanchoredonbothimages stomatallayerwasmadebymanuallyinsertingapointfeaturefor
and the vein image was translated and rotated until exact eachstoma.Thisapproachwasquiteslowbutresultedinabetter
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accuracyofstomatalpatternreplicationcomparedwithanyauto- Thus,directmeasurementsonstomataandareoleswereobtained
matic filtering procedure, which was seen to miss a significant as automatically computed attributes of features in each feature
percentage of features (20–35%). Details of the main steps of class. For each polygon, a binary categorical variable y/n was
imagedigitizationareshowninFig.2. manually added in a new column of the polygon attribute table
to indicate the presence or absence of FEVs within the polygon
(y=present; n=absent). In order to acquire joint attributes of
Measurements
features belonging to different feature classes, the topological
All the polygons completely enclosed by veins were identified as relationships considered here were proximity and containment.
areolesandautomaticallylabelledwithanumericalcode. The number of stomata per areole was obtained with an auto-
The program automatically associates tabular data (or maticoperationofjoiningthetabledattributesofpointandpoly-
attributes)witheachfeatureinalayer:forpointlayers,atableis gon layers based on their spatial relationship, thus obtaining a
automaticallycreatedwithcentroidcoordinates;forpolygonlay- new attribute table with the number of points within each poly-
ers, area, perimeter and centroid coordinates can be computed. gon (this operation is identified as ‘spatial joint’ in ARCGIS).
With the purpose of a new insight on the compromise between
thesizeoftheavailableexchangenetworkandthedensityofsup-
portedevaporativesites,thelinkbetweenthenumberofstomata
per areole andareole contourlengthwasstudied. Given that the
apoplasticflowpathbetweenveinsandstomatahasaparticularly
high resistance (Brodribb etal., 2007), the Euclidean distance to
thenearestveinwallwasautomaticallymeasuredforeachstoma,
and an average distance (L ) representative of each areole was
sv
addedtotheareoleattributes.
Finally,asareolesonlydifferfrompolygonsforFEVpresence,
we selected a subset of species, characterized by >50% FEV
presence in areoles, to further investigate the role of FEV in
reducingthewaterflowpathbetweenveinsandstomata.Forone
sample of each leaf of the subset, the areole layer was edited by
erasingalltheveinletsattheirinsertiononthecontourandthen
restoringcontourcontinuity.AnewL wasthencomputed
sv,edited
forallareolesoftheeditedpatternasfortherealone.
Theoreticalgeometricalmodelsforareolerepresentation
TofurtherquantifytheeffectsofFEVsontheobservedrelation-
ship between areole size and L , we modelled how L would be
sv sv
expected to change in areoles of different geometries without
FEVs. As L is constrained by areole characteristic length (i.e.
sv
L <A1/2, with A being areole area), we hypothesized a general
sv
Fig.1 ExampleofsamplinglocationsonaleafinthespeciesCorylus dependenceofLsvonAfromareolegeometry.
avellana.
(a) (b) (e)
Fig.2 Stepsofimagedigitization.(a)Detail
ofastomatalimpression;(b)veinpattern
(c) (d) afterstainingandimageprocessing;(c)
superpositionoftheveinimageoverthe
stomatalimage;(d)finaldigitalizedfeatures;
(e)enlargementofvectorializedimage
showingareolearea(ingrey),areolecontour
(inred),andstomata(bluedots);green
arrowsindicatefree-endingveinlets.Species:
Quercusrobur.
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ThreetheoreticalmodelsintheformL(A)=cA1/2(c<1)were andveinnetworkgeometryforeachleaf.Statisticalanalyseswere
consideredforcomparison. performed using R.3.0.3 (R Development Core Team, 2014).
Wetestedfordifferencesinslopebetweenrealandmodifiedvein
Circlemodel AleafareoleisapproximatedbyacircleofareaA pattern models for Lsv with the software SMATR (Warton etal.,
andradiusr.Thus,theaveragedistanceL (A)ofinnerpoints 2006)inordertoverifywhetherrealandediteddistancepatterns
circle
tothecontourisafunctionofA,intheclosedform: belongedtodifferentdistributions.
Zr
L ðAÞ¼ 1 ðr (cid:3)xÞ2pxdx ¼1r ffi0:1881A1=2
circle pr2 3 Results
0
Numberofstomataandlengthoftheareolecontour
Hexagon model A honeycomb lattice of regular hexagons of Given that water flows out of the xylem through diffuse pits
sidelapproximatesthelocalveinnetwork(Ellisetal.,2009;Price along the xylem wall, and that stomatal aperture is highly sensi-
etal.,2012).TheaveragedistanceLhexagon(A)ofinnerpointsto tive to pressure gradients in the leaf, it follows that the total
each side of the hexagon is the average distance of points within length of the contour surrounding an areole should strongly
an equilateral triangle, where one side forms the edge of the influencestomatalbehaviour.Toexaminethespatialassociations
hexagonwithsidelength=l: between water supply tissue (veins) and water loss tissue (stom-
ffiffi ata),weanalysedtherelationshipbetweenthenumberofstomata
p
Zl 3(cid:3) pffiffiffi (cid:4) andthecontourlengthofareoles.
2
1 l 3 2 l
L ðA Þ¼ (cid:3)x pffiffiffixdx ¼ pffiffiffi Plots of data and fitting regression line models are shown in
triangle triangle
Atriangle 2 3 2 3 Fig.3 for six representative species (for single species plots, see
0
¼p1ffiffiffiffiffiAtriangle1=2 Fteidg.wSi1t)h;i9n5%Figc.o4nifindteerncceeptisntaenrdvasllso(pCesIsf)o.rWalletshteresspsehceierseatrheaptltohte-
433
areole contours we considered were the outer margins of veins
A surrounding leaf mesophyll (Green etal., 2014) and not the lin-
A ¼ hexagon
triangle ear skeletonization resulting from collapsing vein width on its
6
longitudinalaxis(Priceetal.,2012).
L ðAÞ¼p1ffiffiffiffiffip1ffiffiffiA 1=2 ffi0:179A1=2 Withineachspecies,thenumberofstomatainsideeachareole
hexagon 433 6 hexagon was linearly related to the contour length of the vein (mm). A
highly significant (P<0.0001) relationship was found for all the
species,accountingfor39–98%ofvariation innumberofstom-
Diffusivemodel Anareoleissimplifiedbyaregularhexagonof ataperareole.Theregressionslopesrepresentdensity(numberof
side l and area A with one stoma in the centre. Water leakage is stomata mm(cid:3)1), and appeared to be variable among species
diffuse along each side to the stoma, so that the approximated (Fig.4). Thus, areoles of different species with similar contour
path length canbefound asan average value betweenminimum lengths could host very different numbers of stomata (e.g. SH
(i.e.fromcentretoside)andmaximum(i.e.fromcentretoedge) and AN; see Table S1 for species codes). In addition, similar
distances: slopescouldresultfromspeciesspanningdifferentrangesofcon-
pffiffiffi tourlengthandnumberofstomata(e.g.QCandAN).
L ðAÞ¼1ðl þl 3Þffi0:5788A1=2
diffusive
2 2
L variationwithareolegeometry
sv
Each model focused on a different aspect of the stoma–vein TherelationshipbetweenL (mm)andareolearea(mm2)(Fig.5)
sv
arrangement in leaves: the circle model represents the most was found to be significant for 26 of the 31 species (P<0.05).
genericareolewith infinite sides; thehexagon wasusedin recent However,theslopeoftherelationshipbetweenL andareolearea
sv
worksasthemostsuitablegeometrytomimicalatticeofareoles (d(L )/dA; mmmm(cid:3)2) was closetozeroinalmost allthe species
sv
in a leaf fragment (Price etal., 2012); the diffuse leaking model (slopesof0–0.05for25of31species).Inotherwords,despitethe
accountedforthesupplycomingtoeachstomafromdiffusepits significance of slopes, there was a remarkably constant L over a
sv
alongthewholecontributinglength. verylargerangeofareolearea(Fig.6).Notably,inthethreespecies
(AP, BB and CB) with the highest slopes (>0.1mmmm(cid:3)2), L
sv
changed by 80%, 95% and 33%, respectively, while areole area
Statisticalanalyses
varied550%,692%and617%,respectively.
Outlierswere removedfrom thedata andthe distribution of the In contrast to the uniformity in observed L across areole
sv
datawascheckedfornormality.Measurementsmadeondifferent areas, the theoretical relationships between L and areole size
sv
samples were considered together in order to obtain an average took the form of power-law relationships (Fig.5). Theoretical
trend valid for the whole leaf. Thus, linear regression analysis distancesweremuchgreaterthanthemeasureddistances(2.5-to
allowedustoinvestigatetherelationshipamongstomatalpattern 9.5-foldlargerthanthedistancesmeasuredinleaves).
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Fig.3 Exampleofregressionplotsofnumber
ofstomatawithineachareoleversusareole
contourlength(mm)forsixspecies.
Fig.4 Slopes(upper;innumberofstomatamm(cid:3)1)andintercepts(lower;innumberofstomata)ofthelinearregressionmodelfornumberofstomata
againstareolecontourwith95%confidenceintervals.Thehorizontallineat‘0’stomatalvalues(bluesolidline)hasbeenaddedtoaidcomparisonwith
interceptvalues.Forspeciescodes,seeTable1.
ThemaintenanceofaconstantL acrossarangeofareolecon- c.50%whenaveragedistanceonlytolongitudinalveinswascon-
sv
tours(mm)wasalsoverymarked.Only14of31speciesshowed sidered while excluding transverse bundles from distance mea-
a statistically significant slope (mm mm(cid:3)1), and all slopes were surements(i.e.onlydistancefromstomatatolongitudinalveins).
very small, in the range 0–0.05, in many cases being close to or In BB the slope changed from 0.36 to 0.18 for the relationship
equalto0(Fig.6). distance–area and from 0.041 to 0.029 for the relationship dis-
Amongthethreespeciespresentingastronglysignificantslope tance–contour.InSH,slopevalueswere0.05and0.016,respec-
for the relationship distance–area, AP and CB showed a weak tively,forareoleareaandintheneighbourhoodof0forcontour.
relationship of distance with areole contour. The only exception
was the monocot BB, for which contour and areole size showed
Stomataldensityandareolesize
substantialslopes.
Forthetwoparallelveinmonocotspecies(BBandSH),slopes Given the highly stable values of L found for the leaves of most
sv
ofbothrelationshipswithareaandwithcontourwerereducedby species, we examined whether variation in L among species was
sv
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potentially associated with different capacities to supply water to
Free-endingveinletoccurrenceinareoles
stomata. Using the intercept of the L versus areole area plots
sv
(Fig.S1)asareferenceforcomparingL betweenspecies,wefound In order to determine whether the presence of FEVs within are-
sv
a highly significant correlation between L and stomatal density oles was linked to areole size, FEV distribution among areoles
sv
among species: stomatal density=6.38 (L )(cid:3)0.92; r2=0.42; wasexplored.Monocotspecies(BBandSH)wereexcludedfrom
sv
P<0.005 (Fig.7). Species with smaller L thus were able to sup- the analysis, because they lack FEV. Areoles of the other species
sv
port higher stomatal densities. A similar relationship was observed were organized in five dimensional classes and for each class the
betweenspeciesmeanL andstomataldensity(Fig.7). fractioncoded‘y’(oneormoreFEVsobservedwithintheareole)
sv
wascounted.
Thesizerangeofareoledimensionalclasseswerecharacteristic
foreachspecies,andFEVoccurrencewasnotrelatedtotheabso-
lutedimensionsoftheareoles.However,withinspecies,FEVfre-
quency was found to increase with increasing areole size (i.e.
areolescontainingFEVswerefoundonaveragetobelargerthan
those without). Typical outputs are displayed in Fig.8 for two
species (see Supporting Information for the remaining plots).
FEVswerefoundin38%and57%ofCBandATareoles,respec-
tively, with increasing occurrence with increasing areole dimen-
sions.
Theroleoffree-endingveinletsinstabilizingL
sv
For the analysed species (represented by an asterisk after the
species code in Fig.6), artificial removal of FEVs had a large
effect on the relationship between areole size and L . We com-
sv
Fig.5 Relationshipofaveragedistancefromstomatatoveinsinanareole paredthetrendsofL vsareoleareaforareolesfromwhichFEVs
sv
(Lsv;mm)withareolearea(mm2)forQuercusrobur,aspecieswithahigh werepresentorerased(Fig.9).
regressionslope(>0.05;i.e.abehaviournearertotheoreticalmodels).
Real L data followed in all cases the very flat pattern we
Here,whileareolesizerangesfrom0.01to0.1(oranincreaseofc. sv
observed along the whole leaf in the previous section (Figs5, 6).
900%),realL changesfromc.0.03to0.036(oranincreaseof24%),
sv
andthetheoreticalmodelsexhibitanincreaseof>200%.Aregressionline By contrast, Lsv within edited areoles (without FEVs) was found
andregressionequationarerepresented;dashedlines,theoreticalmodels toincreasewithincreasingareolearea,withextremevaluesupto
ofdistance.Theregressionmodelishighlysignificant(P<0.001). 425% (for BD) the value observed in areoles with FEVs. Edited
Fig.6 Slopesofthelinearregressionmodelforaveragedistancefromstomatatoveinsinanareole,L ,againstareolearea(upper;inmmmm(cid:3)2)and
sv
areolecontour(lower;inmmmm(cid:3)1)with95%confidenceintervals(CI).Horizontallinesat0and0.05slopevalues(reddashedlines)havebeenaddedto
aidcomparison.Forbamboo(BB)andSorghumbicolor(SH),theslopevaluesofdistancetolongitudinalveinsarealsorepresentedwithdottedCIlines.For
speciescodes,seeTable1.Thespeciesforwhichfurtherfree-endingveinleteditingwasperformedareidentifiedwithanasterisk.
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8 Research Phytologist
waythatoptimizesresourceuseintheleaf.Inaddition,ourdata
suggest that the mean distance between veins and stomata
imposes a limitation on the density of stomata that can be irri-
gated by the leaf vascular system, thus supporting functional
models of leaf hydraulic supply (Brodribb etal., 2007; Buckley
etal.,2015).Noneoftheseresultswouldbepredictedfromsepa-
ratedstudiesonveinarchitectureandstomataldistribution.
Isometrictuningbetweencontourveinlengthandnumber
ofstomata
The areole contour represents the effective interface for the
exchangeofwaterbetweentissuescharacterizedbydifferentresis-
tancestowaterflow(xylemandmesophyll).Afewpreviousstud-
ies attempted to introduce areole measurements in topological
studies of vein architecture (Blonder etal., 2011; Price etal.,
Fig.7 Species-specificaveragedistanceofstomatatoveinsinanareole
2011; Sack & Scoffoni, 2013), but none of the previous works
(L ;mm)wasstronglycorrelatedwithstomataldensity(numberof
sv
stomatamm(cid:3)2)amongthespeciessample.Ahighlysignificantregression dealtwiththecontourspecifically.
betweenreferenceL (takenastheinterceptbetweenregressionsofL Wefoundthatineachleaftheareolecontourislinearlyrelated
sv sv
andareolearea(seeFig.5)foreachspecies)andmeanstomataldensity to the number of stomata within each areole, and that the same
plottedonlog–logaxesshowsaslopeof(cid:3)0.93,veryclosetothevalueof
relationshipholdsforalltheareolesindifferentpartsoftheleaf.
(cid:3)1expectedifL wasproportionaltohydraulicresistanceintheleaf.A
sv Hence, on average, it follows that every single stoma is supplied
similarrelationshipbetweenmeanL andstomataldensityisshowninthe
sv
insertgraph. bya‘unit’ofvein(i.e.theslopeofregressionmodel;Fig.3),thus
ensuring homogeneous conditions of water supply across the
wholeleaf.
distance points were best fitted by a power-law relationship (i.e. Basedontheassumptionthatthelengthoftheareoleinterface
y=axb), with 58–78% of distance variance explained by area. is related to the efficiency of xylem water delivery to stomata
Exponentsoftheeditedrelationshiprangedfrom0.323to0.422, (Brodribbetal.,2007;Noblinetal.,2008;Zwieniecki&Boyce,
and notably were closer to the 0.5 exponent of the theoretical 2014), homogeneity in this parameter represents an optimal
relationship distance–area for a hexagonal lattice than the expo- designforleaffunction.Thisremarkableresultmimicswhatwas
nents seen in vein networks without FEVs removed (exponent theoreticallyproposedandobservedinbranchesofanindividual
closeto0). tree(Westetal.,1999;Bettiatietal.,2012).Indeed,theanatomi-
calstructureofthevascularconduitsisdesignedtoguaranteethe
conditionofequi-resistancethroughoutallpaths(i.e.branchesof
Discussion
different length within a crown) from roots to leaf petioles. Our
Inthisstudy,weinvestigatedspatialrelationshipsbetweenveinsand results indicate that the vein network of a leaf behaves like the
stomata in species covering a wide phylogenetic spectrum of living branches of a tree in terms of ensuring conditions of uniform
angiospermleaveswithdiverseveinarchitectures.Thisnewperspec- waterdistributiontotheevaporationsites(stomata).Similarlyto
tiveextendsrecentstudiesonthetopologyoftheveinnetwork(Fu xylem in branches, cell size within the veins increases basipetally
& Chi, 2006; Rolland-Lagan etal., 2009; Cope etal., 2010; Price (i.e. lumens widen from the leaf apex to the base of the petiole)
etal., 2011; Dhondt etal., 2012). We developed an innovative (Coomesetal.,2008;Petit&Anfodillo,2013)andthisanatomi-
methodology, combining image editing and georeferencing opera- cal feature is a key strategy for compensating for the different
tions,thatallowedustoautomaticallymapalargesetoftraitswhile lengths of the path from petioles to areoles. A similar resistance
preservinginformationontheirtopologicalrelationships. withinallpossibleveinpathswouldmeanthata‘unit’ofveinsin
When considering the leaf areole as the fundamental func- anareole,whereveritmaybeintheleaf,wouldreceivethesame
tional unit coupling spatial properties of veins and stomata (the waterfluxperunitofwaterpotentialgradient.
number of stomata, contour length, and the average stoma–vein Itistruethattherearealsoindicationsthatnotallveinstrans-
distance), our results support those of previous work showing fer water in the same way (Altus etal., 1985; Sack & Holbrook,
that stomatal aperture is modulated by hydraulic supply in are- 2006), as a result of modifications such as bundle sheath exten-
ole-discriminated patches (Haefner etal., 1986; Mott & Powell, sions (Nikolopoulos etal., 2002; Shatil-Cohen etal., 2011;
1997; Beyschlag & Eckstein, 2001). Although previous work Sommervilleetal.,2012;Griffithsetal.,2013),theformationof
illustrated how vein development shapes the vein architecture accessory transport elements (Brodribb etal., 2005, 2007) and
(Nelson &Dengler,1997), andhowstomatalandveindensities different tracheary structure (Feild & Brodribb, 2013). Experi-
follow coordinated patterns during adaptation to light (Carins ments with tracers have indicated a subdivision of roles in trans-
Murphy etal., 2012, 2014), here we demonstrated that the pro- port among vein orders in monocot leaves, where vein hierarchy
ductionofstomataandthatofveinsarespatiallycoordinatedina is simplified to two to three orders (Altus & Canny, 1985;
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Phytologist Research 9
Fig.8 Free-endingveinlet(FEV)occurrence
forclassesofareoleareaintwospecies.
Areolesofeachspeciesaredividedintofive
dimensionalclasses.Thepercentage
contributionofeachsizeclass(hatchedbars)
andofareoleswithFEVs(greybars)tothe
totalcountofareolesisshownforeachclass.
Foralmostallthespecies,thepercentageof
areoleswithFEVsineachsizeclassincreases
withprogressivedimensionalclass(inset
graphs).
(a) (b)
Fig.9 Comparisonofaveragedistanceof
stomatatoveinsinanareole(L )withL
sv sv,
(withoutfree-endingveinlets(FEVs))
edited
forsamplesofsevenspecies.Continuous
line:regressionlinearmodelfittingthereal (c) (d)
pattern(opencircles);dashedline:power-
lawmodelfittingtheeditedpattern(closed
circles);dottedline:averagedistanceinsidea
circleasafunctionofcircleareay=0.1881
x0.5.Linearfittingequation;power-law
fittingequation(r2inbrackets):(a) (e) (f)
y=0.008x+0.03(0.009);y=0.139x0.422
(0.71);(b)y=0.11x+0.02(0.004);
y=0.1098x0.323(0.58);(c)
y=0.013x+0.042(0.008);y=0.129x0.35
(0.6);(d)y=0.005x+0.097(0.02); (g) (h)
y=0.168x0.381(0.74);(e)y=0.025x+0.04
(0.023);y=0.123x0.344(0.6);(f)
y=0.008x+0.046(0.01);y=0.104x0.338
(0.68);(g)y=0.0002x+0.106(0.0004);
y=0.147x0.442(0.78).(h)Adetailshowing
areoleswithremovedFEVs.
Russell & Evert, 1985). However, in accordance with Green pressure drop for water flow moving from veins to stomata.
etal.(2014),ourdefinitionofveintissuewasconstrainedtotwo- Thus, the length of the hydraulic path through the mesophyll
dimensional maps of the leaf surface. Thus, no distinction was should be one of the most important parameters in determining
assignedto veinsegmentsbordering anareole,sothatour areole the total hydraulic resistance in the leaf (Brodribb etal., 2010).
contour was a maximum length (surface per unit of leaf thick- However,measurementofthewaterpathoutside thexylempre-
ness)potentiallyirrigatingthemesophyll. sents some difficulties, as different transport mechanisms coexist
or adjust along with leaf developmental stage and physiology
(Sack etal., 2004; Prado & Maurel, 2013; Muller etal., 2014)
Leaveslimitvein–stomaspacingincontrastwiththeoretical
and a change of phase from liquid to vapour occurs along the
modelpredictions
pathway (Rockwell etal., 2014). Thus, the interveinal distance
A major component of the hydraulic resistance, located outside and the inverse of vein density have been used as inexpensive
leafveins,determinesadistributed(i.e.proportionaltodistance) options to assess the extra-xylem flow path length (Brodribb
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