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Transportefficiencythroughuniformity:
Organizationofveinsandstomatain
angiospermleaves
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Research
Transport efficiency through uniformity: organization of veins
and stomata in angiosperm leaves
Lucia Fiorin1, Timothy J. Brodribb2 and Tommaso Anfodillo1
1
Department of Territorio e Sistemi Agro-Forestali (TeSAF), Universita degli Studi di Padova, Viale dell’Universita 16, I-35020, Legnaro (PD), Italy; 2School of Plant Science, University of
Tasmania, Private Bag 55, Hobart, TAS 7001, Australia
Summary
Author for correspondence:
Timothy J. Brodribb
Tel: +61 362261707
Email: [email protected]
Received: 30 March 2015
Accepted: 22 June 2015
New Phytologist (2015)
doi: 10.1111/nph.13577
Key words: angiosperms, free-ending
veinlets, geographic information system
(GIS), leaf hydraulics, stomata, vein network.
Leaves of vascular plants use specific tissues to irrigate the lamina (veins) and to regulate
water loss (stomata), to approach homeostasis in leaf hydration during photosynthesis. As
both tissues come with attendant costs, it would be expected that the synthesis and spacing
of leaf veins and stomata should be coordinated in a way that maximizes benefit to the plant.
We propose an innovative geoprocessing method based on image editing and a geographic
information system to study the quantitative relationships between vein and stomatal spatial
patterns on leaves collected from 31 angiosperm species from different biomes.
The number of stomata within each areole was linearly related to the length of the looping
vein contour. As a consequence of the presence of free-ending veinlets, the minimum mean
distance of stomata from the nearest veins was invariant with areole size in most of the
species, and species with smaller distances carried a higher density of stomata.
Uniformity of spatial patterning was consistent within leaves and species. Our results
demonstrate the existence of an optimal spatial organization of veins and stomata, and suggest their interplay as a key feature for achieving a constant mesophyll hydraulic resistance
throughout the leaf.
Introduction
One of the principal limitations to photosynthesis in terrestrial
plants is the need for continuous replenishment of water transpired through the stomata. Morphotypes producing a denser
and more efficient irrigation system in the leaves were favoured
by natural selection, because this allowed them to achieve higher
photosynthetic rates (Brodribb & Feild, 2010; Brodribb et al.,
2010). This evolutionary process appears to culminate in the production of high-density reticulate vein networks in the leaves of
flowering plants (Brodribb et al., 2007; Boyce et al., 2009), allowing efficient and homogenous delivery of water across the leaf surface (Roth-Nebelsick, 2001; Zwieniecki et al., 2002).
While axial water transport through roots and stems is efficiently achieved by basipetally widening nonliving pipes
(xylem) (Anfodillo et al., 2006), in the leaf the transpiration
stream must move between the xylem and living mesophyll tissues. As a result, the leaf has a disproportionately large
hydraulic resistance, accounting for c. 30% of the total
hydraulic resistance of the plant to water transport (Cochard
et al., 2004; Sack & Holbrook, 2006). Thus, the last few tens
of microns of a hydraulic path that is typically tens of metres
long has a large impact on the transport capacity and photosynthetic performance of the whole plant (Enquist, 2003;
Kikuzawa et al., 2008; McMurtrie & Dewar, 2011; Edwards
et al., 2014), and even on global biogeography (Hetherington
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& Woodward, 2003; Kikuzawa et al., 2008; Baraloto et al.,
2010; Kr€ober et al., 2012; Sack et al., 2012).
Homogeneity in water delivery is achieved in angiosperms by a
highly reticulated structure of widened (tapered) conduits
(Coomes et al., 2008; Beerling & Franks, 2010; Petit &
Anfodillo, 2013), hierarchically organized (McKown et al.,
2010), and including up to 2 m cm2 of minor vein length (Sack
et al., 2012), often terminating in free-ending veinlets (FEVs)
(Sack & Scoffoni, 2013).
The most remarkable and general characteristic of angiosperm
vein architecture is redundancy, where two nodes of the network
are connected by more than one edge, producing loops usually
referred to as ‘areoles’ in leaves (Roth-Nebelsick, 2001). Different
models have been developed to reproduce angiosperm vein networks (Price & Enquist, 2007; Corson, 2010; Mileyko et al.,
2012), redundancy being explained as providing an increase in system resilience to damage (Katifori et al., 2010) or as an adaptation
to fluctuations in loads (Peak et al., 2004; Corson, 2010). These
models focus on the areolated pattern produced by veins, approximating the network as a honeycomb lattice structure of hexagons,
or squares and triangles (Price et al., 2012), while simple areoles
have been modelled as regular polygons (Blonder et al., 2011).
Reducing the length of the hydraulic pathway from vein termini to the sites of evaporation appears to be the principal means
by which plant species achieve higher leaf hydraulic efficiency,
and the most obvious means by which this is achieved is by
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increasing the density of venation (Sack & Frole, 2006; Brodribb
et al., 2007).
Adaptation to improve leaf hydraulic conductance by ramification of the vein network must attract costs in terms of material
investment and displacement of photosynthetic volume (Chapin
et al., 2002). Such a trade-off would imply that maximum economy in terms of net carbon uptake should occur only if plants
coordinate the production of veins with tissues responsible for
photosynthetic gas exchange (Brodribb et al., 2007, 2013;
McKown et al., 2010). High stomatal density is a prerequisite for
achieving the high epidermal conductance to CO2 required for
rapid photosynthesis (Franks & Beerling, 2009), but, unless a
high stomatal density is matched by a high vein density, stomata
will be forced to remain partially closed (Dow & Bergmann,
2014). Evidence for such coordination has been demonstrated in
terms of the densities of vein tissue and stomata on leaves
(Brodribb & Jordan, 2011; Carins Murphy et al., 2012, 2014;
Zhang et al., 2012).
Of course, homogeneity in water delivery by the vein network
is only effective if water loss from the leaf surface is similarly
homogeneous. In general, this is assumed to be the case
(Croxdale, 2000), with stomatal spacing rules thought to guard
against clustering of pores, under nonstressful growth conditions
(Gan et al., 2010). Stomatal clustering in Arabidopsis mutants
has been shown to produce inefficient stomatal function and gas
exchange (Dow et al., 2013).
Thus, spatial relationships between veins and stomata are
demonstrated to have the potential to greatly influence the efficiency of gas exchange relative to carbon investment (Brodribb &
Jordan, 2011). An optimal use of resources requires veins and
stomata to be homogenously distributed in the leaf, and that the
densities of these two tissues should remain coordinated.
It is assumed that veins and stomata follow discrete, but coordinated, developmental pathways, that culminate in an optimal
irrigation of the leaf surface, but this assumption has never been
specifically tested. Recent studies have shown how coordinated
plasticity in vein and stomatal densities allows liquid and vapour
conductances to remain linked during acclimation to sun and
shade (Carins Murphy et al., 2012), but the spatial relationships
between veins and stomata are always assumed.
Here, we used a new geospatial approach to examine the
mutual arrangement of stomata and veins in the leaves of 31
angiosperm species in order to test whether assumptions of optimal spacing of veins and stomata are observed in a diverse sample
of species including monocot and dicot network architectures. In
particular, we focused on the role of FEVs in maintaining uniform water supply to stomata, using simple models of network
geometry to assess the beneficial impact of veinlet presence upon
the homogeneity in vein–stomatal spacing.
Materials and Methods
Data set and sampling
Angiosperm leaves from 31 species and 16 orders were used in
this study. The sample group was phylogenetically diverse and
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species were selected to cover a range of different environments
(tropical, alpine, Mediterranean and temperate), venation architecture (for a classification of vein architecture per species, see
Supporting Information Table S1), and habits (trees, lianas,
grasses and shrubs; Table 1).
Leaves were assumed to be anatomically acclimated to their
microenvironment (i.e. sun and shade leaves; Carins Murphy
et al., 2012), so three to five single mature leaves without visible
damage were collected from a deliberately random position in
the crown of each species.
In view of the unfeasibility of mapping features on a whole leaf
surface, four or more sampling areas of c. 30–40 mm2 were identified along first- and second-order vein directions on each leaf
(i.e. near the leaf base, in the central region and near the tip along
the leaf stem, and in the central position near the margin; Fig. 1).
The margin itself of the leaves was avoided, as some species had
revolute margins associated with mechanical strengthening
(Niklas, 1999) which were thus not completely representative of
the whole leaf vein architecture. Small cuts using a razor were
made on the leaf surface to demarcate sampling areas during further operations.
Image creation and digitization
For the sake of simplicity, only the abaxial side of the leaf was
investigated, as our focus was on the relative spatial distribution
of stomata and veins and not on total conductance measurements. Only a few species were amphistomatic species (Bambusa
sp. and Sorghum bicolour), and in these cases only stomata from
one side were analysed.
A stomatal impression was taken for each sample with transparent nail varnish on adhesive tape on an area of c. 1 cm2,
including the sampling area. A clearing and staining protocol
based on that of Perez-Harguindeguy et al. (2013) was then followed for the same areas in order to make all small veins
detectable. All the pieces of the same leaf were put in a plastic
embedding cassette labelled with a leaf identification code for tissue processing. Chlorophyll was partially extracted using a 50%
solution of ethanol in water, followed by digestion in a weak
solution of 5% NaOH (w/v) in order to erode nonvein tissues.
Digestion was arrested by rinsing in a 10% solution of
CH3COOH (w/v), and then leaf pieces were bleached in 50%
common house bleach (w/v) solution. A 2% solution of
Safranin-O (Sigma) in ethanol was used in order to stain ligninrich tissues. Stained samples were then temporarily mounted on
glass slides.
The best four samples on one leaf per species were chosen for
further operations. Stomatal impressions and stained tissues were
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
lowest magnification needed to clearly detect both physiological
features was adopted.
Partial microscope images were merged with the help of a
commercial graphic editor (Photoshop CS4; Adobe Systems Inc.)
in order to acquire complete representations of stomatal
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Table 1 Species data set and measured features
Code
Species
Family
Origin
Habit
AC
AN
AP
Acer campestre L.
Acer negundo L.
Acer pseudoplatanus L.
Sapindacee
Sapindacee
Sapindacee
T
T
T
BG
BG
BG
D
D
D
58.52
42.46
18.65
55
60
183
2240
7725
2496
AT
AU
BB
BH
BP
BD
CB
CS
CE
CU
CA
CR
FS
FE
FO
HH
OE
Amborellacee
Ericaceae
Poaceae
Berberidacee
Betulacee
Scrophulariacee
Betulacee
Fagacee
Fabacee
Polygonaceae
Betulaceae
Rosaceae
Fagacee
Oleaceae
Oleaceae
Araliaceae
Oleaceae
S
S
T
S
S
S
T
T
T
T
T
T
T
T
T
L
T
TAS
BG
CG
BG
FI
CG
LA
FI
CG
FC
LA
CG
FI
FI
BG
CG
FS
D
D
M
D
D
D
D
D
D
D
D
D
D
D
D
D
D
117.16
21.61
11.58
13.04
34.98
37.22
34.86
47.07
14.51
55.51
45.31
13.45
62.4
140.84
66
12.61
206.5
94
58
969
85
535
255
485
382
125
355
275
181
517
150
589
12
337
18 740
2047
1866
5552
6334
6338
4412
5292
1801
9867
4240
1143
8012
3679
10 750
1912
8524
Fagacee
Fagaceae
Fagaceae
Asparagaceae
Salicaceae
EU, Anatolia
EU, Anatolia, N Africa
N America
EU
Italy
T
T
T
S
T
LA
LA
CG
FI
BG
D
D
D
M
D
61.14
27.68
75.91
31.07
9.59
598
405
279
30
39
23 295
6378
8358
1270
1953
SN
SM
Amborella trichopoda Baill.
Arbutus unedo L.
Bambusa sp.
Berberis hookeri L.
Betula pendula Roth
Buddleja davidii Franch.
Carpinus betulus L.
Castanea sativa Mill.
Cercis siliquastrum L.
Coccoloba uvifera L.
Corylus avellana L.
Crataegus azarolus L.
Fagus sylvatica L.
Fraxinus excelsior L.
Fraxinus ornus L.
Hedera helix L.
Olea europaea L.
subsp. Africana (Mill.)
Quercus cerris L.
Quercus robur L.
Quercus rubra L.
Ruscus aculeatus L.
Salix apennina A. K.
Skvortsov
Sambucus nigra L.
Smilax aspera L.
EU, SW Asia, N Africa
USA
Mediterranean region,
Caucaso, Turkey
New Caledonia
Mediterranean region
China
Nepal, Bhutan, India
EU, SW Asia, Caucasus
Native of China, Japan
W Asia, EU
EU, Asia
S Europe, W Asia
Caribbean
EU, W Asia
Mediterranean region
EU
EU, SW Asia
EU SW Asia
EU, W Asia
Africa, Arabia, SE Asia
Adoxaceae
Smilacaceae
EU
Central Africa,
Mediterranean region,
tropical Asia
S
L
LA
BG
D
M
97.64
220.86
293
181
5769
5335
SH
TC
TI
UG
Sorghum halepense L. D
Tamus communis L.
Tilia cordata Mill.
Ulmus glabra Huds.
Poacee
Dioscoreaceae
Malvaceae
Ulmaceae
G
L
T
T
CG
FI
CG
FI
M
M
D
D
100.04
19.39
62.79
33.26
311
52
475
277
2862
1384
5928
10 014
QC
QR
QU
RA
SA
EU, N Africa, W Asia
EU, W Asia
EU, NE Asia
Major
groups
Analysed
leaf surface
(mm2)
Collecting
place
Areoles
Stomata
Habit: T, tree; S, shrub; G, grass; L, liana. Collecting place: BG, Botanical garden of University of Padua, Padua; Italy; LA, TeSAF Department Arboretum,
University of Padua; TAS, greenhouse of Plant Science Department, University of Tasmania, Australia; FI, field (Italy); FC, field (Costa Rica); FS, field (South
Africa); CG, common garden (Northern Italy, mesic condition in temperate climate); major groups: D, dicots; M, monocots.
distribution and vein pattern. The portion of image corresponding to veins was further extracted from the clearer background by
setting a threshold value of grey, and separately saved.
Image content digitization was central in this work. Data for
the mutual spatial arrangement of stomata and veins were
obtained by applying a georeferencing framework (ARCGIS
10.00; ESRI Inc., Redlands, CA, USA) to the vectorial representation of leaf features. Using this method, c. 103 stomata and c.
102 areoles in each sample were analysed in a semi-automated
fashion (Table 1).
A detailed representation of stomata and vein pattern on the
same surface was obtained by superimposing each aggregated
image of veins over the corresponding aggregated image of stomata with the georeferencing tool ARCVIEW (ESRI Inc.). Some
clearly recognizable control points were anchored on both images
and the vein image was translated and rotated until exact
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superposition. After superposition, the domain contour was
traced along the outer margin of veins in order to avoid introducing artificially shaped areoles, where both stomata and veins were
clearly detectable and undamaged. This operation resulted in different final sample sizes among species (see Fig. S1).
Within the domain, images were then digitized (i.e. transformed from pictures or rasters into vectorial representations) in
separate layers, each one containing only one class of primitive
entities (points, lines, and polygons). The vein layer and the areole layer were automatically generated by taking advantage of the
staining process that enhanced veins relative to the background,
thus permitting easy reclassification of pixels into vein and nonvein. The vein outlines were further converted into polygon features (areole layer) or line features (vein contour layer). The
stomatal layer was made by manually inserting a point feature for
each stoma. This approach was quite slow but resulted in a better
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accuracy of stomatal pattern replication compared with any automatic filtering procedure, which was seen to miss a significant
percentage of features (20–35%). Details of the main steps of
image digitization are shown in Fig. 2.
Measurements
All the polygons completely enclosed by veins were identified as
areoles and automatically labelled with a numerical code.
The program automatically associates tabular data (or
attributes) with each feature in a layer: for point layers, a table is
automatically created with centroid coordinates; for polygon layers, area, perimeter and centroid coordinates can be computed.
Thus, direct measurements on stomata and areoles were obtained
as automatically computed attributes of features in each feature
class. For each polygon, a binary categorical variable y/n was
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
features belonging to different feature classes, the topological
relationships considered here were proximity and containment.
The number of stomata per areole was obtained with an automatic operation of joining the tabled attributes of point and polygon layers based on their spatial relationship, thus obtaining a
new attribute table with the number of points within each polygon (this operation is identified as ‘spatial joint’ in ARCGIS).
With the purpose of a new insight on the compromise between
the size of the available exchange network and the density of supported evaporative sites, the link between the number of stomata
per areole and areole contour length was studied. Given that the
apoplastic flow path between veins and stomata has a particularly
high resistance (Brodribb et al., 2007), the Euclidean distance to
the nearest vein wall was automatically measured for each stoma,
and an average distance (Lsv) representative of each areole was
added to the areole attributes.
Finally, as areoles only differ from polygons for FEV presence,
we selected a subset of species, characterized by >50% FEV
presence in areoles, to further investigate the role of FEV in
reducing the water flow path between veins and stomata. For one
sample of each leaf of the subset, the areole layer was edited by
erasing all the veinlets at their insertion on the contour and then
restoring contour continuity. A new Lsv, edited was then computed
for all areoles of the edited pattern as for the real one.
Theoretical geometrical models for areole representation
To further quantify the effects of FEVs on the observed relationship between areole size and Lsv, we modelled how Lsv would be
expected to change in areoles of different geometries without
FEVs. As Lsv is constrained by areole characteristic length (i.e.
Lsv < A1/2, with A being areole area), we hypothesized a general
dependence of Lsv on A from areole geometry.
Fig. 1 Example of sampling locations on a leaf in the species Corylus
avellana.
(a)
(c)
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(b)
(d)
(e)
Fig. 2 Steps of image digitization. (a) Detail
of a stomatal impression; (b) vein pattern
after staining and image processing; (c)
superposition of the vein image over the
stomatal image; (d) final digitalized features;
(e) enlargement of vectorialized image
showing areole area (in grey), areole contour
(in red), and stomata (blue dots); green
arrows indicate free-ending veinlets. Species:
Quercus robur.
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Three theoretical models in the form L(A) = cA1/2 (c < 1) were
considered for comparison.
Circle model A leaf areole is approximated by a circle of area A
and radius r. Thus, the average distance Lcircle(A) of inner points
to the contour is a function of A, in the closed form:
Zr
1
1
Lcircle ðAÞ ¼ 2 ðr xÞ2pxdx ¼ r ffi 0:1881A 1=2
pr
3
0
and vein network geometry for each leaf. Statistical analyses were
performed using R.3.0.3 (R Development Core Team, 2014).
We tested for differences in slope between real and modified vein
pattern models for Lsv with the software SMATR (Warton et al.,
2006) in order to verify whether real and edited distance patterns
belonged to different distributions.
Results
Number of stomata and length of the areole contour
Hexagon model A honeycomb lattice of regular hexagons of
side l approximates the local vein network (Ellis et al., 2009; Price
et al., 2012). The average distance Lhexagon (A) of inner points to
each side of the hexagon is the average distance of points within
an equilateral triangle, where one side forms the edge of the
hexagon with side length = l:
pffi
l 3
Z 2 pffiffiffi
1
l 3
2
l
Ltriangle ðAtriangle Þ ¼
x pffiffiffi xdx ¼ pffiffiffi
Atriangle
2
3
2 3
0
1
ffiffiffiffiffi Atriangle 1=2
¼p
4
33
Atriangle ¼
Ahexagon
6
1 1
ffiffiffiffiffi pffiffiffi Ahexagon 1=2 ffi 0:179A 1=2
Lhexagon ðAÞ ¼ p
4
33 6
Diffusive model An areole is simplified by a regular hexagon of
side l and area A with one stoma in the centre. Water leakage is
diffuse along each side to the stoma, so that the approximated
path length can be found as an average value between minimum
(i.e. from centre to side) and maximum (i.e. from centre to edge)
distances:
pffiffiffi
1
l 3
Ldiffusive ðAÞ ¼ ðl þ
Þ ffi 0:5788A 1=2
2
2
Each model focused on a different aspect of the stoma–vein
arrangement in leaves: the circle model represents the most
generic areole with infinite sides; the hexagon was used in recent
works as the most suitable geometry to mimic a lattice of areoles
in a leaf fragment (Price et al., 2012); the diffuse leaking model
accounted for the supply coming to each stoma from diffuse pits
along the whole contributing length.
Statistical analyses
Outliers were removed from the data and the distribution of the
data was checked for normality. Measurements made on different
samples were considered together in order to obtain an average
trend valid for the whole leaf. Thus, linear regression analysis
allowed us to investigate the relationship among stomatal pattern
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Given that water flows out of the xylem through diffuse pits
along the xylem wall, and that stomatal aperture is highly sensitive to pressure gradients in the leaf, it follows that the total
length of the contour surrounding an areole should strongly
influence stomatal behaviour. To examine the spatial associations
between water supply tissue (veins) and water loss tissue (stomata), we analysed the relationship between the number of stomata
and the contour length of areoles.
Plots of data and fitting regression line models are shown in
Fig. 3 for six representative species (for single species plots, see
Fig. S1); in Fig. 4 intercepts and slopes for all the species are plotted with 95% confidence intervals (CIs). We stress here that the
areole contours we considered were the outer margins of veins
surrounding leaf mesophyll (Green et al., 2014) and not the linear skeletonization resulting from collapsing vein width on its
longitudinal axis (Price et al., 2012).
Within each species, the number of stomata inside each areole
was linearly related to the contour length of the vein (mm). A
highly significant (P < 0.0001) relationship was found for all the
species, accounting for 39–98% of variation in number of stomata per areole. The regression slopes represent density (number of
stomata mm1), and appeared to be variable among species
(Fig. 4). Thus, areoles of different species with similar contour
lengths could host very different numbers of stomata (e.g. SH
and AN; see Table S1 for species codes). In addition, similar
slopes could result from species spanning different ranges of contour length and number of stomata (e.g. QC and AN).
Lsv variation with areole geometry
The relationship between Lsv (mm) and areole area (mm2) (Fig. 5)
was found to be significant for 26 of the 31 species (P < 0.05).
However, the slope of the relationship between Lsv and areole area
(d(Lsv)/dA; mm mm2) was close to zero in almost all the species
(slopes of 0–0.05 for 25 of 31 species). In other words, despite the
significance of slopes, there was a remarkably constant Lsv over a
very large range of areole area (Fig. 6). Notably, in the three species
(AP, BB and CB) with the highest slopes (> 0.1 mm mm2), Lsv
changed by 80%, 95% and 33%, respectively, while areole area
varied 550%, 692% and 617%, respectively.
In contrast to the uniformity in observed Lsv across areole
areas, the theoretical relationships between Lsv and areole size
took the form of power-law relationships (Fig. 5). Theoretical
distances were much greater than the measured distances (2.5- to
9.5-fold larger than the distances measured in leaves).
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Fig. 3 Example of regression plots of number
of stomata within each areole versus areole
contour length (mm) for six species.
Fig. 4 Slopes (upper; in number of stomata mm1) and intercepts (lower; in number of stomata) of the linear regression model for number of stomata
against areole contour with 95% confidence intervals. The horizontal line at ‘0’ stomatal values (blue solid line) has been added to aid comparison with
intercept values. For species codes, see Table 1.
The maintenance of a constant Lsv across a range of areole contours (mm) was also very marked. Only 14 of 31 species showed
a statistically significant slope (mm mm1), and all slopes were
very small, in the range 0–0.05, in many cases being close to or
equal to 0 (Fig. 6).
Among the three species presenting a strongly significant slope
for the relationship distance–area, AP and CB showed a weak
relationship of distance with areole contour. The only exception
was the monocot BB, for which contour and areole size showed
substantial slopes.
For the two parallel vein monocot species (BB and SH), slopes
of both relationships with area and with contour were reduced by
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c. 50% when average distance only to longitudinal veins was considered while excluding transverse bundles from distance measurements (i.e. only distance from stomata to longitudinal veins).
In BB the slope changed from 0.36 to 0.18 for the relationship
distance–area and from 0.041 to 0.029 for the relationship distance–contour. In SH, slope values were 0.05 and 0.016, respectively, for areole area and in the neighbourhood of 0 for contour.
Stomatal density and areole size
Given the highly stable values of Lsv found for the leaves of most
species, we examined whether variation in Lsv among species was
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potentially associated with different capacities to supply water to
stomata. Using the intercept of the Lsv versus areole area plots
(Fig. S1) as a reference for comparing Lsv between species, we found
a highly significant correlation between Lsv and stomatal density
among species: stomatal density = 6.38 (Lsv)0.92; r2 = 0.42;
P < 0.005 (Fig. 7). Species with smaller Lsv thus were able to support higher stomatal densities. A similar relationship was observed
between species mean Lsv and stomatal density (Fig. 7).
Research 7
Free-ending veinlet occurrence in areoles
In order to determine whether the presence of FEVs within areoles was linked to areole size, FEV distribution among areoles
was explored. Monocot species (BB and SH) were excluded from
the analysis, because they lack FEV. Areoles of the other species
were organized in five dimensional classes and for each class the
fraction coded ‘y’ (one or more FEVs observed within the areole)
was counted.
The size range of areole dimensional classes were characteristic
for each species, and FEV occurrence was not related to the absolute dimensions of the areoles. However, within species, FEV frequency was found to increase with increasing areole size (i.e.
areoles containing FEVs were found on average to be larger than
those without). Typical outputs are displayed in Fig. 8 for two
species (see Supporting Information for the remaining plots).
FEVs were found in 38% and 57% of CB and AT areoles, respectively, with increasing occurrence with increasing areole dimensions.
The role of free-ending veinlets in stabilizing Lsv
Fig. 5 Relationship of average distance from stomata to veins in an areole
(Lsv; mm) with areole area (mm2) for Quercus robur, a species with a high
regression slope (> 0.05; i.e. a behaviour nearer to theoretical models).
Here, while areole size ranges from 0.01 to 0.1 (or an increase of c.
900%), real Lsv changes from c. 0.03 to 0.036 (or an increase of 24%),
and the theoretical models exhibit an increase of > 200%. A regression line
and regression equation are represented; dashed lines, theoretical models
of distance. The regression model is highly significant (P < 0.001).
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 Lsv. We compared the trends of Lsv vs areole area for areoles from which FEVs
were present or erased (Fig. 9).
Real Lsv data followed in all cases the very flat pattern we
observed along the whole leaf in the previous section (Figs 5, 6).
By contrast, Lsv within edited areoles (without FEVs) was found
to increase with increasing areole area, with extreme values up to
425% (for BD) the value observed in areoles with FEVs. Edited
Fig. 6 Slopes of the linear regression model for average distance from stomata to veins in an areole, Lsv, against areole area (upper; in mm mm2) and
areole contour (lower; in mm mm1) with 95% confidence intervals (CI). Horizontal lines at 0 and 0.05 slope values (red dashed lines) have been added to
aid comparison. For bamboo (BB) and Sorghum bicolor (SH), the slope values of distance to longitudinal veins are also represented with dotted CI lines. For
species codes, see Table 1. The species for which further free-ending veinlet editing was performed are identified with an asterisk.
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way that optimizes resource use in the leaf. In addition, our data
suggest that the mean distance between veins and stomata
imposes a limitation on the density of stomata that can be irrigated by the leaf vascular system, thus supporting functional
models of leaf hydraulic supply (Brodribb et al., 2007; Buckley
et al., 2015). None of these results would be predicted from separated studies on vein architecture and stomatal distribution.
Isometric tuning between contour vein length and number
of stomata
Fig. 7 Species-specific average distance of stomata to veins in an areole
(Lsv; mm) was strongly correlated with stomatal density (number of
stomata mm2) among the species sample. A highly significant regression
between reference Lsv (taken as the intercept between regressions of Lsv
and areole area (see Fig. 5) for each species) and mean stomatal density
plotted on log–log axes shows a slope of 0.93, very close to the value of
1 expected if Lsv was proportional to hydraulic resistance in the leaf. A
similar relationship between mean Lsv and stomatal density is shown in the
insert graph.
distance points were best fitted by a power-law relationship (i.e.
y = axb), with 58–78% of distance variance explained by area.
Exponents of the edited relationship ranged from 0.323 to 0.422,
and notably were closer to the 0.5 exponent of the theoretical
relationship distance–area for a hexagonal lattice than the exponents seen in vein networks without FEVs removed (exponent
close to 0).
Discussion
In this study, we investigated spatial relationships between veins and
stomata in species covering a wide phylogenetic spectrum of living
angiosperm leaves with diverse vein architectures. This new perspective extends recent studies on the topology of the vein network (Fu
& Chi, 2006; Rolland-Lagan et al., 2009; Cope et al., 2010; Price
et al., 2011; Dhondt et al., 2012). We developed an innovative
methodology, combining image editing and georeferencing operations, that allowed us to automatically map a large set of traits while
preserving information on their topological relationships.
When considering the leaf areole as the fundamental functional unit coupling spatial properties of veins and stomata (the
number of stomata, contour length, and the average stoma–vein
distance), our results support those of previous work showing
that stomatal aperture is modulated by hydraulic supply in areole-discriminated patches (Haefner et al., 1986; Mott & Powell,
1997; Beyschlag & Eckstein, 2001). Although previous work
illustrated how vein development shapes the vein architecture
(Nelson & Dengler, 1997), and how stomatal and vein densities
follow coordinated patterns during adaptation to light (Carins
Murphy et al., 2012, 2014), here we demonstrated that the production of stomata and that of veins are spatially coordinated in a
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The areole contour represents the effective interface for the
exchange of water between tissues characterized by different resistances to water flow (xylem and mesophyll). A few previous studies attempted to introduce areole measurements in topological
studies of vein architecture (Blonder et al., 2011; Price et al.,
2011; Sack & Scoffoni, 2013), but none of the previous works
dealt with the contour specifically.
We found that in each leaf the areole contour is linearly related
to the number of stomata within each areole, and that the same
relationship holds for all the areoles in different parts of the leaf.
Hence, on average, it follows that every single stoma is supplied
by a ‘unit’ of vein (i.e. the slope of regression model; Fig. 3), thus
ensuring homogeneous conditions of water supply across the
whole leaf.
Based on the assumption that the length of the areole interface
is related to the efficiency of xylem water delivery to stomata
(Brodribb et al., 2007; Noblin et al., 2008; Zwieniecki & Boyce,
2014), homogeneity in this parameter represents an optimal
design for leaf function. This remarkable result mimics what was
theoretically proposed and observed in branches of an individual
tree (West et al., 1999; Bettiati et al., 2012). Indeed, the anatomical structure of the vascular conduits is designed to guarantee the
condition of equi-resistance throughout all paths (i.e. branches of
different length within a crown) from roots to leaf petioles. Our
results indicate that the vein network of a leaf behaves like the
branches of a tree in terms of ensuring conditions of uniform
water distribution to the evaporation sites (stomata). Similarly to
xylem in branches, cell size within the veins increases basipetally
(i.e. lumens widen from the leaf apex to the base of the petiole)
(Coomes et al., 2008; Petit & Anfodillo, 2013) and this anatomical feature is a key strategy for compensating for the different
lengths of the path from petioles to areoles. A similar resistance
within all possible vein paths would mean that a ‘unit’ of veins in
an areole, wherever it may be in the leaf, would receive the same
water flux per unit of water potential gradient.
It is true that there are also indications that not all veins transfer water in the same way (Altus et al., 1985; Sack & Holbrook,
2006), as a result of modifications such as bundle sheath extensions (Nikolopoulos et al., 2002; Shatil-Cohen et al., 2011;
Sommerville et al., 2012; Griffiths et al., 2013), the formation of
accessory transport elements (Brodribb et al., 2005, 2007) and
different tracheary structure (Feild & Brodribb, 2013). Experiments with tracers have indicated a subdivision of roles in transport among vein orders in monocot leaves, where vein hierarchy
is simplified to two to three orders (Altus & Canny, 1985;
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Research 9
Fig. 8 Free-ending veinlet (FEV) occurrence
for classes of areole area in two species.
Areoles of each species are divided into five
dimensional classes. The percentage
contribution of each size class (hatched bars)
and of areoles with FEVs (grey bars) to the
total count of areoles is shown for each class.
For almost all the species, the percentage of
areoles with FEVs in each size class increases
with progressive dimensional class (inset
graphs).
Fig. 9 Comparison of average distance of
stomata to veins in an areole (Lsv) with Lsv,
edited (without free-ending veinlets (FEVs))
for samples of seven species. Continuous
line: regression linear model fitting the real
pattern (open circles); dashed line: powerlaw model fitting the edited pattern (closed
circles); dotted line: average distance inside a
circle as a function of circle area y = 0.1881
x0.5. Linear fitting equation; power-law
fitting equation (r2 in brackets): (a)
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);
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) A detail showing
areoles with removed FEVs.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
Russell & Evert, 1985). However, in accordance with Green
et al. (2014), our definition of vein tissue was constrained to twodimensional maps of the leaf surface. Thus, no distinction was
assigned to vein segments bordering an areole, so that our areole
contour was a maximum length (surface per unit of leaf thickness) potentially irrigating the mesophyll.
Leaves limit vein–stoma spacing in contrast with theoretical
model predictions
A major component of the hydraulic resistance, located outside
leaf veins, determines a distributed (i.e. proportional to distance)
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pressure drop for water flow moving from veins to stomata.
Thus, the length of the hydraulic path through the mesophyll
should be one of the most important parameters in determining
the total hydraulic resistance in the leaf (Brodribb et al., 2010).
However, measurement of the water path outside the xylem presents some difficulties, as different transport mechanisms coexist
or adjust along with leaf developmental stage and physiology
(Sack et al., 2004; Prado & Maurel, 2013; Muller et al., 2014)
and a change of phase from liquid to vapour occurs along the
pathway (Rockwell et al., 2014). Thus, the interveinal distance
and the inverse of vein density have been used as inexpensive
options to assess the extra-xylem flow path length (Brodribb
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10 Research
et al., 2007, 2010; McKown et al., 2010; Blonder et al., 2011;
Sack & Scoffoni, 2013). However, these measurements do not
consider the position of stomata.
Here, still under the assumption that a linear distance can be a
reasonable proxy for the length of the water path (Brodribb et al.,
2007), we performed rigorous measurements of the Euclidean
distance from each stoma to the nearest vein wall, in order to
quantify how stomatal and vein spatial patterning contributes to
efficient water supply.
Contrary to our hypothesis that the average vein-to-stoma distance within an areole (Lsv) would be driven by areole geometry,
Lsv remained highly conserved across increasing areole size. Lsv
was constant irrespective of contour length (slopes of linear relationships in the neighbourhood of zero) and weakly correlated
with areole area (29 of 31 slopes < 5%). Our initial projection
was modelled on three idealizations of a contour line forming a
convex polygon and containing a set of points (one central point
or a continuous set of points), whose distance to the contour was
considered. Theoretical models predict a power-law relationship
with an exponent of 0.5 between the average distance of stomata
to veins and areole area, because the theoretical average distance
of inner points to the contour is proportional to the square root
of the area. Instead, we found that, in leaves, Lsv across areoles of
increasing size was up to 10-fold smaller than the predicted values
of the theoretical models, thus indicating an active modification
of the areole morphology (i.e. the increasing presence of FEVs)
in larger areoles that maintained Lsv relatively constant.
Although Lsv remained relatively constant within species, there
was considerable variation between species. In addition, the number of stomata sustained by a contour was strictly species-specific,
probably reflecting different maximum capacities of photosynthetic rate among the different species. Several studies have suggested that, within and between species, the density of the
venation network is an important determinant of the photosynthetic gas exchange capacity of leaves, with high vein density
often correlated with high photosynthetic rate (Brodribb et al.,
2007). This correlation has been explained by the fact that the
distance water must flow from minor veins to the stomata represents a rate-limiting part of the hydraulic pathway (Brodribb
et al., 2007; Buckley et al., 2015). Here, we confirm this explanation for the link between vein density and stomatal density (and
hence gas exchange) by showing that species with shorter mean
distances between veins and stomata were able to carry higher
stomatal densities.
While conferring robustness to the delivery system of adult
leaves (H€
uve et al., 2002; Sack et al., 2008; Katifori et al., 2010;
Blonder et al., 2011), the highly areolated vein pattern in reticulated angiosperms is probably the most effective structure to
reduce the distance from veins to evaporative sites. As vein-tostoma distance is related to hydraulic resistance across the mesophyll, it follows that the leaves we observed were able to produce
homogeneous average resistance conditions over the entire surface. This suggests that a homogeneous distance between veins is
actively maintained determining during leaf development (Nelson & Dengler, 1997; Dimitrov & Zucker, 2006). This idea
appears valid both for the broad reticulated vasculature of dicots
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and for the parallel vein pattern of monocots, the architecture of
which, consisting of a few orders of parallel veins connected by
small transverse veins at ordered positions, is still essentially reticulated (Nelson & Dengler, 1997). However, for the two monocot species analysed here (bamboo and Sorghum bicolor), the Lsv
value diminished by c. 50% when we considered only distance
from longitudinal veins, thus reflecting a division of labour
among longitudinal and transverse veins, with the latter not
involved in water distribution to the mesophyll, as highlighted by
selective tracer experiments on wheat (Triticum aestivum) leaves
(Altus & Canny, 1985). The general invariance of Lsv we
observed with areole geometry suggests that evolution favours leaf
structures conforming to the principle of spatial uniformity in
water transport and metabolic rate.
Free-ending veinlets and homogeneity in extravenous
distance
Maintenance of homogeneous pressure gradients in the elongated
leaves of monocots appears to be associated with a gradient in
interveinal distance along the leaf axis (Ocheltree et al., 2012).
For dicots, the ultimate way to reduce resistance to flow is by
enlarging the vein surface area for transferring water, so that the
extravenous path is shortened (Brodribb et al., 2007). The architecture of minor vein density is responsible for over 80% of the
total pipe system length in leaves (Sack et al., 2012), and free vein
endings can be considered as the highest vein order, completely
surrounded by mesophyll (Kono & Nakata, 1982). Although the
presence and morphology of FEVs vary across species (Inamdar
& Murthy, 1981), FEV occurrence is usually related to high
minor vein density (Sack & Scoffoni, 2013).
The FEV incidence in areole class sizes shows that FEV occurrence in areoles increased with an increase in areole size in almost
all the species in this study, consistent with observations in other
species (Fisher & Evert, 1982; Korn, 1993). In addition, it has
been noted that FEV density increases during successive leaf
developmental stages in Liriodendron tulipifera leaves (Slade,
1959). Although the mechanism of FEV formation was not
addressed in this study, a tight correlation between large areoles
and FEV presence was apparent.
When one or more FEVs are present within the areole, the
FEV contributes about double its length to the whole contour, as
both sides are potentially leaking surfaces. An areole with many
FEVs will have a greater contour value than an areole with the
same area presenting no FEVs. Thus, FEV construction appears
to be a suitable way for a leaf to increase the supplying surface
within an areole and thus to support the maximum number of
transpiring pores.
Hypothesizing that FEVs would also play an active role in
minimizing the vein to stoma distance, we digitally manipulated
images of vein architecture to model the extravenous path distance in areoles from which FEVs were excised, thus demonstrating that much of the conservatism in extraxylem distance is
attributable to the presence of FEVs. FEVs effectively act by
diminishing the distance from stomata to veins within areoles
without contributing to the areole surface, in such a way that
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distance is almost independent of areole size and positioning on
the leaf.
Our results clearly demonstrate the importance of FEVs as a
means of homogenizing distances between veins and stomata.
This final order of venation appears to be critical for increasing
the available supplying surface of veins to mesophyll and plays a
major role in controlling the vein-to-stoma distance.
Acknowledgements
We are grateful to Ambra Scodro and Matilde Lazzarini for their
help in data collection, and Amos Maritan and Greg Jordan for
valuable discussions. Also we thank very much Alistair Hetherington and five anonymous referees, whose sensitive comments
have significantly improved our manuscript. We acknowledge
funding from the Australian Research Council (T.J.B.) to undertake this research (DP140100666). The research was also funded
by the project UNIFORALL (University of Padova, Progetti di
Ricerca di Ateneo CPDA110234) (T.A.).
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Supporting Information
Additional supporting information may be found in the online
version of this article.
Fig. S1 Result plots for each species.
Table S1 Venation pattern description for the data set
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