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TreesStructure and Function ISSN 0931-1890Volume 26Number 2 Trees (2012) 26:571-579DOI 10.1007/s00468-011-0620-4

Stomatal density distribution patterns inleaves of the Jatobá (Hymenaea courbarilL.)

Giordane Augusto Martins, AngelaMaria Soares, João Paulo RodriguesAlves Delfino Barbosa, José Marcio deMello, Evaristo Mauro de Castro, et al.

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ORIGINAL PAPER

Stomatal density distribution patterns in leaves of the Jatoba(Hymenaea courbaril L.)

Giordane Augusto Martins • Angela Maria Soares •

Joao Paulo Rodrigues Alves Delfino Barbosa • Jose Marcio de Mello •

Evaristo Mauro de Castro • Antonio Carlos Ferraz Jr.

Received: 13 January 2011 / Revised: 22 August 2011 / Accepted: 2 September 2011 / Published online: 28 September 2011

� Springer-Verlag 2011

Abstract Stomata are leaf structures that are essential for

regulating gas exchange and water balance in terrestrial

plants. Accurately quantifying stomatal characteristics is

consequently of great importance for understanding the

physiological processes of plants under different environ-

mental conditions. The objective of this study was to

investigate the spatial distribution pattern of stomata on

leaflet surfaces, and the possible mechanisms that influence

this pattern, particularly leaf expansion. To achieve this,

we used geostatistical tools combined with an analysis of

biometric relationships of leaves from Hymenaea courbaril

L. Our analysis indicates that stomata show a clear spatial

structure in this species: average values of foliar expansion

rates (ERs) were different on right and left-hand sides of

the primary venation of each leaflet and there was a close

relationship between the spatial pattern of stomatal density

and leaf expansion rate. Such differences in lateral

expansion may therefore be partially responsible for the

heterogeneous distribution of stomata documented here

and in other studies.

Keywords Stomata � Geostatistics � Leaf expansion

Introduction

Stomata are structures found in the above ground parts of

all terrestrial plants and account for approximately 95% of

gas exchange. Stomata are epidermal valves that control

the plant’s carbon dioxide input and water output, directly

influencing carbon assimilation, plant water status and

water use efficiency. These structures are therefore key

components for the survival of terrestrial plants (Berger

and Altmann 2000; Nadeau and Sack 2002) and play a

major role in the response of plants to environmental stress

(Slavik 1963).

During development of the leaves, the stomata are

formed by the simultaneous processes of asymmetric cell

division and cell differentiation—the stomatal density

(SD) and spatial distribution of stomata on the leaf surface

being genetically regulated during this period (Nadeau and

Sack 2002). However, the ontogeny of stomata is also

modulated by environmental factors that may change

through time, such as the intensity and quality of radiation,

humidity, temperature, carbon dioxide and ozone levels in

the atmosphere, soil moisture and nutritional availability,

and by internal architecture and leaf position (Garcıa-

Nunez et al. 1995; Maurer et al. 1997; Assmann and Wang

2001; Chen et al. 2001; Gratani et al. 2006; Leroy et al.

2009).

The heterogeneity of the spatial distribution of the

stomata on the epidermis (caused by genetic and environ-

mental factors) is a characteristic of plants that has been

known for some time (Salisbury 1928; Slavik 1963;

Smith et al. 1989; Croxdale 2000; Dong and Zhang 2000;

Zhao et al. 2006). However, there have been few pub-

lished studies that provide detailed information about the

number, size and location of sample sites on the leaf

surface (Poole et al. 1996). Furthermore, the most

Communicated by R. Guy.

G. A. Martins (&) � A. M. Soares �J. P. R. A. D. Barbosa � E. M. de Castro

Departamento de Biologia, Universidade Federal de Lavras,

Caixa Postal 3037, Lavras-MG 37200-000, Brazil

e-mail: giordanemartins@yahoo.com.br

J. P. R. A. D. Barbosa

e-mail: jp.barbosa@dbi.ufla.br

J. M. de Mello � A. C. Ferraz Jr.

Departamento de Ciencias Florestais, Universidade Federal de

Lavras, Caixa Postal 3037, Lavras-MG 37200-000, Brazil

123

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DOI 10.1007/s00468-011-0620-4

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frequently used sampling strategies do not permit a statis-

tical analysis of the spatial characteristics of the stomata:

typical analyses are based on the variance of the mean,

which can lead to a loss in information that could com-

promise interpretations of processes. Indeed, Amzallag

(2001) argues that an analysis based only on the variance of

the mean may exclude important factors of biological

significance for the investigated variable. This also applies

to cases where the investigated variable possesses spatio-

temporal continuity.

The spatial distribution of developing stomata is

reportedly random, although an exclusionary distance is

present around each stomata (Sachs 1974; Rasmussen

1986). However, it is not clear if the term random is being

used by the authors in a strict mathematical sense or sig-

nifies that an ordered pattern is not visually obvious. In the

former case, the assertion that a pattern is mathematically

random must be based on a standard statistical method

(Croxdale 2000). Often the method developed by Clark and

Evans (1954) has been used to determine spatial pattern

possibilities (ordered, random, or clustered). Authors uti-

lizing Clark and Evans’s method have typically found an

ordered patterning of the stomata (cited in Croxdale 2000).

However, while this method indicates the type of pattern, it

yields no detailed quantitative information or spatial

aspects of the pattern. Here, we suggest a new method to

analyze the spatial distribution pattern of stomata on a leaf

surface. We use this method to address the following

fundamental questions: Is spatial stomatal distribution

random, as suggested by Sachs (1974) and Rasmussen

(1986) or ordered, as suggested by Croxdale (2000)? Is it

possible to accurately and precisely quantify this pattern?

How do developmental processes influence the spatial

pattern of stomata?

We conducted a case study using H. courbaril leaflets to

test the method and to address the above questions. Our

new method is based on geostatistics, a relatively recent

statistical analysis tool capable of generating information

regarding the spatial distribution of a given variable.

Geostatistics is one of a number of more sophisticated

mathematical techniques (facilitated by access to comput-

ers with large processing capacity) that has led to better

comprehension of seemingly chaotic phenomena. Geosta-

tistics theory was formalized by the French scientist G.

Matheron at the beginning of the 1960s (Cressie 1989), and

since then it has been applied to a diverse range of phe-

nomena including the spatial distribution of a field’s tin

levels (Clark 1979), behavior of carbon dioxide flow in the

atmosphere (Gourdji et al. 2010), and the distribution of

termite mounds on an African savanna (Pringle et al.

2010).

Materials and methods

Plant material

Hymenaea courbaril (Fabaceae: Caesalpinioideae) is an

evergreen canopy (sometimes emergent) tree of tropical

and subtropical forests and has a distribution that stret-

ches from Mexico and the Caribbean, through Bolivia

to south-central Brazil (Francis 1990). The wood is an

economically valuable hard wood (Patterson 1988;

Francis 1990) that is commercially exploited in the

Peruvian Amazon (Peters et al. 1989). Moreover, the fruit

pulp is edible raw or prepared as a beverage (Francis

1990) and the resinous gum is used in some areas in the

manufacture of varnishes or as incense (Schultes and

Raffauf 1990). Both the bark and pulp are used medici-

nally (Francis 1990).

Leaf samples of H. courbaril were taken from mature

trees and saplings. Eight leaflets were collected from four

mature trees (two leaves per tree, one leaflet per leaf) in a

fragment of Atlantic Rain Forest, in southeastern Brazil

(21�4403800S, 46�2801600W) in September 2008. In October

2008 one mature leaflet was collected from ten H. courb-

aril saplings of 10 months age cultivated under nursery

conditions.

All leaflets were collected from the first fully expanded

leaf. Leaves with signs of herbivore and/or pathogen

attack were excluded. All plants studied were fully sun

exposed.

Sampling and database

To spatially sample SD the leaflet was referenced in a

Cartesian plane, along with the sample points. For this

process, a sheet of graph paper was perforated to form a

sample grid of 5 9 5 mm with random clusters of

2.5 9 2.5 mm (Fig. 1a). Using this sample grid, points on

the abaxial epidermis of the leaflet were marked with a

porous tip pen, transferring the sampling grid to the surface

of the leaflet (Fig. 1b).

The marked leaflet was then scanned at 600 dpi with an

HP Deskjet F4100 (Hewlett-Packard Development Com-

pany, L.P., Brazil (Fig. 1b). With the aid of the software

UTHSCSA ImageTool (University of Texas Health Sci-

ences Center at San Antonio), the leaf blade’s image was

transformed into a Cartesian plane with true dimensions

(Fig. 1d). The x and y coordinates for each point of the

sample grid and a series of points pertaining to the

perimeter of the leaflet were then recorded.

For the assessment of the SD of each point from the

sample grid, ‘‘superglue’’ impressions were made using the

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technique of Wilson (1981). Digital images of the prints

were then captured using a Canon PowerShot A-630 digital

camera (Canon inc., China), coupled to the optic micro-

scope Olympus BX60 (Olympus Optical Corporation, Ltd.,

Tokyo, Japan). The obtained images measured 0.768 9

0.576 mm (Fig. 1c) and consisted of the basic sampling

units used for the geostatistic analyses. Stomata count in

the sampling units was carried out with the software

UTHSCSA ImageTool. Stomata that were only partial in

the image were also counted. Each SD data was associated

with its respective coordinates, thus forming the spatial

database.

Leaf expansion

Hymenaea courbaril mature leaflets are clearly asymmetric

between right and left-hand sides of the primary venation.

However, this asymmetry is less apparent in younger

leaflets (Fig. 2).

Average values of foliar expansion rate (ER) were

estimated on right and left-hand sides of primary venation

of the saplings cultivated under nursery conditions. Mea-

surements of the leaflets were obtained at six positions

(Lr1,2,3 and Ll1,2,3) (Fig. 2). This procedure was performed

in leaflets at two development stages—approximately

10 days old and 50 days old.

The average Lr1,2,3 and Ll1,2,3 at 10 days old (Lri and

Lli) and for mature leaves (Lrm and Llm) was calcu-

lated. Expansion rate was calculated by the following

equation:

ER ¼ Li � Lm

D:

where D is time between two assessments (40 days).

Fig. 1 Mapping of the sampled

points: sampling grid (a); leaflet

with the points to be sampled

(b); leaflet impression under a

microscope (c); leaflet with

sampled points in a Cartesian

plane (d)

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Data analysis

A semivariogram was calculated for each leaflet as follows

(Journel and Huijbregts 1978):

cðhÞ ¼ 1

2NðhÞXNðhÞ

i¼1

zðxðiÞ � zðxi þ hÞ2h i

:

where c(h) is the experimental semivariogram value at the

distance interval h; N(h) is number of sample value pairs

within the distance interval h; z(xi), z(xi ? h) are sample

values at two points separated by the distance interval

h. Semivariograms were calculated both isotropically and

anisotropically. The anisotropic calculations were per-

formed in four directions (0�, 45�, 90� and 135�) with a

tolerance of 22.5� to determine whether semivariogram

functions depended on sampling orientation and direction

(i.e., they were anisotropic) or not (i.e., they were isotro-

pic). The parameters of the model were then determined:

nugget effect (s2), structured variation (r2), sill (s2 ? r2)

and range (U).

The nugget is usually assumed to be non-spatial varia-

tion due to measurement error and variations in the data

that relate to shorter ranges than the minimum sampled

data spacing; sill is the lag distance between measurements

in which one value for a variable does not influence

neighboring values; structured variation is the semivari-

ance range attributed from spatial continuity and range is

the distance in which values of one variable become

spatially independent from the others. Structured variance,

expressed as the percentage of sill, was used to define

spatial dependency of the variables. To define different

classes of spatial dependence for the SD variables, we used

the classification following Cambardella et al. (1994). The

R statistical software (R Development Core Team 2008)

with the GeoR package (Ribeiro and PJ 2001) was used to

conduct semivariogram and spatial structure analysis for

the variables.

Stomatal density was interpolated using the Ordinary

Kriging method (Matheron 1963). Splancs package for R

(Rowlingson and Digglle 1993) was used to plot stomatal

density maps.

We used a t test to compare ER averages on left and

right-hand sides of primary venation in terms of expansion.

Finally, Pearson’s correlation test was conducted to test the

strength of the correlation between the values of the

expansion rate of each side of the leaflets and the range (U)

of the semivariogram.

Results

Stomatal density

Average stomatal density was 308 ± 16.5 (n = 8) for adult

H. courbaril leaflets and 254 ± 22.3 (n = 10) for sapling

H. coubaril leaflets. In both cases there were no differences

in the SD between right and left-hand sides of the primary

vein.

The data obtained in this study provided optimum

conditions for the implementation of geostatistics tech-

niques that depend on a previously established model

(Mello et al. 2005). The variogram analysis of the adult tree

samples demonstrated that stomatal density in H. courbaril

leaflets was characterized by spatial continuity, enabling

the modeling of the semivariance.

The exponential model was the model that best adjusted

to the experimental semivariogram. The spatial depen-

dence of SD in leaflets of H. courbaril can be inferred from

the high level of model accuracy (Fig. 3 illustrates the SD

semivariogram for one of the H. courbaril leaflets and the

model adjusted by the Weighted Least Squares method).

There is a spatial continuity of the data at the micro-

scale, as indicated by low-nugget values (Table 1). The

structured variation values were 1,583–3,260. The combi-

nation of low-nugget effect values and high-structured

variation values is responsible for the high spatial depen-

dence index values (79.4–97.3%)—classified as a strong

level of spatial dependence according to Cambardella et al.

(1994). The range (U) values (3.40–9.34 mm) indicated

that the size of the sampling grid (5 9 5 mm) was

adequate.

Fig. 2 Hymenaea courbaril leaflets at approximately 10 days old

(a) and 50 days old (b). Leaflets were measured at three positions in

right side (Lr1,2,3) and three positions in left side (Ll1,2,3)

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Maps of the SD of the leaflets were plotted using spatial

interpolator Kriging, to allow for a better visualization of

the spatial distribution of that variable (Fig. 4). In addition

to the provision of a visual analysis of the SD distribution

in the leaf surface, the SD maps also allow for the esti-

mation of the spatial average of the variable.

Directional analysis

Directional semivariograms were plotted using the fol-

lowing directions: 0�, 45�, 90� and 135� (Fig. 5). A similar

behavior of semivariance was recorded in all the four

directions for the eight leaflets analyzed. Such a pattern

indicates directional isotropy of SD distribution in the leaf

surface, since the same spatial dependence structure exists

in all the four directions (Cressie 1993). This result reflects

the two-dimensional growth of dicotyledon leaves.

Leaf expansion

The average expansion rate was 0.17 cm day-1 (±0.020)

for the right-hand side of leaflets and 0.06 cm day-1

Sem

ivar

ianc

e

0

400

800

1200

1600

2000

2400

2800

3200

3600

4000

Distance (mm)

Sem

ivar

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0

400

800

1200

1600

2000

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2800

Distance (mm) Distance (mm) Distance (mm)

20 20 200 10 20 30 40 0 10 30 0 10 30 40 0 10 30 40

0 5 10 15 20 25 0 5 10 15 20 25 0 5 10 15 20 0 4 8 12 16

Fig. 3 Stomatal density semivariogram for eigth Hymenaea courbaril (adults) leaflets, along with the exponential model adjusted by the

Weighted Least Squares method. The x and y axes represent distance (mm) and semivariance values, respectively

Table 1 Semivariance model’s

parameters estimate for nugget

effect (s2), structured variation

(r2), sill (s2 ? r2), range (U),

and spatial dependence index

(%) for stomatal density (SD) of

eight leaflets of Jatoba

Leaflets s2 r2 s2 ? r2 U (mm) Spatial dependence

index (%)

A 58 2,112 2,170 6 97.3

B 260 1,930 2,190 3.81 88.1

C 370 2,340 2,710 8.94 86.3

D 110 3,260 3,370 4.52 96.7

E 368 1,902 2,270 8.19 83.8

F 477 1,833 2,310 3.40 79.4

G 407 1,913 2,320 6.12 82.5

H 357 1,583 1,940 9.34 81.6

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(±0.012) for the left-hand side of leaflets. A significant

difference was observed (t = 4.89 and p \ 0.01) between

the right and left average foliar expansion rate.

A strong positive correlation was observed between

the expansion rate values on each side of the leaflet and

the theoretical range values (U) of the semivariograms

(r = 0.84, p = 0.02, n = 20). This result indicates a strong

relationship between expansion rate and the spatial distri-

bution structure of the stomata.

Discussion

Sampling frame

The directional analysis of semivariance is of great

potential importance for planning sampling frames, the

shape of sample units, and in the case of a systematic

sampling, the analysis also informs the definition of best

shape and size of the sample grid. For a variable with

isotropic spatial distribution, rectangle-shaped sampling

units are most frequently indicated. This is because the

largest side of the rectangle ensures a good representivity

of the targeted variable and the smaller side reduces the

area sampled, thereby avoiding excessive sampling effort.

In the case of a variable with an anisotropic spatial distri-

bution the square or the circle is the best sampling unit

shape since it ensures equivalent representativeness in all

directions.

With regard to the sampling grid, a regular grid would

be most appropriate for variables with anisotropic distri-

butions for the same reason that justifies the use of square

or circular sampling units. On the other hand, variables

with an isotropic spatial distribution allow the elimination

of one or more rows (transects) of a sample grid, reducing

the sample intensity without a major loss of representa-

tiveness of the sample. Thus, rectangle-shaped sampling

units are most appropriate for sampling SD in H. courbaril

leaves.

According to the geostatistical analyses, SD cannot be

treated as a random variable, since a strong spatial

dependence index exists (79.4–97.3%). This finding pre-

cludes the use of classical statistics for the analysis of SD,

since these types of tests make the assumption that the

events (samples) are independent. Thus, there are two

possible methods to estimate SD with statistical accuracy:

(1) samples taken from the leaf must have a distance equal

to or greater than the estimated theoretical range of the

semivariogram, and; (2) use the SD estimated by geosta-

tistics, since this provides precise estimates of variance. In

summary, when sampling SD it is necessary to consider the

spatial characteristics of the data for the analysis, or to

formulate a sampling plan that generates data that can be

analyzed with classical statistics.

Spatial and physiological processes

The right side of the leaflet has an ER 2.75 times larger

than the left side. It can therefore be assumed that a

determined area on the right side of the leaflet develops in a

time interval of 2.75 times shorter than the same area on

the left. Thus, all other things being equal, the developed

area on the right side of the leaflet experiences less envi-

ronmental variability than the left side. This finding may

explain the strong relationship among ER and range,

despite there being no differences in stomatal density

between right and left-sides of the primary vein. However,

these observations should be taken with care, since what

we found was a strong correlation between the ER and the

spatial distribution pattern of stomata and not an explicit

relationship between ER and SD. This relationship, as well

as the role of the ER in defining the SD, should be clarified

in further studies.

Smith et al. (1989) found heterogeneous distribution

of stomata in Commelina communis leaves and suggested

three hypotheses to explain this heterogeneity: (1) stomata

differentiation in the leaf surface differs between regions

(differentiation hypothesis); (2) following stomata diff-

erentiation, a differentiated cellular expansion occurs

(expansion hypothesis), and; (3) the two previous hypotheses

are both true (mixed hypothesis). Based on the correlation

between SD and stomatal index in Alnus glutinosa leaves,

Poole et al. (1996) argued that the differentiation hypothesis

is most probable. However, Zhao et al. (2006) investigated

stomata formation and distribution in Cinnamomum cam-

phora leaves and concluded that the mixed hypothesis was

Fig. 4 Stomatal density Kriging map of a Hymenaea courbaril leaflet

with a resolution of 1 9 1 mm

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more probable. In the present study, the rate of leaf expansion

was observed to influence SD distribution patterns in

H. courbaril leaflets thereby supporting the expansion

hypothesis, however, it should be noted that the differenti-

ation hypothesis was not directly evaluated.

The existence of an irregular spatial distribution of

stomata in leaves has long been known, although little

progress has made in identifying the factors that can cause

these variations in SD. This lack of progress is reflected in

the small number of studies dealing with the spatial char-

acteristics of stomata, and is probably also influenced by

the large number of environmental variables which directly

or indirectly influence these characteristics and by the lack

of tools required for this type of research. It is important to

note that the environmental variables that affect stomata

characteristics operate on different timescales.

By differentiating the analysis of SD spatial distribution

in a single leaf (characterized by different rates of expan-

sion between the right and left-hand sides of the primary

venation), the effect of environmental and genetic factors

that cannot be easily controlled in experimental conditions

was minimized. However, the stomatal index was not

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Fig. 5 Directional variograms for eight leaflets. The x and y axes represent distance (mm) and semivariance values, respectively

Trees (2012) 26:571–579 577

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analyzed, which would have enabled an analysis of the

relationship between expansion rate and stomatal initiation.

Moreover, these results are valid only for H. courbaril.

Other plants, such as Sabina vulgaris, have a well-docu-

mented spatial distribution of stomata at a large spatial

scale that is an adaptation to the desert environment where

this species occurs (Dong and Zhang 2000).

In a general analysis, a pattern of SD spatial structure

was detected on small spatial scales (Fig. 3). Such a result

provides no support for the argument of Mott and Buckley

(1998) that ‘‘systematic heterogeneity’’ occurs on large

scales and ‘‘random heterogeneity’’ on small scales.

Environmental factors vary over time and can affect SD

pattern, a fundamentally spatial characteristic. The close

relationship between spatial and environmental variables

means that it is possible to rebuild the temporal pattern of

variability—as done by dendrochronologists. However,

since time is a unidimensional variable, such inferences

can only be made in organs that show unidimensional

growth, such as trunks, roots and monocotyledonous leaves

(Gandar and Hall 1988; Silk 1992; Peters and Bernstein

1997). Indeed, Granier and Tardieu (1998) claim that such

temporal processes cannot be deduced from spatial patterns

of dicotyledonous leaves, since they are characterized by

bidimensional growth. Nonetheless, geostatistical analysis

was able to identify a bidirectional spatial pattern resulting

from temporal processes, indicating a potential mechanism

for rebuilding the history of leaf ontogeny through a single

analytical tool.

The methods developed in this study may be useful for

future investigations that seek to elucidate the mechanisms

that control the spatial distribution pattern of stomata. Such

studies should include an analysis of stomatal index and

epidermal cell density, allowing the separation of mecha-

nisms related to cell differentiation and cell expansion for

different species under a range of environmental conditions.

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