Trees (2012) 26:571–579 DOI 10.1007/s00468-011-0620-4
ORIGINAL PAPER
Stomatal density distribution patterns in leaves of the Jatoba´ (Hymenaea courbaril L.) Giordane Augusto Martins • Angela Maria Soares • Joa˜o 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 Ó 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 environmental 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
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:
[email protected] J. P. R. A. D. Barbosa e-mail:
[email protected] J. M. de Mello A. C. Ferraz Jr. Departamento de Cieˆncias Florestais, Universidade Federal de Lavras, Caixa Postal 3037, Lavras-MG 37200-000, Brazil
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 (Garcı´aNu´n˜ez 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 environmental 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 published 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
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frequently used sampling strategies do not permit a statistical 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 compromise 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 spatiotemporal 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 signifies 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 utilizing 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 computers with large processing capacity) that has led to better comprehension of seemingly chaotic phenomena. Geostatistics 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 phenomena 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).
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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 stretches 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 medicinally (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°440 3800 S, 46°280 1600 W) in September 2008. In October 2008 one mature leaflet was collected from ten H. courbaril 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 Company, L.P., Brazil (Fig. 1b). With the aid of the software UTHSCSA ImageTool (University of Texas Health Sciences 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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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)
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 microscope 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.
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. Measurements 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 calculated. Expansion rate was calculated by the following equation:
Leaf expansion ER ¼ Hymenaea courbaril mature leaflets are clearly asymmetric between right and left-hand sides of the primary venation.
Li Lm : D
where D is time between two assessments (40 days).
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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.
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)
Data analysis A semivariogram was calculated for each leaflet as follows (Journel and Huijbregts 1978): i 1 Xh zðxðiÞ zðxi þ hÞ2 : 2NðhÞ i¼1 NðhÞ
cðhÞ ¼
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 performed 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 isotropic). 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 variation 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 semivariance range attributed from spatial continuity and range is the distance in which values of one variable become
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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 techniques 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 dependence 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 microscale, as indicated by low-nugget values (Table 1). The structured variation values were 1,583–3,260. The combination of low-nugget effect values and high-structured variation values is responsible for the high spatial dependence 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.
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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 Ja´toba
Leaflets
s2
r2
s2 ? r2
U (mm)
Spatial dependence index (%)
A
58
2,112
2,170
6
97.3
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260
1,930
2,190
3.81
88.1
C
370
2,340
2,710
8.94
86.3
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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
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 estimation of the spatial average of the variable.
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.
Directional analysis
Leaf expansion
Directional semivariograms were plotted using the following directions: 0°, 45°, 90° and 135° (Fig. 5). A similar
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
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Fig. 4 Stomatal density Kriging map of a Hymenaea courbaril leaflet with a resolution of 1 9 1 mm
(±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 distribution 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 distribution 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 distributions for the same reason that justifies the use of square or circular sampling units. On the other hand, variables
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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 representativeness 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 precludes 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 geostatistics, 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 environmental 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 differentiation, 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 camphora leaves and concluded that the mixed hypothesis was
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Fig. 5 Directional variograms for eight leaflets. The x and y axes represent distance (mm) and semivariance values, respectively
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 differentiation 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 characteristics 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 expansion 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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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-documented 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 mechanisms related to cell differentiation and cell expansion for different species under a range of environmental conditions.
References Amzallag GN (2001) Data analysis in plant physiology: are we missing the reality? Plant Cell Environ 24:881–890 Assmann SM, Wang XQ (2001) From milliseconds to millions of years: guard cells and environmental responses. Curr Opin Plant Biol 4:421–428 Berger D, Altmann TA (2000) Subtilisin-like serine protease involved in the regulation of stomatal density and distribution in Arabidopsis thaliana. Gene Dev 14:1119–1131 Cambardella CA, Moorman TB, Novak JM, Parkin TB, Karlen DL, Turco RF, Konopka AE (1994) Field scale variability of soil properties in central Iowa soils. Soil Sci Soc Am J 58:1501–1511 Chen LQ, Chaloner WG, Beerling DJ, Sun QG, Collinson ME, Mitchell PL (2001) The stomatal frequency of extant and fossil Ginkgo leaves as biosensors of atmospheric CO2 levels. Am J Bot 88:1309–1315
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Trees (2012) 26:571–579 Clark I (1979) Practical geostatistics. Applied Science Publishers, London Clark PJ, Evans FC (1954) Distance to nearest neighbor as a measure of spatial relationships in populations. Ecology 35:445–453 Cressie N (1989) The origins of kriging. Math Geol 22:239–252 Cressie N (1993) Statistics for spatial data. John Wiley, New York Croxdale J (2000) Stomatal pattern in angiosperms. Am J Bot 87:1069–1080 Dong X, Zhang X (2000) Special stomatal distribution in Sabina vulgaris in relation to its survival in a desert environment. Trees 14:369–375. doi:10.1007/s004680000054 Francis JK (1990) Hymenaea courbaril (L.). USDA Forest Service. SO-ITF-SM-27 Gandar PW, Hall AJ (1988) Estimating position–time relationships in steady state one-dimensional growth zones. Planta 175:121–129 Garcı´a-Nu´n˜ez C, Azo´car A, Rada F (1995) Photosynthetic acclimation to light in juveniles of two cloud forest tree species. Trees 10:114–124. doi:10.1007/BF00192192 Gourdji SM, Hirsch AI, Mueller KL, Yadav V, Andrews AE, Michalak AM (2010) Regional-scale geostatistical inverse modeling of North American CO2 fluxes: a synthetic data study. Atmos Chem Phys 10:6151–6167 Granier C, Tardieu F (1998) Spatial and temporal analyses of expansion and cell cycle in sunflower leaves: a common pattern of development for all zones of a leaf and different leaves of a plant. Plant Phys 116:991–1001 Gratani L, Covone F, Larcher W (2006) Leaf plasticity in response to light of three evergreen species of the Mediterranean maquis. Trees 20:549–558 Journel AG, Huijbregts CJ (1978) Mining geostatistics. Academic Press, London Leroy C, Gue´roult M, Wahyune NS, Escoute J, Ce´re´ghino R, Sabatier S, Auclair D (2009) Morphogenetic trends in the morphological, optical and biochemical features of phyllodes in Acacia mangium Willd (Mimosaceae). Trees 23:37–49 Matheron G (1963) Principles of geostatistics. Econ Geol 58:1246– 1266 Maurer S, Matyssek R, Gu¨nthardt GMS, Landolt W, Eining W (1997) Nutrition and the ozone sensitivity of birch (Betula pendula). Trees 12:1–10 Mello JM, Batista JLF, Oliveira MS, Ribeiro PJ Jr (2005) Estudo da dependeˆncia espacial de caracterı´sticas dendrome´tricas para Eucalyptus grandis. Cerne 11:113–126 Mott K, Buckley TN (1998) Stomatal heterogeneity. J Exp Bot 49:407–417 Nadeau JA, Sack FD (2002) Control of stomatal distribution on the Arabidopsis leaf surface. Sci 296:1697–1700 Patterson D (1988) Commercial timbers of the world, 5th edn. Gower Technical Press, Aldershot Peters WS, Bernstein N (1997) The determination of relative elemental growth rate profiles from segmental growth rates. Plant Physiol 113:1395–1404 Peters CM, Gentry AH, Mendelsohn RO (1989) Valuation of an Amazonian rainforest. Nature 339:655–656 Poole I, Weyers JDB, Lawson T, Raven JA (1996) Variations in stomatal density and index: implications for paleoclimatic reconstructions. Plant Cell Environ 19:705–712 Pringle RM, Doak DF, Brody AK, Jocque R, Palmer TM (2010) Spatial pattern enhances ecosystem functioning in an African Savanna. Plos Biol 8:e1000377. doi:10.1371/journal.pbio.1000377 R Development Core Team (2008) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna Rasmussen H (1986) Pattern formation and cell interactions in epidermal development of Anemarrhena asphodeloides (Liliaceae). Nord J Bot 6:467–477
Trees (2012) 26:571–579 Ribeiro PJ, Diggle PJ (2001) The geoR package functions for geostatistical data analysis: R. News 1:15–18 Rowlingson B, Digglle P (1993) Splancs: spatial point pattern analysis code in S-Plus. Comput Geosci 9:627–655 Sachs T (1974) The developmental origin of stomata pattern in Crinum. Bot Gaz 135:314–318 Salisbury EJ (1928) On the causes and ecological significance of stomatal frequency with special reference to the woodland flora. Phil Trans R Soc B 216:1–65 Schultes R, Raffauf R (1990) The healing forest: medicinal and toxic plants of northwestern Amazonia. Dioscorides Press, Portland Silk WK (1992) Steady form from changing cells. Int J Plant Sci 153:49–58
579 Slavik B (1963) The distribution pattern of transpiration rate, water saturation deficit, stomata number and size, photosynthetic respiration rate in the area of the tobacco leaf blade. Biol Plant 5:143–153 Smith S, Weyers DB, Berry WG (1989) Variation in stomatal characteristics over the lower surface of Commelina communis leaves. Plant Cell Environ 12:653–659 Wilson CL (1981) Plant epidermal sections and imprints using cyanoacrylate adhesives. Can J Plant Sci 61:781–783 Zhao XZ, Daı´ XF, Wang GX, Shen ZX, Zhang H, Qiu MQ (2006) Developmental mechanism and distribution pattern of stomatal clusters in Cinnamomum camphora. Russ J Plant Physl 53:89–98
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