Published online 27 October 2005
Published in Crop Sci 45:2552-2556 (2005)
© 2005 Crop Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
FORAGE & GRAZINGLANDS
Nondestructive Estimates of Leaf Area in White Clover Using Predictive Formulae
The Contribution of Genotype Identity to Trifoliate Leaf Area
Hannes Gamper*
Dep. of Biology, P.O. Box 373, Univ. of York, Heslington, York, YO10 5YW, UK
* Corresponding author (hag500{at}york.ac.uk)
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ABSTRACT
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Studies on plant development in ecology and agriculture typically assess the formation of leaf area. Plants studied here were clonal propagates of nine genets of Trifolium repens cv. Milkanova (white clover), a common species of grasslands and an important forage legume. A simple predictive mathematical relationship is introduced that can be used to estimate the area of trifoliate leaves nondestructively from the lengths of the corresponding middle leaflets. Since differences in the correlative relationship between area and length were found among all nine investigated plant genets, genet-specific coefficients are reported. Our findings suggest that before nondestructive growth analyses are undertaken on the leaf area of clonal propagates of white clover, appropriate genet-specific coefficients for individual predictive formulae should be determined. However, for studies in the field or mathematical modeling on a larger scale, where ecological factors may have much greater influence on leaf development than genotypes, the common predictive equation calculated for all nine genets appears to be a reasonable approximation.
Abbreviations: ANCOVA, analysis of covariance
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INTRODUCTION
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MANY ECOLOGICAL and agronomic studies on single plant individuals rely on growth analysis (Hunt, 1982). Total leaf area is a key ecophysiological trait, involved in photosynthesis and aboveground biomass production. It may serve as an indicator of potential prospective dry mass production. There are various methodological approaches to measure the leaf area of plants (Marshall, 1968). Leaf area is most often estimated nondestructively by applying mathematical formulae, which require only simple linear measurements of leaf laminae. Alternatively, the area of leaf laminae are rated after comparison with graphical leaf templates of a known size (Williams et al., 1964). Wendt (1967) proposed a log–log relationship between leaf length and leaf area for all plants. Logarithmic transformation of both leaf area and leaf length translates the sigmoid into an analytically much easier linear correlation.
In the extensive literature on white clover, equations to estimate its leaf area nondestructively are lacking, although this plant species is one of the most common legumes in temperate grasslands worldwide (Baker and Williams, 1987). For the congeneric T. subterraneum L. (subterranean clover), Black (1958) established a polynomial relationship to estimate the area of its trifoliate leaves. He used straight-line fitting to determine the appropriate coefficients in the polynomial formula of the form A = aLb from double ln-transformed paired measures of midrib length of the central leaflet and trifoliate leaf area. In a comprehensive study assessing the predictive ability of individual linear measurements on all leaflets and leaves of the trifoliate leaves of Glycine max (L.) Merr. (soybean), Wiersma and Bailey (1975) concluded that considerable time could be saved with little loss of predictive ability when only length or width of leaflets was measured.
Vast heritable morphological diversity has been established for the obligate outcrossing legume, white clover (Hamilton and Harper, 1989; Caradus et al., 1993; Hutchings et al., 1997). It is therefore unlikely that for clonal propagates of different genets of this plant species, one single predictive mathematical equation would be sufficient to estimate leaf area from leaf-length measurements. Moreover, high morphological plasticity of white clover leaves in relation to seasonal changes in environment and phosphorus supply may question the use of a single mathematical relationship even for one single genet (Brougham, 1962; Caradus et al., 1993).
The aim of the present study was to investigate variation in leaf shape among nine genets of white clover and the consequence for nondestructive estimates of leaf area. We tested whether the area of trifoliate leaves could be inferred using a single predictive equation for all genets together or whether individual equations would serve this purpose better. On the basis of measurements of dry leaves, we established mathematical relations for white clover that allow estimation of the area of trifoliate leaves from the length of their middle leaflets. It is shown that leaf shape may vary among genets, which would suggest that appropriate coefficients for predictive formulae might have to be determined for each genet used in physiological growth experiments. However, with only a small error, the established common predictive equation may be used to nondestructively estimate the leaf area of white clover, both in large-scale experimental or modeling studies on the effects of ecological factors under field conditions or in studies comparing leaf development of different plant species. Using comparative measurements on fresh and dry leaves of one selected genet, an approximate conversion factor for correcting shrinkage in leaf area due to drying could be suggested.
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MATERIALS AND METHODS
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Plant Material and Culturing Conditions
Nine out of 150 8-wk-old genets of white clover (Dansk Planteforaedling, Research Division, Store Heddinge, Denmark) were selected for clonal micropropagation due to particularly high numbers of leaf nodes. Pieces of stolon with single nodes from these nine plants (genets A, B, F–L) were surface disinfected (70% ethanol for 10 s, 1% bleach for 10 min) and placed on cellulose filter paper over 1 x Hoagland nutrient solution agar (0.7% w/w) (Hoagland and Arnon, 1938). After 10 d of growth in constant conditions (16-h light and 23°C), micropropagates were transplanted into finely grained Perlite and adapted gradually to ambient air humidity under plastic foil. A fortnight later, the 80 most vigorous plantlets were transplanted singly to 1-L pots (14 x 10 cm), filled with pasteurized field soil [clay loam, pH (H2O) = 5.8; available P (Olson) = 52 mg P kg–1] silica sand (0.7–1.2 mm) and expanded, attapulgite clay (Oil Dry Chem-Sorb WR 24/18, Brenntag Mediterranée Export, Vitrolles Cedex, France), mixed in a volumetric ratio of 1:2:2. Each of the nine genets was represented in approximately equal proportions. They were inoculated with a dense aqueous suspension of Rhizobium leguminosarum bv. trifolii (strain RBL 5020, Leiden, the Netherlands), prepared using plate washes from 3-d-old bacterial layers grown on solidified malt agar-soil extract.
Plants were irrigated with deionized water through an automatic tensiometer-controlled drip-irrigation system (Tropf Blumat, Telf, Austria), which maintained substrate humidity at about 40%, or 50–60% of its water holding capacity. During the growth period of 10 wk, 50 mL of 0.1 x Hoagland nutrient solution, lacking P, were applied to each pot on three separate occasions. Climate chamber (Conviron, PGV-36, Winnipeg, Manitoba, Canada) conditions were cycled between 16-h light (450–550 µmol m–2 s–1 photosynthetic fluence rate at plant height), with an actual temperature of 23°C at plant height, and 8-h darkness, with temperature of 15°C at plant height. Relative air humidity was kept at 70–80%. Four pots with ramets of genet G were kept outdoors until the following year at full sunlight without any further fertilization.
Leaf Measurements
Three hundred and thirteen to 1004 fully expanded leaves (second leaf from the stolon tip or older) per genet were destructively harvested during a period of 1 to 10 wk posttransplantation, covering the whole range of leaf sizes. The following year we harvested and measured 279 regrown leaves of genet G in the fresh (fully hydrated) as well as dry state. Laminae of trifoliate leaves were cut off at the site of petiole attachment and pressed dry between blotting paper. Grayscale digital pictures (TIFF-format, 300 dpi resolution, no LZW compression) of the leaves were scanned on a 1-mm gridded background and contrast-enhanced (60%) in Adobe Photoshop v. 7.0 (Adobe Systems, Inc., San Jose, CA). Length of the spine, running through the terminal leaflet of the trifoliate leaf (termed midrib length) and corresponding area of the trifoliate leaf were measured using the straight line and wand (tracing) tool in the public domain software, Image J v. 1.29x (National Institutes of Health, USA, http://rsb.info.nih.gov/ij/, verified 8 Aug. 2005).
Statistical Analyses
The ln-transforming of both paired measures (midrib length and leaf area) accounted for increasing variation with larger values. This data transformation translated the sigmoid into an approximately linear relationship. At the same time, it lead to an approximately equal scattering of the data points along regression lines of the form ln(area) = s + t x ln(midrib length).
An analysis of covariance (ANCOVA) was performed, using the statistical software package JMP v.5.1 (SAS Institute, Inc., Cary, NC), to test whether overall the slopes of the linear regression lines on the ln(area) vs. ln(midrib length) data differed among individual genets. In this analysis plant genet was a categorial factor with nine levels, and midrib length was a continuous variable used as covariate. Similarly, ANCOVAs were used to examine whether drying the leaves or plant age affected the slope of the linear relationship between ln(area) and ln(midrib length). For these analyses, midrib length was defined again as the covariate and either leaf state (fresh vs. dry), or plant age (young vs. old) with two levels each as a factor. In all these ANCOVAs, the interaction term between factor and covariate tested for overall difference in slopes of the linear ln(area) vs. ln(midrib length) relationship among the factorial treatment groups. Paired t tests were applied for individual comparisons of leaf length and area before and after leaf drying.
For further analyses, we followed the procedure described in Zar (1999)(chapter 18) to compare two or multiple linear regression equations. The statistical procedure for multiple regressions employs total and residual sum of squares of so-called pooled and common regressions. Multiple comparisons among slopes were performed using the Tukey-Kramer test, which accounts for unequal sample sizes.
To further assess whether one common correlative relationship as opposed to individual correlative relationships would be significantly worse, we statistically compared the linear fit for pooled data to the fits for individual genets using the variance-ratio test (Zar, 1999). Thereby, variance of squared residuals (i.e., scattering of measures around the fitted line) is compared for the cases when a single regression line (pooled data) or individual regression lines for each genet are fitted.
As an approximate estimate of the relative error made when using predictive equations, the relative deviation of the estimates compared with the actual trifoliate leaf areas was calculated. This measure of deviation was estimated as the average of the absolute ratio between the residuals from a linear fit to the observed leaf area plotted against estimated leaf area and observed area. The quality of the common predictive equation for the data of all nine genets was further analyzed by calculating this relative deviation for four size classes of the range of studied midrib lengths.
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RESULTS
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Genet identity of white clover plants significantly contributed to the variance in trifoliate leaf area and interacted with midrib length, indicating differences in leaf shape (ANCOVA: F17, 4989 = 7038.49, P < 0.001; genet: F8, 4989 = 171.18, P 
0.001; ln(length): F1, 4989 = 82899.13, P 0.001; interaction: F8, 4989 = 14.02, P 0.001). Genet-specific differences in the slope of the linear relationship ln(area) = s + t x ln(length) were particularly pronounced for the genets G and J, but also present for the genets K and L, when compared with genet G (Fig. 1 and Table 1). A highly significant F ratio test (F8, 4989 = 28.765, P 0.001), which analyses overall differences among the slopes of the nine individual leaf data sets, motivated further multiple pairwise comparisons to identify differences between individual pairs of slopes. However, none of the pairs of slopes was significantly different at 
= 0.05 (Tukey-Kramer test), although the slopes of regression lines for genets G and J differed at = 0.1 (Fig. 1, q4989, 9 = 4.148; 95% confidence interval for bJ–bG: 0.213 ± 0.226). Regression slopes of genets A/J, F/J and G/K differed at = 0.5 (data not shown). Furthermore, variance-ratio tests revealed that individual linear fits for each genet are superior to a single linear regression line for pooled data. Variances of squared residuals for individual regression lines were in all cases significantly (P 0.001) smaller than the variance of residuals when a single line was fitted (Table 1). The relative deviation of the estimates from the actual measurements of leaf area increased by a maximum of 3.7% for estimates based on the individual genet-specific predictive equations as opposed to the common equation for all nine genets (Table 1, for calculations see Materials and Methods). In addition, the linear regression coefficient for the common line (b = 1.929) lies well within the range of values for the individual regression lines (1.884 b 2.191). The quality of prediction of the trifoliate leaf areas improves with increasing midrib length as evident from decreasing relative deviations of the estimates from the actual measurements for the four length (L) classes 2.4 mm L 10.2 mm [21.1% (27.5% SD, n = 424)], 10.2 mm < L 18.0 mm [11.9% (9.7% SD, n = 2400)], 18.0 mm < L 25.8 mm [9.3% (6.9% SD, n = 1891)], and 25.8 mm < L 33.6 mm [6.6% (4.8% SD, n = 292)].
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Fig. 1. The linear relationship between area (cm2) and midrib length (cm) of the central leaflet of trifoliate leaves of white clover (Trifolium repens cv. Milkanova) after double ln transformation. Data for individual leaves of genet G (n = 410, closed circles, full line) and J (n = 728, open circles, broken line) are shown. The slopes of linear regressions on these data (bG = 2.191, bJ = 1.884) differed according to a Tukey-Kramer pairwise comparison test at = 0.1 (q4989, 9 = 4.148; 95% confidence interval for bJ–bG: 0.213 ± 0.226).
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Table 1. Coefficients for the formula (trifoliate leaf area) = a(midrib length)b, as determined by orthogonal fits of ln-transformed paired data for midrib lengths (cm) and areas (cm2) of the trifoliate leaf of white clover (Trifolium repens cv. Milkanova). Values are based on dry and pressed leaves and are given for each genet along with the pooled data.
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Factors a and b (Table 1) in the polynomial predictive formulae of the form (trifoliate leaf area) = a(midrib length)b were derived via back-transformation (a = es, b = t) from intercept s and slope t of linear regressions of the ln(area) vs. ln(midrib length).
Leaf-drying significantly reduced mean midrib length by 2.3% from 1.85 ± 0.02 cm to 1.81 ± 0.02 cm (t = 6.26, df = 278, P < 0.001) and mean leaf area by 12.6% from 4.97 ± 0.12 cm2 to 4.35 ± 0.111 cm2 [t = 20.06, df = 278, P < 0.001; ANCOVA: F2, 555 = 2122.95, P < 0.001, fresh/dry: F1, 555 = 61.68, P < 0.001, ln(length): F1, 555 = 4113.86, P < 0.001]. Foliar shape of genet G differed significantly after 1 yr of growth under full sunlight and without further fertilization. Mean midrib length increased by 2.63% and mean leaf area decreased by 8.14% [ANCOVA: F3, 685 = 2221.76, P < 0.001; old/young: F1, 685 = 32.41, P < 0.001, ln(length): F1, 685 = 4515.54, P < 0.001, interaction: F1, 685 = 4.12, P = 0.043].
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DISCUSSION
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The area of trifoliate leaves of white clover can be adequately predicted from nondestructive measurements on the midrib lengths of the terminal leaflet of the trifoliate leaf, using simple polynomial formulae. However, predictions have to account for genotypic differences. Nondestructive estimates on leaf area are key to many ecophysiological and agronomic studies, analyzing whole plant growth in response to altered environmental conditions. They represent an index of growth capacity in the near future, since whole plant leaf area is strongly correlated with total plant yield (Black, 1958).
This study shows that midrib length of the terminal leaflet of trifoliate leaves of white clover has high potential for accurately estimating whole leaf area (Fig. 1 and Table 1). High correlation coefficients (0.959 r2 
0.986, for ln-transformed data of individual genets) confirmed the strong association between midrib length of the terminal leaflet and the area of whole trifoliate leaves. I suggest coefficients for predictive formulae to be determined from dry and pressed leaves, particularly for small and nonplanar leaves, because measurements are more precise than when made using fresh leaf material. Such coefficients obtained from dry leaves, as reported in Table 1, apply only when relative differences in leaf area are to be assessed. For estimates of absolute leaf area, correction factors, to account for leaf shrinkage, would have to be determined in addition. For example, genet G shrank by a factor of 12.6%. Maintenance of leaf shape in the course of drying, a precondition for simple factorial correction, was confirmed in an ANCOVA on leaf area by the absence of a significant statistical interaction between midrib length and drying.
Variation in leaf morphology among different genets of white clover makes it incompatible with a single equation to accurately estimate the area of trifoliate leaves. A larger variance of corresponding residuals, when a common line was fitted compared with individual lines, suggested that appropriate genet-specific coefficients should instead be calculated to increase the precision of the estimates (Table 1 and Fig. 2)
. The significant statistical interaction between genet and midrib length on leaf area, as shown in the ANCOVA test, indicates that leaf shape differs among genets of white clover. This difference stresses the necessity to determine individual coefficients for each particular white clover genet. Therefore, the use of genet-specific predictive equations would increase the precision of leaf area estimates and simultaneously increase accuracy.
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Fig. 2. Coefficients t of linear regression slopes of the form ln(trifoliate leaf area) = s + t x ln(midrib length), corresponding to exponents b in the predictive formulae (trifoliate leaf area) = a(midrib length)b with associated 95% confidence limits for nine genets of white clover (Trifolium repens cv. Milkanova).
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The finding of considerable differences in leaf geometry among the genets of white clover in this study was unexpected, since varieties of white clover are usually examined for visual homogeneity in breeding programs to narrow genetic variability. Moreover, these differences in leaf shape contrast with the high similarity found by Wiersma and Bailey (1975) for 12 cultivars of soybean. Greater genetic uniformity due to selfing in soybean vs. outcrossing in white clover may explain these contrasting findings in regard to leaf shape among respective varieties. However, given the fact that all our nine genets were selected from the same bred seed pool, differences caused by genotype in leaf measurements might be even more pronounced among plants of white clover from natural populations.
In physiological studies of growth, one could follow leaf area formation of whole white clover plants by summing up all estimates for the individual trifoliate leaves, although leaf position and plant aging also may influence the estimates. Indeed, we observed a change in leaf geometry in one selected genotype after 1 yr of growth under different light and soil nutrient conditions. This observation highlights that even for the same genet of white clover, predictive coefficients might have to be adjusted for plants grown under different environmental conditions. Seasonal- and P-nutrition-dependent variation in leaf size of white clover were previously observed, although these and other studies did not specifically account for leaf shape (Brougham, 1962; Caradus et al., 1993). White clover is known to optimize its leaf size for maximal photosynthesis within constraints of the soil resources (Baker and Williams, 1987). The statistical differences in leaf morphology of nine genets of white clover detected in this study under artificial, but controlled conditions (e.g., relatively low light intensity), may thus be of much less importance under natural conditions.
In the light of all the environmental factors that can affect leaf morphology and the rather small bias introduced by the use of a common, instead of individual predictive equations (Table 1), it might be justified for large-scale studies under field conditions or simulation studies at the pasture scale to apply the common equation derived from the pooled data of all nine genets as a reasonable approximation. This common predictive equation impairs the accuracy of the estimates for the trifoliate leaf areas by <4% and gives estimates well within the range covered by the equations established for the individual genets. Under field conditions, the magnitude of the effects of environmental factors on the phenotypically plastic trait, leaf area, may be much bigger than that of the genotype so that the latter might become negligible. Moreover, this common formula based on the pooled data may be sufficient for comparative studies of leaf area development among different plant species. Both the steepness and curvature of the polynomial function determined in this study for white clover seem to be smaller than for the congeneric subterranean clover (Black, 1958).
The present work is unique in applying the log–log relationship for nondestructive estimates on leaf area in the common forage legume white clover. It highlights that even for clonal propagates of the same bred variety, coefficients of predictive equations for trifoliate leaf area need to be adjusted to account for genotypic differences. However, nondestructive measurements on leaf length, together with the reported predictive formulae, are a cost-effective and precise method for estimating leaf area in studies on plant development. The proposed predictive equation, based on the pooled data of all nine studied genets, might serve as a general equation applicable for studies under natural conditions at the pasture-scale or comparative studies of leaf development among different plant species. However, for studies at the level of individual plants, further analyses on the importance of environmental factors relative to genotypic differences may provide more appropriate coefficients for the reported polynomial correlative relationship between midrib length of the terminal leaflet and the whole trifoliate leaf of white clover.
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ACKNOWLEDGMENTS
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I gratefully acknowledge technical assistance with leaf preparation by Yolanda Callau, valuable comments on an earlier version by Prof. Dr. J. Nösberger and PD Dr. U.A. Hartwig, and proofreading by Joanne Leigh.
Received for publication February 2, 2005.
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REFERENCES
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ABSTRACT
INTRODUCTION
