Application of linear models for estimation of leaf area in soybean [<Emphasis Type="Italic">Glycine max</Emphasis> (L.) Merr]

Leaf area estimation is an important measurement for comparing plant growth in field and pot experiments. In this study, determination of the leaf area (LA, cm²) in soybean [Glycine max (L.) Merr] involves measurements of leaf parameters such as maximum terminal leaflet length (L, cm), width (W, cm), product of length and width (LW), green leaf dry matter (GLDM) and the total number of green leaflets per plant (TNLP) as independent variables. A two-year study was carried out during 2009 (three cultivars) and 2010 (four cultivars) under field conditions to build a model for estimation of LA across soybean cultivars. Regression analysis of LA vs. L and W revealed several functions that could be used to estimate the area of individual leaflet (LE), trifoliate (T) and total leaf area (TLA). Results showed that the LW-based models were better (highest R ² and smallest RMSE) than models based on L or W and models that used GLDM and TNLP as independent variables. The proposed linear models are: LE = 0.754 + 0.655 LW, (R ² = 0.98), T = −4.869 + 1.923 LW, (R ² = 0.97), and TLA = 6.876 + 1.813 ΣLW (summed product of L and W terminal leaflets per plant), (R ² = 0.99). The validation of the models based on LW and developed on cv. DPX showed that the correlation between calculated and measured LA was strong. Therefore, the proposed models can estimate accurately and massively the LA in soybeans without the use of expensive instrumentation.     

Allometric models for leaf area estimation across different leaf-age groups of evergreen broadleaved trees in a subtropical forest

The accurate and nondestructive determination of individual leaf area (LA) of plants, by using leaf length (L) and width (W) measurement or combinations of them, is important for many experimental comparisons. Here, we propose reliable and simple regressions for estimating LA across different leaf-age groups of eight common evergreen broadleaved trees in a subtropical forest in Gutianshan Natural Reserve, eastern China. During July 2007, the L, W, and LA of 2,923 leaves (202 to 476 leaves for each species) were measured for model construction and the respective measurements on 1,299 leaves were used for model validation. Mean L, W, LA and leaf shape (L:W ratio) differed significantly between current and older leaves in four out of the eight species. The coefficients of one-dimension LA models were affected by leaf age for most species while those incorporating both leaf dimensions (L and W) were independent of leaf age for all the species. Therefore, the regressions encompassing both L and W (LA = a L W + b), which were independent of leaf age and also allowed reliable LA estimations, were developed. Comparison between observed and predicted LA using these equations in another dataset, conducted for model validation, exhibited a high degree of correlation (R ² = 0.96−0.99). Accordingly, these models can accurately estimate the LA of different age groups for the eight evergreen tree species without using instruments.     

Allometric model for nondestructive leaf area estimation in clary sage (<Emphasis Type="Italic">Salvia sclarea</Emphasis> L.)

Leaf area estimation is an important biometrical observation recorded for evaluating plant growth in field and pot experiments. In this study, conducted in 2009, a leaf area estimation model was developed for aromatic crop clary sage (Salvia sclarea L.), using linear measurements of leaf length (L) and maximum width (W). Leaves from four genotypes of clary sage, collected at different stages, were used to develop the model. The actual leaf area (LA) and leaf dimensions were measured with a Laser Area meter. Different combinations of prediction equations were obtained from L, W, product of LW and dry mass of leaves (DM) to create linear (y = a + bx), quadratic (y = a + bx + cx²), exponential (y = ae^bx), logarithmic (y = a + bLnx), and power models (y = ax^b) for each genotype. Data for all four genotypes were pooled and compared with earlier models by graphical procedures and statistical measures viz. Mean Square Error (MSE) and Prediction Sum of Squares (PRESS). A linear model having LW as the independent variables (y = −3.4444 + 0.729 LW) provided the most accurate estimate (R ² = 0.99, MSE = 50.05, PRESS = 12.51) of clary sage leaf area. Validation of the regression model using the data from another experiment showed that the correlation between measured and predicted values was very high (R ² = 0.98) with low MSE (107.74) and PRESS (26.96).     

Leaf area estimation of sunflower leaves from simple linear measurements

Simple, accurate, and non-destructive methods for determining leaf area (LA) of plants are important for many experimental comparisons. Determining the individual LA of sunflower (Helianthus annuus L.) involves measurements of leaf parameters such as length (L) and width (W), or some combinations of these parameters. Two field experiments were carried out during 2003 and 2004 to compare predictive equations of sunflower LAs using simple linear measurements. Regression analyses of LA vs. L and W revealed several equations that could be used for estimating the area of individual sunflower leaves. A linear equation having W² as the independent variable provided the most accurate estimate (r ² = 0.98, MSE = 985) of sunflower LA. Validation of the equation having W² of leaves measured in the 2004 experiment showed that the correlation between calculated and measured areas was very high.     

Leaf area prediction model for sugar beet (<Emphasis Type="Italic">Beta vulgaris</Emphasis> L.) cultivars

In two successive years (2003 and 2004), a set of 16 commercial sugar beet cultivars was established in Randomized Complete Block experiments at two sites in central Greece. Cultivar combination was different between years, but not between sites. Leaf sampling took place once during the growing season and leaf area, LA [cm²], leaf midvein length, L [cm] and maximum leaf width, W [cm] were determined using an image analysis system. Leaf parameters were mainly affected by cultivars. Leaf dimensions and their squares (L², W²) did not provide an accurate model for LA predictions. Using L×W as an independent variable, a quadratic model (y = 0.003 x² − 1.3027 x + 296.84, r ² = 0.970, p<0.001, n = 32) provided the most accurate estimation of LA. With compromises in accuracy, the linear relationship between L×W and LA (y = 0.5083 x + 31.928, r ² = 0.948, p<0.001, n = 32) could be used as a prediction model thanks to its simplicity.     

Evaluation of a leaf area prediction model proposed for sunflower

Six leaf samplings were conducted in two sunflower (Helianthus annuus L.) hybrids during the 2006 growing season in order to evaluate a simple model proposed for leaf area (LA) estimation. A total of 144 leaves were processed using an image analysis system and LA, maximum leaf width (W) [cm], and midvein length (L) [cm] were measured. Also, LA was estimated using the model proposed by Rouphael et al. (2007). Measured LA was exponentially related with L and W, and the W-LA relationships showed higher r ². Estimated LA was strongly and exponentially related with L. Strong, linear relationships with high r ² between estimated and measured LA confirmed the high predictability of the proposed model.     

Modeling individual leaf area of rose (<Emphasis Type="Italic">Rosa hybrida</Emphasis> L.) based on leaf length and width measurement

Accurate and nondestructive methods to determine individual leaf areas of plants are a useful tool in physiological and agronomic research. Determining the individual leaf area (LA) of rose (Rosa hybrida L.) involves measurements of leaf parameters such as length (L) and width (W), or some combinations of these parameters. Two-year investigation was carried out during 2007 (on thirteen cultivars) and 2008 (on one cultivar) under greenhouse conditions, respectively, to test whether a model could be developed to estimate LA of rose across cultivars. Regression analysis of LA vs. L and W revealed several models that could be used for estimating the area of individual rose leaves. A linear model having L×W as the independent variable provided the most accurate estimate (highest r ² , smallest MSE, and the smallest PRESS) of LA in rose. Validation of the model having L×W of leaves measured in the 2008 experiment coming from other cultivars of rose showed that the correlation between calculated and measured rose LA was very high. Therefore, this model can estimate accurately and in large quantities the LA of rose plants in many experimental comparisons without the use of any expensive instruments.     

Leaf shape and its relationship with Leaf Area Index in a sugar beet (<Emphasis Type="Italic">Beta vulgaris</Emphasis> L.) cultivar

Heteroblasty of sugar beet cultivar Rizor was studied under field conditions for three growing seasons (2003, 2005, 2006) in a Randomized Complete Block (RCB) design experiment. Eleven leaf samplings, from early June till the end of October, were conducted each year and leaf shape parameters [leaf area (LA), centroid X or Y (CX or CY), length (L), width (W), average radial (AR), elongation (EL), shape factor (SF)] were determined by an image analysis system. During samplings, Leaf Area Index (LAI) was measured non-destructively. Significant year and sampling effects were found for all traits determined. With the progress of the growing season, leaves became smaller (LA, L, W, and AR were decreased) and rounded. The largest leaves were sampled in 2006 when LAI was highest. LA was strongly correlated with L and W with simple functions (y = 0.1933 x^2.2238, r ² = 0.96, p<0.001, and y = 28.693 x − 192.33, r ² = 0.97, p< 0.001, respectively), which could be used for non-destructive LA determination. Also, LAI was significantly related with LA and leaf dimensions (L, W) suggesting that an easy, non-destructive determination of LAI under field conditions is feasible for sugar beet cv. Rizor. An erratum to this article is available at .     

Nondestructive,simple, and accurate model for estimation of the individual leaf area of som (<Emphasis Type="Italic">Persea bombycina</Emphasis>)

Nondestructive approach of modeling leaf area could be useful for plant growth estimation especially when number of available plants is limited and/or experiment demands repeated estimation of leaf area over a time scale. A total of 1,280 leaves were selected randomly from eight different morphotypes of som (Persea bombycina) established at randomized complete block design under recommended cultural regimes in field. Maximum leaf laminar width (B), length (L) and their squares B², L²; leaf area (LA), and lamina length × width (L×B) were determined over two successive seasons. Leaf parameters were significantly affected by morphotypes; but seasons had nonsignificant impacts on tested features. Therefore, pooled seasonal morphotype means of each parameter were used to establish relationship with LA. L and its square L² did not provide accurate models for LA predictions. Considerably better models were obtained by using B (y = 2.984 + 7.9664 x, R ² = 0.615, P≥0.001, n = 119) and B² (y = 12.784+ 0.9604 x, R ² = 0.605, P≥0.001, n = 119) as independent variables. However, maximum accuracy of prediction of LA could be achieved through a simple linear relationship of L×B (y = 8.2203 + 0.4224 x, R ² = 0.843, P≥0.0001, n = 119). The model (LA:L×B) was validated with randomly selected leaf samples (n = 360) of som morphotypes and highly significant (P≤0.001) linear function was found between actual and predicted LAs. Therefore, the last model may consider adequate to predict leaf area of all cultivars of som with sufficient fidelity.     

五种火棘属植物的叶面积回归分析

以采集于贵州、云南、广西、湖南等地的火棘、密花火棘、全缘火棘、细圆齿火棘和窄叶火棘共5种火棘属植物26 401个成熟叶样为材料,利用WinFOLIA软件测量叶的多项形态指标并与叶面积进行11种模拟方程回归分析。结果表明:五种火棘属植物的叶面积(LA)与叶长×叶宽(LW)相关性最高,幂函数方程、三次方程、二次方程和线性方程能较好拟合其关系,且均以幂函数方程的解释程度最高(R²均大于0.970),5个物种的幂函数方程分别为LA=0.743(LW)0.936、LA=0.748(LW)0.936、LA=0.742(LW)0.955、LA=0.732(LW)0.952、LA=0.766(LW)0.954。这说明基于叶长×叶宽的叶面积幂函数方程能很好地来模拟五种火棘属植物的叶面积。     

Assessment of a non-destructive method to estimate the leaf area of <Emphasis Type="Italic">Armoracia rusticana</Emphasis>

The aim of the study was to analyze horseradish growth for developing a mathematical model to estimate the leaf area based on linear measurements of the leaf surface. Leaf area (LA), number, and morphometric characteristics of the leaves including lamina length (L) and width (W) were evaluated on two horseradish accessions (Cor and Mon) throughout a 2 year growing cycle. In both accessions, increased values of LA and leaf number were found by comparing the second with the first-growing season. Leaf development occurs along with variations in size and not in shape during the plant growth. The leaves are elliptical in shape but tend to be wider and bigger in Cor accession and tapered and similar to narrow ellipses in Mon showing different length/width relationship. Consequently, several regression models relating to the LA and L, W, L², and W² individually or in combination were fitted for each accession based on a set of 1000 leaves. The horseradish LA can be predicted based on either length or width alone. However, the regression linear model LA?=?aLW?+?b (LA?=?0.71LW ??0.27 and LA?=?0.76LW ??3.22 for Cor and Mon, respectively) provided the best LA estimation (R²?>?0.95). The validation of this latter model showed high correlation between LA measured and LA predicted in both accessions (R²?=?0.98). Considering the type of foliage of horseradish, the proposed model can be used to estimate the leaf area throughout the entire crop cycle.     

Nitrogen fertilization effects on leaf morphology and evaluation of leaf area and leaf area index prediction models in sugar beet

In a two-year experiment (2002–2003), five N application rates [0, 60, 120, 180, and 240 kg(N) ha⁻¹, marked N₀, N₆₀, N₁₂₀, N₁₈₀, and N₂₄₀, respectively] were applied to sugar beet cv. Rizor arranged in a Randomized Complete Block design with six replications. Leaf shape parameters [leaf area (LA), maximum length (L), maximum width (W), average radial (AR), elongation (EL), and shape factor (SF)] were determined using an image analysis system, and leaf area index (LAI) was non-destructively measured every two weeks, from early August till mid-September (four times). Years, samplings, and their interaction had significant effects on the determined parameters. Fertilization at the highest dose (N₂₄₀) increased L and sampling×fertilization interaction had significant effects on LA, L, W, and SF. For this interaction, W was the best-correlated parameter with LA and LAI meaning that W is a good predictor of these parameters. Two proposed models for LA estimation were tested. The model based on both leaf dimensions [LA = 0.5083 (L×W) + 31.928] predicted LA better than that using only W (LA = 21.686 W − 112.88). Instrumentally measured LAI was highly correlated with predicted LAI values derived from a quadratic function [LAI = −0.00001 (LA)² + 0.0327 LA − 2.0413]. Thus, both LA and LAI can be reliably predicted non-destructively by using easily applied functions based on leaf dimensions (L, W) and LA estimations, respectively.     

Predicting the Leaf Area and Leaf Dry Weight of Elaeagnus mollis in Shanxi

Non destructive and mathematical approaches of modeling can be very convenient and useful for plant growth estimation. The leaf of Elaeagnus mollis was taken as the object of research. Leaf length、 leaf width、SPAD value and different combinations of these variables were developed models to predict individual leaf area, saturated fresh weight, and dry weight of Elaeagnus mollis. Ten regression equations were compared. Select fitting the best model as a predictive model in leaf area, saturated fresh weight and dry weight. The three models were as follows: individual leaf area LA=3647+0383LW+0001LWS (R=0968), saturated fresh weight SFW=-0464+0081L+000008LWS (R=0963), and dry weight DW=-0094+0032W+00001LS (R=0960). The best prediction model of LA, SFW and DW was validated with the measured value. The results showed that the predicted values and measured values were highly consistent. It could be used to predict the LA, SFW and DW of actual unknown leaves.     

Leaf area estimation in muskmelon by allometry

This study developed a method for estimating the leaf area (LA) of muskmelon by using allometry. The best linear measure was evaluated first, testing both a leaf length and width (W). Leaf samples were collected from plants grown in containers of different sizes, leaves of four cultivars, at different develpoment stages, and of different leaf sizes. Two constants of a power equation were determined for relating allometrically a linear leaf measure and LA, in a greenhouse crop. W proved to be a better fit than the leaf length. The maximum attainable W and LA were estimated at W_x = 15.4 cm and LA_x = 174.1 cm². The indicators of fit quality showed that the function was properly related to LA and W as: LA/LA_x = A_o × (W/W_Lx)^b; the allometric exponent was b = 1.89, where R ² = 0.9809 (n = 484), the absolute sum of squares, 0.4584, and the standard deviation of residues, 0.03084, based on relative values calculations (LA/LA _x and W/W_Lx). The relationship was not affected by the cultivar, crop age, leaf size or stress treatment in the seedling stage. The empirical value of allometric constant (A₀) was estimated as 0.963.     

A simple model for nondestructive leaf area estimation in bedding plants

Measurement of leaf area is commonly used in many horticultural research experiments, but it is generally destructive, requiring leaves to be removed for measurement. Determining the individual leaf area (LA) of bedding plants like pot marigold (Calendula officinalis L.), dahlia (Dahlia pinnata), sweet William (Dianthus barbatus L.), geranium (Pelargonium × hortorum), petunia (Petunia × hybrida), and pansy (Viola wittrockiana) involves measurements of leaf parameters such as length (L) and width (W) or some combinations of these parameters. Two experiments were carried out during spring 2010 (on two pot marigold, four dahlia, three sweet William, four geranium, three petunia, and three pansy cultivars) and summer 2010 (on one cultivar per species) under greenhouse conditions to test whether a model could be developed to estimate LA of bedding plants across cultivars. Regression analysis of LA versus L and W revealed several models that could be used for estimating the area of individual bedding plants leaves. A linear model having LW as the independent variable provided the most accurate estimate (highest R ², smallest mean square error, and the smallest predicted residual error sum of squares) of LA in all bedding plants. Validation of the model having LW of leaves measured in the summer 2010 experiment coming from other cultivars of bedding plants showed that the correlation between calculated and measured bedding plants leaf areas was very high. Therefore, these allometric models could be considered simple and useful tools in many experimental comparisons without the use of any expensive instruments.     

Leaf shape alters the coefficients of leaf area estimation models for Saussurea stoliczkai in central Tibet

Nondestructive methods to estimate individual leaf area (LA) accurately, by leaf length (L) and/or width (W), is helpful for the in situ and successive LA measurements. However, leaf shape and size may covary with environment and thus alter the coefficients of LA estimation models. To test such hypothesis, we carried out an experiment by measuring Saussurea stoliczkai C. B. Clarke leaves along an altitudinal transect in Damxung county, central Tibet. In July 2011, we selected seven sites at about every 150 m in altitude from 4,350 m to 5,250 m a.s.l. A total of 1,389 leaves (182 to 203 leaves for each site) were measured. For each site, models developed by two leaf dimensions [LA = a (L×W) + b] could estimate LA more accurately than those by single dimension. L, W, LA and leaf shape index (L:W ratio) all decreased with increasing altitude, leading to significant differences in coefficients of two-dimension model between almost every two sites. Accordingly, a common two-dimension model is unlikely to occur for S. stoliczkai across the whole altitudinal transect, indicating that the varying leaf shape may alter the coefficient of LA estimation models.     

EFFECTS OF ELEVATED CARBON DIOXIDE ON ESTIMATION OF LEAF AREA AND LEAF DRY WEIGHT OF SOYBEAN

The objectives of this study were to determine the effects of elevated CO₂ on relationships between leaf area (A) and linear leaf dimensions (length [L] and width [W]) and leaf dry weight (M) in soybeans (Glycine max (L.) Merr. cv. Bragg). Based on dimensional measurements made on trifoliolates 1–6 for plants grown under three CO₂ levels (348, 502 and 645 μl l^−-1), the best predictor for both trifoliolate leaf area and for fully expanded central leaflets of the trifoliolates was an equation of the form A = b_o + b₁L·W; these relationships were unaffected by CO₂, although there was a small effect of leaf position. For expanding central leaflets of the fifth trifoliolate, no CO₂, leaf size (age) or CO₂ × leaf size effect was found. Specific leaf weight (i.e., M/A) was significantly affected by CO₂, increasing with increasing CO₂. Hence, trifoliolate dry weight can be nondestructively estimated from trifoliolate area using the equation M = 0.097 + (6.71 × 10^−-3 + 1.04 × 10^−-6[CO₂])A, where [CO₂] is mean daytime CO₂ concentration of the growth environment.     

Leaf allometry and prediction of specific leaf area (SLA) in a sugar beet (<Emphasis Type="Italic">Beta vulgaris</Emphasis> L.) cultivar

Sugar beet cv. Rizor was grown for five growing seasons (2002–2006) in field conditions in Thessaly, central Greece. A total of 55 samplings took place during the growing seasons and allometric growth of the leaves was monitored. Highly significant (p<0.001) quadratic relationships were found between individual leaf mass (LM), individual leaf area (LA), aboveground dry biomass (ADB), and leaf area index (LAI). Only the LM-LA relationship (LA = 43.444 LM² − 10.693 LM + 118.34) showed a relatively high r ² (0.63) and thus could be used for prediction of LA. Specific leaf area (SLA) was significantly related with leaf water content (LWC) (SLA = 26 279 LWC² − 44 498 LWC + 18 951, r ² = 0.91, p<0.001) and thus LWC could be a good indirect predictor of SLA in this cultivar.     

龙船花两变种叶面积回归方程的建立

以龙船花两变种橙红龙船花Ixora coccinea var. coccinea、邦德胡卡红仙丹草I. coccinea var. bandhuca的成熟叶为材料,利用WinFolia软件测定多项叶形态指标,并对叶面积进行回归分析,分别建立其8种回归方程以及总的适用回归方程。结果表明,龙船花两变种的叶片长×叶水平宽、叶周长、叶垂直长、叶片长、叶水平宽、叶片长×叶片长以及叶水平宽×叶水平宽与叶面积之间的相关系数及复相关系数均呈极显著水平(P＜0.01),可分别用来建立龙船花的叶面积回归方程;叶面积与叶片长×叶水平宽的相关系数及复相关系数最高,基于叶片长×叶水平宽的8种叶面积回归方程更好地估测两种龙船花的叶面积。经检验发现,二次函数、复合函数、幂函数能更准确地估测叶面积;由两种龙船花共同建立的3种总的回归方程中,复合函数与幂函数能更好地模拟估测叶面积。     

辽东栎（Quercus liaotungensis ）叶特性沿海拔梯度的变化及其环境解释

植物对环境的适应一直是生态学研究的核心问题之一。山地由于海拔剧烈变化造成显著的环境差异,成为研究植物对环境适应性变化的理想对象。为阐明辽东栎(Quercus liaotungensis Koidz.)叶对环境的适应性变化,在北京东灵山地区辽东栎海拔分布范围(1000~1800 m)内研究了叶特性的变化规律及其与地形和土壤养分的关系。回归分析发现：辽东栎气孔密度、气孔长度和叶面积随海拔的升高呈现曲线变化形式。在海拔约1400m处,气孔密度最小而气孔长度和叶面积最大;气孔密度和长度成反比;叶长宽比没有明显变化;叶绿素(a+b)含量和单位干重叶氮、磷和钾含量沿海拔梯度呈上升趋势,同时叶绿素含量和叶氮含量有较弱的正相关。偏相关分析显示：叶绿素含量和坡位有显著的相关关系,叶磷含量与坡度关系显著,但叶养分与土壤养分之间未表现出明显的相关关系;地形和土壤养分与气孔密度、长度和叶面积等形态指标的关系均不显著。方差分析表明上坡位与中、下坡位的叶绿素含量有显著差异,上坡位的叶绿素含量最高。辽东栎大部分叶特性在其海拔分布范围内有显著的变化,并且形态特征和养分特征的变化形式不同,海拔1400 m左右是辽东栎叶形态特征变化最显著的范围。这些叶特征的变化与土壤养分的关系不明显。