Essay: Leaf area index estimation from allometric …

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Leaf area index estimation from allometric relationships in Cucurbita pepo L.

Prediction of leaf area is essential in crop simulation models. The objective of this study was to find relationships between leaf area index (LAI) and numbers of leaves (NL), leaf dry weight (LDW), leaf fresh weight (LFW), number of nodes (NN) and plant height (PH), in Pumpkin (Cucurbita pepo L.). For this purpose, an experiment was conducted using three planting date (20 April, 21 May, 21 June) at the research field of Abooreihan Campus, the University of Tehran, Pakdasht, Tehran, Iran, in 2009-2010 cropping season. The experimental design was randomized complete block with three replication. Sampling was performed during the whole growing season. In each sampling LA, NL, LDW, LFW, NN and PH, were measured. Various equations were used to describe relationships between LAI and afore mentioned characteristics. The best result was obtained a simple ln-transformed linear equation

{ln(y)= a+b*ln(x)}. Results showed that significant relationships were found between LAI and LA

(R2 = 90), LAI and NL (R2 = 90), LAI and NN (R2 = 90), LAI and LDW (R2 = 98) and LAI and LFW

(R2 = 98). These equations LAI can be used for estimation in simulation models of Pumpkin as well as for the fast and easy estimation of LAI, especially where there is no LAI-meter available.

Keywords: Pumpkin, Allometric relationships, Leaf area, Vegetative characteristics

Introduction

The genus Cucurbita L. (pumpkins and squash) is native to the Americas where there is evidence of their culture more than 10000 years ago (Smith, 1997), according to archaeological recordings, where Cucurbita pepo L. appears to be one of the first domesticated species (Aliu et al., 2011; Hern _ ando-Bermejo & Le _ on, 1994). (1) It is an important vegetable food crop with medicinal value, including treatment for benign prostatic hyperplasia and leprosy (Hamissou and others 2013), that is consumed either raw in salads or cooked in soups.(7)

The oil content of the medicinal pumpkin seed varies from 42-54% and the composition of fatty acids is dependent on several factors (variety, area in which the plants are grown, climate, state of ripeness). The dominant fatty acids comprise palmitic, stearic acid, oleic acid and linoleic acid (Murkovic et al., 2004). The content of vitamin E in medicinal pumpkin seeds is very high (Murkovic et al., 1996). (5)

The leaf area index (LAI), defined as the ratio of the leaf area of a plant population to the ground area it occupies, is an important variable of the canopy, which determines plant growth and development. It expresses the effect of the emergence and expansion of leaves, interaction with the input of CO2 and energy flow, and directly affects the interception of solar radiation, photosynthesis, accumulation of biomass, transpiration and gas exchange in the crop canopies (JONCKHEERE et al., 2004; KANDIANNAN et al., 2009).(4)

LAI is an excellent indicator of crop development and health, and is used as an input variable for crop growth and yield forecasting models. Various ground methods are used to measure LAI including hemispherical photography (Demarez, Duthoit, Baret, Weiss, & Dedieu, 2008; Tang et al., 2014), optical sensors with the LAI-2000/2200 (Tang et al., 2014) and terrestrial Light Detection and Ranging (LIDAR) scanning (Riano, 2004; Jensen, Humes, Vierling, & Hudak, 2008).(12)

Of the regression models available, those classified as nonlinear are useful for describing growth over time as they use biological interpretation parameters that make analyses easier. According to Seber and Wild (1989), Smyth (2002), Bates and Watts (2007), nonlinear models are generally adopted when it is suspected that the relationship between the response variable and the predictors follows a particular function.

The application of nonlinear growth models can be found in a range of studies in the literature in various areas. In the agricultural sciences, the studies in this area evaluate the entire cycle of a specified species or growth model according to the application of different crop management techniques or comparison between genotypes, as can be seen in Hernلndez et al. (2007), Barrera et al. (2008) , Tarara et al. (2009), Akpo et al. (2014) and Carson et al. (2014). (2)

The aim of this study was to obtain a mathematical model that would estimate leaf area index (LAI) in a Cucurbita pepo as a function of allometric relationships.

Material and methods

The present study was performed in Abooreihan campus – Tehran University Research Farm at Pakdasht in 2011. The test altitude is 1003 m above sea level, latitude and longitude are 35º 28′ N and 44º 51′ E. The test area has loamy soil texture and the climate based on Do marten classification is arid. This area has hot, dry summers, mild winters and an average annual rainfall of 170 mm.

The experiment was carried in a randomized complete block design with three replication, planting date treatment included May, June, and July the first. Each experimental unit consisted of 6 planting rows of 7 m length, row spacing of 30 cm and 150 cm distance between rows. While planting, 5 seeds were planted in each hole and were thinned in 4-leaf seedlings stage. All weeds and their roots were removed manually at the beginning of the experiment, and re-grown weeds were removed weekly during the experiment. Based on soil chemical analysis, the fertilizer amount consumption was calculated on 100 kg of nitrogen per hectare using urea fertilizer (46% N) and 100 kg per hectare triple super phosphate fertilizers and potassium phosphate. The application of fertilizers was in a way that all phosphate fertilizers and potassium fertilizers and one-third of urea fertilizers were used excessively in the beginning of flowering and fruit set. Irrigation and pest and probable disease control operations carried out in a way that no effects of drought, blight, and disease is found in pumpkin.

Plant measurements include leaf area using a leaf area meter, shoot dry weight for each limb, plant height, number of nodes on the main stem and number of leaves. For this purpose, destructive samplings started two weeks after planting and were done once every 10-14 days until the end of the growing season (Planting date May and June 7 samples and July 6 samples). 3 plants of each plot was harvested and evaluated at each sampling.

Various models (Table 1) were used to describe the relationship between LAI and dry weight of leaf, fresh weight of leaf, number of leaves per plant, number of nodes on the main stem and plant height. Equation fitting and examining it was done for all planting dates individually and eventually, a general equation was fitted for all planting dates. Root mean square error (RMSE), the standard error of the estimate (SE) and the coefficient of determination R^2 was used to compare the accuracy of equations estimating the leaf area from the plant growth characteristics. Statistical analysis was performed using the Sigma Plot 11 program.

Table1- Used equation for explanation of relationships between leaf area index and leaf dry and fresh weight, leaf no. per plant, node no. per main stem and plant height in pumpkin

Equation Category Equation name Equation

Exponential Rise to Max Single, 2 parameter Y=a*(1-exp(-b*x))

Peak Gaussian, 3 parameter Y=a*exp(-.5*((x-x0)/b)^2)

Polynomial Linear Y= y0+a*x

Polynomial Linear (x)ln*b+a=(Y)ln

Polynomial Quadratic ln(Y)=y0+a*x+b*x^2

Power 2 parameter Y=a*x^b

Power Symmetric, 4 parameter Y=y0+a*abs(x-x0)^b

Sigmoidal Sigmoid, 3 parameter Y= a/(1+exp(-(x-x0)/b))

Results and Discussion

Domain (time change characteristics during the growing season), mean and standard deviation has shown in Table 2 for LAI, number of leaves per plant, number of nodes per stem, plant height, fresh weight and dry weight of leaves in each sowing levels. July allocated the lowest growth traits measured, probably due to the late cultivation of pumpkin and shortened growth period. Since the linear equation ln⁡〖(Y)〗=a+b×ln⁡〖(x)〗 (where the logarithm of x and y is taken) had a lower coefficient of determination and root mean square compared to the other models, so this relationship was used to estimate LAI in all fields (The results are not provided). In this equation, (a) is width of the origin and (b) is the slope of the line (Allometric factor).

Table2- The value of mean, standard deviation and min-max leaf area index and leaf dry and fresh weight, leaf no. per plant, node no. per main stem and plant height in pumpkin

Mean Standard deviation Range Planting dates Trait

Leaf area index

0.7114 0.6709 0.01 – 1.86 20 April

0.7736 0.7756 0.01 – 2.48 21 May

0.5989 0.5504 0.02 – 1.58 21 June

0.6979 0.6679 0.01 – 2.48 Sum

Leaf no. Per plant

45.6984 42.9552 2.67 – 123.67 20 April

46.5317 39.589 4.50 – 135.67 21 May

32.9753 26.869 5.67 – 100.33 21 June

42.1731 37.4403 2.67 – 135.67 Sum

Node no. Per main stem

19.8095 15.7397 1 – 45.33 20 April

21.1111 14.037 2 – 41 21 May

19.1235 12.0174 2.33 – 36.33 21 June

20.0593 13.8949 1 – 45.33 Sum

Plant height (cm)

90.473 86.442 2.50 – 267 20 April

80.8952 68.5831 4.50 – 202.17 21 May

75.9759 64.5764 5 – 189 21 June

80.1011 70.8706 2.50 – 267 Sum

Leaf fresh weight (g\\m2)

303.4214 321.2354 2.31 – 1081.44 20 April

282.3287 307.6384 5.33 – 1139.33 21 May

197.7301 203.9678 6.62 – 738.88 21 June

264.3316 284.7138 2.31 – 1139.33 Sum

Leaf dry weight (g\\m2)

59.1787 68.006 0.24 – 245.03 20 April

52.9987 57.1837 0.77 – 206.89 21 May

36.1203 36.8467 1 – 132.03 21 June

50.0982 56.208 0.24 – 245.03 Sum

Model fitting was done separately in each sowing date to describe the relationship between leaf area index and number of leaves per plant and the results showed no significant difference between sowing dates and Allometric factor (b) varied from 1.37 to 1.50 (Table 3). Among the date of sowing, June fitting equation allocated the best prediction with the lowest root mean square error (3.86) and standard error (0.45) and highest coefficient of determination (0.94).

Table3- Coefficient of equation a and b in Y)ln) =a+b*ln(x) between leaf area index and leaf dry and fresh weight, leaf no. per plant, node no. per main stem and plant height in pumpkin

R2 SE RMSE b±se a±se n Planting dates Trait

Leaf no. Per plant

0.910 0.59 6.70 1.42±0.10 -5.72±0.35 21 20 April

0.945 0.45 3.86 1.50±0.08 -6.08±0.29 21 21 May

0.828 0.64 6.46 1.37±0.16 -5.49±0.51 18 21 June

0.904 0.55 17.52 1.44±0.06 -5.78±0.21 60 Sum

Node no. Per main stem

0.947 0.45 3.93 1.33±0.07 -4.34±0.20 21 20 April

0.915 0.56 6.02 1.70±0.12 -5.66±0.34 21 21 May

0.828 0.64 3.42 1.37±0.16 -5.49±0.51 18 21 June

0.901 0.56 18.05 1.46±0.06 -4.92±0.18 60 Sum

Plant height (cm)

0.931 0.52 5.13 1.10±0.07 -5.16±0.27 21 20 April

0.932 0.50 4.81 1.37±0.08 -6.30±0.34 21 21 May

0.909 0.46 4.79 1.57±0.12 -5.40±0.35 18 21 June

0.907 0.54 17.02 1.18±0.05 -5.57±0.20 60 Sum

Leaf fresh weight (g\\m2)

0.990 0.20 0.77 1.01±0.02 -5.92±0.12 21 20 April

0.997 0.11 0.22 1.05±0.01 -5.98±0.07 21 21 May

0.948 0.35 1.93 0.97±0.06 -5.63±0.27 18 21 June

0.982 0.24 3.22 1.01±0.02 -5.86±0.09 60 Sum

Leaf dry weight (g\\m2)

0.989 0.21 0.81 0.90±0.02 -3.75±0.08 21 20 April

0.998 0.09 0.15 1.01±0.01 -4.10±0.04 21 21 May

0.965 0.28 1.30 0.91±0.04 -3.72±0.14 18 21 June

0.984 0.22 2.91 0.94±0.02 -3.85±0.05 60 Sum

n: Number of Sampling, RMSE: Root Mean Square Error, SE: Standard Error of Estimate, R2: Coefficient of Determination

Figure 1 shows the relationship between the natural logarithm of observed and estimated LAI using the number of leaves per plant in different sowing dates. There is a proper relationship between LAI and number of leaves per plant in different cultures. Significant differences between different sowing dates’ allometric coefficients in the level of 5% did not exist (Table 3). The effective use of the number of leaves is emphasized in studies conducted by other researchers to estimate the leaf area of different plants. So that Soltani et al., (2006) and Rahemi et al., (2006) about peas and Maddah-Yazdi et al., (2008) about peas and wheat reported that leaf area in plant has a strong relationship with the number of nodes (leaves) on the main stem. Bakhshandeh et al., (2012) used a non-linear two-pieced regression model to estimate leaf area from number of leaves per plant in wheat and predicted a good estimation of leaf area.

Fig. 1- Relationship between observed and predicted Leaf Area Index and Leaf Number of pumpkin at 20 April (a), 21 May (b), 21 June (c) and all planting dates (d)

As seen in Table 3, the number of nodes on the main stem indicates a good estimation of the LAI as well as the number of leaves in the bushes in May and June planting dates. Root mean square error for different sowing dates was variable between 3.42 to 6.02 and equation estimation standard error from 0.45 to 0.64 (Table 3). Figure 2 shows the relationship between the natural and estimated logarithm of leaf area index using the number of nodes on the main stem on different sowing dates. An equation cannot be used to predict LAI used in all sowing dates due to allometric factor signification in the given fitting equations. Sinclair (1984) for soybeans and Wahabi and Sinclair (2005) for wheat and barley used an exponential equation describing the leaf surface via the number of nodes on the main stem. Rahemi et al., (2006) for peas and Maddah-Yazdi et al., (2008) for wheat and peas used the power equation y=ax^b and Hammer et al., (1993) for grain sorghum and Soltani et al., (2006) for peas used y=x^b to estimate the leaf surface via the number of nodes on the main stem and reported proper estimation of the leaf surface. Results of this experiment is consistent with the results of other researchers in terms of a proper estimation of leaf area index using the number of nodes, but the equation for the best estimation is different.

Fig. 2- Relationship between observed and predicted Leaf Area Index and Number of Node of pumpkin at 20 April (a), 21 May (b), 21 June (c) and all planting dates (d)

Relations of LAI with plant height have been brought for each planting date in table 3. Coefficient of determination varied from 0.909 to 0.932 in different planting dates. Allometric coefficients showed no significant difference as seen; therefore one equation can be used to fit the LAI using the plant height in all planting dates. Figure 3 shows the relationship between the natural logarithm of estimated leaf area index based on plant height in different plant dates, with natural logarithm of observed LAI. Bakhshandeh et al., (2012) reported the existence of a significant relationship between leaf surfaces of wheat cultivars plant height with a higher Coefficient of determination than 0.91, with fitting the two pieced non-linear model. Rahemi et al., (2006) on peas, Akram-Ghaderi and Soltani (2007) on cotton and Lieth et al., (1986) on soy used nonlinear equations and Dwyer et al., (1992) on corn used third degree equation to describe the relationship between leaf surfaces and plant height. Lieth et al (1986) stated that in his research conducted on the soybean, plant height is not a good estimator for leaf surface; which is not consistent with the results obtained in this study.

Fig. 3- Relationship between observed and predicted Leaf Area Index and Plant Height of pumpkin at 20 April (a), 21 May (b), 21 June (c) and all planting dates (d)

Relations between the fresh weight of leaves and LAI for each plant date have been brought separately in Table 3. Root mean square error varied from 0.22 to 1.93 and standard error of the estimated equations from 0.11 to 0.35. Coefficient of determination varied from 0.948 to 0.997 in different cultivations which indicates the proper relationship between LAI and fresh weight of leaves (Table 2). Predicted and observed LAI fitting using the leaf fresh weight on different culture dates confirms the mentioned results (Figure 4). None of the investigated sources used leaf fresh weight to estimate leaf area because of the leaf fresh weight’s fast influence from temperature, irrigation, time of sampling, sampling interval and weighting the leaves. But the results of this study showed that the leaf fresh weight has a strong relationship with LAI as well as leaf dry weight is able to predict LAI with fewer facilities (only needs scales, without the need for oven) and faster than the dry weight.

Fig. 4- Relationship between observed and predicted Leaf Area Index and Leaf Fresh Weight of pumpkin at 20 April (a), 21 May (b), 21 June (c) and all planting dates (d)

Using leaf dry weight to estimate LAI was successful as leaf fresh weight so that the Coefficient of determination for equations was variable from 0.965 to 0.998 (Table 3). It seems that one equation can be used to estimate the LAI from leaf dry weight according to the allometric coefficients and standard errors of estimating equations. Figure 5 shows the appropriateness of the leaf dry weight to estimate LAI. Awal et al., (2004) on oil palm and Ma et al., (1992) on peanuts reported high correlation between leaf dry weight and leaf area using the linear and non-linear regression equations. Bakhshandeh et al., (2010) on soybeans, Tsialtas and Maslaris (2008) on sugar beets and Retta et al., (2000) on several grass species used non-linear equations to describe the relations of green leaf dry weight and total dry weight of vegetative parts with the leaf surface which among their results, can be referred to the results of Rahemi et al., (2006) for peas, Akram-Ghaderi and Soltani (2007) for cotton, Payne et al., (1991) for millet, Sharrett and Baker (1985) for lucerne, Romas et al., (1983) for barley, Zrust et al., (1974) for potato, Shin et al., (1981) for sweet sorghum, Lieth et al., (1986) for soybean and Aase (1978) for wheat. Since measuring the assessed traits is simpler and gets measured fast without the use of equipped instruments compared to measuring leaf surface, therefore the traits can be used to estimate leaf area.

Fig. 5- Relationship between observed and predicted Leaf Area Index and Leaf Dry Weight of pumpkin at 20 April (a), 21 May (b), 21 June (c) and all planting dates (d)

Conclusion

The results showed that there are very high Allometric relations between leaf area index and number of leaves per plant, number of nodes on the main stem, plant height, dry weight and leaf wet weight (With coefficients of determination 0.90, 0.90, 0.90, 0.98 and 0.98 respectively). The wet and dry weight were better able to estimate leaf area and between them, wet leaf weight was selected as the best attribute due to the speed, ease of measurement and fewer required facilities (only needs scales, without the need for oven). These relationships can be used in pumpkin simulation models and a quick and easy estimation of the LAI when leaf area measurement instruments are not available.

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