Introduction

Leaf area (AF, for its acronym in Spanish) is the surface in which energy and matter are exchanged between a plant and the atmosphere; it is considered a key variable to model the growth of trees and the conditions of a forest (^{Guangjian et al., 2019}). Its dynamics can be analyzed by parameters such as the leaf area index (IAF, for its acronym in Spanish), defined as the number of leaves present per unit area (m² m^-2) (^{Sun et al., 2019}). IAF is used as an indicator to assess the productivity of ecosystems and forest plantations (^{Papamija and García, 2012}).

The methods to estimate the IAF are direct or indirect. The former require destructive sampling and involve the direct measurement of the tree's foliage or the collection of litter over a period, which makes them costly and slow to apply (^{Muñoz et al., 2008}), which limits their use to large scale. Indirect methods can be based on the measurement of solar radiation that penetrates the forest floor through the canopy of the trees (^{Hu et al., 2014}). These methods are an efficient alternative for measuring IAF in different types of forest vegetation (^{Martínez et al., 2006}; ^{Chen et al., 2018}). However, despite their efficiency, indirect methods tend to present bias in the estimates, so it is common to turn to the use of mixed methods that establish precise mathematical relationships between allometric estimates (direct) and optical measurements (indirect) (^{Aguirre-Salado et al., 2011}; ^{Guangjian et al., 2019}).

The estimation of IAF in commercial forest plantations (PFC) is important to determine their productive potential and to establish possible growth responses due to forestry management (^{Papamija and García, 2012}). For this reason, it is justified to determine the most efficient and precise method to estimate this index for each species used in plantations. In Mexico, the Eucalyptus genus is the second most frequent in PFC (^{Conafor, 2014}), in particular E. urophylla S. T. Blake, a well-adapted and fast-growing species in tropical regions (^{Wright, 1997}).

The main objective of this study was to estimate IAF by direct and indirect methods in E. urophylla commercial forest plantations, based on the hypothesis that indirect measurements of IAF can provide reliable information and with less effort to measure the dynamics of growth and status of forest plantations. At the same time, it was sought to analyze the seasonal dynamics of IAF for one year.

Materials and Methods

Study area

The study was carried out in commercial forest plantations of E. urophylla established in Huimanguillo, Tabasco, Mexico (17°55' N, 94°06' W) (Figure 1), where the average altitude is 30 m. The climate is warm humid (A_m (f)), with rains in summer, 2 500 mm average annual rainfall and average annual temperature around 26 °C (^{García, 1998}). Soils are of the Feozem type (^{INEGI, 2005}). The surrounding vegetation is composed of remnants of high evergreen forest and secondary vegetation (^{Conafor, 2012}). The plantations are between one and seven years old and were established at an average spacing of 2.5 m × 3.5 m between plants and rows, at an average density of 1 367 trees ha^-1 with E. urophylla clonal plants.

Figure 1 Location of Eucalyptus urophylla S. T. Blake comercial forest plantations. 

Data collection in the field. Through selective sampling, with special attention to respecting the original plantation density or with the least possible loss of trees, four rectangular sites of 500 m² per plantation were demarcated. In total, 28 sampling sites were established distributed in seven plantations, each one with a different age - from one to seven years old. At the beginning and end of the study (July 2014 and August 2015, respectively) the normal diameter (Dn, cm) was measured with a 95 cm Mantax Black caliper and the total height (At, m) with a SUUNTO clinometer of all trees within the sampling sites.

To estimate the IAF by means of the litter collection method, circular capture traps of 1 m² of surface were placed, 1 m above the ground. In total, 112 traps were placed (16 per plantation, 4 per sampling site). On a monthly basis, from August 2014 to July 2015, the litter present in the traps was collected and dehydrated until reaching constant weight (about 72 hrs) in a drying SHEL LAB SMO14-2 oven at 70 °C. Subsequently, dry weight (g) was obtained by a 0.01 g precision OHAUS Navigator^TM scale.

The optical method involved obtaining five hemispheric photographs (FH, for its acronym in Spanish) at each sampling site by using a Nikon Coolpix D3100 camera (Figure 2), equipped with a 5 mm “fish eye” type lens. The FHs were obtained according to the minimum sample size defined by ^{Whitford et al. (1995)}. Each sampling site was divided into four sections to take one FH per section and one more in the center. The monthly sample was 140 FH, which were analyzed with the Hemisfer^© Patrick Schleppi version 2.13 application, an application that integrates a wide variety of methodologies to estimate the IAF (^{Schleppi et al., 2007}).

Figure 2 Examples of hemispheric photographs taken in one-year (a) and seven-year (b) old plantations. 

The IAF allometric estimation involved the destructive sampling of 93 trees selected from seven plantations of different age (15, 13, 12, 12, 12, 15 and 14 individuals in the plantations of one to seven years, respectively), distributed in a 7.8 to 33.2 cm interval of normal diameter and in total height between 8.5 and 33.3 m. According to ^{Jonckheere et al. (2004)}, the sample obtained is representative to estimate the specific leaf area (AFE, for its acronym in Spanish, m² kg^-1) and the projected leaf area (AFP, for its acronym in Spanish, m²). The total weight of the green foliage of each felled tree was recorded and a sample (0.5 kg) of foliage was extracted from different parts of the crown per tree, which was dehydrated at 72 °C to determine its dry weight on a 0.01g OHAUS Navigator^TM precision scale. The felled trees were measured for stump diameter (Dt, cm) and normal diameter (Dn, cm) with a 95 cm Mantax Black^TM caliper; in addition to the total height (At, m) with a 30 m Truper 12639 measuring tape. With these data, allometric equations were generated to estimate AFE and AFP.

Estimation of the specific leaf area. The AFE was estimated at the tree level (AFE _Individual , m² kg^-1) by the arithmetic calculation used by ^{Cano et al. (1996)} and ^{Muñoz et al. (2008)}. In a subsample of 60 leaves, of the initial sample of foliage collected from each felled tree, the adaxial leaf area of each leaf (AF _Hoja ) (m²) was measured with a foliar integrator (Li-COR 3000C). They were then dried and weighed to obtain the dry biomass per leaf (BS _Hoja ) (kg). Through the quotient of AF _Hoja and BS _Hoja (Equation 1) the individual AFE of each tree was obtained. After that, the values were averaged to obtain a value by plantation age:

AFEIndividual=∑i=1nAFHoja∑i=1nBSHoja (1)

Estimation of the projected leaf area. The AFP _Individual (m²) per tree was estimated as a result of AFE _Individual and the dry leaf biomass (BFS _Total ) (kg) (Equation 2). BFS _Total was calculated by the methodology recommended by ^{Muñoz et al. (2008)}, which comes from multiplying the green leaf weight (PFV _individual ) by the dry weight/green weight quotient (R _Muestra ) of leaves from the foliage simple per felled tree (Equation 3).

AFPIndividual=AFEIndividual BFSTotal (2)

BFSTotal=PFVIndividual RMuestra (3)

Estimation of the leaf area index. The IAF was estimated by the allometric, litter collection and optic methods. For the first one, the BFS _Total for each tree at the sampling sites was initially calculated with the equations suggested by ^{Hernández-Ramos et al. (2017)} for the species, using the allometric variables. After that, with the calculated BFS _Total , the AFP _Individual was estimated for each tree in the site, from the model adjusted in this document and described in the results. These estimations allowed to obtain IAF_Alométrico (m² m^-2) (Equation 4) to the site level for the two measurement dates (Initial: July, 2014 and final: August, 2015).

IAFAlométrico=∑i=1nAFPIndividualAS (4)

Where:

IAF _Alométrico = Leaf area index per site calculated through allometric relations

AFP _Individual = Projected leaf area estimated per tree (m²)

AS = Area of the site (m²)

n = Number of trees at the site

The IAF estimation by means of litter collection (IAF _Hojarasca ) for each sampling site resulted from the weight of the dry litter accumulated during a year in a trap and the value of the average AFE _Individual for a plantation of the same age; at the end, the four values obtained per trap were averaged to obtain an IAF value per site (^{Liu et al., 2015}).

The optical IAF (IAF _Óptico ) was estimated monthly with the Hemisfer^© Patrick Schleppi version 2.13 program, from the individual processing of the FHs taken at each site, with the ^{Thimonier et al. (2010)} method, which consists of weighting the IAF values estimated from the Norman and Campbell Ellipsoidal method with a regression model that integrates the leaf insertion angle and the solar radiation under the canopy as predictive variables (^{Lang and Yueqin, 1986}). The result of the previous process was applied a correction factor for clustering of the canopy and foliage not randomly distributed, to reduce the underestimation of the IAF caused by a greater input of solar radiation (^{Chen and Cihlar, 1995}; ^{Liu et al., 2015}). The IAF _Óptico value per site corresponds to the average of the values calculated for the five FHs taken at the site.

In spite of the corrections made to the optical method, the calculated values tend to underestimate the real IAF values (^{Weiss et al., 2004}). To reduce this bias, the calibration proposed by ^{Aguirre-Salado et al. (2011)} was made, which consists of adjusting regression models in which the IAF _Alométrico or IAF _Hojarasca are dependent variables and the IAF _Óptico is the independent variable. The result is a calibrated IAF value (IAF _Calibrado ).

Statistical analysis. The values of AFE _Individual and AFP _Individual obtained from destructive sampling data were analyzed using an ANOVA, defining the planting age as the primary factor. Differences between means were evaluated with the Tukey test. The correlation between the AFP and AFE variables with the Dn, At and BFS _Total variables was analyzed with the Pearson's correlation coefficient. The variables related to a greater degree with the AFP and the AFE served as the basis to adjust the non-linear regression models (Table 1) (^{Cano et al., 1996}; ^{Aguirre-Salado et al., 2011}).

Table 1 Adjusted models to estimate the projected leaf area (AFP) and the calibrated leaf area index in Eucalyptus urophylla S. T. Blake.plantations. 

Model	Type of model	Structure
1	Chapman-Richards	y=β01-e-β1X1β2
2	Monserud y Sterba	y=X1eβ0X1β1X2
3	Power	y=β0X1β1
4	Schumacher Cobb-Webb	y=β0X1β1X2β2
5	Schumacher´s exponential	y=β0e-β1X1

y = Dependient variable; χ _n = Normal diameter (Dn); At = Total height; Ab = Basimetric area; Vt = Total volume; BFS _Total = Dry leaf biomass; B _n = Parameters of the model.

For IAF, the estimated values by the three methods used were plotted and compared by means of a Pearson correlation analysis. It should be noted that for the comparison of the allometric and optical IAF, the values and FH corresponding to the same measurement date were used to avoid a temporality error. The direct and indirect methods mostly related were used to generate a calibrated IAF _Calibrado from a non-linear regression model, with the models in Table 1. The selection of the models with the best fit was made considering the highest adjusted R ² value and the lowest value of the root mean square error (RECM), in addition to the significance of its parameters. The selected models were analyzed to corroborate compliance with the regression assumptions using the Shapiro-Wilk test for normality and the White test to detect heteroskedasticity (p≥0.05). Given that the data presented this last problem, specifically the IAF, a residual correction was applied using the AFP/ROOT variable (BFS ² ). Finally, the Durbin-Watson test was applied to detect collinearity between variables. The analysis was carried out using the PROC MODEL procedure of SAS 9.4 Institute Inc. (^{SAS, 2014}).

Results and Discussion

Specific leaf area and projected leaf area. The average value of AFE _Individual and AFP was 8.024 m² kg^-1 and 35.995 m², respectively, for the sample. Both variables showed significant differences (P = 0.0001) between the averages of the trees with different ages (Figure 3). The comparison of means showed a higher value of AFE (8.56 m² kg^-1) in the one-year-old plantation. In contrast, the four-year plantation yielded the lowest value (7.36 m² kg^-1). The highest value of individual AFP was presented by the seven-year plantation (52.23 m²) and the lowest value (14.18 m²) was calculated for four-year plantations, coinciding with the lowest value of AFE. The AFE is lower at the age of four and five years of planting (Figure 3A). This tendency can be explained by the adaptation of the leaves to competition for light, water stress and management practices at intermediate ages of growth (^{Vega et al., 2010}). Other species show a similar trend. For example, Pinus patula Schiede ex Schltdl. et Cham. showed a 6 % reduction when going from one to two years of age, which was attributed to the increase in structural components and substances in the older foliage, making it heavier (^{Cano et al., 1996}). On the other hand, the AFE values obtained in this study that vary between 7.36 and 8.56 m² kg^-1 are high, which may be related to the high density of the plantations (1 367 trees ha^-1), as demonstrated by ^{Muñoz et al. (2008)} for Eucalyptus nitens H. Deane & Maiden, who calculated the highest AFE values in plantations with higher densities.

Different letters indicate statistical difference (Tukey, p≤0.05) in their mean.

Figure 3 Trend of (A) specific leaf area (AFE, m² kg^-1) and (B) projected leaf area (AFP, m²) in regard to the age of the plantation. 

In the AFP an irregular behavior was observed, since it increased in the first years of growth, later it decreased and then increased again (Figure 3B). This variation is due to the mortality that is registered in the plantations, in which, by losing individuals, the AFP decreases in the short term and then increases due to the increase in the availability of nutrients, water and light, which allows generating more foliage per unit area (^{Rodríguez-Ortiz et al., 2011}), which favors capturing more solar radiation to increase the photosynthetic rate.

Relationship of the AFE and AFP with structural variables of the plantation. In the case of AFE, this relationship is negative and not significant, so no regression models were adjusted. For AFP, the correlation is positive (BFS _Total [0.97] and Dn [0.50]), which indicates a greater amount of leaves as the dimensions of the tree increase, especially the width of the normal diameter and, consequently, the crown diameter (^{Rodríguez-Ortiz et al., 2011}).

Model 3 exhibited R ² _ajustada high values, low for RCME, highly significant parameters, normality (Shapiro-Wilk with a 0.95 value), inexistence of collinearity (Durbin-Watson test (1.67) and logical estimations of AFP for the low study sites (Table 2). However heterocedasticity problems occurred, which were solved by correction for weighting residuals with the AFP/RAÍZ (BFS ² ) variable. The correction of the model improved the fit statistics (R ² _ajustada = 0.9526, RECM= 0.9077 and its structure: AFPIndividual=7.952315(BFSTotal)1.006678) making it statistically stable and reliable to estimate AFP in E. urophylla plantations.

Leaf area index. The estimated values of average IAF that include the seven plantations are 2.7, 2.6 and 1.6 m² m^-2, within the ranges 1.8 to 3.7, 1.3 to 4.2 and 1.0 to 2.6 m² m^-2, for IAF _Alométrico , IAF _Hojarasca e IAF _Óptico , respectively. The allometric method estimated the highest value of IAF in the one-year plantation and the lowest was recorded for the three-year old (Figure 4). The highest IAF _Hojarasca value was recorded in the seven-year-old plantation and the lowest in the four-year-old. The IAF _Óptico value was higher in the seven- and one-year-old plantations and the rest presented homogeneous values of less than 1.7 m² m^-2.

Figure 4 Leaf area index (IAF) estimated by direct and indirect methods for Eucalyptus urophylla S.T. Blake plantations. 

If the direct methods are considered as a reference, the IAF _Óptico presented an average underestimation of -39 and -37 % in the evaluated plantations, with the IAF _Alométrico and the IAF _Hojarasca , respectively. Although an average percentage difference of 8 % was verified between the direct methods, for all plantations, the IAF _Hojarasca value was taken as a reference parameter since, in addition to estimating the IAF with precision; it allows describing its dynamics during a growth cycle. In addition, its measurement is not destructive of the trees, as demonstrated by ^{Castellanos and León (2010)} when modeling the monthly foliar production of Acacia mangium Willd. In other words, the IAF _Hojarasca value was considered the basis for the comparisons between methods and for the calibration of the values obtained using the indirect method (IAF _Óptico ), since this method predicts the mean and spatial variability of IAF with greater precision (^{Iwamoto and Hiura, 2011}).

The correlation of the IAF _Alométrico values with the IAF _Óptico and the IAF _Hojarasca is 0.30 and 0.33 respectively, which are inadequate to fit a regression model. However, the correlation between the IAF _Óptico and IAF _Hojarasca is 0.75. Therefore, the models presented in Table 1 were adjusted to calibrate the IAF _Óptico using the IAF _Hojarasca . The time of measurement of the allometric method corresponded to the beginning of leaf production, which surely influenced the low values of the IAF _Alométrico compared to the IAF _Hojarasca .

Except for the power type model (Table 1, model 3), the models tested to calibrate the IAF presented low adjustments. Model 3 had a reasonable adjustment in the calibration of the IAF _Óptico in regard to the IAF _Hojarasca (Table 3). These two techniques can be compared at the site level since the litter collection and hemispheric photographs were made without spatial difference (Figure 5). The selected model showed normality with a statistic of W = 0.94, the White test indicated homoscedasticity and the Durbin-Watson statistic was 1.78, which means there is non-collinearity between variables.

Figure 5 Scatter diagram of the leaf area index, real data (litter collection) and estimates (IAF _Calibrado ) (IAFCalibrado=1.650636*IAFÓptico0.956617) for Eucalyptus urophylla S. T. Blake. 

The estimated IAF values are similar to those of E. nitens plantations in the Central Zone of Chile, with + values between 1.63 and 2.55 m² m^-2 for densities of 1 100 trees ha^-1. At the same time, these values are low compared to lower density plantations due to the competition for space among the trees for the development of the crown (^{Muñoz et al., 2008}). ^{Papamija and García (2012)} recorded IAF _Alométrico values of 2.30 to 3.20 m² m^-2 for Eucalyptus grandis W. Hill ex Maiden plantations established in Colombia and even higher with the optical method, from 2.42 to 3.64 m² m^-2, which differs from that calculated in this study, in which the IAF _Óptico underestimates the value obtained by allometry, in addition to obtaining a correlation coefficient between the two methods equal to 0.011.

^{Macfarlane et al. (2007)} determined an IAF of 3.0 m² m^-2 for Eucalyptus marginata Donn ex Sm. plantations of 12-years old using the allometric method and 1.77 m² m^-2 using the optical method with correction for FH agglutination, which represents a 41 % underestimation. In a similar way, ^{Chen and Cihlar (1995)} determined underestimations of the IAF in a range of 15 to 25 % by means of the optical method due to the agglutination of the foliage, for which they recommended applying a correction to reduce the error by integrating a parameter of branch area index. This variation in the low estimates of the IAF _Óptico is due to factors such as the automatic exposure of the lens towards the light (^{Thimonier et al., 2010}); the clumping effect of the tree canopies (^{Weiss et al., 2004}) and the subjective choice of threshold when analyzing images with any program (^{Coops et al., 2004}).

Monthly dynamics of the leaf area index. With the adjusted model (IAF _Calibrado ) and the IAF _Óptico measurements, the monthly IAF values were calculated (Figure 6). As expected, these values presented a negative relationship with the fall of litter, that is, the maximum peaks of leaf collection agree with low values of IAF in the plantations. During the months of February to May, there was an increase in the fall of litter and consequently a decrease in the IAF in E. urophylla (Figure 6), the values varied between 2.14 and 2.20 m² m^-2 in the season of lower production. In June and July an increase in the IAF was observed, corresponding to the time of maximum leaf production and the beginning of the growth stage, when they reached maximum values from July to September of 2.65 to 2.71 m² m^-2.

Figure 6 Monthly dynamics of litter fall (A) and leaf area index (B) for Eucalyptus urophylla S. T. Blake plantations. 

In November took place a steep decline in the IAF value from an increment in litter fall in October; however, the following month a foliar recovery was observed, indicating that during the rainy or growing season E. urophylla presents a continuous replacement of foliage according to water availability. This behavior is similar to that described by ^{Castellanos and León (2010)} for Acacia mangium forest plantations, in which the highest peak of foliar production occurred at the beginning and during the rainy season (July to October).

Theoretically, older plantations should have a high IAF, however, for the case studied, the highest IAF value was presented in younger plantations, with a decreasing trend as age increases. If the mentioned by ^{Peduzzi et al. (2010)} regarding that the IAF is an indicator of the productivity of the land, the values found indicate that the evaluated plantations of four and five years are the ones with the lowest production by registering the lowest values of IAF in comparison with the plantations of other ages. Greater efficiency in activities such as fertilization, weed control and thinning is expected when carried out in young plantations due to the greater amount of foliage they have.

Conclusions

The litter collection method (IAF _Hojarasca ) was considered the most accurate for the purpose because it involved the monthly collection of litter during an annual growth cycle of the species, which also allowed a detailed description of the dynamics of the index of leaf area. Based on the results obtained by this method, and in order to recommend an alternative to estimate the IAF efficiently and accurately, a regression model was generated that calibrates initial measurements of IAF obtained through an indirect method (IAF _Óptico ), easy to obtain but with low precision, to make a more adequate and efficient estimation of the leaf area index (IAF _Calibrado ).

In regard to the dynamics of IAF, the analysis carried out allows to conclude that the highest production of leaves occurs in the rainy season (from June to October), which corresponds to the season of greatest growth of E. urophylla. Therefore, it is reasonable to assume that the application of forestry management practices such as fertilization and weeding would be more effective if applied at this time.