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Revista mexicana de ciencias forestales
versão impressa ISSN 2007-1132
Rev. mex. de cienc. forestales vol.11 no.58 México Mar./Abr. 2020 Epub 17-Jun-2020
https://doi.org/10.29298/rmcf.v11i58.642
Scientific article
Model for estimating Litsea parvifolia (Hemsl.) Mez. dry leaf biomass
1Campo Experimental Saltillo. CIR-Noreste, Instituto Nacional de Investigaciones Forestales, Agrícolas y Pecuarias. México.
2Departamento Forestal, Universidad Autónoma Agraria Antonio Narro. México.
Litsea parvifolia is an ever-green shrub of the Lauraceae family whose foliar biomass is its main component. Its leaves are harvested and marketed in and around the southeastern region of Saltillo municipality, Coahuila State. Fresh, it has culinary and medicinal use; dry, it is used as condiment. In order to regulate its use and determining its stock, an allometric model was selected to estimate the dry foliar biomass and the elaboration of a production table of the standing shrubs was planned as well. Natural populations were evaluated, recording the total height (H, cm) and mean diameter (Dp, cm) of the shrub crown, considering all categories of height and cover of standing shrubs and dry leaf biomass (Bfs, g). Ten allometric models were evaluated using the PROC MODEL procedure in SAS, version 9.4. Dp and H are correlated with laurel Bfs. The Schumacher-Hall model in its non-linear form is statistically reliable (p <0.0001) as it records the best statistics, with presence of heteroscedasticity, corrected effect with a weighted regression with variance structure (Dp 2 H) -0.5 , obtaining an R 2 aj . of 0.82, S xy of 18.41 g and a CV of 44.93 %. The model can be used to estimate the production of Bfs in places with similar ecological characteristics to the study area.
Key words Allometry; biomass; dry leaf; forest management; non-timber; weighted regression
Litsea parvifolia es un arbusto, perenne de la familia
Lauraceae, cuya biomasa foliar es su componente principal. Sus hojas se
aprovechan y comercializan en el sureste de Saltillo y alrededores. En fresco,
tiene uso culinario y medicinal; en seco, como condimento. Con el propósito de
generar información básica para la regulación de su aprovechamiento, se planteó
seleccionar un modelo alométrico para predecir la biomasa foliar seca y elaborar
una tabla de producción para arbustos en pie. Se evaluaron algunas poblaciones
naturales, en las que se registró la altura total (H) y
diámetro promedio (Dp) de todos los individuos en pie y se
determinó la biomasa foliar seca (Bfs). Se probaron nueve
modelos alométricos mediante el procedimiento PROC MODEL en SAS
9.4, para elegir aquel con el mayor coeficiente de determinación ajustado (
Palabras clave Alometría; biomasa; hoja seca; manejo forestal; no maderable; regresión ponderada
Introduction
Non-timber forest products (NTFPs) are vastly important as goods and services, primarily in rural communities, as they have a variety of uses -nutritional, cultural, medicinal, and industrial-, and, in general, they are in high demand in foreign trade (Chandrasekharan et al., 1996).
The native distribution area of Litsea parvifolia (Hemsl.) Mez. (laurel) is northeastern Mexico, with seven recognized species of this genus. It grows in humid areas, pine-oak forests, and semi-desert shrublands; it grows at altitudes of 1 000 to 3 000 m, but with a restricted distribution in the states of Coahuila, Nuevo León and Tamaulipas (Van Der Werff and Lorea, 1997; Jiménez-Pérez and Lorea-Hernández, 2009).
According to the Codex Alimentarius Commission of the United Nations’ Food and Agriculture Organization (FAO) and the Mexican Official Norm PROY-NOM-000-SCFI/SADER-2019 on Spices and Cooking or Aromatic Herbs, dry Mexican bay leaves -whole, crushed or ground- are used in cooking due to their flavor, aroma and visual aspect, and their primary function is to provide a fragrant, aromatic or pungent seasoning to foods (CODEX, 2017).
From the medicinal point of view, it is prepared as an infusion tea in order to relieve digestive disorders such as diarrhea and indigestion, as well as fever and nervousness; in addition, its maceration in alcohol is used for healing rheumatism. In some cases, the plant is given a ceremonial and ornamental use (Jiménez-Pérez et al., 2011).
Biomass is the amount of living organic matter present in the stems, leave and bark (aerial biomass), as well as in the roots (underground biomass) (Brown, 1997). In forest terms, biomass is utilized to determine the carbon content per unit of surface area and, thus, to calculate the fixing capacity of the ecosystems (Ordóñez et al., 2015).
Allometric models are tools for predicting biomass components of the plant (leaves, branches, roots, etc.) based on one or more easily measured variables (diameter, height) and thus express their mean content at the genus or species level (Avery and Burkhart, 1983; Picard et al., 2012; Gaillard et al., 2013). A production table summarizes these calculations, whose application, however, is restricted to regions with similar ecological characteristics to those of the area for which they were made (Ramos-Uvilla et al., 2014).
Several allometric models have been generated in arid zones for predicting the biomass of trees and shrubs like Prosopis glandulosa Torr. (Méndez et al., 2012), Acacia pennatula (Schltdl. & Cham.) Benth. (López-Merlín et al., 2003), Larrea tridentata (DC.) Coville (Ludwig et al., 1975), Atriplex canescens (Pursh) Nutt. var. canescens (Thomson et al., 1998), Lippia graveolens Kunth (Villavicencio et al., 2018), and in fiber producing species such as Yucca carnerosana Trel. (Villavicencio and Franco, 1992), Agave lechuguilla Torr. (Berlanga et al., 1992; Velasco et al., 2009) and Nolina cespitifera Trel. (Sáenz and Castillo, 1992), or even the weight of the stem or “cone” in Dasylirion cedrosanum Trel. (Cano et al., 2006).
Because leaves of L. parvifolia are one of the most exploited and commercialized components in arid zones, the objective of the present study was to determine the mensuration variable or variables of the plant that are directly correlated to dry leaf biomass, once the most suitable allometric model for predicting the weight of the dry leaves has been selected, and, based on it, to develop a production table that may serve to evaluate the natural Mexican bay populations existing in Saltillo municipality, Coahuila State, Mexico.
Materials and Methods
Study area
The study was carried out in Cuauhtémoc ejido, in Saltillo, Coahuila, located at 25°17'3.61" N and 100°56'57.99" W (RAN, 2018) (Figure 1). The soil type is Leptosol (Inegi, 2006a); the climate is BS1kw (semi-arid, temperate); the mean annual temperature ranges between 12 and 18 °C, and the precipitation, between 500 and 800 mm (Inegi, 2006b; Inegi, 2007; Inegi, 2008). The vegetation consists of conifer forests, rosetophile scrubs, sub-montane shrubs and grasslands (Profauna, 2008).
Sampling design and estimation of variables
According to a directed sampling, a total of 156 L. parvifolia plants were selected, considering all the categories of height and crown diameter. The measured variables were total height from ground level (H, cm), and larger (DM, from its acronym in Spanish) and smaller (Dm, from its acronym in Spanish) crown diameter, which were made with a 21601 Pretul™ professional flexometer. The mean diameter (Dp, from its acronym in Spanish) of the leaf coverage of the shrub was estimated in terms of the measurement of two perpendicular diameters (DM and Dm) of each shrub, both of which were expressed in centimeters (cm). A destructive sampling was applied, in which the stems and leaves of each selected plant were cut. The samples were kept in paper bags with their corresponding label and were subsequently dehydrated in the greenhouse of the Saltillo Experimental Station of the Instituto Nacional de Investigaciones Forestales, Agrícolas y Pecuarias, INIFAP at ambient temperature during five days, after which the stems were separated from the leaves. The dry leaf biomass (Bfs) was determined using an ADAMTM analytical scale with 0.001 g accuracy. Thus, the dependent variable was Bfs, and the independent variables, H and Dp.
Statistical analysis
The data of the dry leaf biomass and the variables height and mean diameter were analyzed using the PROC MODEL of SAS (Statistical Analysis System) software, version 9.4 (SAS, 2017), with Ordinary Least Squares (OLS) regression. Nine allometric models were fitted; these had been previously evaluated in similar studies on oregano (Villavicencio et al., 2018), lechuguilla (Velasco et al., 2009), mesquite (Méndez et al., 2012), and acacias (López-Merlín et al., 2003) (Table 1). These models provide a perfect description of the relationship between forest mensuration variables and the biomass.
Model | Name | Equation |
---|---|---|
1 | Allometric |
|
2 | Constant morphic coefficient |
|
3 | Australian |
|
4 | Combined linear variable |
|
5 | Spurr |
|
6 | Schumacher-Hall |
|
7 | Potency |
|
8 | Takata |
|
9 | Thornber |
|
Sources: Segura and Andrade (2008); Picard et al. (2012).
Bfs = Dry leaf biomass (g); Dp = Mean crown diameter (cm); H = Total height (cm); Β 0 ..., β n = Regression coefficients, Exp = Exponential of the expression.
Model selection criteria
The statistical parameters for the selection of the best model were: a higher
value of the adjusted coefficient of determination (
Where:
EMP = Percentage mean error
Y i = Observed values
Y est = Estimated values
DA = Added difference
Results and Discussion
The average dry leaf biomass of L. parvifolia per plant in the study area was 40.99 g. with a variation of 1.80 to 246.32 g, and it became evident that the morphological variation and factors such as competition determined its production (Foroughbakhch et al., 2009); furthermore, it is indicative of the productivity of the forest ecosystem as mentioned by Huff et al. (2018) (Table 2).
Variable | Average | Minimum | Maximum | DE | CV |
---|---|---|---|---|---|
H (cm) | 71.25 | 27.00 | 201.00 | 26.59 | 37.32 |
Dp (cm) | 53.54 | 16.50 | 120.50 | 22.09 | 41.26 |
Bfs (g) | 40.99 | 1.80 | 246.32 | 44.05 | 107.47 |
H = Total height; Dp = Mean diameter per crown (DM + Dm) /2; Bfs = Dry leaf biomass; DE = Standard deviation (g); CV = Coefficient of variation (%).
According to the results of the nine adjusted models: seven had a higher adj R 2 above 0.70, which indicates that the variability of the dry leaf biomass of L. parvifolia can be accounted for in 70 % by the average crown diameter and the total height of the plant. The S xy varied from 17.56 to 25.81 g, and the CV was 42.84 to 62.96 % G (Table 3). According to the selection criteria, the Schumacher-Hall model (6) was the one that best estimated the foliar biomass of L. parvifolia.
Model | Coefficient | Estimate | P value | adj R 2 | S xy | CV | QSR |
---|---|---|---|---|---|---|---|
1 | β 0 | 0.0070 | 0.062 | 0.6568 | 25.81 | 62.96 | 93243.4 |
β 1 | 1.0482 | <0.0001 | |||||
2 | β 1 | 0.0001 | <0.0001 | 0.6794 | 24.94 | 60.86 | 87731.7 |
3 | β 0 | -15.4778 | 0.0116 | 0.8391 | 17.67 | 43.11 | 43090.8 |
β 1 | 0.0119 | <0.0001 | |||||
β 2 | 0.1977 | 0.0206 | |||||
β 3 | 0.0000 | 0.4754 | |||||
4 | β 0 | 11.6173 | <0.0001 | 0.7206 | 23.28 | 56.80 | 75898.5 |
β 1 | 0.0001 | <0.0001 | |||||
5 | β 1 | 0.0039 | 0.0266 | 0.7754 | 20.95 | 51.11 | 61452.8 |
β 2 | 0.7516 | <0.0001 | |||||
6 | β 0 | 0.0029 | 0.0174 | 0.8411 | 17.56 | 42.84 | 42853.1 |
β 1 | 2.0836 | <0.0001 | |||||
β 2 | 0.2512 | 0.0006 | |||||
7 | β 0 | 0.0043 | 0.0196 | 0.8275 | 18.29 | 44.63 | 46857.4 |
β 1 | 2.2459 | <0.0001 | |||||
8 | β 0 | 3767.9430 | <0.0001 | 0.7163 | 23.46 | 57.24 | 77069.7 |
β 1 | 44.1444 | <0.0001 | |||||
9 | β 0 | 0.000138 | <0.0001 | 0.7915 | 20.1176 | 49.08 | 56660.5 |
β 1 | -0.704540 | <0.0001 |
adj R 2 = Adjusted coefficient of determination; S xy = Standard error of the model (g); CV = Coefficient of variation (%); QSR = Quadratic sum of the residuals.
Due to its simplicity and to its good fit, the Schumacher-Hall model is widely utilized to predict the volume, the carbon content (Cruz et al., 2016), and the leaf biomass in shrub taxa (Villavicencio et al., 2018). In models generated for aromatic species such as oregano (Villavicencio et al., 2018) and thyme (Belmonte and López, 2003), the variables height and diameter are also the best biomass predictors, as was the case of L. parvifolia.
The Durbin-Watson statistic (d) (2.03) with n =
142, k = 3,
|
Variable | Sxy |
|
|
Heteroskedasticity | Normality | ||
---|---|---|---|---|---|---|---|---|
|
|
|
|
|||||
|
|
17.75 | 0.8376 | 2.15 | 53.39 | <0.0001 | 0.96 | 0.0006 |
|
0.97 | |||||||
|
|
17.83 | 0.8361 | 2.25 | 55.45 | <0.0001 | 0.96 | 0.0002 |
|
0.98 | |||||||
|
|
18.82 | 0.8174 | 1.81 | 5.69 | 0.7702 | 0.95 | <0.0001 |
|
1.02 | |||||||
|
|
19.26 | 0.8089 | 1.95 | 14.81 | 0.0962 | 0.94 | <0.0001 |
|
1.02 | |||||||
|
|
17.63 | 0.8399 | 2.19 | 61.28 | <0.0001 | 0.96 | 0.0002 |
|
2.01 | |||||||
|
|
18.04 | 0.8324 | 2.19 | 40.90 | <0.0001 | 0.96 | 0.0008 |
|
0.23 | |||||||
|
|
18.42 | 0.8252 | 2.03 | 16.20 | 0.0629 | 0.97 | 0.0011 |
|
0.03 | |||||||
|
|
17.79 | 0.8368 | 2.22 | 54.88 | <0.0001 | 0.96 | 0.0004 |
|
0.98 | |||||||
|
|
19.23 | 0.8094 | 1.87 | 6.42 | 0.6977 | 0.94 | <0.0001 |
|
1.02 |
F.P. = Weighting factor; Dp c = Average diameter of the leaf coverage of the shrub; H = Total height; c and k = parameters of the variance model; Resid. = Residuals; Bfs = Dry leaf biomass.
Weighted regression with variance structure
In order to correct the heteroskedasticity of the Schumacher-Hall model,
several weighting factors were tested according to Álvarez-González (2007), Gómez-García (2013), and Pedrosa
et al., (2015); the variables
Dp and H were utilized as a weighting
factor (
Biomasa foliar seca estimada = Estimated dry leaf biomass; Residuales = Residuals; Diámetro promedio = Mean diameter; Observados = Observed; Predichos = Predicted.
Differences were observed between the predicted weighted and unweighted values, in absolute (i.e. observed minus predicted) terms. The weighted values overestimate the dry leaf biomass by 9.5 g, while the unweighted ones overestimate it only by 6.3 g, less than 0.10 % of the total. Nevertheless, fulfillment of the assumptions of the regression models (for the weighted model) is preferable, as it ensures efficient predictions. Because the Schumacher-Hall model corrects the heteroskedasticity completely and is statistically reliable (P < 0.0001), it can be utilized to predict the production of L. parvifolia dry leaf biomass.
The corrected goodness-of-fit statistics were: adj R 2 = 0.8252, estimation error = 18.42 g (Table 4), and statistical significance in all the parameters (P ≤ 0.05). These results adjust to the requirements of Picard et al. (2012) for the selection of a model; furthermore, they are within the interval cited by Návar et al. (2002) and Návar et al. (2004) for 18 shrub species of the Tamaulipan shrub, where leaf biomass prediction models with R 2 = 0.56 to 0.93, error = 0.026 to 0.396 kg, and C. V. = 14 to 81 % were generated. Similar values have also been documented for shrub taxa used as forage, as firewood, and for medicinal purposes, in which R 2 varies between 0.45 and 0.99 (Foroughbakhch et al., 2005; Foroughbakhch et al., 2009). Huff et al. (2018) register a S xy of 33.2 to 441.9 g for shrubs. In most cases, the diameter and coverage were the independent variables utilized for predicting the production of leaf biomass; in the present study, the heterosedasticity was corrected by including the height variable.
In the face of the lack of normality and the presence of heterosedasticity,
as in the case of L. parvifolia, authors like Gómez-García (2013) carried out a
weighted regression with a variance model, based on the diameter, the height (
Model for predecting Litsea parvifolia (Hemsl.) Mez. dry leaf biomass
Unweighted Schumacher-Hall model:
Schumacher-Hall model corrected by a weighting factor:
The results evidenced an added difference (DA) of 0.06 g of average error in the estimation of the dry leaf biomass per plant, with a mean percentage error (EMP) of 0.16 %. According to Prodan et al. (1997), an EMP of less than 1 % ensures the validity of the model; thus, the Schumacher-Hall model is adequate for the interval of observed values, and it is statistically effective for predicting the dry leaf biomass of L. parvifolia.
A double-entry table with an operation interval is 5 to 120 cm for both independent variables (H and Dp) based on the selected variables in the Schumaher-Hall model. Within this model, there are intervals every 5 cm in which the dry leaf biomass (Bfs) (g) of the standing L. parvifolia plants can be predicted (Table 5). This prediction table facilitates the quantification in the field and is easy to use.
Diameter (cm) | Height (cm) | |||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 | 65 | 70 | 75 | 80 | 85 | 90 | 95 | 100 | 105 | 110 | 115 | 120 | |
5 | 0.1 | 0.1 | 0.1 | 0.2 | 0.2 | |||||||||||||||||||
10 | 0.3 | 0.5 | 0.5 | 0.6 | 0.7 | 0.8 | ||||||||||||||||||
15 | 0.7 | 1.0 | 1.2 | 1.4 | 1.6 | 1.7 | ||||||||||||||||||
20 | 2.2 | 2.5 | 2.8 | 3.1 | 3.3 | 3.5 | ||||||||||||||||||
25 | 3.9 | 4.4 | 4.8 | 5.2 | 5.5 | 5.9 | ||||||||||||||||||
30 | 6.3 | 6.9 | 7.5 | 8.0 | 8.4 | 8.9 | 9.3 | 9.7 | 10.1 | |||||||||||||||
35 | 9.4 | 10.1 | 10.8 | 11.5 | 12.1 | 12.7 | 13.2 | 13.8 | 14.3 | 14.8 | 15.2 | |||||||||||||
40 | 12.3 | 13.2 | 14.1 | 15.0 | 15.8 | 16.5 | 17.3 | 17.9 | 18.6 | 19.3 | 19.9 | 20.5 | 21.1 | |||||||||||
45 | 15.5 | 16.7 | 17.9 | 18.9 | 19.9 | 20.9 | 21.8 | 22.7 | 23.5 | 24.4 | 25.1 | 25.9 | 26.6 | 27.4 | 28.1 | |||||||||
50 | 20.6 | 22.1 | 23.4 | 24.6 | 25.8 | 26.9 | 28.0 | 29.0 | 30.1 | 31.0 | 32.0 | 32.9 | 33.8 | 34.6 | 35.5 | 36.3 | 37.1 | 37.9 | ||||||
55 | 25.0 | 26.7 | 28.3 | 29.8 | 31.2 | 32.6 | 33.9 | 35.1 | 36.3 | 37.5 | 38.7 | 39.8 | 40.8 | 41.9 | 42.9 | 43.9 | 44.9 | 45.8 | ||||||
60 | 31.7 | 33.6 | 35.4 | 37.1 | 38.7 | 40.3 | 41.8 | 43.2 | 44.6 | 46.0 | 47.3 | 48.6 | 49.8 | 51.0 | 52.2 | 53.3 | 54.5 | |||||||
65 | 39.4 | 41.5 | 43.5 | 45.4 | 47.3 | 49.0 | 50.7 | 52.3 | 53.9 | 55.5 | 57.0 | 58.4 | 59.8 | 61.2 | 62.6 | 63.9 | ||||||||
70 | 45.7 | 48.1 | 50.5 | 52.7 | 54.8 | 56.8 | 58.8 | 60.7 | 62.5 | 64.3 | 66.0 | 67.7 | 69.4 | 71.0 | 72.5 | 74.1 | ||||||||
75 | 52.4 | 55.2 | 57.9 | 60.4 | 62.9 | 65.2 | 67.4 | 69.6 | 71.7 | 73.8 | 75.8 | 77.7 | 79.6 | 81.4 | 83.2 | 85.0 | ||||||||
80 | 59.7 | 62.8 | 65.8 | 68.7 | 71.5 | 74.1 | 76.7 | 79.2 | 81.6 | 83.9 | 86.2 | 88.4 | 90.5 | 92.6 | 94.7 | 96.7 | ||||||||
85 | 70.9 | 74.3 | 77.6 | 80.7 | 83.7 | 86.6 | 89.4 | 92.1 | 94.7 | 97.2 | 99.7 | 102.2 | 104.5 | 106.8 | 109.1 | |||||||||
90 | 83.3 | 86.9 | 90.4 | 93.8 | 97.0 | 100.1 | 103.2 | 106.1 | 109.0 | 111.8 | 114.5 | 117.1 | 119.7 | 122.3 | ||||||||||
95 | 96.8 | 100.7 | 104.4 | 108.1 | 111.5 | 114.9 | 118.2 | 121.4 | 124.5 | 127.5 | 130.5 | 133.4 | 136.2 | |||||||||||
100 | 115.7 | 119.7 | 123.6 | 127.3 | 130.9 | 134.5 | 137.9 | 141.3 | 144.5 | 147.7 | 150.9 | |||||||||||||
105 | 136.2 | 140.3 | 144.3 | 148.2 | 152.0 | 155.7 | 159.3 | 162.8 | 166.3 | |||||||||||||||
110 | 153.9 | 158.3 | 162.6 | 166.8 | 170.8 | 174.8 | 178.6 | 182.4 | ||||||||||||||||
115 | 177.7 | 182.2 | 186.6 | 191.0 | 195.2 | 199.3 | ||||||||||||||||||
120 | 198.4 | 203.2 | 207.9 | 212.5 | 217.0 |
Conclusions
The Schumacher-Hall model is the one that best predicts the dry leaf biomass of the standing Litsea parvifolia (Hemsl.) Mez. bushes, based on simple measurements of variables as the mean diameter of the crown and total height of the bush. The double-entry prediction table generated can be applied in areas where plants of this species occur with structures of similar diameter, height and climate conditions to those observed in this study.
Acknowledgements
The authors wish to thank the Conafor-Conacyt Sectoral Fund for its support to the project registered with the SIGI number 13271734312 titled: “Development and implementation of two processing systems for a) the extraction of essential oils and b) the extraction of ixtle fiber: generation of high quality products”. To the Saltillo CIRNE-INIFAP Experimental Station for the complementary support for the realization of the said project, and to the Universidad Autónoma Agraria Antonio Narro for facilitating the training of human resources.
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Received: August 12, 2019; Accepted: January 29, 2020