Equations to estimate aerial biomass of candelilla (Euphorbia antisyphilitica Zucc.) in Chihuahua

Maldonado-Ortiz, Margarito; López-Serrano, Pablito Marcelo; Valdez-Cepeda, Ricardo D.; Mata-González, Ricardo; García-González, Fabián; Martínez-Salvador, Martín; Maldonado-Ortiz, Margarito; López-Serrano, Pablito Marcelo; Valdez-Cepeda, Ricardo D.; Mata-González, Ricardo; García-González, Fabián; Martínez-Salvador, Martín

doi:10.29298/rmcf.v13i72.1231

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Revista mexicana de ciencias forestales

versión impresa ISSN 2007-1132

Rev. mex. de cienc. forestales vol.13 no.72 México jul./ago. 2022 Epub 22-Ago-2022

https://doi.org/10.29298/rmcf.v13i72.1231

Scientific article

Equations to estimate aerial biomass of candelilla (Euphorbia antisyphilitica Zucc.) in Chihuahua

Margarito Maldonado-Ortiz¹

Pablito Marcelo López-Serrano²
http://orcid.org/0000-0003-0640-0606

Ricardo D. Valdez-Cepeda¹
http://orcid.org/0000-0002-6990-3502

Ricardo Mata-González³
http://orcid.org/0000-0003-2053-7027

Fabián García-González¹

Martín Martínez-Salvador⁴^*
http://orcid.org/0000-0002-2679-5070

^¹Unidad Regional Universitaria de Zonas Áridas, Universidad Autónoma Chapingo. México.

^²Falcultad de Ciencias Forestales, Universidad Juárez del Estado de Durango. México.

^³Department of Animal and Rangeland Sciences, Oregon State University. USA.

^⁴Facultad de Zootecnia y Ecología, Universidad Autónoma de Chihuahua. México.

Abstract

Candelilla (Euphorbia antisyphilitica Zucc.) is a shrub that grows in the arid zones of northern Mexico. This species is harvested for the purpose of extracting a wax that it produces in response to water stress. In order to authorize the harvesting of plants, it is necessary to estimate their biomass indirectly through predictive equations. The objective of this study was to generate allometric equations to estimate the biomass of candelilla based on morphometric variables. The work was carried out in the region of Aldama and Coyame del Sotol in northeastern Chihuahua, Mexico. A selective and destructive sampling of 198 individuals of candelilla was applied, which were obtained in ejidos with forest management programs in force. Four models and different combinations of biomass predictor variables were tested to fit the best equation. Variables were transformed to logarithmic scale. The Schumacher and Hall model was selected in the logarithmic form determined by the crown diameter and base diameter of the plant, since it exhibited the best statistical adjustments (R ² _adj =0.83), as well as by the root mean square of the error (RMSE=0.042), and the model parameters were significant (p<0.0001) in their correction of the regression assumptions. The equation thus obtained is reliable for estimating the biomass of candelilla in the northeastern state of Chihuahua, Mexico.

Key words Shrub biomass; Candelilla wax; allometric equations; models; biomass prediction; arid zones

Resumen

La candelilla (Euphorbia antisyphilitica) es un arbusto que crece en las zonas áridas del norte de México. Esta especie se cosecha para extraer una cera que produce como respuesta al estrés hídrico. Para autorizar la recolección de las plantas, es necesario realizar estimaciones indirectas mediante ecuaciones predictivas de su biomasa. El objetivo del presente estudio fue generar ecuaciones alométricas para estimar biomasa de candelilla a partir de variables morfométricas. El trabajo se llevó a cabo en la región de Aldama y Coyame del Sotol en el noreste de Chihuahua, México. Se aplicó un muestro selectivo y destructivo de 198 individuos de candelilla, los cuales se obtuvieron en ejidos con programas de manejo forestal vigente. Para ajustar la mejor ecuación se probaron cuatro modelos y diferentes combinaciones de variables predictoras de biomasa. Las variables se transformaron a escala logarítmica. Se seleccionó el modelo de Schumacher y Hall en la forma logarítmica con el uso del diámetro de copa y diámetro de la base de la planta, ya que fue el que presentó los mejores ajustes estadísticos (R ² _adj =0.83), la raíz del cuadrado medio del error (RCME=0.042), y los parámetros del modelo fueron significativos (p<0.0001) en su corrección de los supuestos de regresión. La ecuación obtenida es confiable para estimar biomasa de candelilla en el noreste del estado de Chihuahua, México.

Palabras clave Biomasa de arbustos; cera de candelilla; ecuaciones alométricas; modelos; predicción de biomasa; zonas áridas

Introduction

Candelilla (Euphorbia antisyphilitica Zucc.) reproduces by rhizomes, forming clusters of stems in patches of plants that grow in the semi-desert of northern Mexico (^{Arato
et al., 2014}). As a mechanism to tolerate water deficit, this species produces a natural wax which is harvested for commercialization in national and international markets (^{Rojas et al., 2011}; ^{Muñoz-Ruiz et al., 2016}).

In Mexico, candelilla harvesting is carried out mainly by inhabitants of villages in the arid zones of the states of San Luis Potosí, Zacatecas, Coahuila and Chihuahua (^{Villa-Castorena
et al., 2010}; ^{Becerra-López et al., 2020}). Extraction procedures, biomass estimation, harvesting intensities, and regeneration of the taxon have been studied for conservation and management purposes, since alterations in its distribution and abundance are caused by inappropriate use and by the influence of climate change (^{Vargas-Piedra et
al., 2020}).

The generation of allometric equations to estimate biomass or volumes is a widely studied topic for tree species in temperate and tropical forests, not only in Mexico, but also internationally (^{Vargas-Larreta
et al., 2017}; ^{Martínez-Domínguez et al., 2020}; ^{Martínez-Sánchez et al.,
2020}). However, in shrub taxa and plants from semi-arid zones, the generation of these equations is little studied, even for species that are commercially exploited (^{Flores-Hernández
et al., 2020}; ^{Villavicencio-Gutierrez et al., 2020}). In addition, it is necessary to develop them at the level of ecological regions, due to the wide variation of environmental conditions in which the semi-desert taxa grow; such is the case of candelilla (^{Hernández-Ramos et al., 2019}; ^{Luo et al., 2020}; ^{Vargas-Piedra et al., 2020}).

Prominent among the published works related to equations for estimating candelilla biomass ―generated from data of average plant height and crown diameters― are those produced for certain regions in the state of Coahuila (^{Flores del Angel,
2013}). Recently, ^{Hernández-Ramos
et al. (2019)} have documented equations for some municipalities in the state of Coahuila with acceptable adjustments in the statistical estimators, allowing reliable estimation of the biomass of the species in these regions; however, there are no scientifically valid equations for Chihuahua.

The objective of this study was to generate allometric equations to estimate total biomass using morphometric variables of Euphorbia antisyphylitica for the region of Aldama and Coyame del Sotol in northeastern Chihuahua, Mexico.

Materials and Methods

Study area

The research was carried out in Coyame del Sotol and Aldama municipalities in the state of Chihuahua, Mexico (Figure 1). The predominant shrub vegetation is composed of desert microphyllous and rosetophytic shrubs, with a predominance of Euphorbia antisyphilitica, Agave lechuguilla Torr., Larrea tridentata DC. Coville, and Dasylirion sp. (^{Granados-Sánchez et al.,
2011}). The altimetric altitudes of the area range between 940 and 1 500 m; the average annual rainfall is 200 to 400 mm and the average annual temperature is 24 °C (Granados-Sánchez et al., 2011; ^{González-Medrano,
2012}).

Figure 1 Location of the study area in the municipalities of Aldama and Coyame del Sotol in the state of Chihuahua, Mexico.

Data collection

The data were collected in ejidos and communities with currently valid technical studies on the use of candelilla (Table 1). For this work, the term "plant" is understood as a compact colony of catkins growing in independent patches, with at least 20 cm of separation between the bases of the colonies. Individuals were selected according to their health and size characteristics; diseased or sparse plants were avoided. Samples were obtained considering the variability of growth conditions that exist in plant populations. A destructive measurement procedure was carried out on 198 plants, distributed among seven ejidos with forest harvesting permits for candelilla. Morphometric variables were measured for each specimen: mean total height (Mth), average height of the tips of the shrub’s crown, without considering the central height of the plant, which is usually higher; total height (Th), total height of the plant including the longest stem of the central portion of the crown; base diameter (Bd), diameter of the base of the plant measured 10 cm above the soil surface; crown diameter (Cd), average of the smallest and largest diameter of the crown width measured perpendicularly in north-south and east-west directions. Subsequently, each plant was extracted to obtain the weight of total green biomass (kg) including the root (^{Villavicencio-Gutiérrez et
al., 2018}).

Table 1 Distribution of samples of Euphorbia antisyphilitica Zucc. populations in the study area.

Municipality	Plots	Samples
Aldama	Chorreras	92
Coyame del Sotol	Cañón de Barrera	58
	El Táscate	19
	Francisco Portillo	6
	San Pedro	23
Total		198

Database

In the laboratory, the mean crown diameter (Cd) and crown cover (Cc) variables were estimated, the latter was calculated as the surface area of a circle with the mean crown diameter.

Descriptive summary of variables

Table 2 shows that the biomass of candelilla plants ranged from 0.09 to 12.89 kg per plant. The wide range in the size of the sampled plants was also observed, which allowed the use of the resulting equation for most of the plant sizes to be found in the field.

Table 2 Statistical summary of Euphorbia antisyphilitica Zucc. in the municipalities of Coyame del Sotol and Aldama, state of Chihuahua.

Variable	n	Minimum	Maximum	Mean	SD	CV (%)
Bd (cm)	198	7	91.00	29.20	18.41	63.05
Th (cm)	198	17	105.00	46.43	15.33	33.02
Mth (cm)	198	10	80.00	30.00	11.05	36.83
Cd (cm)	198	14.5	147.50	50.53	25.88	51.22
Cc (m²)	198	0.02	1.71	0.25	0.27	108.00
Biomass(kg)	198	0.09	12.89	1.85	2.33	125.95

Bd = Base diameter; Th = Total height; Mth = Mean height; Cd = Crown diameter; Cc = Crown cover; n = Sample size; SD = Standard deviation; CV = Coefficient of variation.

Selection of predictor variables

Pearson's correlation test was performed including all variables in order to determine their relationship with plant biomass. The purpose is to identify the variables correlated with biomass and the predictor variables. Distribution plots were used to visualize the relationship between the dependent variable (biomass) and the independent variables (crown diameter, base diameter, crown cover and height) (Figures 2 and 3).

Figure 2 Correlation test of morphometric variables and candelilla biomass.

Figure 3 Relationship of biomass with predictor variables of Euphorbia antisyphilitica Zucc.

Model selection

Equations with flexibility criteria with different combinations of variables were selected for the purpose of determining the biomass of E. antisyphilitica (Table 3). These equations have allowed good biomass predictions for several forest species (^{Návar, 2010}; ^{Noulèkoun et al.,
2018}; ^{Altanzagas et
al., 2019}). In the allometric biomass studies, error variances for nonlinear equations based on arithmetic units are not constant (heteroscedasticity) for all observations (^{Chave et al., 2005}). This issue can be addressed by means of logarithmic transformations, which are one of the most widely used methods for reducing the influence of errors (^{Moussa and Mahamene, 2018}; ^{Zhao et al., 2018}). Consequently, logarithmic equations were used to estimate the candelilla’s biomass (Table 3). Allometric equations in their logarithmic form, the predictions lead to a systematic bias; in order to minimize this, the correction factor (CF) was calculated for each model (^{Sprugel, 1983}).

Table 3 Proposed logarithmic equations for determining the biomass of Euphorbia antisyphilitica Zucc.

Eq.	Logarithmic equation	Original equation	Type
1.1	ln(B)=ln⁡(B0)+(B1) ln(Dc)	B=β0DcB1	Allometric
1.2	ln(B)=ln⁡(B0)+(B1) ln(Ca)	B=β0CaB1	Allometric
1.3	ln(B)=ln⁡(B0)+(B1) ln(Db)	B=β0DbB1	Allometric
2.1	ln(B)=ln⁡(B0)+B1 ln(Db)+B2 ln(At)	B=β0DbB1 AtB2	Schumacher and Hall
2.2	ln(B)=ln⁡(B0)+B1 ln(Dc)+B2 ln(Db)	B=β0DcB1 DbB2	Schumacher and Hall
2.3	ln(B)=ln⁡(B0)+B1 ln(Db)+B2 ln(Atm)	B=β0DbB1 AtmB2	Schumacher and Hall
3.1	ln(B)=ln⁡(B0)+(B1) ln(Dc2*At)	B=β0(Dc2*At)B1	Spurr
3.2	ln(B)=ln⁡(B0)+(B1) ln(Dc2*Db)	B=β0(Dc2*Db)B1	Spurr
3.3	ln(B)=ln⁡(B0)+(B1) ln(Db2*Dc)	B=β0(Db2*Dc)B1	Spurr
4.1	ln(B)=ln⁡(B0)+(B1) ln(At*Ca)	B=β0(At*Ca)B1	Spurr
4.2	ln(B)=ln⁡(B0)+(B1) ln(Dc*Db)	B=β0(Dc*Db)β1	Spurr

Fuente: ^{Návar, 2010}; ^{Noulèkoun et
al., 2018}; ^{Altanzagas et al.,
2019}.

Eq = Equation; B = Biomass; B0, B1 and B2 = Model parameters; nl = Natural logarithm.

CF=exp⁡SEest22

Where:

CF = Correction factor

SEest = Standard error of estimation

exp = Exponential function

Statistical analysis

The models were fitted using the Ordinary Least Squares method (OLS) (^{Montgomery et al.,
2021}). The selection of the model was based on equation-fitting criteria, specifically the significance of the parameters (p≤0.05). In addition, the evaluation of the equations considered the adjusted coefficient of determination (R ² _adj ), the root mean square error (RMSE), the Akaike information criterion (AIC), the Bayesian information criterion (BIC), and the mean absolute percentage error (MAPE) (^{Picard
et al., 2015}; ^{Islam et al., 2021}). Subsequently, in order to validate the equations, the assumptions of the regressions were verified according to their predictions; normality was verified with the Lilierfors test, while compliance with homoscedasticity was evaluated with the Breusch-Pagan test (^{Villavicencio-Gutiérrez et al., 2018}; ^{Flores-Hernández et al.,
2020}; ^{Villavicencio-Gutierrez
et al., 2020}). The autocorrelation correction was performed using the cochrane.orcutt method (^{Kutner et al., 2005}) with the orcutt library of R Project, which provides for a continuous-time autoregressive model (^{Quiñonez-Barraza
et al., 2015}). Finally, the variance inflation factor (VIF) was used to detect multicollinearity (^{Mahmood et al.,
2019}). All statistical and graphical analyses were performed with the lm and plot functions in the R Project software (^{R Core Team, 2021}).

Results

Basic statistics of the morphometric variables

The result of the Pearson correlation analysis shows that the variables that registered the highest correlation with biomass were crown cover (r=0.86), crown diameter (r=0.85) and base diameter (r=0.80) (Figure 2). However, in the linear regression analysis, all selected variables were used to obtain the best fits.

Biomass equations

The estimated parameters were significantly different from zero at a significance level of 5 % (p<0.0001). The fit statistics (R ² _adj , RMSE, AIC and BIC) exhibited similar values in the different equations (Table 4). In keeping with the selection criteria, Equations 2.2 and 3.2 were selected to estimate the biomass, given that they both had the highest R ² _adj (0.84) and registered the lowest values for the RMSE, AIC and BIC. The regression assumptions were verified; the Lillierfos test showed normality of the residuals, while the Lillierfos test showed normality of the residuals: D=0.047, p value=0.345 and D=0.039, p value=0.0641 for equations 2.2 and 3.2, respectively (Table 5). The Breusch-Pagan test showed a slight presence of heteroscedasticity: BP=9.180, p value=0.050 and BP=8.697, p value=0.003, for equations 2.2 and 3.2, respectively. The Durbin-Watson test was 1.34 for the two equations, indicating that there was some consideration of autocorrelation between the variables. In view of this evidence, the equations were corrected in order to obtain reliable estimates in the prediction of the candelilla’s biomass (Table 5).

Table 4 Estimated parameter values and their goodness-of-fit statistics of the logarithmic equations for predicting biomass in Euphorbia antisyphilitica Zucc.

Equation	Parameter	Estimator	Standard error	t value	p value	Variable	R ² _adj	RMSE	AIC	BIC	CF
1.1	B1	-8.12	0.27	-30.05	0.0001	Cd	0.82	0.47	268.38	278.25	1.12
	B2	2.13	0.07	30.29	0.0001
1.2	B1	1.96	0.07	26.91	0.0001	Cc	0.82	0.47	268.38	278.25	1.12
	B2	1.06	0.03	30.29	0.0001
1.3	B1	-5.19	0.20	-25.01	0.0001	Bd	0.77	0.54	323.30	333.17	1.16
	B2	1.62	0.06	25.45	0.0001
2.1	B1	-7.04	0.41	-16.803	0.0001	Bd, Th	0.79	0.51	301.59	314.74	1.14
	B2	1.45	0.06	20.752	0.0001
	B3	0.63	0.12	4.981	0.0001
2.2*	B1	-7.46	0.28	-25.741	0.0001	Cd, Bd	0.84	0.45	247.66	260.81	1.10
	B2	1.46	0.15	9.676	0.0001
	B3	0.58	0.12	4.87	0.0001
2.3	B1	-6.66	0.35	-18.643	0.0001	Bd, Mth	0.79	0.51	302.22	315.37	1.14
	B2	1.42	0.07	19.427	0.0001
	B3	0.62	0.12	4.911	0.0001
3.1	B1	-9.58	0.35	-27.32	0.0001	Cd ² *Th	0.79	0.51	299.75	309.61	1.14
	B2	0.84	0.03	27.47	0.0001
3.2*	B1	-7.32	0.22	-32.39	0.0001	Cd ² *Bd	0.84	0.45	246.28	256.15	1.10
	B2	0.677	0.02	32.39	0.0001
3.3	B1	-6.26	0.21	-29.21	0.0001	Bd ² *Cd	0.82	0.48	275.91	285.78	1.12
	B2	0.614	0.02	29.60	0.0001
4.1	B1	-1.63	0.06	-23.45	0.0001	Th*Cc	0.79	0.51	299.75	309.61	1.14
	B2	0.84	0.03	27.4	0.0001
4.2	B1	-6.80	0.21	-31.04	0.0001	Cd*Bd	0.83	0.46	256.67	266.53	1.11
	B2	0.97	0.03	31.39	0.0001

R² _adj = Adjusted coefficient of determination; RMSE = Root mean square error; AIC = Akaike information criteria; BIC = Bayesian information criterion; CF = Correction factor; Bd = Base diameter; Cd = Crown diameter; Th = Total height; Mth = Mean height; Cc = Crown cover; * = Selected model.

Table 5 Assumptions of normality, heteroscedasticity, and inflation value of the equations tested.

Equation	Lilierfors	p value	Breusch Pagan	p value	Durbin Watson	VIF
1.1	0.042	0.521	9.227	0.002	1.350
1.2	0.042	0.521	9.227	0.002	1.357
1.3	0.039	0.632	1.102	0.293	1.299
2.1	0.042	0.507	3.181	0.203	1.193	1.342
2.2	0.047	0.345	9.180	0.050	1.346	5.186
2.3	0.031	0.900	1.728	0.410	1.260	1.469
3.1	0.040	0.581	5.910	0.015	1.028
3.2	0.039	0.641	8.697	0.003	1.340
3.3	0.030	0.910	4.027	0.044	1.308
4.1	0.040	0.580	5.910	0.015	1.028
4.2	0.042	0.510	6.448	0.011	1.322

The correction was performed with the Cochrane Orcutt test. Correcting for autocorrelation led to reliable estimates for biomass prediction (Table 6). Durbin-Watson test increased 2.19 for the two selected equations. The Breusch-Pagan test indicated the absence of heteroscedasticity: BP=3.689, p value=0.15 and BP=3.286, p value= 0.47 for Equations 2.2 and 3.2, respectively.

Table 6 Estimates obtained by correcting the autocorrelation and heteroscedasticity of equations 2.2 and 3.2.

Equation	Parameter	Estimator	Standard error	t value	p value	R ² _adj	RMSE	CF
2.2	B1	-7.03	0.27	-25.157	0.0001	0.83	0.42	1.09
	B2	1.36	0.14	9.484	0.0001
	B3	0.57	0.11	4.897	0.0001
3.2	B1	-6.93	0.23	-30.134	0.0001	0.83	0.42	1.09
	B2	0.64	0.02	30.814	0.0001

R²_adj = Adjusted coefficient of determination; RMSE = Root mean square error; CF = correction factor.

The predictive capacity of model 2.2 showed a mean absolute percentage error of 3.6 %, and of 3.8 % for equation 3.2. Thus, the analyzed criteria favor Equations 2.2 for estimating the green biomass of candelilla. The estimates obtained are alternatives for predicting candelilla biomass using the inverse transformation to a logarithmic scale; therefore, we suggest using the following equation for the estimation of the biomass of in the study region:

B=exp⁡-7.03+1.36*nlCd+0.57*nlBd* 1.15 Eq. 2.2

Where:

B = Biomass (kg)

nl = Natural logarithm

exp = Exponential function

Cd = Crown diameter (cm)

Bd = Base diameter (cm).

Discussion

The independent variables of candelilla plants showed a good correlation with biomass, mainly crown cover, crown diameter and base diameter. Total height and average height exhibited a weaker relationship. In this regard, it should be noted that, unlike in most tree species, whose biomass and volume prediction is made with data on the height and diameter of individuals, in shrub taxa there are other predictor variables that depend on the shape of the plant.

For example, ^{Pando-Moreno et al.
(2004)} tested several variables for predicting the biomass of lechuguilla (Agave lechuguilla Torr.) and determined that bud volume, as an independent variable, had a higher correlation coefficient than bud biomass. For their part, ^{Villavicencio-Gutierrez et al. (2018)} identified a reliable relationship between the average crown diameter and the base diameter with the biomass of Lippia graveolens Kunth in arid zones, using the Schumacher and Hall equation. It stands out that, in shrub species with irregular shapes, avoiding multicollinearity and performing an analysis of variables is more necessary in order to obtain those that best predict the biomass (^{Daryanto et al.,
2013}; ^{Dai et al.,
2020}).

In this study, allometric equations using the variables crown diameter and base diameter led to a more accurate estimation of the biomass of candelilla. These equations had a low RMSE (0.42) and a statistically acceptable R² _adj (0.82) (p<0.0001). In this regard, some studies indicate that crown diameter is a reliable variable for estimating shrub biomass in arid and semi-arid zones (^{Ali
et al., 2015}; ^{Sione et al., 2019}; ^{Aranha et al., 2020}; ^{Chieppa et al., 2020}).

The prediction of the biomass or volume of shrub species usually presents acceptable values. However, test statistics commonly present lower values than the prediction of the biomass of tree taxa, especially of conifers, which generally maintain conical and solid shapes, as opposed to shrubs, which are highly branched and not very uniform (^{Pando-Moreno et al., 2004}; ^{Zhang et al., 2016}; ^{Vargas-Larreta et al., 2017}; ^{Yao et al., 2021} ). In this sense, the present study was no exception, since the maximum values of the coefficient of determination (R ² _adj ) were 0.84, compared to the model equations for tree species, whose coefficients are generally above 0.90 (^{Vargas-Larreta et al., 2017}).

In the documented case of candelilla, the model of Schumacher and Hall (Equations 2.2) in its logarithmic form predicted a candelilla biomass with statistically acceptable coefficients. The general forms of these equations have been used in other research studies in arid and semi-arid environments (^{Návar et al., 2004}; ^{Flores-Hernández et al.,
2020}), its effectiveness is ratified. In addition, it is important to note that the crown and base diameters of the shrubs are easy to measure in candelilla, which grows in colonies or small groups of stems forming wide patches from the base (^{Flores-del Angel et al., 2013}; ^{Bañuelos-Revilla et al.,
2019}). Finally, the estimates obtained can be used to calculate the areal biomass of E. antisyphilitica for the arid zones of the state of Chihuahua.

Conclusions

The allometric equation of Schumacher and Hall in its logarithmic form can be used to estimate the biomass of Euphorbia antisyphilitica in the northeastern region of Chihuahua. The selected equation includes easily measured morphometric variables such as the crown variable and the base diameter of the plants.

The models tested in this study are recommended for estimating the green biomass of candelilla, which is required in technical studies and management programs of the species in Aldama and Coyame del Sotol municipalities in northeastern Chihuahua, Mexico.

Acknowledgments

The authors would like to thank the Conacyt-Conafor sectorial fund for financing the project "Best practices and generation of volume and biomass tables for the main non-timber forest species of economic importance in arid and semi-arid ecosystems of Mexico".

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Received: May 12, 2021; Accepted: March 31, 2022

^{Conflict of interest}

The authors declare no conflict of interest with any person or institution.

^{Contributions by author}

Margarito Maldonado Ortiz and Martín Martínez Salvador: data processing and analysis, planning and drafting of manuscript; Pablito Marcelo López Serrano: overall project coordination and information storage support; Ricardo D. Valdez Cepeda: data analysis; Ricardo Mata González: review and editing of the contribution; Fabián García González: review and editing of the manuscript.

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