Biomass and fiber yield tables were generated obtained from the bud of Agave lechuguilla at northern Zacatecas, Mexico. Regression models were evaluated to estimate green weight (pv, g) and dry weight of fiber (ps, g) by plant, respectively. The method of quadrants centered on a point was used as sampling to obtain information at 74 sites randomly located. In each plant it was measured, the smallest diameter (smd, cm), the largest aerial diameter (lad, cm), bud height (h, cm), pv (g) and ps (g). 296 buds were collected and they were manually carved to obtain the fiber, which was sun-dried in for 3-5 h. The average pv was 287.2 g bud^-1, ps 19.1 g bud^-1, average density was 2 149 plants ha^-1. The correlation showed high statistical significance (P<0.01) for pv with lad (R=0.968) and ps with h (R²=0.945). The model pv=21.920(1.054)^hwas selected to estimate the green biomass performance table for presenting better adjustment statistics (R²_aj=0.960, RCME=0.095, CV=1.688 %, Cp=2.002, │PRESS│=0.012 and PRESS=0.0001). For the fiber dry weight the selected model was ps=0.0003(h)^2.812 (R²_aj=0.921, RCME=0.164, CV=5.708 %, Cp=2.004, │PRESS│=0.123 y PRESS=0.015). The statistical criteria used gave certainty in the selection of models to generate biomass and fiber yield tables in the study area.

Keywords: Agave lechuguilla Torr., plant density, ixtle, lechuguilla, allometric model, biomass and fiber yield table.

Se generaron tablas de rendimiento de biomasa y fibra del cogollo de Agave lechuguilla en el norte de Zacatecas, México. Se evaluaron modelos de regresión para estimar el peso verde (pv, g) y peso seco de fibra (ps, g) por planta, respectivamente. Se utilizó el método de muestreo de cuadrantes centrados en un punto para obtener información en 74 sitios ubicados al azar. En cada planta se midió el diámetro menor (dme, cm), el diámetro aéreo mayor (dma, cm), la altura del cogollo (h, cm), pv (g) y ps (g). Se recolectaron 296 cogollos, se tallaron manualmente para obtener la fibra y se secaron al sol por 3–5 horas. El pv promedio fue de 287.2 g cogollo^-1, el de ps de 19.1 g cogollo^-1 y la densidad promedio de 2 149 plantas ha^-1. La correlación mostró alta significancia estadística (P<0.01) para pv con dma (R=0.968) y ps con h (R=0.945). Se seleccionó el modelo pv=21.920(1.054)^h para estimar la tabla de rendimiento de biomasa verde por presentar mejores estadísticos de ajuste (R²_aj=0.960, RCME=0.095, CV=1.688 %, Cp=2.002, │PRESS│=0.012 y PRESS=0.0001). Para el peso seco de fibra se seleccionó el modelo ps=0.0003(h)^2.812 (R²_aj=0.921, RCME=0.164, CV=5.708 %, Cp=2.004, │PRESS│=0.123 y PRESS=0.015). Los criterios estadísticos utilizados dieron certidumbre en la selección de los modelos para generar tablas de rendimiento de biomasa y fibra en el área de estudio.

Palabras clave: Agave lechuguilla Torr., densidad de plantas, ixtle, lechuguilla, modelo alométrico, tabla de rendimiento de biomasa y fibra.

An economic activity carried out by the inhabitants of arid and semi-arid areas of Mexico is the use of natural resources, which provide raw materials, goods and additional services to satisfy their needs (Martínez, 2013). Non-woody products are known as non-timber forest resources, which would be, for example, lichens, mosses, fungi, resins, gums, seeds, fibers, waxes, rhizomes, leaves, stalks, stems; including also the soils of many wild lands; their harvest amounts to 32% of the country's production (Chandrasekharan et al., 1996; Martínez, 2013). Of the 2 200 non-timber species, 450 are considered useful, 100 of them are marketed under official control and 25 are for commercial, domestic and regional use, however, changing market conditions influence their demand (Chandrasekharan et al., 1996; Tapia-Tapia y Reyes-Chilpa, 2008; Semarnat, 2018).

The species of the Agave genus are relevant since they provide socioeconomic and agroecological benefits to the inhabitants of rural areas and to the environment where they grow; Agave lechuguilla Torr. in particular, is a plant from which a tight cone formed by the young leaves covered by the older ones located in the center of the plant is obtained, commonly known as the bud (Figure 1); there, high fiber contents are taken by cutting and carving or by manual-mechanical pulping where the parenchyma of the leaves is extracted (Martínez, 2013). This activity represents an important source of income and in many cases, the only one (Mayorga-Hernández et al., 2004). The lack of management plans has caused the decline of the natural populations of A. lechuguilla, mainly due to the type of harvest that is practiced, which does not consider the replacement of individuals and that, in general, plants of all sizes are extracted, which misleads the use of this natural resource (Semarnat, 1996; Mayorga-Hernández et al., 2004).

Figure 1. a) Agave lechuguilla Torr. plant. to the bud center; b) Storage yard; c) Location of the study area in the El Rodeo ejido, Mazapil municipality, Zacatecas State.

In Mexico, A. lechuguilla is distributed in the states of Chihuahua, Coahuila, Nuevo León, Tamaulipas, Durango, Zacatecas, San Luis Potosí, Hidalgo and Oaxaca (Sagarpa, 2009; Martínez, 2013). There are few studies to estimate the biomass and fiber production potential of the species, which can be known through statistical methodologies such as the evaluation of allometric models through regression. These models are fed with data from the field measurement of morphometric variables recommended in current regulations (Semarnat, 1996).

For the use of this type of species, the regulatory entity requests, previously, a technical study to have information on the real stocks of the natural population and then a use plan must be defined (Semarnat, 1996; Semarnat, 2018; Cano et al., 2005; Velasco et al., 2009; Martínez, 2013). This is useful to generate biomass and fiber yield tables for A. lechuguilla, because it is a tool that supports the description and conservation of the resource in arid and semi-arid zones (Cano et al., 2005; Velasco et al., 2009).

The objective of this study was to adjust models to predict the green weight (biomass) and dry weight (fiber) of Agave lechuguilla and, based on the selection of the best ones, develop performance tables that use morphometric variables that are easy to measure in wild populations. in the north of Zacatecas.

The research was carried out in 2020 in the El Rodeo ejido, Mazapil municipality, located north of the state of Zacatecas, Mexico. Important natural populations of A. lechuguilla are found in this area. It is located between 23º08'00" North and 101º07'00" West (Figure 1), at an average altitude of 2 200 m (Conabio, 2014), with an area of 10 317.553 ha.

In order to cover the total variation of biological development of the plants and to know the fiber productivity due to altitudinal oscillations of the terrain and sampling sites, areas close to being exploited and also those that are not customary to harvest were considered (Semarnat, 1996).

For data collection in the field, 74 points were used as sampling units or sites (n=74), spaced at a distance of 100 m between them, randomly distributed. Starting from the center of the site, two axes were drawn, one north-south and the other east-west, which resulted in four quadrants centered on a point (Bonham, 2013; González et al., 2022). There, measurements were taken of one plant per quadrant (the closest one) with usable characteristics, such as that they had not been harvested in previous years, that they were free of biological and mechanical damage. In addition, the current forest legislation was applied and those specimens whose minimum length or height of the top was 25 cm were collected (Berlanga et al., 1992; Semarnat, 1996; Velasco et al., 2009).

In each of the quadrats derived from each sampling point and aided by a tape measure 700 model MBZ^®, the distance from the point to the closest plant (m) was taken, which was a total of 296 measured plants (r=296). To estimate the density of lechuguilla plants ha^-1 (d) the unbiased estimators (1) and (2) were used (Bonham, 2013).

The morphometric variables measured in each A. lechuguilla plant were the minor diameter (dme, cm) or bud base, which was measured with a tape measure after cutting the basal part of the plant. The greatest aerial diameter (dma, cm), which was obtained by putting a wooden ruler graduated in cm 5010 model Arly^® over the widest part of the aerial cover of the plant. The height of the shoot (h, cm) was measured from the base to the tip of each of the leaves; the curved ones were fitted with a tape measure lengthwise.

Each bud was individually labeled to keep an orderly control and easy identification. The sample of collected specimens was transported to storage yards to obtain the green weight of the individual bud (pv, g) with a Torrey L-EQ 5/10 model digital scale 20 kg capacity. The dry weight of the fiber (ps, g) of each bud was determined after manual carving, labeling and direct exposure to the sun for 3 to 5 hours; to record the weight, the criteria that there was no moisture to the touch was applied. A SPX model portable scale with a 180×190 mm diameter plate and 2 000 g×0.01 g precision capacity was used.

The sample mean and intervals

, s the standard deviation, as well as the minimum and maximum values of each morphometric variable were calculated from the 296 individuals collected. In addition, the data normality test was performed with the Shapiro-Wilk W statistic in Excel^® (Zar, 1999).

In order to know the linear relationship between the measured variables, the simple correlation coefficient (R) was estimated in Excel^® (Pearson, P<0.01) for the pairs of variables in the data matrix (Zar, 1999). The associations of pv (g) and ps (g) with respect to dme (cm), dma (cm) and h (cm) were mainly considered, the highest value was selected to organize the information in ranges (Zar, 1999; Walpole et al., 2012).

To predict biomass production in terms of pv and fiber yield given by ps, the regression adjustment of 18 linear and non-linear allometric models (9 for each dependent variable) was evaluated (Table 1), the method of least squares in Excel^® was applied; for this end, the variables best correlated with the pv (g) and ps (g) were used. For the selection of the best models, the following criteria were used: Probability of committing the Type I Error (P<0.01) in the regression, the highest value of the adjusted coefficient of determination (R²_aj), minimum values for the root of the Mean Square of the Error (RCME), Coefficient of Variation (CV), Cp Mallows statistic (Cp), absolute value of the prediction sum of squares (│PRESS│), and prediction sum of squares (PRESS) (Zar, 1999; Walpole et al., 2012). Subsequently, the Breusch-Pagan (BP) test (P<0.01) for homoscedasticity was applied (Breusch and Pagan, 1979; Maldonado-Ortiz et al., 2022). It was sought that the model used included within its confidence bands (99 %) all the observations organized in intervals for new values of pv (g) and ps (g), respectively (Semarnat, 1996; Zar, 1999; Walpole et al., 2012).

Table 1. Tested models to estimate biomass yield pv (g) and fiber ps (g) of Agave lechuguilla Torr.

No.	Model	No.	Model
1	pv=a+b(dme)	10	ps=a+b(dme)
2	pv=a+b(dma)	11	ps=a+b(dma)
3	pv=a+b(h)	12	ps=a+b(h)
4	pv=ab^dme	13	ps=ab^dme
5	pv=ab^dma	14	ps=ab^dma
6	pv=ab^h	15	ps=ab^h
7	pv=a(dme)^b	16	ps=a(dme)^b
8	pv=a(dma)^b	17	ps=a(dma)^b
9	pv=ah^b	18	ps=ah^b

pv = Green weight of the bud (g); ps = Dry weight of the fiber (g); a and b = Estimators of the regression parameters; dme = Minor diameter (cm); dma = Major aerial diameter (cm); h = Bud height (cm).

Once the two regression models were selected (Table 1), a green biomass yield table for pv (g) and fiber for ps (g), respectively, was estimated.

The average density of A. lechuguilla was 2 149±126 usable plants ha^-1, with an interval of 2 023-2 275 plants ha^-1, limits given by the unbiased estimators (1) and (2) of the quadrant sampling method centered on a point made in the field (Bonham, 2013) and that are only applicable to the study area.

The data analysis of A. lechuguilla resulted in the statistics presented in Table 2. The mean pv was 287.2±118.8 g bud^-1; for ps it was 19.1±10.0 g, which represented a yield of 6.65 % fiber, similar to that recorded by Berlanga et al. (1992) and Martínez (2013). It should be considered that the study areas were different, so the performance figures may differ. On the other hand, the morphometric variables dme (cm), dma (cm), h (cm), pv (g) and ps (g) showed a normal distribution (W>P) (Table 2).

Table 2. Data exploration analysis for the morphometric variables of Agave lechuguilla Torr.

dme = Minor diameter (cm); dma = Greatest aerial diameter (cm); h = Height of the bud (cm); pv = Green weight (g); ps = Dry weight (g); W = Shapiro-Wilk statistic.

The correlation between the variables (Table 3) was estimated with the averages of the 296 A. lechuguilla plants. It was determined that the linear relationship between pairs of variables was statistically significant at 99 % (P<0.01). Attention was focused on pv (g) and ps (g) as dependent variables with the morphometric variables; the highest values, with a positive and significant relationship (P<0.01), were for pv and dma (R=0.968), as well as ps and h (R=0.945), the intervals were ordered from 35-215 cm for dma and from 30–65 cm for h.

Table 3. Linear correlation coefficients (R) between the morphometric variables of Agave lechuguilla Torr.

	*dme*	*dma*	h	pv	ps
dme
dma	0.878**
h	0.936**	0.967**
pv	0.895**	0.968**	0.952**
ps	0.904**	0.919**	0.945**	0.965**

dme = Minor diameter (cm); dma = Greatest aerial diameter (cm); h = Height of the bud (cm); pv = Green weight (g); ps = Dry weight (g); **P<0.01.

Table estimation of biomass yield of pv (g) and fiber ps (g) for Agave lechuguilla Torr.

The evaluation of the fitted models to estimate the biomass and fiber production of A. lechuguilla is shown in Table 4. The values of the regression estimators a and b are presented as exponential for the non-linear models of pv (4-6) and ps (13–15); only for a in pv (7-9) and ps (16-18) the selection criteria are shown in Table 5. The best were the non-linear ones for green biomass, pv=21.920(1.054)^h (model 6, Table 1) and for fiber, ps=0.0003(h)^2.812 (model 18, Table 1), respectively. The choice of models was similar to what has been done for studies in other areas with the same species (Berlanga et al., 1992; Pando et al., 2004). They complied with homoscedasticity (P>0.01), that is, the selected models did not have the heteroscedasticity problem (Breusch and Pagan, 1979; Maldonado-Ortiz et al., 2022). For the selected models, tables of biomass production pv (g) and fiber yield ps (g) were generated, respectively (Table 6); in addition, the confidence intervals (99 %) for the data are displayed (Figure 2), which gives the possibility of making estimates within the observed range of the data for the study area.

Table 4. Analysis of variance for the biomass models of pv (g) and fiber ps (g) for Agave lechuguilla Torr.

Model	a	b	sa	sb	Pa<0.01	Pb<0.01
1	-355.969	139.848	81.675	16.904	**	**
2	24.242	2.282	19.613	0.144	NS	**
3	-366.712	13.918	53.371	1.080	**	**
4	21.276	1.719	0.214	0.044	**	**
5	99.790	1.008	0.082	0.0005	**	**
6	21.920	1.054	0.124	0.002	**	**
7	8.334	2.279	0.326	0.209	**	**
8	4.042	0.899	0.214	0.045	**	**
9	0.320	2.351	0.470	0.121	**	**
10	-24.765	9.363	5.189	1.074	**	**
11	1.841	0.144	2.040	0.014	NS	**
12	-24.672	0.915	3.805	0.077	**	**
13	0.783	1.919	0.284	0.058	NS	**
14	5.528	1.009	0.168	0.001	**	**
15	0.881	1.063	0.256	0.005	NS	**
16	0.231	2.800	0.365	0.235	**	**
17	0.124	1.048	0.442	0.093	**	**
18	0.0003	2.812	0.749	0.194	**	**

sa = Standard error for a; sb = Standard error for b; **Pa<0.01; **Pb<0.01; NS = Non-significant.

Table 5. Regression models adjusted for the variables pv and ps based on morphometric variables of Agave lechuguilla Torr.

Model	P<0.01	*R²_aj*	*RCME*	*CV (%)*	Cp	*│PRESS│*	*PRESS*	BP<0.01
1	**	0.789	59.896	19.315	599.919	48.445	2 346.959	NS
2	**	0.933	33.773	10.891	192.108	5.697	32.459	**
3	**	0.902	40.933	13.200	281.246	29.112	847.483	NS
4	**	0.892	0.158	2.780	2.004	0.049	0.0020	**
5	**	0.913	0.141	2.495	2.003	0.114	0.0130	NS
6	**	0.960	0.095	1.688	2.002	0.012	0.0001	NS
7	**	0.867	0.173	3.087	2.005	0.176	0.0310	NS
8	**	0.957	0.100	1.762	2.002	0.017	0.0003	NS
9	**	0.954	0.100	1.816	2.002	0.065	0.0040	NS
10	**	0.806	3.805	19.191	4.413	1.167	1.3620	NS
11	**	0.835	3.514	17.720	4.057	1.990	3.9580	NS
12	**	0.886	2.918	14.717	3.419	0.199	0.0390	NS
13	**	0.871	0.207	7.288	2.007	0.121	0.0150	NS
14	**	0.751	0.290	10.138	2.014	0.244	0.0590	NS
15	**	0.885	0.197	6.879	2.006	0.180	0.0320	NS
16	**	0.887	0.195	6.832	2.006	0.029	0.0010	NS
17	**	0.875	0.205	7.187	2.007	0.147	0.0220	NS
18	**	0.921	0.164	5.708	2.004	0.123	0.0150	NS

Table 6. Yield tables for green biomass (g) and dry fiber (g) for Agave lechuguilla Torr. depending on the bud height (h).

BCI = Lower confidence band; BCS = Upper confidence band; h = Shoot height (cm); pv = Green weight (g); ps = Dry weight (g); e_i = Residual

= i-^th estimated value of y (pv or ps).

Figure 2. Average curve, bands that reproduce the confidence intervals (P<0.01) and residual graphs for the selected models.

The morphometric variable height of the shoot (h) measured in wild populations of A. lechuguilla to the north of Zacatecas allowed to estimate the green biomass yield of the shoot (g) in terms of green weight (pv, g), as well as the fiber yield in terms of their respective dry weight (ps, g) using regression equations. For the first case the function pv=21.920(1.054)^h was selected and in the second the expression ps=0.0003(h)^2.812, respectively. The statistical criteria used gave certainty in the selection of the best model for each variable of interest. Green biomass production and fiber yield tables were generated, which make up quantitative work tools that will contribute to the development of management plans for the species in areas with ecological-environmental characteristics similar to those studied.

Héctor Darío González López and Dino Ulises González Uribe: research planning and development, field sampling, data capture, data analysis and exploration, writing and review of the manuscript structure.

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Estimators	Variables
Estimators	*dme*	*dma*	h	pv	ps
Mean	4.8±1.1	114.8±34.4	48.2±9.9	287.2±118.8	19.1±10.0
Minimum	2.3	36.8	27.0	81.0	4.0
Maximum	7.5	215.0	82.0	666.0	54.0
W>P	0.1373	0.6179	0.2666	0.3904	0.5815

h (cm)	30	35	40	45	50	55	60	65
Green biomass (pv, g)	106.18	138.12	179.66	233.70	303.99	395.43	514.37	669.08
Dry fiber (ps, g)	4.27	6.59	9.59	13.36	17.97	23.49	30.01	37.58