Study area

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}).

Sampling design and assessed variables

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}).

Where:

d = Estimator of plant density

n = Number of sampling points

r _ij = Individual distances in each quadrant

π = Value of pi (3.14159)

s ² (d) = Variance of plant density

The confidence interval for the density (d) was determined by the expression:

Where:

√s ² (d) = Square root of the variance of the density

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.

Statistic analysis

The sample mean and intervals (X-±s), 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 (R ² _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}).

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.

Statistical analysis of the information

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).

Correlation between morphometric variables

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 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.

BCI = Lower confidence band; BCS = Upper confidence band; h = Shoot height (cm); pv = Green weight (g); ps = Dry weight (g); e _i = Residual (y _i - y^ _i ); y^ _i = 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.