Study area

The research was conducted in natural populations of oregano distributed in General Cepeda, Parras de la Fuente and Ramos Arizpe municipalities, located between the coordinates 25°22'41" - 25°26'27 N and 100°57'2" - 102°11'10" W, with an altitudinal range of 1 000 to 1 400 m. The predominant soil types are Lithosol, Xerosol and (calcic and haplic) Yermosol with a medium texture and without salinity issues (^{Inegi, 2005}). The climate of the region, according to Köeppen’s classification modified by ^{García (2004)} and ^{Inegi (2005)} is of the BS₁hw (semi-arid and semi-warm) and BS_ohw (very arid semi-warm) types, with a mean temperature of 18 to 20 °C, and extreme values from -4 to 45 °C, with an annual precipitation of 125 to 400 mm.

Oregano is a shrubby plant with annual sprouts, associated to the vegetation consisting of rosetophilous scrub with agave of Salm (Agave salmiana Otto ex Salm-Dyck), lechuguilla (Agave lechuguilla Torr.), xoconostle (Opuntia imbricata (Haw.) DC.), candelilla (Euphorbia antisyphilitica Zucc.), sotol (Dasylirion cedrosanum Trel.), Prickly Pear Cactus (Opuntia spp.), espadín (Agave striata Zucc.), and maguey (Agave spp.).

In the microphyllic shrub, with hojasen (Flourencia cernua DC.), skeletonleaf goldeneye (Viguiera stenoloba S.F. Blake), mariola (Parthenium incanum Kunth), gobernadora, tasajillo (Opuntia leptocaulis DC.), ocotillo or coachwhip (Fouquieria splendens Engelm.), guayule (Parthenium argentatum A. Gray), giant Spanish dagger (Yucca carnerosana (Trel.) McKelvey), coyotillo (Karwinskia humboldtiana (Schult.) Zucc.), leatherstem or sangre de drago (Jatropha dioica Sessé), woody crinklemat (Tiquilia canescens (A. DC.) A.T. Richardson) and Polieria angustifolia (Engelm.) A. Gray.

In both types of vegetation, oregano is associated with different species of cacti and with the stratum of taxa, such as wicker (Chilopsis linearis (Cav.) Sweet), mesquite (Prosopis sp.) and huisache (Acacia farnesiana (L.) Willd. and Acacia constricta Benth.) (^{Berlanga et al., 2005}).

Data collection and sampling design

The sample was composed of 706 individuals distributed in 20 populations located in three municipalities of southeastern Coahuila. The sampling was carried out during the harvesting period of the plant (July to October), and each population was georeferenced for its location (Table 1 and Figure 1).

Table 1 Number of sampled oregano populations and plants in General Cepeda, Parras de la Fuente and Ramos Arizpe municipalities, corresponding to the oregano corridor in Coahuila. 

Figure 1 Geographical distribution of the sampling localities in General Cepeda, Parras de la Fuente and Ramos Arizpe municipalities, Coahuila. 

Independent Variables

The total height (TH cm), the larger diameter (LD, cm) and smaller diameter (SD, cm) of the shrub cover were measured in each sampled individual with a Truper™ tape model 21601 (Figure 2b, c). In order to take into account the variability of the growth of the species, all the categories of height and cover of the standing shrubs present in the populations were included. The TH of the plant was measured from the base of the soil to the tip of the highest branches (Figure 2a), the LD and SD were measured taking into account the shrub cover (Figure 2b and 2c). The mean diameter (MD, cm) of the cover was estimated based on the larger and smaller diameters.

Figure 2 Measurement of a) height (TH), b) larger diameter (LD) and (c) smaller diameter (SD) of Lippia graveolens Kunth shrub. 

Dependent Variable

The dry leaf biomass (DLB, gr) was calculated based on a destructive sampling of the assessed individuals; for this purpose, the whole aerial part of the plants (stems and leaves) was harvested and stored in paper bags. The samples were then dehydrated in situ at room temperature for five days -a drying method used by the producer. The dry biomass was subsequently separated by components: stems and leaves. The weight of dry leaves per sample was determined on a Schientech analytical balance with an accuracy of 0.001 g. The DLB per plant -i.e. the usable component with commercial importance- was thus estimated.

Statistical Analysis

The set of data on the DLB and the allometric variables TH, LD and SD were analyzed, first, through a Pearson's correlation test in order to select those variables most related to the DLB that were used to adjust linear and non-linear regression models (^{SAS, 2015}) (Table 2).

Table 2 Models adjusted to estimate the dry leaf biomass in natural populations of Lippia graveolens Kunth, in General Cepeda, Parras de la Fuente and Ramos Arizpe municipalities, Coahuila. 

MD = Mean diameter of the cover (cm); TH = Total height (cm); B_n = Model parameters; e = Exponential expression.

The database used for the regression analysis was purged through the detection of Outlier with the r-influence of the SAS 9.4 software (^{SAS, 2015}), in order to eliminate potential errors in the data base that might affect the statistical regression. The selected model was the one that exhibited the highest values for the adjusted determination coefficient (R² _adj) and the lowest value for the root mean square error (RMSE), in addition to the significance of its parameters (P ≤ 0.001). The regression assumptions were verified using the Shapiro-Wilk test for normality; the White test, to detect heteroskedasticity, in which, due to the nature of the data, a correction was assumed and applied by weighting the form residuals, 1 𝑀𝐷∗𝑇𝐻 , whereby this problem was eliminated; finally, the Durbin-Watson statistic test was carried out in order to test the co-linearity between variables. The regression models were adjusted with the the PROC MODEL procedure to generate consistent estimators (^{SAS, 2015}).

Equation for estimating DLB

The correlation test determined that the variables MD and TH, and the interaction between them, have a significant relationship with the DLB (p< 0.001), of 0.82, 0.53 and 0.83, respectively, with the rest of the evaluated variables, and therefore they were used as the basis for the adjustment of the models. The statistical adjustment was similar for all models, particularly models 3 and the 6, which exhibited higher R² _adj values and lower RMSEs. However, these had heteroskedasticity issues and therefore were corrected; thus, the correlation was obtained only for model 6, and for the adjustment values of R² _adj (0.81) and of the RMSE (21.5256), which was selected to estimate the DLB of oregano.

The structure of the chosen model corresponds to that of Schumacher-Hall, which is sigmoidal (Table 3); furthermore, the model uses the MD and TH that characterize the shape of the oregano shrub and based on which a double-entry table was built enabling the primary producers to estimate the DLBs.

The Schumacher-Hall model is applicable for these conditions and study sites; this type of model has been used to predict the timber volume of temperate species, as well as their total biomass and components (^{Velasco et al., 2007}; ^{Ramos-Uvilla et al., 2014}), while the potency model has been used in Acacia pennatula and Guazuma ulmiflora to predict the forage biomass and fuelwood production, considering the mean basal diameter as a variable (^{López-Merlín et al., 2003}).

The results show that the composition of the shrub exerts an influence on the allometric relationships of the plant; the TH and MD are related variables that show a phenotypic plasticity in response to environmental heterogeneity with morphological and physiological adjustments (^{Camargo et al., 2008}). The same variables were also considered in Lysioma divaricatum (Jacq.) J.F.Macbr. (^{Breceda and Ortiz, 2005}) and in Cercidium floridum Benth. ex A.Gray (forage plant) in order to predict the forage production (^{Guillen et al., 2007}); these variables are therefore easy to measure in field and can help evaluate the populations of oregano for exploitation.

The Schumacher-Hall model for estimating the DLB was structured as follows:

DLB = 0.00599(MD)^1.935454(TH)^0.256803

The MD and TH are significantly correlated with the dry leaf biomass of oregano; therefore, their estimates are reliable and can be used by the Providers of Professional Services (PPSs) to estimate the dry leaf biomass in the region of the three municipalities considered. Graphically, there is a good dispersion of the estimated data against the observed data, as well as a good fit (Figure 3).

Biomasa foliar = Dry leaf biomass; Diámetro promedio = Mean diameter; Biomasa foliar predicha = Dry leaf biomass predicted; Biomasa foliar observada= Dry leaf biomass observed

Figure 3 Dry leaf biomass (DLB) values observed and predicted for Lippia graveolens Kunth with the Schumacher-Hall Model. 

Table of production (g) of dry leaves of Lippia graveolens Kunth

The Schumacher-Hall model was used to develop a double-entry table for estimating the DLB of oregano in three municipalities of Coahuila. The measurement variables that serve as input are the height and mean diameter of the shrub’s cover, both of which are expressed in centimeters. Based on these variables, it is possible to determine the weight in grams of the dry leaves in the standing shrubs without having to cut them (Table 4).

Table 4 Production (g) of dry Lippia graveolens Kunth leaves in terms of the diameter of the cover and the height of the shrubs in natural stands located in Parras de la Fuente, General Cepeda and Ramos Arizpe municipalities, Coahuila.