Introduction

The rangelands distributed around the world cover more than 50 % of the earth’s surface and provide biomass that supplies a fundamental ecosystem service on which wildlife, population, and livestock farming, the main economic activity in this ecosystem, depend^1,2. In the last century, rangelands have suffered degradation due to episodes of drought and overgrazing due to an excessive stocking rate^3,4, due to failures in efficient and sustainable use of the rangeland to cover the forage biomass requirements of the cattle herd⁵. Therefore, it is essential to have reliable estimates of the amount of forage available for cattle that allow the proper use of forage, avoidance of overgrazing, and the satisfaction of the needs of animals^6,7.

The traditional method for estimating aerial biomass production is that of cutting and weighing grass; although this destructive method is accurate, it is usually expensive and time-consuming^8,9. In addition, the random distribution of vegetation makes it necessary to increase the recommended number of samples per site (15-20 samples¹⁰), ideally collected at each forage growing season⁸.

Indirect methods (non-destructive, since they do not require cutting the grass present) arise as an alternative to the traditional one (destructive, which involves cutting and weighing the grass present) to determine the aerial biomass of forage in the rangeland since they have the advantage of achieving estimates of the biomass of large areas in a faster way^11,12. Subjective empirical methods of visual estimation have the disadvantage of a high variation in results among people who perform them in different periods of time¹³. Graduated plates or sticks have been used in recent decades to estimate forage biomass in meadows with homogeneous vegetation^14,15. New methodologies for biomass estimation have been developed through the use of satellite images¹⁶, radar images¹⁷, and unmanned vehicles¹⁸; however, these are mainly carried out in cultivated areas.

The rangelands have different types of vegetation with heterogeneous distribution. For example, in the Tamaulipan thornscrub (TTS), shrub and semi-shrub species predominate, sometimes constituting more than 80 % of the botanical composition, while grass species and other weeds hardly exceed 10 and 6 %, respectively^19,20. Under these conditions, allometric models developed by relating the biomass production data obtained from the traditional method with the measurements made in morphological characteristics of the individual are a good option to estimate the biomass of grasses objectively. Once the model is generated, biomass estimation can only be done by measuring the necessary vegetative variables, without the need to cut the plants^5,9.

Studies prior to this work have been conducted in meadows under irrigated and monoculture conditions^15,21,22. For rangeland conditions, results obtained under arid conditions in Arizona²³ and multispecies conditions in Argentina⁹ have been published. There are reports of equations generated specifically for estimating the biomass of certain grass species, such as those reported based on 40 plants from C. ciliaris grass meadows in southern Arizona, relating biomass with basal diameter and plant height²⁴, as well as equations generated for A. purpurea in a previous study²⁵, using the diameter of the plant at different heights as variables.

In Europe, an indirect estimation methodology was developed for grass species²¹, which used a measure called minimum volume, obtained by joining all the stems of the plant by applying a subjective, non-standardized force to form a minimum volume.

The present study aimed to generate new equations to estimate the aerial biomass of five species of grasses present in the rangelands of Nuevo León, Mexico, based on the measurement of their morphological variables, which could serve as an alternative to replace the need to cut grass as in the traditional method.

Material and methods

The study was conducted in an area of 132 ha of rangelands in the municipality of Marín, Nuevo León (25°52'28"N; 100°03'24"W), in which precipitation varies between 400 and 600 mm per year, and the average temperature ranges from 20 to 22 °C²⁶. The primary vegetation type is Tamaulipan thornscrub (TTS), in addition to having areas of induced grassland and agriculture.

In January 2021, 31 sampling plots of 100 square meters (10 m x 10 m) were randomly established within the study area with vegetation typical of the Tamaulipan thornscrub, and five 1 m² subplots were delimited within each plot, in which was collected and weighed (dry matter basis) all the individuals of grasses present in each of the 155 subplots evaluated, in a design similar to that previously used in areas of rangeland²⁷. A perimeter fence was placed around each plot to prevent disturbances. All plots were cut at 3 to 5 cm height at the beginning of the study and in each sampling. The first sampling was conducted from June 15 to July 15, 2021, and the second was conducted in the autumn from October 18 to November 8, 2021. In both cases, the sampling was carried out 30 to 40 d after a rainfall greater than 150 mm (in the first sampling) and 231 mm (in the case of the second sampling) since, according to previous studies²⁸, the flowering of the Cenchrus ciliaris grass occurs between 25 and 35 d after regrowth as a result of precipitation of 150 mm, which is considered as the threshold for the productivity of the species Cenchrus ciliaris²⁹ during the summer and autumn.

In each subplot, all plants of the grass species present were sampled and identified individually at the genus and species level. A Truper® pro-Lock FX-5M tape measure was used to measure the variables described below and shown in Figure 1A:

H= height ; Hvs= height of vegetative stems ; Bd= basal diameter; Cd= compressed diameter; Ad= aerial diameter.

Figure 1 Variables measured in grass plants (A) and shapes of estimated volumes (B) 

Each of the 745 plants sampled was identified, measured, and cut with hand scissors at ground level to record its fresh weight (g) in the field and stored in a Kraft paper bag. Subsequently, the samples were taken to the laboratory and dried in a forced air oven at 60 °C until reaching a constant weight in order to obtain their dry weight (g) by using a scale with a capacity of 500 g with a minimum division of 0.1 g (Torrey brand, model Lab-500).

The 745 individuals found in the sampling subplots were identified, measured, and cut. The plants of the five grass species present in the study area: Cenchrus ciliaris (n= 424 individuals), Pappophorum bicolor (n= 125 individuals), Aristida purpurea (n= 107 individuals), Tridens texanus (n= 59 individuals) and Paspalum pubiflorum (n= 30 individuals) were collected for the generation of equations.

A total of 19 independent variables (aerial diameter, basal diameter, compressed diameter, height, vegetative stem height, circular basal cover, elliptical basal cover, circular aerial cover, elliptical aerial cover, volume of cylinder 1, volume of cylinder 2, volume of cylinder 3, volume of cylinder 4, volume of cylinder 5, volume of cone 1, volume of cone 2, volume of cone 3, volume of cone 4, volume of cone 5) and a dependent variable (measured biomass [g DM] per individual of the grass species) were subjected to linear regression, stepwise regression⁹ and nonlinear regression (logarithmic, inverse, quadratic, cubic, power, exponential) analysis in the IBM SPSS software to generate biomass prediction equations both generally and specifically (for each of the five grass species found in the samplings).

To assess the quality of the biomass estimate achieved with the new general and specific equations, each of the values recorded in the destructive sampling was compared with the predicted values of each of the equations. The coefficient of determination of the regression (R²)²⁷, the standard error (SE)³⁰, Pearson’s correlation (r)¹⁸, the normalized root mean squared error (NRMSE)²¹, and the Akaike information criterion (AIC)²⁷ were calculated.

The six general equations developed with the best statistical fits of AIC, NRMSE, R², SE, and r were selected to estimate the total species collected, and a specific equation was selected for each of the five recorded grass species.

Results

The grasses Cenchrus ciliaris and Paspalum pubiflorum presented values of aerial and basal cover, aerial and basal diameter, and fresh and dry weight (P<0.05) higher than the rest of the species (Table 1). Cenchrus ciliaris recorded an average value of dry weight per individual higher than that of Aristida purpurea and Tridens texanus (P<0.05), while Paspalum pubiflorum and Pappophorum bicolor obtained intermediate values.

The estimates of aerial biomass calculated with the six new general equations generated in the present study had coefficients of determination (R²) that varied between 0.77 and 0.90, while Pearson’s correlation coefficient (r) ranged from 0.88 to 0.94. The normalized root mean squared error (NRMSE) ranged from 0.68 to 0.48, and the Akaike information criterion (AIC) took values from 3553 to 3079 (Table 2).

Equation I is a linear model that incorporates the measurement of cone 5 (Figure 1B), which is calculated based on three direct variables (aerial diameter, compressed diameter, and height of the vegetative stems), and whose estimates have an R² of 0.77, r=0.88, NRMSE=0.64, AIC=3469. The estimates calculated with equation II (linear) from the data generated by the variables aerial diameter, compressed diameter, height, and height of the vegetative stems have an R² of 0.87, r= 0.93, NRMSE= 0.49, and AIC= 3108. Equation III (linear) incorporates the data of the five measured variables to calculate estimates that have an R² of 0.88, r= 0.94, NRMSE= 0.48, AIC= 3079 (Figure 2A).

A) General equation III (Table 2). B) General equation IV (compressed diameter). C) Specific equation for Cenchrus ciliaris. D) Specific equation for Pappophorum bicolor (Table 2). E) Specific equation of Aristida purpurea. F) Specific equation of Tridens texanus (Table 2). All graphs were set to zero.

Figure 2 Regression of predicted values and observed values 

Nonlinear equations IV (R²= 0.86, r= 0.88, NRMSE= 0.67, AIC= 3530; Figure 2B), V (R²= 0.89, r= 0.88, NRMSE= 0.68, AIC= 3553) and VI (0.90, r= 0.88, NRMSE= 0.67, AIC= 3530) are from the power model and use fewer variables. The estimates calculated using equation IV, which uses the compressed diameter as the only variable, have an R²=0.86 (Figure 2B). Equation V uses cylinder 3, calculated from the compressed diameter and height of the plant, to estimate aerial grass biomass with R²=0.89. Equation VI uses cylinder 5 (Figure 1B), calculated from the compressed diameter and height of the vegetative stems, to estimate aerial biomass with R²= 0.90 (Table 2).

In the case of equations generated specifically for each of the grass species, comparisons between the estimated values and the results recorded directly from aerial biomass yielded R² values from 0.86 to 0.93. The values of r (Pearson) ranged from 0.92 to 0.97. For NRMSE, values from 0.40 to 0.24 were recorded, and AIC took values from 1603 to -18 (Table 2). In the specific case of the equation generated for Cenchrus ciliaris, a good fit of the estimated values of aerial biomass was achieved, with R² of 0.88, r= 0.94, NRMSE= 0.40, AIC= 1603, using the five variables measured (Figure 2C).

The results estimated using the five variables with the specific equation for the species Pappophorum bicolor (Table 2) had a fit of (R²= 0.86, r =0.92, NRMSE= 0.29, AIC= 287) (Figure 2D).

The information collected from 107 individuals of Aristida purpurea allowed the generation of a specific equation for this grass species (Table 2), whose estimates, based on the five variables measured, had a fit with a coefficient of determination of 0.92, r=0.96, NRMSE= 0.27, AIC= 87. (Figure 2E).

Discussion

The linear and polynomial equations generated in the present study based on the sampling of vegetative measurements and biomass weight records of grasses present in the rangeland allowed the estimation of the aerial biomass of grasses present in the rangeland with a high degree of precision.

The new general allometric equations established in the present study had values of R² (0.77 to 0.93) higher than those previously reported (R² from 0.25 to 0.85) for estimates of general equations for two grasses and two pseudo-grasses in the Peruvian Andes²⁷. Allometric equations generated in Chubut, Argentina²³, by evaluating 50 individuals from three species of grasses, had R² values (between 0.72 and 0.86) similar to those obtained in the present study.

The number of plots established in the present study was similar to that previously used²⁷; however, in the present study, there were plots of 100 m², while in the previous study²⁷, they had plots of 4 m². In addition, in each of the 31 plots of the present study, the values of botanical composition, vegetative measurements, and biomass of the grasses present in five subplots were recorded. With this, there was greater reliability of the recorded measurements and the calculated averages for the generation of the equations.

The species C. ciliaris had a significant presence in the grass vegetation observed in the rangeland evaluated since it represented 57 % of the total number (n= 745) of individuals collected and its biomass, calculated considering the number of individuals and the average weight of the individuals of the species shown in Table 1, represented 80 % of the biomass recorded in the rangeland evaluated. In the areas assessed in the present study, the C. ciliaris grass present was established by natural dispersion, evidencing its high potential to establish itself in the rangelands in Mexico³¹. The native species with the highest presence in the present study was Pappophorum bicolor, which had a record of 125 individuals, that is, 17 % of the total, whose biomass represented only 11 % of the total biomass (Table 1).

The compressed diameter was the variable included in 100 % of the general allometric equations and in 97 % of the specific equations, both for the linear and nonlinear model, generated in the present study for each grass species. The height of the vegetative stems was included in 87 % of the general equations. The variables vegetative stem height and plant height were included in 71 % of the specific equations. These variables have been directly related to forage density³². Some authors³⁰ reported that, in meadows with optimal conditions for their development, the variable vegetation cover is the one that can best indirectly estimate the biomass. Mahood et al²² determined that vegetation cover is a good predictor for biomass estimation, with an R² of up to 0.89 in Bromus tectorum plant communities.

An indirect estimation methodology implemented for grass species in Western Europe²¹ used a measure called minimum volume as a variable, consisting of manually joining all the stems of the plant until forming a minimum volume; nevertheless, the applied force was subjective, varying according to the person performing the measurement and it could even vary when the same person exerts different pressure due to fatigue when repeatedly making the sampling. By applying the same compression force, the compaction device used in the present work generated greater certainty of the results obtained.

The NRMSE values calculated in each of the new equations generated in the present study determine the dispersion of the estimated data with respect to the observed data, with 0 being the ideal fit³³. In contrast, the Akaike criterion compares and selects from a group of prediction models that use the same experimental data the most appropriate to forecast the expected values compared to the observed values, which in this case should be the model with the lowest AIC value^34,35. The values of NRMSE and AIC are very useful in the selection of the best models.

The specific equation generated in the present study for Cenchrus ciliaris had a value of R²=0.87, and with it, an R² similar to that reported in a study (R² of 0.82²⁴) to generate allometric equations relating biomass with the measurement of basal diameter and height of 40 plants of C. ciliaris grass meadows in southern Arizona. The equation generated in the present study for A. purpurea resulted in an R²= 0.89, similar to those reported (R² from 0.82 to 0.90) in a previous study²⁵, for the species A. purpurea, using the diameter of the plant at different heights. Some authors³⁰ generated equations to estimate aerial biomass from the analysis of 93 plants of Agropyron desertorum and reported coefficients of variation (R² from 0.76 to 0.88) slightly lower than those of the present study. The new equations generated in this study are potential candidates to replace the cutting, drying, and weighing phases performed in the traditional method³⁶.

The development of allometric equations with application in rangelands is of utmost importance to achieve sustainable ecosystem management²⁷. These non-destructive vegetation samplings have advantages in terms of time and budget compared to traditional sampling and also allow growth monitoring at the individual level^21,37.

Conclusions and implications

The importance of 19 variables related to the morphological characteristics of grasses present in the rangeland was evaluated to estimate the production of aerial biomass per plant. This information was used to generate 6 new general equations for five grass species present in the study area and 5 new specific equations (one for each grass species Cenchrus ciliaris, Pappophorum bicolor, Aristida purpurea, Tridens texanus, and Paspalum pubiflorum), which reliably and practically estimate the production of biomass without destroying (cutting) the plant. The new equations generated in this study are a viable option to replace the cutting phase of the samples in the traditional method of estimating the production of aerial biomass of grasses in the rangeland. The development of general (multispecies) and specific (for a particular grass species) allometric equations is a reliable alternative to indirectly estimate the aerial biomass of the grasses of the rangelands of northeastern Mexico more quickly and less expensively than the traditional method.