Overton (32.29˚N, 94.97˚W) in the US state of Texas, where a Texas A&M AgriLife Research and Extension Center mandated to conduct long-term forage, grazing, and beef cattle research trials and provide Extension services for the Pineywoods region in East Texas is situated, was used as a representative site for this region and the southern United States (Figure 2). This region covers about 141,000 km² in eastern Texas, southern Arkansas, and western Louisiana. Beef cattle production on pastures is a major economic activity in this region.

Figure 2. Map showing Overton, TX in the Pineywoods region (the darker area) of the southern United States.

In this study, the effects of beef cattle SR on several variables associated with bermudagrass growth and stocker performance as influenced by ENSO and soil moisture conditions were assessed using the DGESS. For SR, three levels were considered: low (5 hd∙ha⁻¹), medium (8 hd∙ha⁻¹), and high (11 hd∙ha⁻¹). The body weight of each animal at stocking was assumed to be 250 kg. These numbers were based on the prevailing practices in the study region. For moisture conditions, dryland (rainfed) and fully-irrigated management strategies were studied as these options would allow one to assess the drought-induced losses of the dependent variables considered.

The effects of SR on multiple variables as influenced by ENSO and moisture condition were studied using the long-term historical daily weather data spanning 76 years (1950-2025) collected at Overton, Texas. The weather data comprised daily values of ambient temperatures (minimum, maximum, and dewpoint), precipitation, and windspeed. The weather data were needed for simulation and drought analysis purposes. The daily values of solar radiation, another important meteorological variable for simulations, were generated using a reliable global solar radiation model for the southeastern United States [26].

Using the DGESS, the SR effects were simulated for 456 scenarios, comprising 76 years × 3 SRs × 2 moisture conditions. Eventually, a data matrix of 456 rows and 9 columns (one for each variable: ENSO phase, SR, moisture condition, year, HM, GHM_P, GHM_A, SWG, and ADG) was created, which later was used for further analyses such as significance tests and drought effect assessments.

Of the 456 scenarios, 228 scenarios (76 years × 3 SRs) belonged to the bermudagrass forage grown under rainfed conditions and the remaining scenarios to the forage grown under irrigated conditions. While no irrigation was applied under rainfed conditions, irrigation was provided automatically so as to maintain soil moisture at the field capacity level under irrigated conditions.

Using the R software environment [27], statistical significance tests were conducted to examine if the values of each of the dependent variables studied were different across the three SRs under each ENSO phase and under each soil moisture condition (p < 0.05). For significance tests, the pairwise Wilcoxon rank sum test [28], a non-parametric alternative to the two-sample t-test, was used, with Holm as the p-value adjustment method [29]. The tests were performed at the significance level (α) of 0.05. In this study, the Wilcoxon test was used because the assumption of normality was not met for each ENSO phase and each moisture condition for the classic “analysis of variance” test. To extract separate main effects and an interaction effect from non-normal data with multiple categorical variables, the Aligned Ranks Transformation ANOVA (ART ANOVA), a non-parametric alternative to a Two-Way ANOVA, was used. The ART ANOVA is the most robust non-parametric method for testing interactions [30][31]. It aligns data before ranking so that main effects do not contaminate the interaction test.

For ENSO analyses, the 76 years (1950-2025) were assigned to a specific ENSO phase as categorized by the Japan Meteorological Agency (JMA) index [32][33]. Based on this index, an El Niño (or La Niña) phase occurs if the 5-month running mean sea surface temperature deviation from the long-term average in the Niño 3 region (5˚S - 5˚N, 150˚W - 90˚W) is ≥0.5˚C (or ≤−0.5˚C) for at least six consecutive months. Accordingly, the total number of years available under El Niño, La Niña, and Neutral phases during the 1950-2025 period was 22, 18, and 36, respectively. For ENSO classification, the JMA index was used as it is more sensitive to El Niño and La Niña conditions than other similar indices [34]. The ENSO influence was studied under rainfed conditions only, as irrigated conditions would mask the ENSO effect.

For drought effect analyses, the Agricultural Reference Index for Drought (ARID) [35] was used. The ARID is computationally simple, physically and physiologically sound, and generally applicable to a wide range of crops, soils, topographies, and management to characterize an agricultural drought [36]. The values of ARID range from zero, meaning no water stress, to one, meaning complete water stress. From the daily weather data, the daily values of ARID were computed for all 76 years (seasons), which then were averaged over the grazing season (May 15 through October 31) to convert them into the seasonal values. Accordingly, there were 76 ARID values available for drought effect analyses.

To truly represent the effect of water stress on an agricultural commodity, its relative value must be used [37]. This relative value is the amount of a commodity produced under water-stressed conditions relative to that which could be produced under non-water-stressed conditions, the other inputs or factors remaining the same. This relative value was obtained by dividing the water-stressed amount by the non-water-stressed amount. This division process eliminated the effects of the other factors involved, except water, thus representing the effect of only water stress on the produce.

To assess the effects of drought on HM, GHM, SWG, and ADG as influenced by SR, the relative values of a given variable were calculated for each SR by dividing its corresponding rainfed values by irrigated ones (Equation (1)).

where V R y , s , V U y , s , and V I y , s , respectively, are the relative, unirrigated (rainfed), and irrigated values of a given variable (V: HM, GHM, SWG, or ADG) in the y-th year under the s-th SR.

The relative values were then subtracted from 1.0 to compute the fraction of loss of that variable due to drought (Equation (2)).

where V L y , s is the drought-induced loss fraction of the variable V in the y-th year under the s-th SR. Accordingly, there were 76 V L values available for drought effect analysis for each variable under each SR. Finally, these fractional values were converted into percentages by multiplying the former by 100.

Under irrigated conditions, the SR effect on bermudagrass HM produced was statistically significant (p < 0.05) (Table 1). The values of HM produced increased considerably with an increase in SR (Figure 3). The likely reasons for this increase were as follows. As stated above, the three SRs considered for the study belonged to moderate grazing. Under moderate grazing, animals remove about 40% to 50% of the annual forage growth, opening up the canopy and allowing sunlight to reach the base of the plant [38][39]. This grazing intensity acts as a catalyst for growth and stimulates dormant buds to produce new vegetative shoots and diverts energy toward active, nutritious leaf production rather than reproductive stem growth [38]-[41]. At low stocking (light grazing), animals select a small fraction of the available forage, leaving most of the leaf canopy intact and letting plants prioritize vertical stem elongation and flowering and ungrazed canopies restrict new basal leaf development [42]-[44].

Table 1. The effect of stocking rate on various variables associated with bermudagrass herbage mass (HM) and stocker performance as influenced by El Niño-Southern Oscillation and soil moisture condition at Overton, Texas, USA during 1950-2025.

*Means followed by the same letter across stocking rates (horizontally) within a factor-level-variable combination are not significantly different at the significance level (α) of 0.05.

Figure 3. Effects of stocking rate on bermudagrass herbage mass produced and grazed and the average daily gain of stockers under irrigated and rainfed conditions at Overton, TX, USA during 1950-2025.

With an increase in SR within moderate grazing, animals defoliate more forage, and more new vegetative shoots and nourishing leaves are produced. An increase in leaf mass but a decrease in stem mass with an increase in SR confirmed these phenomena (Figure 4). The significant increase in HM with increased SR under irrigated conditions was due to non-water-limited production conditions. Under these conditions, the potential benefits of moderate grazing and other inputs, such as manures and fertilizers, were fully realized.

Figure 4. Effects of stocking rate on the bermudagrass herbage mass, leaf mass, and stem mass produced under rainfed and irrigated conditions at Overton, TX, USA during 1950-2025.

Figure 5. Effects of stocking rate on bermudagrass herbage mass produced and grazed under rainfed and irrigated conditions at Overton, TX, USA during 1950-2025.

Under rainfed conditions, the effect of SR on bermudagrass HM was not statistically significant (p > 0.05), but the HM values tended to increase with an increase in SR (Table 1). As discussed above, this pattern was likely because of stimulated new leaf growth and tillering under moderate grazing [38]-[41]. The non-significant increase in HM with increased SR, however, was due to dryland conditions. Water limitation reduced leaf growth and tillering stimulated by an increase in defoliation.

Under both rainfed and irrigated conditions, the effect of SR on GHM_P, GHM_A, SWG, and ADG each was significant (Table 1). With an increase in SR, the values of GHM_P increased, whereas those of GHM_A, SWG, and ADG decreased significantly (Figure 3). However, the increase in HM grazed per hectare (GHM_P) was linear under irrigated conditions but curvilinear under rainfed conditions (Figure 5). The increase in GHM_P with increased SR under both conditions was due to more animals on a pasture consuming a larger quantity of HM on that pasture. The curvilinear increase in GHM_P under rainfed conditions was likely because the HM produced was almost constant across all SRs. This situation led to the plateauing of the HM grazed (Figure 5). With an increase in SR, the animal grazing need increased, but the forage availability did not change much. The linear increase in GHM_P under irrigated conditions was due to the following reasons. The HM produced linearly increased with SR for the reasons explained in previous paragraphs. This situation did not allow for the plateauing of the HM grazed. The animal grazing needs increased linearly with SR, and so did the availability of forage for grazing (Figure 5).

The gap (difference) in each variable (bermudagrass HM, GHM_P, GHM_A, SWG, or ADG) between rainfed and irrigated conditions increased with an increase in SR (Figure 3). These trends as well as the p-values presented in the ART ANOVA tables (Table 2) indicated that the SR effect was significantly influenced by soil moisture conditions (p < 0.05). The SR effect was stronger under high moisture (irrigated) conditions. The slopes of HM and GHM_P to SR were steeper under irrigated conditions than those under rainfed conditions, whereas the slopes of GHM_A, SWG, and ADG to SR were steeper under rainfed conditions than those under irrigated conditions.

Table 2. The ART ANOVA tables showing the main effects of stocking rate (SR) as well as the interaction effects between SR and MC (soil moisture condition) or ENSO (El Niño-Southern Oscillation) on various variables associated with bermudagrass herbage mass and stocker performance at Overton, Texas, USA during 1950-2025.

*DF = degrees of freedom, Res. = residuals, Sq. = square, Pr (>F) = p-value.

The effect of SR on bermudagrass HM was not statistically significant under each ENSO phase (Table 1). However, the HM values tended to be larger with an increase in SR. This pattern was likely because moderate grazing stimulated new leaf growth and tillering [38]-[41]. However, the HM increase with an increase in SR within moderate grazing was not significant because of dryland conditions. The shortage of sufficient soil moisture, as the limiting factor for forage production, led to insignificant new leaf growth and tillering.

However, the effect of SR on GHM_P, GHM_A, SWG, and ADG each was significant under all ENSO phases (Table 1). That is, with an increase in SR, the values of GHM_P increased significantly, whereas those of GHM_A, SWG, and ADG had significant decreases (Figure 6). In the case of GHM_P, its values increased at a decreasing rate with an increase in SR. The likely reason for this increase was as follows. As expected, more animals on a given pasture consumed a larger amount of HM on that pasture as long as the pasture had enough herbage allowance to sustain the grazers. However, with an increase in SR, the availability of forage for grazing, that is, the HM produced per unit of the HM grazed (needed by the animals) or the gap between the HM produced on a pasture and the HM grazed on that pasture, became less (Figure 7).

With the amount of HM produced on a pasture being almost constant at all SRs, the herbage allowance (HM per animal) decreased with an increase in SR. Accordingly, the amount of HM grazed by each stocker (GHM_A) also decreased. The decrease in GHM_A, in turn, led to the decrease of both SWG and ADG.

Although the value of each dependent variable under La Niña was the smallest of all the ENSO phases at each SR (Figure 6) due to the driest grazing conditions (represented by the greatest seasonal average value of ARID) under this phase (Figure 8), the differences (gaps) in each variable across the ENSO phases at each SR were not significant (p > 0.05). Moreover, these ENSO gaps across SRs were about the same (Figure 6). These trends as well as the p-values presented in

Figure 6. Effects of stocking rate on bermudagrass herbage mass produced and grazed and the average daily gain of stockers under three ENSO phases at Overton, TX during 1950-2025.

Figure 7. Effects of stocking rate on bermudagrass herbage mass produced and grazed under the El Niño and La Niña phases of ENSO at Overton, TX, USA during 1950-2025.

Figure 8. The El Niño-Southern Oscillation (ENSO) phase-specific monthly and seasonal average values of the drought index ARID at Overton, TX, USA during 1950-2025.

the ART ANOVA tables (Table 2) suggested that the SR effect on HM, GHM_P, GHM_A, SWG, and ADG each was not significantly influenced by ENSO (p > 0.05).

The likely reason for non-significant ENSO influence was that, although the sub-seasonal (monthly) weather conditions represented by ARID were considerably different across the ENSO phases, the seasonal average values of weather conditions did not significantly vary across the ENSO phases (the dotted lines in Figure 8). Since this study involved the seasonal values of dependent variables, they were naturally impacted by the seasonal average weather conditions.

The loss of bermudagrass HM due to drought increased exponentially with an increase in drought intensity, represented by the larger values of the drought index ARID (Figure 9). This exponential relationship between ARID and HM loss was expected. Previous researchers have also demonstrated that the relationship between drought intensity and forage production is strongly non-linear and negative. As drought severity increases, forage biomass declines sharply, often by more than 50% in arid environments. As water scarcity worsens, plant growth stunts, root systems impair, and cellular functions collapse, thus severely limiting the available biomass for livestock [45]-[48]. Incremental increases in drought intensity limit the water available for photosynthesis [45][49]. Forage plants exhibit leaf rolling, drooping, and accelerated senescence to conserve water, directly shrinking the total herbage mass [47][50][51]. Research has shown that under critical drought intensity, biomass drops steeply, leaving grasslands with depleted forage [52][53].

Results further showed that the relationship between ARID and the drought-induced loss of HM was independent of SR. That is, the HM loss caused by drought was not influenced by SR. This result was expected because the total HM produced in a season was the sum of total HM grazed by the animals during that season and the leftover HM after the grazing season. Although the total HM grazed during a given grazing season (GHM_P) was larger with a higher SR (Figure 5), the residual HM after the grazing season decreased with an increase in SR. Thus, the amounts of total HM produced in a season were about the same across SRs.

The drought-induced losses of grazed herbage mass (GHM), including both GHM_P and GHM_A, SWG, and ADG also showed similar trends. These results were likely because, regardless of SR, these variables were based on the total amount of HM produced in the grazing season, the loss of which had an exponential relationship with drought severity. However, the loss trends became more pronounced with an increase in SR (Figure 9) because the values of each of these variables under rainfed conditions relative to those under irrigated conditions decreased quadratically with an increase in SR. The above results further validated the robustness of the DGESS interface model [21].

Figure 9. Relationships between the drought index ARID values and the drought-induced loss of bermudagrass herbage mass (HM), grazed HM (GHM), and stocker seasonal weight gain (SWG) and average daily gain (ADG) at three stocking rates (SR) at Overton, TX, USA during 1950-2025. The dots and dotted lines in figure represent magnitudes and trends, respectively.