Introduction

Oats (Avena sativa L.) are the seventh most important cereal worldwide, with an annual production of 18.7 million tons of grain. The importance of this crop lies in its hardiness and adaptability to diverse environments, its versatility for forage uses, and its use of grain for human consumption (^{FAO, 2024}). Since the beginning of crop breeding, there has been an effort to privilege the development of varieties with genetic combinations that combine high yield, higher quality, and adaptability to various production environments (^{Liu et al., 2016}; ^{Mehraj et al., 2017}). Plant breeders have worked to develop good-quality, consistent, and high-yielding cultivars; such cultivars are highly desired to adapt to a wide range of environments (^{Mut et al., 2018}). It is a crop that stands out for being more suitable than others in marginal lands, such as high and cold areas, as well as in infertile and arid areas (^{Buerstmayr et al., 2007}).

In Mexico, in 2023, about 352 000 ha of forage oats were planted, with a production of 2.9 million tons with an average yield of 8.23 t ha^-1; in contrast, in the High Valleys of Mexico, that year, about 104 000 ha were planted for forage, obtaining an average yield of 16.6 t ha^-1 and about 37 000 ha for grain, with an average yield of 2.4 t ha^-1 (^{SIAP, 2024}); at the national level, this crop is highly adaptable to high, cold and rainy areas, as well as to semi-arid environments and is an alternative when crops such as corn, beans, wheat, or barley are damaged by drought or early frosts (^{Villaseñor et al., 2021}).

Yield stability cannot be directly measured in a field experiment in one year, it must be evaluated in various locations or environments for several years (^{Reckling et al., 2021}); this concept is useful for plant breeders who develop genotypes adapted to a wide range of environmental conditions (^{Mühleisen et al., 2014}); in addition, in recent years, there has been a greater variability in climatic conditions, which is associated with lower stability of crop yields (^{Müller et al., 2018}; ^{Tigchelaar et al., 2018}).

For the study of genotype × environment interaction (GEI), among all the statistical analyses developed, the most used are the GGE biplot and the Additive Main Effects and Multiplicative Interaction (AMMI) models (^{Dyulgerova et al., 2020}). The AMMI model is efficient because it captures much of the sum of squares of the GEI, accurately separates the main effects, and provides a meaningful interpretation of the data (^{Ebdon and Gauch, 2002}); it also allowed us to understand the interactions of the GEI of genotypes in multiple environments (^{Luo et al., 2015}).

Given this scenario, studies are needed to develop oat materials that meet the aforementioned requirements. This work is conceptualized as a tool for the selection of materials to be planted and thus achieve a positive impact on production; therefore, the objectives were to determine the stability of grain yield of oat varieties across rainfed environments in the High Valleys of Central Mexico and to identify high-yielding, stable and consistent varieties.

Materials and methods

The study utilized information from 12 oat varieties released by INIFAP’s Oat Genetic Improvement Program, which were evaluated under rainfed conditions using an experimental design in complete blocks with randomized treatments (DCBRT) with two replications. The size of the experimental plot was four rows, each measuring three meters in length and spaced 30 cm apart, with the useful plot being the total of the experimental plot (4.5 m²). The agronomic variables evaluated were days to flowering (DF), days to physiological maturity (DM), plant height (PH), and grain yield (YIE); however, for the present study, the variable of interest is YIE.

The agronomic management of the crop followed guidelines recommended by INIFAP according to each region. Each variety was established in 23 environments, which have been cataloged depending on the conditions they present; the classification proposed by ^{Villaseñor and Espitia (2000)} considers the following: favorable environments, those with rainfall greater than 600 mm during the growing season and well distributed, soils with good moisture retention, low temperatures at the end of the cycle and high relative humidity; intermediate environments, with precipitation ranging from 400 to 600 mm during the growing season and regularly distributed, soils with regular moisture retention and low temperatures at the end of the cycle. Critical environments, with rainfall of less than 400 mm during the growing season and poorly distributed, thin soils with low moisture retention, and low temperatures at the end of the cycle. Table 1 groups the evaluated localities by the type of environment to which they belong, as well as the average of the variables evaluated for the 12 varieties.

Results and discussion

Table 2 presents the values obtained for each methodology, where it is possible to observe that for ^{Eberhart and Russell (1966)}, the regression coefficients and the deviation of the regression are used. Likewise, the possible situations of the values of the stability parameters were considered.

Figure 1 shows the results plotted and obtained through the stability parameters of Eberhart and Russell, where the behavior of the 12 varieties is observed by means of the regression coefficients and the deviation of the regression; if the regression coefficient (bi) is close to 1, they are considered to be adaptive genotypes; if the deviation of the regression (S²di) is close to zero, they are stable genotypes.

Figure 1 Yield stability parameters (regression coefficient, bi and variability or deviation of the regression, S²di) obtained through the analysis of ^{Eberhart and Russell (1966)}. 

Eberhart and Russell emphasized considering the linear (bi) and nonlinear (S²di) components of GxE interactions when judging the stability of a genotype (^{Akcura et al., 2005}). According to what was obtained, it is highlighted that variety 3 (Cuauhtémoc) is considered stable, but with low yield, whereas variety 8 (Karma), considering the classification of ^{Carballo and Márquez (1970)}, responds well in all environments, but is inconsistent; the rest of the varieties do not show significant behavior. Similarly, the regression deviations are non-zero, which aligns with ^{Rodríguez et al. (2002)}, who determined that the linear model is not appropriate for describing the response of genotypes as a function of environmental effect; according to this criterion, the genotypes mentioned would not be stable.

^{Rodríguez et al. (2002)} stated that lower regression coefficients, bi< 1, indicate genotypes with relative adaptation to unfavorable environments, while genotypes with values of bi> 1 indicate that they respond adequately to environmental improvements. In the present study, the Obsidiana, Teporaca, Diamante R31 and Papigochi varieties have regression coefficients lower than 1, which makes them varieties that respond better in unfavorable environments; for their part, Avemex, Chihuahua, Karma, Turquesa and Menonita, with regression coefficients equal to or greater than 1, are considered genotypes that respond adequately to better environments.

Table 3 presents the results obtained from the AMMI analysis, in which, according to the Gollob test (^{Vargas and Crossa, 2000}), five principal components represent important variability; the first only considers 34.57% of the variability of the GEI or of the sum of squares of this source of variation, so the discrimination of genotypes using this study technique may be somewhat limited, coinciding with the results reported by ^{Dyulgerova et al. (2020)}, which demonstrates the need to perform tests in various environments to identify stable and high-yielding lines; likewise, ^{García et al. (2021)} mention that the advantage of the AMMI model can be seen in identifying genotypes with superior yields and high stability from those with medium yields, but with specific adaptation.

Figure 2 shows the results of the AMMI analysis for the 12 varieties evaluated in the 23 environments, which were obtained from Table 2. The results are easier to interpret when genotypes and environments are presented graphically (GGE Biplot). The grain yield of the genotypes and environments is read on the x-axis.

Figure 2 GGE biplot of the AMMI analysis for grain yield of 12 oat varieties evaluated in 23 rainfed environments of the High Valleys. 

The line perpendicular to this axis indicates the average yield, so the inputs with the lowest yield are plotted to the left of this axis, and the varieties and environments with the highest yield are located to the right. On the other hand, the y-axis measures the stability of genotypes and environments: those with values close to zero are stable, while those with high values of the first principal component are unstable. Generally, the recommendations of the best are based on the average performance of the genotypes across environments (^{Adnan et al., 2020}); likewise, the biplot allows the selection of stable and superior genotypes in multiple environments, as stated by ^{Khan et al. (2021)}.

According to the information generated, the Chihuahua and Avemex varieties were the most stable, but they registered low yields; in contrast, the Ágata, Menonita and Turquesa varieties were the most stable and those that registered the highest yields, although the higher productivity of Ágata is evident. On the other hand, the Cuauhtémoc, Diamante R31, Papigochi, Karma, Obsidiana and Jade were the most unstable varieties as they were far from the zero value of the y-axis (2) and some of them registered the lowest yields.

Environment 20 (Tlalmanalco, Mexico) had the highest yield, and since it has the longest vector, it is inferred that it discriminated the genotypes better compared to environment 13 (Soltepec, Tlaxcala), which registered the lowest yield. Environments 5, 6, 7, 8 and 14 had the shortest vectors, indicating that they did not discriminate genotypes; that is, most of them showed a similar response.

Through the AMMI analysis, the varieties that were the most stable and yielding were Ágata, Turquesa, and Menonita, as their values in the yield component fell within the parameters established by this model, which in turn allows us to indicate that the test is adequate for the present research.

One of the most common tests to determine stability in genotypes across environments is that of ^{Eberhart and Russell (1966)}, through which, for the present study, it was determined that the varieties that showed stability were Ágata, Jade and Cuauhtémoc, whereas the least stable varieties, but with adaptation to unfavorable environments, were Obsidiana, Teporaca, Diamante R31 and Papigochi; for their part, the Chihuahua, Karma, Turquesa, Menonita and Avemex varieties improved their performance in response to improved environmental conditions, combination of precipitation, soil moisture, as reported by ^{Villaseñor and Espitia (2000)}, since in the latter, their bi was greater than one.

Ágata was the most outstanding variety with conventional analyses of variance, expressing itself as a high-yielding variety, as pointed out by ^{Villaseñor et al. (2018)}, who described it as a variety with the best response in all environments, but inconsistent, which is not adequate, since consistency across environments is important in the High Valleys of Mexico.

Conclusions

The evaluation of the varieties in various contrasting environments enabled us to discriminate among them in the best way, as they all presented significance in the GEI. The results of the methods to determine stability were not consistent; nevertheless, they agree in pointing to the Ágata variety as the most stable and high-yielding, and the Papigochi, Jade and Karma varieties were the most unstable. With the implementation of these methodologies, it is proposed to continue recommending stable and high-yielding varieties, such as Ágata and to stop using Papigochi, Cuauhtémoc, and Avemex because they are unstable, inconsistent, and low-yielding.

Acknowledgements

We thank INIFAP for financing the research through the fiscal project: ‘generation of oat varieties to increase productivity in Mexico’ with SIGI number 9165636496.