Introduction

As global food demand is constantly increasing, minor cereals and pseudocereal proteins are gaining increasing attention (^{Guerrieri and Cavaletto, 2018}). Amaranth is a pseudocereal of multipurpose cultivation with good potential for exploitation of grain, vegetable and fodder, the crop has high levels of proteins (14-17%) and minerals, compared to other cereals such as sorghum, rice, wheat and corn (^{Mustafa et al., 2011}).

Currently, 70 species of Amaranthus have been documented, among these are Amaranthus hypochondriacus L., Amaranthus cruentus L. and Amaranthus caudatus L., which are the main grain-producing species (^{Trucco and Tranel, 2011}). The amaranth grain is widely used for food in the country, the best known is as popped grain for the preparation of traditional candies known as ‘alegría’, brittles, granola, cookies and flakes.

It is rich in essential amino acids such as lysine and methionine (^{Januszewska and Synowiecki, 2008}), gluten-free (^{Aderibigbe et al., 2022}), and contains squalene, a terpenoid that helps reduce cholesterol levels in the body (^{Shin et al., 2004}). Popping is a process that is carried out under vapor pressure. The micropores present in the grain structure cause the vapor to be expelled at high pressure because they expand or inflate. Inflating the grain results in a porous structure that increases their flavor and aroma (^{Nath et al., 2007}).

However, the quality of the popping is at risk when working during the process with inadequate temperatures and with immature seeds derived from indeterminate inflorescences and plants susceptible to lodging. Therefore, it is necessary to carry out research focused on studying the effect of genotype and environment on the popping of amaranth grain, in order to determine the best genotypes for these environments and the respective quality characteristics of the harvested grain and its processing.

Popping is influenced by the genotype, by the size of the seed and by the method of popping (^{Vázquez et al., 1988}), within the genotype there is the variant of varieties with binding and non-binding starch, determined by type of perisperm, which is a function of the composition of the starch and influences its physicochemical properties and the popping capacity of the amaranth seed, opaque perisperm genotypes popped better than crystalline ones (^{Aguilar et al., 2022}).

Conventional improvement methods for autogamous species, in a general way, lead to a progressive and intense reduction of opportunities for genetic recombination, resulting in a reduction of genetic variability and restriction of selection gains. In addition to this, an excessive narrowing of the genetic base of the populations used has been verified (^{Servellón, 1996}). Heritability and genetic advancement are important selection parameters, which, when studied, allow the evaluation and identification of superior genotypes (^{Tasiguano et al., 2019}).

Heritability values help in the selection of outstanding genotypes from various genetic populations. Genetic advancement measures the amount of progress that might be expected with the selection. In population improvement, only the additive genetic component is passed on to the next generation. The level of improvement also depends on the rigor of selection and the genetic advancement obtained from the population (^{Lovely and Vijayaraghava, 2017}).

In contrast, the selection of suitable varieties is difficult due to their different levels of response to the environment (^{Ferreira et al., 2006}). Nevertheless, it is necessary to identify which varieties have high grain yield, agronomic characteristics suitable for a certain environment and high expansion volume of popped grain (^{Ortiz et al., 2018}). Therefore, the objective of the present research was to evaluate amaranth genotypes for their popping capacity, in addition to genetic variability, heritability and the association of quality variables that favor the popping volume.

Materials and methods

Results and discussion

Table 2 shows the mean squares of the combined analysis of variance for the variables under study. Highly significant differences (p≤ 0.1) were detected for environments in all the variables analyzed. For genotypes, there were only highly significant differences (p≤ 0.1) in weight of one thousand grains, popping volume and volume increase. For the genotype-environment interaction, the variables weight of one thousand grains, seed diameter, popping volume and volume increase were highly significant (p≤ 0.1).

Genotype, environment and their interaction play an important role in the final expression of grain yield and quality attributes (^{Kaya and Akcura, 2014}). Such interaction indicated that genotypes performed differently in different environments and that genotypes should be selected to adapt to specific environments.

Table 3 shows the comparison of means between localities in each of the environments. When analyzing the influence of the environment of the different localities, it is observed that it influenced the weight of one thousand grains, seed diameter and popping volume. The environment that resulted with the greatest weight of one thousand grains was that of Cuapiaxtla (0.813 g) and those of the lowest weight were Santa Lucía 2017 in the two sowing dates (0.753 with and 0.746 without), the seeds with the largest diameter were found in the environments of Santa Lucía 16 2F and Santa Lucía 17.

The environment that presented the highest popping volume was Santa Lucía 2017 with (214 cm³). The least favorable locality for amaranth popping volume were Cuapiaxtla and Santa Lucía 2017 without, while Santa Lucía 16 1F was the most favorable environment for volume increase (6.45). According to ^{Guy (2001}), popped grains must generally contain more than 60% starch to ensure the desired expansion, so that any structural damage to the perisperm affects the expansion process and this can produce two effects: the non-popping of the grain or the reduction of the final volume of the expanded product (^{Tandjung et al., 2005}), this information coincides with the results of this research.

Therefore, the relationship between the environment and the effect on the variables studied may be due to the shortening of the carbon assimilation cycle and the grain filling period (^{Awasthi et al., 2014}), which produces smaller seeds. Table 4 shows the comparison of means by genotype. Tlahuicole, Revancha, Areli, Determinada and L145 presented the highest weight of one thousand grains (0.871 to 0.838 g), contrary to the Chichiltic genotype which was the one with the lowest weight (0.661 g), followed by AGIM (0.685 g).

The genotype with the largest seed diameter was Areli (1.347 mm) and those with the smallest diameter were Chichiltic, Benito and Amaranteca. In the variable of popping volume, all varieties showed a good yield, except for the genotype L145, although all are within the acceptable range. In volume increase, the most outstanding genotype was Tlahuicole, followed by AGIM, both had the largest increase in popping volume (6 and 5.93), respectively.

The analysis of different genotypes in different environments allows determining the agronomic potential for each of them in order to obtain the best yields and industrialization characteristics. In this sense, according to ^{Bishaw et al. (2007}), seeds obtained from different geographical areas are modified in their viability by the conditions present at the time of their formation, development and maturation.

Deficiency in water (^{Dornbos et al., 1989}; ^{Ghassemi et al., 1997}), minerals and extreme temperatures (^{Grass and Burris, 1995}) are the most common and have the greatest effect on seed quality. In contrast, genotype is not associated with seed diameter and weight of non-popped seed. Only this last variable does not show significance in the genotype-environment interaction. Therefore, it is important to determine and quantify how environmental factors and the genotype-environment interaction influence the variation in each grain quality parameter (^{Kaya and Akcura, 2014}).

Figure 1 shows the origin of the variation of the characteristics studied. It can be observed that variation due to environmental effects was the main source of 4 of the 5 variables studied; this coincides with studies reported in other crops (^{Papastylianou et al., 2021}). Weight of one thousand grains was the one that showed the highest variation due to genetic effects (65.96%), which means that this genetic variability could be capitalized in a selection scheme.

Figure 1 Proportion of variability by source of variation in 12 amaranth genotypes evaluated in six rainfed environments in the Central Plateau. AMB= environment; AMB(REP)= repetitions within the environment; GEN= genotypes; AMB*GEN= environment by genotype interaction. 

This variable is important because it is related to heavier grains, that is, grains with greater storage of starch, which represents about 63% of the seed content, and it is associated with grain yield, this trait is closely linked to solar radiation and accumulation of dry matter in the plant, that is, there is also an environmental effect. On the other hand, some studies show that the starch content is connected to the popping volume, so the physicochemical characteristics have an important function in the quality of the popping, therefore, this also causes some grains not to pop (^{Núñez Limón, 2018}).

For the variables seed diameter, popping volume and volume increase, they presented a variation due to genetic effects, between 4.46 and 6.5%, while the variable of weight of non-popped grain showed only a variation consequence of the genetic effects of 0.55%. Therefore, the variation of these four variables was predominantly due to environmental effects; where the largest was due to environments in seed diameter (29.87%) and volume increase (18.99%).

The magnitude of the variation due to the experimental error is remarkable, this could occur due to the low genetic variability in the traits studied. This can be explained by the high percentage of self-pollination that occurs in the plant (^{Agong and Ayiecho, 1991}) and because gene flow between species is very limited (^{Ruiz et al., 2018}).

In relation to the effects due to the genotype-environment interaction, this was higher in volume increase (16.4%) and popping volume (13%), for seed diameter it was medium (9.8%), while for weight of one thousand grains (7.3%) and weight of non-popped seed (1.9%) it was low. The variation due to interaction was less than that of the two main sources and less than 20%. The similarity in the environments, characterized by similar precipitation, and the inclusion of only two localities of the High Valleys of Mexico with little longitudinal variation, altitude and latitude, could be the cause to understand the low variation of the genotype-environment interaction.

Table 5 shows the results obtained from the coefficient of genetic variation and heritability for the variables evaluated. The variables seed diameter (0.065), weight of non-popped seed (0.006), popping volume (0.045) and volume increase (0.053) presented low heritability values, which indicates that there is an influence of the environment as they present values close to zero. ^{Joshi and Rana (1992}) found high values (0.60 to 0.76) for different genotypes of A. hypochondriacus, for variables such as plant height and inflorescence length and intermediate values (0.26 to 0.47) for yield (^{Pandey, 1982}).

Plant breeders use heritability estimates to determine the influence of environmental and genetic factors on the trait of interest and choose the selection procedure that should be implemented to make improvements to crops (^{Kaya and Akcura, 2014}).

Knowing the correlations between the variables and their heritability allows improving the efficiency of selection programs. Correlations often depend on heritabilities, so that, if both correlated traits have low heritabilities, the phenotypic correlation will be determined mainly by the environmental correlation; but if they have high heritabilities, then the genetic correlation is the most important (^{Falconer, 1984}).

Therefore, for the variables evaluated, only the weight of one thousand grains is determined by the genotype (Table 5) and it can be used to carry out genetic improvement and increase the efficiency of selection programs. Table 6 shows low negative correlations between the different variables, except for seed diameter and weight of one thousand grains, which indicates that the diameter influences the weight of one thousand grains and the volume of popping favors the increase in volume.

According to ^{Mishra et al. (2014}), the variety is a factor that significantly affects the volume of popped seeds, this agrees with the results obtained in this study, which was also corroborated by ^{Ortiz et al. (2018}); likewise, the type of starch of the genotypes influences the popping capacity (^{Aguilar et al., 2022}).

This may be related to the moisture content of the seed at the time of popping (^{Haught et al., 1976}) or the method of popping (^{Vázquez et al., 1988}; ^{Dofing et al., 1990}). It is clear that the genotype has a slight effect on the popping capacity, which is not comparable with the effect of the environment; this indicates that the popping capacity in amaranth is not an easy trait to improve.

Conclusions

The genotype component was the main cause of variation for weight of one thousand grains, in addition to presenting the highest coefficient of genetic variability and the highest heritability. Weight of one thousand grains was the variable that showed the highest variation due to genetic effects, so it is a characteristic that can be used in plant breeding.

The environment factor was the most important component for seed diameter, weight of non-popped seed, popping volume and volume increase, so they are traits difficult to improve, at least for this group of genotypes. The positive correlation between seed diameter and weight of non-popped seed with popping volume and volume increase indicate that these characteristics can be used as selection criteria to improve popping volume.