Introduction

In Mexico, corn is the most important crop for being the main food of the population, for its sown area and for generating 36% of the value of agricultural production. The main use is direct consumption in its different forms in human diet. The national area in 2018 was 7.95 million hectares, of which 7.345 million were for grain, with an average yield of 3.748 t ha^-1 and a production of 26.67 million tonnes, of which 12.6 million tonnes are used for direct consumption, 35% is through the flour industry and 65% through the dough and tortilla industry in the process of nixtamalization. However, during 2018 17.095 million tonnes of yellow grain were imported for the feed industry, which generated an apparent per capita consumption of 345.6 kg (^{SAGARPA 2018}).

In the tropical region of the country, 2.8 million hectares are sown with corn, of which one million are located within agronomic provinces of good and very good productivity and 91 000 ha are sown under irrigation conditions (^{Espinosa et al., 2019}), in this area the use of improved seed of hybrids and synthetic varieties is feasible since these have good yield potential under favorable conditions of climate, soil and management by farmers (^{Sierra et al., 2019}).

In the genetic improvement of corn for the tropics, by-products such as free-pollinated varieties, synthetic varieties and corn hybrids are generated (^{Sierra et al., 2019}), in the formation of hybrids it is important to identify parents with good general (GCA) and specific combining ability (SCA), good yield per se, tolerance to biotic and abiotic stress, ease and profitability in the commercial production of seed (^{Tadeo et al., 2015a}; ^{Tadeo et al., 2015b}; ^{Trachsel et al., 2016}; ^{Gómez et al., 2017}; Sierra et al., 2018).

Regarding the use of hybrid seed, the genetic variance, deviation of additivity and the advantages offered by heterosis in the commercial production of corn, given by the heterozygosity when crossing corn parents with relative genetic divergence, are taken advantage of (^{Reyes, 1985}; ^{Esquivel et al., 2011}; ^{Sierra et al., 2018}; ^{Sierra et al., 2019}). ^{Chuquija and Huanuqueño (2015}), from a study on the behavior of eight populations of yellow corn, found that populations 28 and 24 were good parents, because their descendants were more yielding, of lower plant height and earlier than the tester.

From a study with corn germplasm adapted to High Valleys, ^{Velasco et al. (2019}) found that the cross F1p9*P8 presented the highest value of heterosis (26.19%). ^{Reyes (1971}) used the heterotic pattern humid tropics x dry tropics in the formation of the hybrids H-503 and H-507. ^{Córdova et al. (2007}) report that the cross CML247xCML254 has been used as a control in several experiments in national programs in Latin America, in which it has expressed good yield and favorable agronomic characteristics, it has also been used by several seed producing companies. ^{Sierra et al. (2004}) used as testers inbred lines of good specific combining ability (SCA), LT154, LT155, CML247 and CML254, which allowed identifying advanced lines and separating heterotic groups. ^{De la Cruz et al. (2010}), from a study on heterosis and combining ability in tropical corn populations, found that additive effects were the main component in the expression of grain yield. ^{Gómez et al. (2015}), in crosses of local varieties of temperate climate with adapted varieties of the tropics, found crosses of the Chalqueño race with Tepecintle with the highest values of heterosis.

Varietal crosses represent an alternative in commercial corn production due, among other reasons, to the heterosis that results from crossing two parents free-pollinated varieties, and to the fact that only two parents have to be kept; therefore, commercial seed production is easier and more profitable (^{Sierra et al., 2016}; ^{Sierra et al., 2018}). For their part, ^{Tadeo et al. (2015}b) mention that although the varieties V-54A and V-55A represent a good option for rainfed producers in the High Valleys of Mexico, the cross 156xV-54A was found, which exceeded by 38.1% the yield of the variety V-54A, which can represent advantages in commercial sowings.

According to the values of Heterosis, GCA and SCA for yield, ^{Palemón et al. (2012}) selected the varietal crosses VS-529*VE1 and VS-529*VE3 for mass promotion in the semi-warm region of the state of Guerrero. The adaptability of genotypes allows knowing the response to different environments defined by climate, soil and agronomic management (^{Eberhart and Russell, 1966}). The environment-genotype interaction is the relative differential behavior exhibited by genotypes across different environments (^{Reyes, 1990}; ^{Andrés et al., 2017}; ^{Sierra et al., 2018}).

The model by ^{Eberhart and Russell (1966}) uses the regression coefficient to measure the response of a variety to different environments and the regression deviation that measures the consistency of said response, it is necessary to select genotypes that interact as little as possible with the environment. A stable variety is one with a coefficient of variation equal to 1 and regression deviation equal to 0. The statistical model is: Y¯ ij = μi+ βiI_j+ δ_ij. Where, Y ¯ _ij= mean of variety i in environment j; μ_i= mean of variety i in all environments; β_i= regression coefficient; I_j= environmental index; δ_ij= regression deviation.

The objectives of the research were to know the yield, adaptability and agronomic characteristics of varietal crosses of corn across environments in the states of Veracruz and Tabasco and to determine heterosis with respect to the best parent. The hypotheses were to verify that, in the varietal crosses of corn in evaluation, there are differences in adaptability and agronomic characteristics across environments, as well as values of heterosis with respect to the best parent.

Materials and methods

Location. The formation of varietal crosses of corn was carried out in the Cotaxtla Experimental Field, belonging to the National Institute of Forestry, Agricultural and Livestock Research (INIFAP, for its acronym in Spanish), located in the municipality of Medellín de Bravo, Veracruz, located at 18° 56’ north latitude and 96° 11’ west longitude and an altitude of 15 masl, the climate, according to the Köppen classification modified by ^{García (1981}), with area of influence in the humid tropics of Mexico, includes the climatic group A (Aw, Am and Af), humid and subhumid warm with average temperature of 25 °C and annual rainfall of 1 400 mm, distributed from June to November.

The soil is of alluvial origin, deep, with medium texture throughout the profile, slope less than 1%, good drainage and slightly acidic pH (6.6). The evaluation localities of the varietal crosses were: Cotaxtla Experimental Field, CBTA 84 of the municipality of Carlos A. Carrillo in Veracruz and Huimanguillo in the state of Tabasco, with climate Aw1, Aw2 and Am for each locality, respectively.

Germplasm used. The corn germplasm used in the present research is experimental material in different degrees of advance in genetic improvement, particularly they are varietal crosses of corn formed with experimental synthetic varieties belonging to the Tuxpeño race, 28 genotypes were evaluated, of which 20 are varietal crosses, five experimental synthetics, the varieties VS-536 and V-537C and the hybrid H-520, used as controls for their commercial use (^{Sierra et al., 2019}).

Description of the experiments. During the spring-summer cycles 2016, 2017 and 2018, 20 varietal crosses of corn, five experimental synthetics, the varieties VS-536 and V-537C and the hybrid H-520 used as controls, were evaluated, which were distributed under a randomized complete block design with 28 treatments and three repetitions in plots of 2 furrows 5 m long, 80 cm apart, at a density of 62 500 plants ha^-1, for weed control Atrazine was applied in a pre-emergent way, and the fertilization was carried out with the formula 161-46-00, using urea as a nitrogen source and foliage pests were controlled during the development of the crop.

Variables and data recording. Due to their economic importance and reduction in the risks in production, the main agronomic variables recorded in the experiments were: days to male and female flowering, plant and ear height, rating of appearance and health of plant and ear using a rating scale of 1 to 5, where 1 is the best and 5 is the worst, total number of plants, % of lodged plants, % of ears with poor cover, at harvest the variables of grain yield, total number of ears, % of rotten ears and % of dry matter in the grain were recorded.

Statistical methods. The designs used were randomized complete blocks with 28 treatments and three repetitions in plots of two furrows 5 m long, 80 cm apart, with a density of 62 500 plants ha^-1. An individual analysis for each experiment and a combined analysis of the varietal crosses in the six evaluation environments were performed. For the separation of means, the least significant difference (LSD) test was applied, at 0.05 and 0.01 probability (^{Reyes, 1990}).

An analysis of stability parameters was made (^{Eberhart and Russell, 1966}). Comparisons and t-tests at 0.05 and 0.01 probability were made for varietal crosses and their parents’ synthetic varieties. Likewise, the percentages of heterosis with respect to the best parent were calculated (^{Reyes, 1985}), as follows:

Results and discussion

From the combined analysis of variance for grain yield in the varietal crosses (Table 1), statistical significance at 0.01 probability was found for genotypes (G), for environments (E) and for the GxE interaction, the significance for the interaction suggests that the genotypes outstanding in one environment are not necessarily outstanding in other environments. In Table 1, it can be observed that the variance due to the factor environments was more important, which means that the environment is important in the expression of varietal crosses; likewise, the coefficient of variation recorded was 13.97%, a relatively low value, which suggests that the management of the experiments and the data obtained are reliable (^{Reyes, 1990}).

In the genotype-environment interaction and according to the parameters of stability (^{Eberhart and Russell, 1966}), the 28 genotypes were characterized as stable (^{Reyes 1990}; ^{Andrés et al., 2017}; ^{Sierra et al., 2018}). The varietal hybrids outstanding in yield at 0.01 probability were: SINT-2BxVS-536, SINT-4BxVS-536, SINT-4BxSINT-2B, SINT-5BxVS-537C, VS-536xV-537C, SINT-3BxSINT-1BQ, SINT-2BxVS-537C, SINT-5BxVS-536, SINT-1BQxVS-536, SINT-5BxSINT-1BQ, with grain yield of 6.45 to 7.21 t ha^-1 (Table 2). Also, this group of varietal hybrids was superior in yield by 1 to 13% more in relation to the commercial control H-520.

These varietal crosses have the additional advantage represented from the point of view of keeping only two parents, which are free-pollinated varieties with greater profitability and ease in the commercial production of seed (^{Tadeo et al., 2015a}; ^{Tadeo et al., 2015b}; ^{Sierra et al., 2016}; ^{Gómez et al., 2017}; ^{Sierra et al., 2018}).

In the best crosses, the presence of VS-536, a variety of greater commercial use in southeastern Mexico (^{Sierra et al., 2016}), is observed. Also, the percentages of heterosis with respect to the best parent were: 19.76, 13.46, 11.29, 8.54, 16.9, 5.46, 7.64, 6.24, 6.07 and 5.91% for each varietal hybrid, respectively (Table 2 and Figure 1) (^{Reyes, 1971}; ^{Reyes, 1985}; ^{Sierra et al., 2004}; ^{Córdova et al., 2007}; ^{De la Cruz et al., 2010}; ^{Esquivel et al., 2011}; ^{Palemón et al., 2012}; ^{Chuquija and Huanuqueño, 2015}; ^{Gómez et al., 2015}; ^{Velasco et al., 2019}).

Figure 1 Heterosis in outstanding varietal crosses of corn, Veracruz and Tabasco 2016-2018. 

Environmental indices. Regarding the environmental indices, according to ^{Eberhart and Russell (1966}), the environments of Carlos A. Carrillo, Veracruz, in 2016B and Cotaxtla, Veracruz in 2016B had significantly higher average yields with 7.29^** and 7.27^** t ha^-1 and positive values in the environmental indices with 1.01 and 0.99 for each environment respectively, while Cotaxtla in 2017B and the locality of Huimanguillo, Tabasco in 2018 and 2016B had the lowest average yields with negative environmental indices of -0.25, -0.88 and -1.1 for each environment, respectively (Table 3).

Conclusions

The outstanding varietal hybrids were: SINT-2BxVS-536, SINT-4BxVS-536, SINT-4BxSINT-2B, SINT-5BxVS-537C, VS-536xV-537C, SINT-3BxSINT-1BQ, SINT-2BxVS-537C, SINT-5BxVS-536, SINT-1BQxVS-536, SINT-5BxSINT-1BQ, with grain yield of 6.45 to 7.21 t ha^-1 and they were superior to the commercial control H-520. The percentages of heterosis with respect to the best parent in the outstanding varietal crosses were: 19.76, 13.46, 11.29, 8.54, 16.9, 5.46, 7.64, 6.24, 6.07 and 5.91% for each varietal hybrid, respectively.

The crosses had an average yield of 6.39 t ha^-1, 8% more in relation to the parents, as well as better rating of appearance of plant and ear. The outstanding crosses showed low plant and ear, good appearance and health of plant and ear, tolerant to lodging, with good ear cover, low percentage of rotten ears. The variety VS-536, of greater commercial use and adapted to the tropical region in southeastern Mexico, participates in five of the 10 outstanding crosses.

Outstanding varietal crosses represent an important advantage from the point of view of keeping both parents, free-pollinated varieties with greater profitability and ease in the commercial production of seed.