Introduction

Horticulture is an agricultural activity of great economic importance for foreign exchange earnings and job creation. The tomato is the second largest in the world after the potato horticultural crop. Globally, the main producers are China, India and the United States. Mexico is located in tenth place with 2 838 69 tons annually (^{FAOSTAT, 2012}), is the vegetable crop wider distribution, it is sown in all entities of the country under a wide variety of weather conditions and farming systems. In 2013 there were 2 694 358 tonnes, with a value of $15 045 508. In that year the major producing states were; Sinaloa, Baja California, Zacatecas, San Luis Potosi and Jalisco, with an average yield of 57.21 t ha^-1 in open field and greenhouse. Currently it is relevant to note that the Laguna region of northern Mexico, about 900 ha of tomatoes planted under irrigation and temporal (^{SIAP-SAGARPA, 2013}).

The steady growth of the population and therefore the growing demand for food, it has become necessary to produce food and raw materials industrializable as much per unit of arable land. Faced with this demand the main aim of breeding is to increase production and quality of agricultural products per unit area in the shortest time with the least possible effort and cost. This can be achieved by obtaining new varieties or hybrids with higher productive skills in grains, fruits, stems and leaves or roots, and responsive to the needs of farmers and consumers.

One alternative to achieve an increase in production per plant, is evaluating new hybrids or varieties leading in terms of combining ability parameters for important agronomic traits. Among the most commonly used genetic designs to find genotypes with outstanding characteristics judging by his general combining ability (ACG) and specific (ACE) were proposed by ^{Haynman (1954)}, ^{Griffing (1956)} or by ^{Gardner and Eberhart (1966)} by which greater efficiency in the breeding program is achieved, allowing select lines or genotypes from a series of diallel crosses.

The ACG analysis allows parents to properly identify their ability to transmit desirable traits to offspring and ACE possible to know all the outstanding hybrid F₁ combinations, originated from crosses between varieties, lines or populations. This type of analysis also provides information on the type of gene action that affects the expression of a character, which is basic to choose the most appropriate method to follow. Determining the ACG and ACE, it allows to know how genes act on certain characteristics, as well as the relative importance of each, making it possible to obtain rapid progress in breeding if greater fitness genotypes used combinatorics. When the values of ACG outweigh the ACE means the supremacy of additive effects. If not, they are more important dominance effects non-additives (^{Peña et al., 1999}; ^{Elizondo, 2000}; ^{Espitia et al., 2006}).

^{Sanchez et al. (2010)} to assess the genetic effects of four parents and six direct crosses tomato in field and greenhouse for variables of performance and quality, they found differences in the combined analysis of variance (p≤ 0.01) environments to average weight of result and performance as well as significant (p≤ 0.05) for days to first cut. The environmental conditions of each locality were different genotypes in general, including parents and hybrids, average fruit weight and yield, indicating that genotypes behaved different and hybrids differ in their behavior due to the genetic diversity of the parents. ^{Mendoza et al. (2010)} found in a study of 9 Saladette tomato hybrids evaluated under greenhouse and hydroponics six crosses that matched shelf life (p≤ 0.05) from their parents and exceeded total fruit yield, with effects of heterosis with respect to best parent and parent average fluctuated between 9 and 11 and between 7 and 16 kg parcela^-1 eight plants respectively (p≤ 0.01 o p≤ 0.05), noting that genotypes can be hired attributes of combining ability and parcel additive, for use as varieties; also they possess specific skills favorable to produce combinatorial dominance effects and be operated in hybrid combinations.

In Bangladesh 10 parents and 45 possible crosses of tomato genotypes were studied to analyze the heterosis of yield components, significant differences (p≤ 0.01) among genotypes for all the characteristics evaluated performance, these results were found three hybrids were selected by high performance heterotic (^{Hannan et al., 2007}). In a study of heterosis and combining ability in five parents and his 10 crosses tomato with adaptation to high temperatures, it was found that hybrid outperformed parents for fruit yield of large and medium size, suggesting the presence of effects additives, noting that the presence of heterosis in tomato hybrids is associated with increased plant biomass and hence fruit production (^{Moreira et al., 2003}).

Based on the above, this study raised the following objective: identify and select outstanding genotypes on important agronomic characteristics of performance and assess the genetic effects between parents and hybrids of tomato (Solanum lycopersicum L.) under field conditions following analysis methodology II of ^{Gardner and Eberhart (1966)}.

Materials and methods

The genetic material was used in this research were eight lines of tomato as parents and 28 direct crosses. Crosses were performed based on the method II of Griffing model I (1956), which involved parents and direct crosses (Table 1). The formation of hybrids was conducted in a greenhouse of the Universidad Autonoma Agraria Antonio Narro (UAAAN), Coahuila state, during the cycle autumnwinter 2011. The fruits from each cross were harvested at physiological maturity stage and stored until complete ripening, for extraction of seed, and hybrids subsequently evaluated.

Evaluation of the genetic material. The evaluation of the 36 materials (progenitors and cross) was held in the springsummer cycle, 2012, in an experimental batch of UAAAN, located in the village of Buenavista, south of Saltillo, Coahuila, Mexico, located at 25° 23' north latitude and 101° degrees 00' west longitude and an altitude of 1 743 meters above sea level, with a climate (Bshw) very dry, semi, and rainfall of 350-450 mm annual average (^{INEGI, 2000}).

Planting of parents and hybrids was held on april 21, 2012 in polystyrene trays 200 cavities containing peat moss (Premier, Pro-mix. PGX. Professional), seeding 20 seeds of each genotype, applying a light watering and subsequently they placed in the greenhouse for germination and development. The transplant was carried out in an open field on june 5, 2012.

After transplantation, the irrigation applications began at three times per week, the frequency being increased according to the needs of the plant. Pruning started at 20 days after transplantation, they went to a single stem for materials of undetermined habit and two stems for certain habit. They were held every week and continued to complete the cycle of the crop in tomatoes indeterminate and determinate growth only until the beginning of fruiting.

As for fertilization before transplantation were applied manually to the ground 4g m² triple 17; subsequently diluted fertilizer in irrigation water (Table 2) applying a volume of 6.28 L per m² once a week for three hours, increasing the frequency to two per week during flowering and production.

Variables evaluated. Phenological variables: days to first cut (DPC), days last cut (DUC) and number of cuts (NC). Performance variables: number of fruits per plant (NFP), average fruit weight (PPF) in grams (g), polar diameter (DP) in centimeters (cm), equatorial diameter (OD) in centimeters (cm) and performance (REND) in tonnes per hectare (t ha^-1).

Data collection. For days to first cut a count it was done in days from the date of transplant and harvest beginning of each genotype to determine their precocity. For days last cut was determined in days from the date of transplant through the end of the last cut. Cut numbers were taken by counting the days from the first to the last cut. To estimate the average weight of the fruit in each material the weight of each of the cuts made and divided by the number of total fruits added. The sixth cut five fruits at random from each genotype and repetition were taken, he took their individual weight, polar and equatorial diameter of the fruit and end the average of the 5 fruits are reported. For performance in tonnes per hectare, the yield per plant multiplied by the density of the population, which was 18 939 plants per hectare.

Experimental design. An experimental design was used in a randomized complete block with 3 replications. The experimental unit consisted of 5 plants in rows 2 m long at a distance of 0.33 m between plants and 1.60 m between rows. The 3 central plants were evaluated with full competition.

The overall analysis of genetic effects used was the analysis II ^{Gardner and Eberhart (1966)} which includes parents and their n(n^-1)/² possible crosses, was used to estimate the effects of heterosis. The average for the parent population or cross is described by the model:

Where: Mv= average parent varieties; Vi= varietal effect of the j-th variety; hij= heterosis effect when the variety j intersects the j` variety.

The effect of heterosis (hij`) is described as follows: hjj`= h+ hj + hj` + sjj`.

Where: h= average heterosis; hj= varietal heterosis contributed by the variety j; hj'= varietal heterosis contributed by the variety j'; sjj`= effect of heterosis specified corresponding to the cross j and j`.

For comparison of means test (DMS) it was performed at the level of probability p≤ 0.05. The data processing and statistical analysis was performed with the Statitical Analysis System (SAS) version 9.0 program. Using Diallel-SAS (^{Zhang et al., 2005}), which was followed by analysis of variance and estimation of genetic effects of this experiment.

Results and discussion

In Table 3, 4 and 5 mean squares analyzes of variance under the model II of ^{Gardner and Eberhart (1966)} for the evaluated characteristics, which allowed us to know the differences between parents and their crosses are shown, as well as the different effects of heterosis. Table 3 differences (p≤ 0.05) were observed in repetitions variables polar diameter and equatorial diameter, this may be because the parents used to form their crosses, were saladette fruit type and ball respectively. For genotypes significant difference (p≤ 0.05) in number of cuts, the total weight of fruit per plant and yield. Likewise differences (p≤ 0.01) for days last cut, polar diameter, equatorial diameter, number of fruit per plant and average fruit weight, which indicates that at least one crosses behaved differently from parents, results Similar were found by ^{Dorantes et al. (2008)}; ^{Sánchez et al. (2010)} and De la Rosa et al. (2010).

For the source of variation varieties differences (p≤ 0.01) for polar diameter, equatorial diameter significantly (p≤ 0.05) in number of fruits per plant, total weight of fruit per plant and demonstrated performance, this indicates that at least one crossing behaved differently from the other way, this due to the different genetic backgrounds of the parents. At the source of heterosis discrepancies variation (p≤ 0.01) for days last cut, polar diameter, equatorial diameter, number of fruit per plant, average fruit weight also contrasts (p≤ 0.05) to cut number were found, which indicates a difference in behavior of crosses with respect to their parents so that matches ^{Martin et al. (1995=} which states that in some self-pollinated crops heterotic earnings are considerably lower in this character.

With respect to the average power variation heterosis, significance (p≤ 0.01) for equatorial diameter, the total fruit weight per plant, average fruit weight and yield, which indicates at least one cross that differs from the average it was obtained experiment. In varietal heterosis only differences (p≤ 0.01) in variables polar diameter, equatorial diameter and fruit weight average, which shows that for the source of variation genotype had a very similar behavior in other characteristics evaluated. As corresponding to specific heterosis, differences were achieved (p≤ 0.05) for cutting number, number of fruit per plant and differences (p≤ 0.01) for days last cut, polar diameter, equatorial diameter and average weight of fruit which it indicates that at least one crosses these features differs from the rest of the crosses.

In the Table 4 you can see the estimated average heterosis and varietal heterosis values, presenting differences (p≤ 0.01) for average heterosis in variables equatorial diameter, average fruit weight and performance, which highlights the importance of genetic effects additives that determine these variables. The average heterosis is a first indicator of the existence of heterosis in all the hybrids F₁ formed with respect parents used. The existence of average heterosis can be interpreted as a consequence of genetic divergence between parents commercial hybrids, and numerous experimental studies several authors have shown that the higher genetic divergence between parents, there is greater heterosis in crosses (^{Gutiérrez del Río et al., 2002}), if the materials used have different characteristics and in some cases even opposite will allow sorting lines into heterotic groups, thereby achieving more efficient management of crosses for best hybrid combinations (^{Fehr, 1982}; ^{Sierra et al., 1991}).

In estimating varietal heterosis, for variable days to first cut (DPC) line D4 was the one that obtained the highest value (3.12), presenting significant (p≤ 0.05). The existence of these positive effects DPC is a disadvantage if desired improve that character to precocity, since positive effects indicating more late cycles; on the contrary the line with less negative value of varietal heterosis were IR9 and IR14 both with no statistical difference -1.87, indicating the precocity of these parents, a situation that makes it desirable to enhance this genotype in future studies that character. Regarding days last cut (DUC) progenitors with best varietal heterosis were D1, D4, D6, IR13, IR14 and lower are D3, D10 and IR9 without any difference, indicating that the genotypes for this feature behave similarly. The difference expressed between genotypes in variable DPC and DUC is due to the characteristics of the varieties used to classify the different tomato cultivars, ie through the length of their growth cycle within which are the early, intermediate and late (^{Elkind et al., 1991}).

The varietal heterosis for number of cut (NC) on lines more positive value corresponded IR9 both 0.75 and IR14 no statistical differences and the parent who provided significant (p≤ 0.05) with a negative value was -0.91 D4 with these differences may be due to genotype D4 is determined habit while IR9 and IR14 were indeterminate. ^{Elkind et al. (1991)} mentions that a continuous production of tomato fruit is characteristic of indeterminate habit, however a concentrated production in short periods of time is determined habit.

For polar diameter (DP) most parents expressed varietal heterosis to show differences (p≤ 0.01 and p≤ 0.05) of IR9, IR14 and IR13 parents with positive values of 0.70, 0.41 and 0.21 each and genotypes D3, D4, D6 and D10 showed negative values of -0.23, -0.37, -0.32 and -0.28 respectively with significant (p≤ 0.01). For the equatorial diameter (OD), the lines were varietal heterosis D3 and D10, with significance (p≤ 0.01) with values of 0.38, 0.37 and difference (p≤ 0.05) D1 material to a value of 0.20 respectively, further three parents showed significant (p≤ 0.01) but negative for IR9, both with IR13 and IR14 value of -0.32 to -0.39. This indicates that the materials have wide genetic diversity for these two features, because half of the genotypes used as parents was the type of fruit ball and saladette another type.

As for the varietal heterosis for fruit number per plant (NFP), the parent with highest value was 1.95 and the D1 with less varietal parent heterosis D10 value was -3.37 showing significance (p≤ 0.05). For average fruit weight (PPF) only parent worth 191.72 D10 showed significant difference (p≤ 0.01) varietal heterosis, otherwise the lines D1, D4, D6, IR13 and IR14 were negative and no statistical differences. With respect to variable performance (REND), it was observed that more varietal lines were heterosis IR9, D10 and D3 show positive values of 15.73, 7.66 and 4.77 respectively, meanwhile D1, D4 and IR14 lines had negative values -13.99, -13.76 and -3.51. This means that the additive effects were influencing the D10, IR9 and D3 line to present the highest and positive values for the PPF and REND variables, indicating that these materials are a good source of germplasm to develop future breeding programs these two variables. He found similar result ^{Lopez et al. (2012)} to estimate the performance variable to the General Combining Ability (ACG) and specific (ACE) in seven tomato lines where IR17, IR24, IR14 and IR9 lines were those that were more positive value of ACG.

In the Table 5 shows the estimate of the effects of Combining Ability Specifies (ACE) of diallel crossing, where significant difference (p≤ 0.01) was found in the cross IR9*IR13 value of 2.40 for variable days to first cut occurs (DPC) and the crosses are less heterosis specified D10*IR13, IR9*D3 and D10*D1 values of -2.33, -2.04, -2.0, respectively. Regarding the variable days to last cut (DUC) hybrids are more positive value D10*D6 and D6*D1 with both 0.31 and no significant differences crosses lowest value differences (p≤ 0.01) were D10*D1, IR13*D3 and IR14*D6 with values of -1.52, -0.86 and -0.84. Regarding the number of cutting (NC) hybrids with greater effect of ACE were D10*D1, D10*IR13 and IR9*D3 values of 1.02, 0.94 and 0.84 with differences (p≤ 0.01 and p≤ 0.05), otherwise the crosses less heterosis was specified D10*IR14 with -1.05 showing significant difference (p≤ 0.01). According to the results of the DPC, DUC and NC variables, you can select and discard hybrids according to their phenological development, in which early, intermediate and late genotypes (^{Elkind et al., 1991}).

With respect to these variables ^{Santiago et al. (1998)} mentions that the days to the first cut makes a material has some precocity, getting off before most of the product is on the market, this will result in better source of income; these authors found that the earliest genotype was the hybrid Bingo with 99.5 days from sowing to first cut and has 134.5 days later and belongs to the hybrid Burpees Supersteak; also mention the days to crop allow genotype have a longer time in obtaining fruits, making outstanding genotype, in this case, the hybrid Bingo had a higher harvest period.

The effects of ACE for polar diameter (DP), differences (p≤ 0.01) in D10*IR13, IR14*D6 hybrids, with values of 0.27 and 0.22, were observed in turn crosses D6*D3, D4*D1 value of 0.17 and 0.18 were different (p≤ 0.05). For this same variable crosses with negative values are IR9 *D4 and D10* D1 (-0.22 and -0.18) with significance p≤ 0.01 and p≤ 0.05, respectively. As for equatorial diameter (DE) crosses higher value of ACE were IR9*D4, IR14*D6, IR13*D1 and IR13*D3, (0.43, 0.29, 0.23 y 0.18) expressing significant contrasts with p≤ 0.01 and p≤ 0.05. Hybrids with minor negative effects and differences (p ≤ 0.01) from ACE were IR14*D4 (-0.38), D10*IR13 (-0.29), IR9*IR14 (-0.28) and crosses D4*D6 (-0.20) differing (p≤ 0.05) from the rest of the materials, which was reflected in the size of the fruits, which were smaller. The DP-DE ratio indicates the type of the result of each genotype, polar diameters larger indicates that the materials are saladette fruit type and equatorial diameters show large fruit genotypes ball type.

The variable number of fruit per plant (NFP) crosses higher value of ACE and significant differences (p≤ 0.01 and p≤ 0.05) were IR9 * IR14 and IR13 * D3 with values of 4.92 and 0.86, also contrasts were observed (p≤ 0.05) for the cross IR9*IR13, D10*IR14, D4*D1, IR9*D4 negative values (-5.01, -3.30, -3.24 and -3.23). Compared to the average weight of fruit (PPF) outstanding hybrids (p≤ 0.01 yp≤ 0.05) were IR14*D6 (229.34), D4*D1 (137.90), IR13*D1 (129.92) and D4*D3 (98.65), among crosses with differences (p≤ 0.01) and negative results were found IR14*D4, D3*D1 and the D6*D1 but significant (p≤ 0.05). It was found in the variable performance (REND) to cross IR14*D6 (34.78), IR13*D1 (28.56), IR13*D4 (26.54) with the highest value of specific heterosis (ACE) showing these contrasts p≤ 0.01 and p≤ 0.05, respectively, followed by hybrid IR9*D10 and D4*D3 without statistical differences; further interbreeding with lower value was IR14 * IR13 with significance (p≤ 0.05), with the specific heterosis -29.44. The high performance of a cross may be due to the amount of additive effects of genes from both parents, or the interaction effects of the dominant allele from one parent to the other parent recessive alleles (^{Falconer, 1981}).

Table 6 shows the behavior of genotypes involved in the analysis for fruit yield in tonnes per hectare is (t ha^-1), which is observed at the line IR9 more performance with 81.6 t ha-1 and they hybrids with higher yield potential were D4*D3, IR14*D6, IR13*D4, IR13*D3 and IR9*D10, having potential yields above 100 t ha^-1 in the open, above the national average reported in 2013 that was 57.21 t ha^-1 (^{SIAP-SAGARPA, 2013}). ^{Bazan et al. (2005)} evaluated five genotypes tomato under greenhouse conditions, finding that the Yaqui cultivar showed the highest fruit yield (37.5 t ha^-1) and was also the tallest (68.8 cm). ^{Moreira et al. (2003)} found that hybrids outperformed parents in tomato yield at high temperatures. With regard to these results ^{Zewdie et al. (2000)} mentioned that based on the ACG of parents can predict the contribution that each hacea their progeny. This allows you to select plants that combine the superior characteristics of the parents, also predict the crosses with the greatest potential. The same author mentions that with high values of ACG and ACE of parents and their crosses, you can define the most appropriate methods of improvement to take advantage of favorable alleles.

Conclusions

Considering the variables of study, there is great variability between genotypes. Combine fitness general and specific, in most genotypes showed outstanding features that make them eligible to advance them to the next generation. The crosses were higher potential yield D4*D3, IR14*D6, IR13*D4, IR13*D3 and IR9*D10, exceeding 100 t ha^-1 in open field; these crosses showed an ACE for greater performance than other hybrids; Also, IR9 and D10 lines exhibited high values of ACG. Lines and crosses showed the highest effect of GCA and SCA regarding performance, could be used in breeding programs, in order to successfully exploit both additive and dominance gene action.