Introduction

The formation of synthetic varieties and hybrids of corn (Zea mays L.) is an ongoing process that involves the development of lines and identifying the best hybrid combinations (^{De la Cruz et al., 2010}; ^{Borghi et al., 2012}; ^{Badu et al., 2013}). ^{Gardner and Eberhart (1966)} report that use analysis diallel crosses to estimate the components of the genetic variance, as well as specified (ACE) genetic parameters of general combining ability (ACG) and which are used to identify superior combinations and thus able to select the best parents for the design of more efficient breeding strategies (^{Gutierrez et al., 2002}; ^{Yao et al., 2013}). According to ^{Sprague and Tatum (1942)}, the average GCA corresponds to the behavior of a parent in a series of crosses and ACE as the deviation of each crossing over the average behavior of the parents involved in the crosses. The information in the diallel crosses is also useful to study the heterosis of yield and its components.

Corn, other studies have indicated the importance of increasing performance by heterosis (^{Vasal et al., 1992}; ^{Vasal et al., 1995}; ^{Antuna et al., 2003}; ^{Reyes et al., 2004}; ^{De la Cruz et al., 2010}). Heterosis is the result of adding and interaction of a large number of genetic factors, provided by parents and assembled in the resulting hybrid, based on the assumption of dominance and Overdominance (^{Allard, 1999}), so that, in terms gene action, heterosis is mainly due to interaction effects between alleles and dominance (^{Crown, 1999}). Thus, to achieve the positive effects of heterosis in the formation of hybrid corn is to identify sources of germplasm heterotic potential (^{Márquez, 1988}; ^{Gutiérrez et al., 2004}; ^{Esquivel et al., 2011}).

Tamaulipas state is considered within the areas that are centers of origin and genetic diversity of corn (Zea mays L.) in Mexico (^{Ortega et al., 1991}; ^{SAGARPA, 2012}), which is established in most municipalities; in tropical regions of central and southern native germplasm it is still used, mainly because improved cultivars represent high investment and sometimes do not show adaptation to the specific weather conditions and production systems (^{Reyes and Cantú, 2005}; ^{Castro et al., 2011}), even if it is proven agronomic potential and heterotic they have some native populations of Tamaulipas (^{Pecina et al., 2011}; ^{Pecina et al., 2013}), its use has been minimal, due inter alia to lack continuity in research, and little information on their behavior and use of native corn populations in these regions.

In this context, it is a pressing need to generate specific improvement programs, with particular purposes and avoid a likely loss of this germplasm (^{Castro et al., 2013}). The objectives of this study were to analyze the effects of general combining ability (ACG) and specific (ACE) on yield and its components six corn lines and their hybrid combinations also estimate the degree of dominance, heterosis and heritability to identify and evaluate the heterotic patterns among corn inbred lines developed from the native germplasm central and southern Tamaulipas.

Materials and methods

Results and discussion

Analysis of variance showed that the effect of localities was significant (p≤ 0.01) for all variables except for PIG (Table 2), demonstrating significant contrast between the towns of culture, where in addition to the natural features influenced of each locality, different planting dates and crop management in each. The effect of genotypes presented statistical differences (p≤ 0.01) in all variables, so it is inferred the existence of genetic diversity of the origin of the parents, enabling the identification of crosses with contrasting performances, as well as differences in the porte plant varieties and patterns.

Regarding the effects of ACG and ACE found that the ACG had significant effects (p≤ 0.01) for all variables, whereas ACE showed only significant variables AP and DFM, the value of the mean squares of ACG were higher for all traits, indicating that the effects of ACG contribute more to the genetic variation of yield and its components to the effects of ACE. This indicates the importance of additive gene action on non-additive effects in the characters evaluated (^{Pswarayi and Vivek, 2008}), these results are consistent with those reported by ^{Antuna et al. (2003)}, ^{De la Cruz et al. (2010)}, ^{Vasal et al. (1992) Pech et al. (2010)} who found that the additive genetic action is the most important yield and plant height genetic component. When the effects of additive gene action outweigh the non additive gene action, it is suggested to improve the recurrent selection population, this mode ^{Reyes et al. (2004)} and ^{De la Cruz et al. (2010)} mention that first you have to exploit the additive variance for selection and then the non-additive variance by hybridization.

Interaction L × ACG not statistically affect the evaluated variables, indicating that the effects of ACG parents are specific according to each location, and suggests parents choose the best ACG effects for each locality. As for the interaction L × ACE significances (p≤ 0.05) for LMZ, NGM and AP indicate that the cross did not keep their ACE across locations for these variables, while RGha, DMZ, PIG and DFM maintained their ACE in each locality. On the other hand, the interaction L× L×ER and EM only affected significantly (p≤ 0.05) to the DFM and PIG (Table 2).

Estimates of the effects of GCA and SCA for the six lines and 15 direct crosses values are shown in Tables 3 and 4. For ACG in RGha per hectare, L5, L6 and L4 parents had the highest positive values with 455.0, 239.3 and 154.2 kg ha^-1, respectively (Table 3). Registered GCA values are indicators of variability in parents, which is transmitted to their progeny, in addition to the knowledge of this variability contributes to the prediction that will each parent with their respective offspring (^{Zewdie et al., 2000}), and so selecting plants that combine superior characteristics between parents. Regarding the effects of ACE RGR, the best crosses were L1 × L5, L5 × L6, L2 × L4 and L3 × L5, with values of 293.0, 203.4, 101.5 and 23.0 kg ha^-1, respectively, while the rest of the crosses had negative values (Table 4).

The fluctuations of the effects of ACE in all traits, indicating that they can not be predicted based on the values of ACG effects of the parents, as indicated by ^{Revilla et al. (1999)}; however, ^{Reyes et al. (2004)} note that the single cross will be high value of ACE if at least one of its parental lines is high ACG, which coincides with the findings in this study.

Heterosis values found ranged between -12.0 and 36.4%, eight of the 15 crosses studied showed positive heterosis for grain yield per hectare and were cross L1 × L5, L1 × L3, L2 × L3, L2 × L5, L2 × L4, L2 × L6, L5 × L6 and L4 × L6 with heterosis of 36.4, 13.4, 12.8, 10.1, 7.7, 7.4, 7.0 and 4.3, respectively (Table 4). These values are higher than those reported by ^{Vasal et al. (1992)}; but lower than those reported by ^{De la Cruz et al. (2010)}. Negative heterosis generally insufficient genetic diversity among populations (^{Han et al., 1991}), or possibly to the presence of interalélicos intraalélicos effects or reducing the expression of the measured attribute character. Crossing a progenitor of low value of ACG with other effects ACG high a hybrid of good response from ACE was obtained, as in the case of cross L1 × L5, L2 × L4 and L3 × L5, but also showed good response ACE crosses × L5 L6 having good ACG progenitors.

In estimating the components of genetic variance, heritability and average dominance degree (Table 5), it was found that the additive variance was expressed mainly by additive effects in all the variables evaluated, as they had shown the significances in the mean squares of ACG in Table 2; Also, the dominance variance showed negative values in LMZ and PIG, indicating that these variables effects additives are interacting with these variables forming performance components presented. These results can be attributed to the proportion of additive genetic variance is greater than the genetic variance of dominance (as found in this study), but it could exploit both additive and dominance, variances by combining selection methodologies and hybridization. According to the results evaluated all variables presented low heritability values, characters DFM, AP and RGha expressed heritability values of 0.42, 0.34 and 0.30, respectively, which for this study were higher heritability values. The average degree of dominance d-) of DFM, AP and NGM according to variables ^{Molina, (1992)} are considered as partial dominance, which is manifested in crosses to be formed with parents and while the variables RGha, LMZ, DMZ and PIG showed values of 0.29, 0.32, 0.62 and 0.80, respectively. These results show that you can exploit the effects of dominance and additive effects of the lines evaluated in this work.

Genetic crosses showed response set by the average values of the variables under study, expressed significant variation. Such a response is mainly due to inherited by parents for hybrid superior character, through crossbreeding (^{Esquivel et al., 2011}). Regarding RGha, as the main component of interest, six of the cross (20%) exceeded 4 900 kg ha^-1 performance which L6 × L4, L6 × L5 were the most outstanding (Table 6). Good expression presented these crosses is due to the origin of the parents (Table 1), which come from native populations that have been cultivated by farmers, adapting to adverse weather conditions and which have accumulated favorable genes that have allowed them adapt to these environmental conditions in the center of Tamaulipas (^{Castro et al., 2011}; ^{Pecina et al., 2013}).

For NGM outstanding cross was four, with L4 × L2 crosses the highest number of grains per ear 475.0 expressed, that value is higher than reported for lines and collections of native populations in this area (^{Pecina et al., 2009}; ^{Pecina et al., 2011}). To LMZ seven crosses (23.3%) had values greater than the mean plus the corresponding standard error (15.4 cm), these values are similar to those reported by ^{Pecina et al. (2013)}, who evaluated groups of crosses, with different paternal origin for the same geographic area. The DMZ was the least affected variable, ranging from 0.1 to 0.5 cm, L4 × L5 being the only crossing that exceeded the mean plus one standard error instead, similar values reported ^{Pecina et al. (2011)} and ^{Pecina et al. (2013}), who mentioned that this feature is distinctive in Olotillo and Tuxpeño races.

Higher prices for AP exceeded the average values and the corresponding standard error ranged between 211.1 and 213.7 cm which corresponded to the cross L6 × L1 and L4 × L2 respectively, which were higher than those reported by ^{Pecina et al. (2009)} who indicate that agronomically greater heights is undesirable because it presents a high correlation with the flattens of plants, which is a problem in native populations; however, in this study no such problem arose. The PIG showed higher values in crosses L5 × L6, L3 × L6, L6 × L5 and L4 × L6 securities 258.7, 248.0, 247.0, 249.2 respectively, which L5 × L6 was the most important though was not affected by changes in the environment (^{Andrade et al., 1996}). It notes that L6 is expressed expressively on all outstanding cross.

For DFM five crossbreds (16.6%) exceeded 79 days, increasing the number of days for this area, in which lower values (67-73 days) (^{Pecina et al., 2013}) are reported. Note that the hybrid H-439 behaved in a superior manner in grain yield (5 876.5 kg ha^-1) and size of the cob, cross L6 × L4 and L6 × L5 they showed RGha of 5 063.3 and 205.9 kg ha^-1, respectively, which they are lower than those obtained in return for the commercial hybrid, but are an acceptable option for further improvement, as L6, L4 and L5 parents behave expressively in their crosses in grain yield.

Conclusions

The combined analysis showed significant differences for genotypes. Progenitor L4, L5 and L6 lines showed the greatest effects of ACG to RGha to 154.2, 455 and 239.3, respectively, which can be used for hybrid formation.

The L1, L2, L4, L5 and L6 parents were involved in the best crosses for grain yield (L1 × L5, L2 × L4 and L5 × L6) with positive effects of heterosis and ACE. Crosses L1 × L2, L2 × L3, L5 × L1 and L6 × L1 shown precocity of 74.3, 74, 74.3, 74.2 and 74.8 respectively, but with yields in excess of 4 000 kg ha^-1 which can be used as cross outstanding.

Crosses L4 × L3, L4 × L5, L5 × L4, L5 × L6, L6 × L4 and L6 × L5 showed higher grain yields 4 924.1, 5 012.0, 4 945.9, 4 939.1, 5 063.3 and 5 205.9 kg ha^-1 respectively. Additive effects were the principal for the expression of the variables evaluated component, making it possible to exploit the effects of additive by selection.