The understanding of the genetic basis of quantitative characters has its peak of complexity in grain yield because the interaction of different yield components and the environmental effects hamper the direct selection of the character. In this case, the indirect selection through yield components is a more efficient criterion for genetic gain (Novoselovic et al., 2004). Genetic parameters that can estimate the performance of quantitative characters with higher accuracy have been greatly pursued by breeders aiming at a higher efficiency in the selection process. In this sense, generation analysis is an important tool for the estimation of genic effects, besides enabling the measurement of episthatic effects that interfere in the expression of the character (Bertan et al., 2009). The major need for estimating genetic parameters is based on two reasons: i) to obtain information on the action of genes involved in the inheritance of characters and ii) to establish the basis for choosing breeding methods (Hayes and Thill, 2002).

In measurable characters, the primary genetic questions are formulated in terms of variance and its partitioning into components attributable to different causes (Falconer and Mackay, 1996). The first partition of genetic variance (σ_G²) was determined in 1918, in three components: i) additive variance, due to average gene effects; ii) dominance variance, due to the interaction between alleles from the same locus and iii) episthatic variance, originating from the interaction between alleles from distinct loci (Fisher, 1984). The analysis of generation parameters has contributed for the understanding of genetic parameters associated to many important agronomic characters, leading to gains in selection efficiency. Therefore, the present work had as objective to estimate the genetic parameters involved in oat grain yield and its components through the analyses of different generations, supplying information for the selection of high yielding genotypes at early selfing generations.

1 Results
A significant difference between all parents (P₁ and P₂), individually evaluated for the three target characters, except for CR2 (UPF 16/UFRGS 7) and CR3 (UPF 16/URPEL 15) for the character PP was observed with the t test analysis (Table 1). Higher values were observed for segregating generations, especially F₂, as opposed to the F₁ generation, where more reduced values were observed. For the characters GY P^-1 and PP, a probable expression of heterosis on the F₁ generation was observed, for all crosses, with a highlight for CR1 (UPF 16/UPF 18) in the character GY P^-1. For the character NP P^-1, however, the same behavior was not observed but still CR1 was the only combination showing a heterotic effect for the character. The cultivar UPF 16 deserves some special credit, since when it was present in the evaluated combinations. It influenced decisively the increase in the character GY P^-1 as revealed by the high performance of its F₁ hybrids, suggesting that this parent transfers to its progeny alleles that contribute to the superior performance.

Table 1 Number of plants (n), means and variances for P1, RC1F1, F1, F2, RC2F1 and P2 generations for three characters in five oat crosses (+) Grain yield per plant (GY P-1)

The performance of the hybrid generations compared to the parents is presented in Table 2, where a high magnitude and positive sign was found for the characters GY P^-1 and PP in all crosses. The maximum expression of vigor was observed for CR1 (120.96% and 82.68%, for GY P^-1 and PP, respectively), revealing a large decrease when comparing the F₂ and F₁ generation means. Regarding the character NP P^-1, a reduced heterosis expression was observed, except for CR1, which showed positive values. Based on the genetic parameters of each population, a high and distinct phenotypic variance (σ_P²) was observed for each of the different crosses analyzed and for the three target characters (Table 2). When compared the values of σ_G² and σ_E², it can be observed a lower contribution of the environment (σ_E²) for the total phenotypic variance (σ_P²).  The additive variance (σ_A²) was, in general, the major genetic effect on the genetic variance (σ_G²). Regarding the character GY P^-1, the crosses presented a distinct behavior for σ_P² and σ_G² values, however, the variance attributed to the genetic effects (σ_G²) expressed higher magnitude when compared to σ_E² for all crosses. The most significant contribution of σ_D² (60%) to σ_G² for the character GY P^-1, was found in CR3. In this case, the σ_A² (40%) resulted in the highest value found for the broad sense heritability (h_a²), reaching 73.18%. Regarding σ_A², the major contribution of this component was found in CR1, reaching 83% of σ_G², therefore overcoming the dominance variance (σ_D²), leading to a higher h_r² (53.08%). The higher values for σ_G² found for the character NP P^-1 were obtained in CR1, where a large contribution from σ_D² was also detected. The cross CR5 (UPF 18/UFRGS 17), revealed that 76% of σ_G² was due to σ_D², showing a reduced h_r² (13.90%). Only the crosses CR3 and CR4 (UPF 18/UFRGS 7), revealed a superior effect of σ_A² over σ_D², and consequently higher h_r². The character PP in cross CR5 was the only case to show negative σ_D² values. Its values were recalculated in order to eliminate the error estimates caused by super estimating the additivity. The same character showed, in crosses CR4 and CR5, the higher σ_A² values.

Table 2 Phenotypic (σP2), genetic (σG2) and environment (σE2) variance, additive (σA2), dominance (σD2), broad (ha2) and strict (hr2) sense heritability and heterosis (H) and loss of vigor (LV) estimates for three characters in five oat crosses (CR)

For the three target characters, the complete six-parameter model (m, a, d, aa, ad and dd) was first tested (Table 3). Additionally, for crosses in which the episthatic effects were non-significant, the reduced three-parameter model (m, a and d) was used. For the character GY P^-1, at least one type of epistasis (a x a, a x d or d x d) was detected in the five evaluated crosses, being the episthatic effect (a x a) present in all crosses. Only CR5 and CR3 presented all three interaction effects significant for this character.  For the character NP P^-1, in CR3 and CR5 episthatic interactions were not detected, therefore only the reduced model is presented. Thus, the additive component was significant for both crosses, but dominance effects were detected only for CR3. In CR1, CR2 and CR4 at least one type of epistasis was detected, being the a x a effect significant in all three crosses. For the character PP, only in CR1 significant interactions were detected by the six-parameter analysis. Despite the non-orthogonal decomposition, the measure denoted by R2 allows the idea of the contribution of a particular genetic effect on the available variability for the target character (Table 3). Thus, besides the effect of the mean, the most important genetic effect contributing GY P^-1 was additive, with 47.79%, 29.92% and 31.21% for CR1, CR3 and CR4, respectively, while the interactions caused by dominance were of reduced magnitude among the single effects.

Considering the significant episthatic interactions present in these crosses, contributing values of 15.65%, 47.96% and 15.04% on the means of studied generations were detected in CR1, CR3 and CR4, respectively. For  GY P^-1, the larger contributions of episthatic interactions were observed in CR2 and CR5, with 56.53% and 35.01%, respectively (Table 3). Besides, CR5 indicated effects of higher complexity, since it did not present a significant additive (a) effect, and considerable magnitudes in all episthatic interactions. For the character NP P^-1, significant interactions can be observed for CR1, CR2 and CR4, with different contributions of these effects on the generation means: 14.31%, 45.87% and 7.61%, respectively. Also, additive significant effects influencing the generation means were found in CR1 (64.07%) and CR4 (88.89%). Regarding the character PP, CR4 was distinguished by a higher contribution of the additive when compared to the dominant component in the genetic control of the character (Table 3).

Table 3 Genetic parameter estimates for the simple (additive-dominant) and complete (additive-dominant-epistatic) models and Relative contribution of parameters (“m”, “a”, “d”, “aa”, “ad” and “dd”) for the simple and complete models, adjusted based on the mean of evaluated characters, in six generations (P1, P2, F1, F2, RC1F1 and RC2F2) obtained from five oat crosses (CR)

2 Discussion
Besides the use of mean and variances, genetic parameter estimates such as heritability and phenotypic variance components have been considered as of great importance in validating populations with high genetic potential in breeding programs, serving to guide towards more efficient selection (Vencovsky, 1969; Lorencetti et al., 2005). In this sense, through the parameters analyzed, it can be observed the presence of genetic variability for the majority of the crosses studied, suggesting that there is a great potential for hybrid combinations in the rescue of superior individuals in segregant oat populations.

The occurrence of a higher genetic variability in segregating generations, especially in F₂, is supported by the hypothesis of a larger number of segregating loci when compared to the backcross generation. On the other hand, the observation of reduced variance values in the F₁ generation, according to Carvalho et al. (2001), is due to the fact that this generation presents a more stable behavior (higher homeostasis), which can lead to the observation of plants in the population with lower environment variation when compared to the other fixed genotypes. The analysis of mean and heterosis values at the F₁ generation for the characters GY P^-1 and PP, reveals the presence of positive heterosis for all crosses evaluated. According to Fehr (1987), heterosis or hybrid vigor can be defined as the superiority of individuals from F₁ generation, which can be significant in oat (self-pollinated), since it can lead to higher genetic class amplitudes for selection in the next generation. Regarding to F₂, it can be highlighted in all crosses, for the characters GY P^-1 and PP, the presence of transgressive segregation, except in CR4, for GY P^-1. The transgressive segregation occurs when the phenotype of a segregating population is much higher than the parental mean value (Ibrahim and Quick, 2001), and in many cases surpassing the best performing parent. This phenomenon is suggested to come from contributions of complementary genes from both parents, which is routinely exploited in plant breeding when superior individuals are selected (Ibrahim and Quick, 2001). However, it was possible to obtain genetic variability from crosses involving parents with similar means, as observed in CR2 and CR3, for the character PP. This is probably due to the fact that genes controlling this character are complementary distributed between the parents, i.e., present in distinct loci between both parents, which, at the time of the cross are reunited and accumulate as favorable alleles in the progenies.

The positive heterotic effect found in CR1 is an indication of the presence of a large number of dominant alleles at heterozygous loci in the F₁ generation, resulting in higher vigor loss for GY P^-1, NP P^-1 and PP in the F₂ generation. Crosses that reveal heterosis in F₁, followed by loss of vigor loss (LV) in F₂, can produce a higher number of genotypic classes for selection, and these information can be extremely useful for the breeder, especially regarding selection intensity and the most adequate moment for its application (Allard, 1960; Crestani et al., 2012).

The small contribution of σ_E² was due to the reduced variances obtained for the fixed generations (P₁, P₂ and F₁) observed in this study. This parameter is extremely important, because the variance caused by the environment cannot be removed, since it represents, by definition, all the non-genetic variation, and a large proportion of it is outside experimental control (Falconer and Mackay, 1996). Therefore, for all crosses evaluated a larger contribution of genetic variance for the total (phenotypic) variance. However, a small value for σ_G²  (GY P^-1) was observed, resulting in the lowest H₂ (58.63%) estimate among all characters in all crosses. In this case, higher selection efficiency is only obtained in advanced generations, since the increase in homozygosis, as a consequence of selfing, leads to an increase in the strict sense heritability (Falconer and Mackay, 1996; Bertan et al., 2009). On the other hand, the adjustment to the environment can proportionate higher success in the H₂ values, since the environment factor in this case, has a large contribution to the total variation.

σ_G² is generally the result of adding σ_A², σ_D² and epistasis, however, in the present work, σ_A² was the major factor contributing to σ_G² for all characters, in the majority of crosses. This is very helpful to the breeders, since it is the only genetic effect quickly fixable along succeeding selfing generations. The major contribution of σ_A² for GY P^-1 was observed in CR1, indicating the presence of similar alleles among the parents, increasing the magnitude of the additive component (Saleem et al., 2005). Thus, greater success is obtained in the selection process, due to a higher h_r² (53.08%). On the other hand, a high σ_A² does not mean that the character is only under influence of additive genic action, i.e., that the genes act additively, without any dominance or epistasis. The σ_A² can originate from genes with any degree of dominance or epistasis, and only if all σ_G² is additive, it will be possible to conclude that there is neither dominance nor episthasis.

The high σ_G² found in CR3 for GY P^-1 can be explained by the genetic distance between these parents. A study performed by our group detected, using morphological markers, a large distance between the genotypes used as parents in CR3, suggesting that a higher genetic variability would be obtained in the populations formed from this combination (Lorencetti et al., 2005). This combination will certainly provide a high h_a² value, since a higher σ_G² will be generated from this combination. On the other hand, the breeder would face some difficulties on early generations, due to the higher contribution of σ_D²  to σ_G² in this character. This result is corroborated by the reduced narrow sense heritability (h_a²) values found, resulting from the reduced contribution of additive gene effects for the character. Reduced h_a² coefficients can be associated with a lower additive genetic variance, higher environment variance and higher genotype vs. environment (G x E) interactions (Fehr, 1987).

Heritability has a predictive role, which expresses the reliability of the phenotypic value as an estimator of the genetic value, such as the higher the heritability, the higher the genetic gain through selection (Hayes and Thill, 2002). Thus, CR3 showed interesting results for NP P^-1, with higher h_a² (>70%), which can favor larger selection gains and would be prioritized for indirect selection aiming to increase GY P^-1. Recent observations have shown that the character NP P^-1 has high positive correlation with GY P^-1 (Benin et al., 2005). Besides, the efficiency of indirect selection is increased when the secondary has a higher heritability than the primary character (Fehr, 1987), as observed here, with heritability values of 48.92% and 29.64%, respectively for NP P^-1 and GY P^-1, in CR3.For the character PP, a higher contribution of σ_A²  to σ_G² and a negative value for σ_D² was observed in CR5.This result can be due to estimates coming from distinct populations, since for the estimation of σ_G², both parents and  F₁ are used, while for σ_A², backcross generations are included (Silva et al., 2002). On the other hand, Carvalho et al. (2001) pointed out the need for the correction of this result, since the simple subtraction of the additive variance from the genetic variance to obtain the dominance variance can lead to errors, expressing negative values for the dominance action due to a superestimation of additivity. Therefore, even with corrected values, CR5 is superior to CR4, showing higher σ_A² than σD2 for the character PP. As observed in the model adjustments for the three target characters, in some cases, the additive effect was non-significant. This can be explained by the fact that additivity effects represent the sum of individual additive gene effects and, since their values can be positive or negative, their estimates may turn out to be non-significant, even when each of the genes involved, individually, shows substantial additivity. This could occur in cases where the genes act in opposing directions, mutually cancelling their effects (Mather and Jinks, 1982; Saleem et al., 2005).

Exploring the character GY P^-1 in early generations can be troublesome, since episthatic effects were observed in the five crosses tested. The episthatic effect “a x a” always seemed inferior to one or two interactions (“a x d” or “d x d”), which can lead to major problems for the breeder of self-pollinating plants, where one expects “a x a” interaction values to be higher than “a x d” and “d x d” values. Theoretically, in a linear direction, the episthatic effect “a x a” can be a fixable component of the genetic variation, easily explored for some characters through single hybridizations and selection procedures. Episthatic interactions such as “a x d” and “d x d”, are not directional and can not be fixed through selfing in self-pollinating plants and, therefore, would not be favorable to the development of inbred lines for GY P^-1. They could be, however, interesting for hybrid development (Saleem et al., 2005).

The detection of at least one type of epistasis in the five crosses evaluated for GY P^-1, gives support to the idea of using the complete model for the analysis of complex inheritance characters. On the other hand, in the breeding of self-pollinating crops, the techniques that beneficiate from a higher σ_A² and from the interaction “a x a” are the most important in obtaining genetic gains. As observed in this work, for the character GY P^-1, the effects “a” and “a x a” were significant in all crosses, with exception of CR5. In the crosses CR1 and CR4, only the interaction “a x a” was detected as a significant episthatic effect, reaching higher selection gains. The detection of a reduced contribution of episthatic effects for the control of GY P^-1 in CR1 and CR4 can not be disregarded, even if the episthatic effect in this crosses is of  “a x a” type, showing the importance of an analysis considering the complete additive-dominant-episthatic model, for quantitative characters. Genic interactions between non-allelic or episthatic genes can not be disregarded in the elucidation of basic genetic mechanisms (Gravina et al., 2004) and genetic models that disregard epistasis can have some kind of bias (Cockerham, 1954; Valério, 2008). On the other hand, estimates obtained from genetic parameter analyses are only valid for the population from which the samples are taken and also only for the environmental conditions in which the study was conducted (Gravina et al., 2004). Contrasting results found for the significance of episthatic effects for the characters NP P^-1 and PP in the different crosses, reveal some direct environmental influence. This is more important when only one environment is studied, where the g x e interaction can have some influence on the episthatic effect. The presence or absence of epistasis can be environmentally dependent and, therefore, not related to the genotype’s inheritance (Saleem et al., 2005).

As observed for the characters NP P^-1, in CR3 and CR5, where there was no significant episthatic interaction detected, interpretations have to be made cautiously since they present differences in sign and significance of dominance effects, because the negative and significant “d” effect (CR3) reduces the character, therefore, not being a priority for breeding programs, even if the three parameter model is sufficient to explain variations for the genetic control of this character.  Thus, CR5 appears to be quite interesting, since the “d” effect was non-significant, even if the cross shows higher contribution of σ_D² to σ_G² for this character. This is due to the fact that variance and genic effect tests make use of different information bits, which should be interpreted as complementary data and should not be mixed. CR1 displays the highest difficulty for the selection of PP in initial generations, due to the higher complexity of genic effects that influence this character in this cross. For the other crosses, substantial genetic gains can be observed at early generations, since no significant episthatic effects are detected. The best performance was observed for CR4, which had the highest additive/dominance ratio in the genetic control of the character. As observed in this study, for the character GY P^-1, CR3 and CR5 crosses showed higher complexity, having significant non-allelic interactions (“a x a”, “a x d” and “d x d”). Many authors point out the prevalence of epistasis in the genic effect of quantitative characters in a range of populations (Falconer and Mackay, 1996; Allard, 1960). Recent results reveal large contributions of epistatic effects of “a x d” and “d x d” type for the genetic control of PG P^-1 (Saleem et al., 2005). Therefore, episthatic interactions were substantially significant and should be taken into account for the better understanding of the genic effects acting in each cross, requiring attention from the breeder when selection is performed.

There is presence of significant episthatic interactions for the character grain yield per plant. The results suggest that specific crosses in oats can lead to high genetic gains in the selection at early generations. The characters number of panicle per plant and panicle weight presented the lowest complexity for the estimated genic effects to more effective in selection.

3 Material and Methods
The experiment was installed in the years 2002 and 2003 in the experimental field located at Capão do Leão County-Rio Grande do Sul State (RS). In this work, five oat cultivars (UPF 16, UPF 18, UFRGS 7, UFRGS 17 and URPel 15) were crossed forming five hybrid combinations. F₁ seeds from each combination were obtained in greenhouse in the fall/winter 2002. In the same year (spring/summer), the first backcross generation [RC₁F₁ (F₁ x P₁) and RC₂F₁ (F₁ x P₂)] as well as F₂ seeds were obtained. In 2003, three fixed (P₁, P₂ e F₁) and three segregating (F₂, RC₁F₁ e RC₂F₁) generations were sowed in the field. Plants were conducted in 3 m long rows with 0.3 m spacing between plants and rows. The experimental design used was random blocks with three replications, considering one plant as an observation unit. After harvesting, the following characters were evaluated in the laboratory: i) number of panicles per plant (NP P^-1), through the counting of fertile tillers of individual plants; ii) production of grains per plant (GY P^-1), through the individual threshing of plants, in grams; and iii) panicle weight (PP), obtained by weighing the main panicle, in grams. From plant individual values were estimated the means and variances for each generation in the distinct crosses.

The phenotypic (σ_P²), genetic (σ_G²), additive (σ_A²), dominant (σ_D²) and environment (σ_E²) variances and the heritabilities in the broad (h_a²) and narrow (h_r²) senses were estimated according to Allard (1960), where: σ_P²=σ_F2²; σ_G²=σ_F2²-σ_E²; σ_A²=2σ_F2²-(σ_RC1²+ σ_RC2²); σ_D²=σ_G²-σ_A²; σ_E²=(σ_P1²+2σ_F1²+σ_P2²)/4; h_a²=σ_G²/σ_P² and h_r²=σ_A²/σ_P². When negative values for dominance variance (σ_D²) were found, the following alternative formula was used, according to Carvalho et al. (2001): σ_D²=4(σ_F2²-σ_A²/2-σ_E²).

The heterosis estimate was based on a model similar to the initially proposed by Matzingeret al. (1962) and described by Gardner and Eberhart (1966): H₁(%)=(F₁-MP)/MP*100, where: H₁(%)=heterosis relative to the parental mean, F₁=hybrid mean and MP=parental mean, obtained as: MP=(P₁+P₂)/2. The loss of vigor (LV) was calculated based on the model described by Vencovsky and Barriga (1992): LV(%)=(MF₁-MF₂)/MF₁*100, where: LV(%)=loss of vigor, MF₁=mean of F₁ generation, MF₂=mean of F₂ generation.

The genic effects for each cross were estimated for the characters GY P^-1, NP P^-1 and PP, using the generalized weighted least square method and testing the adjustment of the model of six parameters  (complete model: mean “m”, additivity “a”, dominance “d”, additivity x additivity “a x a”, additivity x dominance “a x d” and dominance x dominance “d x d”) and three parameters (reduced model: mean “m”, additivity “a” and dominance “d”), according to Mather and Jinks (1982). The significance of the genetic parameter was verified by the t test, as follows: t=ê/DP, where: ê=parameter estimate and DP= parameters standard deviation.

Authors’ contribution
IV, CL, JS and HL participated in the design of the study, in the experimental conduction of essays, in the statistic analysis and in the manuscript writing. ACO and FIFC participated in the design and supervision of the study and preparation of the final manuscript. All authors have read and approved the final manuscript.

Acknowledgements
The authors are thankful to the Brazilian Council for Research and Development (CNPq), Higher Education Improvement Bureau (CAPES) and Rio Grande do Sul State Research Assistance Foundation (FAPERGS) for grants and fellowship support.

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