Genetic analysis of F6 and F6:7 soybean generations

For estimating genetic parameters and selecting superior lines for grain yield, forty-five soybean ( Glyci e max L.) crosses in F6 and F6:7 generations were evaluated. The soybean lines FT-Cristalina, EMGOPA-301, IAC-4, IAC-5, IAC-6, IAC-8, IAC-9, IAC-11, Santa Rosa, and OCEPAR-9-SS-1 were used in the crosses. The F 6 progenies of 44 crosses (except EMGOPA-301 x IAC-5) and the ten parents were evaluated as well as the F 6:7 progenies from all 45 crosses and the ten parents in the next crop. The number of days to maturity (NDM), plant height at maturity (PHM), agronomic value (AV) and grain yield (GY) were evaluated for both generations. There was some difficulty to select early top yield lines due to the high posi tive genotypic correlation between GY and NDM. The heritability estimates were high (> 0.70) and moderate (0.40 – 0.70) for NDM and PHM, respectively. The presence of transgressive segregates indicated the possibility of selecting lines with high grain yield.


INTRODUCTION
Research into genetics and improvement of soybean has offered a somewhat significant contribution to agriculture. The developed methodologies for the selection of parents and crosses with a high genetic potential to produce superior populations now allow a more precise choice of lines in relation to quantitative traits.
Results of genetic improvement of cultivated plants have become more predictable due to the awareness and understanding of genetic parameters. The estimate of the correlation coefficient is essential for selection, mainly if one of the desirable traits presents low heritability or problems with evaluation and identification (Cruz and Regazzi 1994). The magnitude of heritability helps predict selection gains and define the best strategy for an improvement program (Fehr 1987). For the selection of inbred lines, low heritability traits must be selected in more advanced generations (F 6 , F 7 , F 8 ...), since there is an increase in heritability in the course of inbreeding generations, owing to the increase of additive genetic variance and decrease of the dominance variance (Ramalho and Vencovsky 1978). Besides, there is the possibility to use a higher number of replications to reduce the experimental error.
The goal set for this study was the evaluation of 45 diallel soybean crosses in advanced generations, aiming to estimate genetic parameters of agronomic traits, which support the selection of superior seed yield lines.
Generations F 1 and F 2 were conducted by Nass (1989), generation F 3 by Moreira (1992) and generations F 4 and F 5 by the Setor de Genética Aplicada às Espécies Autógamas do Departamento de Genética -ESALQ/USP. The SHDT (Single Hill Descent Thinned; Vello 1992) method was employed to advance the populations until obtaining F 6 generation seeds.
In generation F 6 , 72 plants derived from each of the 44 crosses (with exception of cross EMGOPA-301 x IAC-5, due to the delay in the achievement of F 2 seeds) and the ten parents were evaluated. The trial was established in randomized block design with six replications, sown November 6, 1991, Piracicaba, SP (lat 22º 45' S, long 47º 38' W, altitude 540m asl). Every plot consisted of 12 individual hills spaced 0.5 x 0.6 m.
In generation F 6:7, 24 lines of each one of the 45 crosses (1080 lines), originated by one individual F 6 plant and the ten parents were evaluated in an augmented block design (Federer 1956) with 24 blocks. Each block consisted of 55 plots (one line of each cross and the ten parents), and every plot held a 2.0 m row spaced 0.5 m. In this generation, cross EMGOPA-301 x IAC-5, which had been advanced separately up to F 6 , was included by the SHDT method, too. The trial was sown December 4, 1992, in Piracicaba.
In view of the soil analysis, the crop was fertilized with 25 g m -1 in furrows (500 kg ha -1 ) with the formula 4-20-20 of N-P 2 O 5 -K 2 O, respectively. Seeds were inoculated with Bradyrhizobium japonicum, which was diluted in water (800 g 20 L -1 ) and applied by a back sprayer minutes before sowing into the furrows. Initial additional irrigation helped guarantee the establishment of the crop. Weeds were controlled with two applications of postemergent herbicides and manual weeding. Insecticides were applied to control pests, mainly bugs. No diseases occurred which would have required control.
In both generations the following traits were evaluated: NDM -number of days to maturity, referring to the period between the sowing date and stage R8 of the Fehr and Caviness (1977) scale; PHM -plant height at maturity, measured in centimeters from the plant base to the plant tip of the main stem; AV -agronomic value, based on the evaluation realized at maturity, in a visual grading system from 1 to 5. Score 1 refers to a plant or row with no agronomic value, and score 5 to a plant or row with excellent agronomic traits (high number of full pods, height above 60 cm, vigorous, no bending, absence of green stems and leaf retention, without opening of pods or disease symptoms); and GY -grain yield transformed in kg ha -1 , which corresponds to g plant -1 or g 0.3 m -2 in generation F 6 since the analyses were based on the mean of the 12 planting hills of individual plants of each plot; and corresponds to g m -2 in F 6:7 , as the analyses were based on the total plot yield.
Variance and covariance analyses in generation F 6 were based on plot means for each trait, with posterior inclusion of within variance and covariance, considering the fixed effect of treatments.
Data of generation F 6:7 were initially analyzed for intra-block variance, considering a fixed effect of parents and a random effect of lines. Since the intra-block error ( 2 ê σ ) from the referred analysis can only be used for comparisons among lines tested in the same block, a comparison among lines of a same cross, placed in different blocks must be carried out with the inter-block error ( ' 2 ê σ ), using the adjusted means of regular treatments. However, to avoid the use of two different errors, the mean effective error ( 2 ef σ ) was estimated in analogy to the procedure of Cochran and Cox (1957) for the classic square lattice designs, whose mean square (MS) was given by the following expression, based on Vencovsky (1994) where: B is the number of blocks; C 1 the number of line combinations in block j, considered in pairs; C 2 is the number of possible contrasts between the lines of any block j with the lines of another block j′, considered in pairs; 2 ê σ is the mean square of the intra-block error; and c is the number of common treatments according to Vizoni (1984).
Coefficients of genotypic correlation between the trait pairs were estimated by the variance and covariance estimates expressed by the equation (Vencovsky and Barriga 1992): is the genetic covariance between traits x and Y estimated according to the methodology of Kempthorne (1973); and are genetic variances of traits x and Y, respectively.
Broad-sense heritability was estimated in generation F 6 , according to Mahmud and Kramer (1951): σ is the phenotypic variance estimate among lines; 2 σ the error variance, estimated on the base of the geometric mean of the environmental variances among hills of the two parents involved in the cross; 2 1 P σ and 2 2 P σ are environmental variances estimates among hills of parents 1 and 2. In generation F 6:7 , the heritability was estimated according to the following equation: where 2 F σ is the phenotypic variance estimated among lines of one cross; 2 ef σ is the estimate of the mean effective error, according to the augmented block design.
For the grain yield (GY) in generation F 6:7 the percentage of lines with a superior mean to the parent mean for each cross (observed positive selection gain) was calculated and the proportional selection gain (Gs %) of the best line in relation to the mean of the parents involved in the cross, by the following expression: Gs % = [(best line yield -parent mean)/parent mean] x 100

RESULTS AND DISCUSSION
In the variance analyses of generation F 6 , significant effects of parents and crosses in all traits were observed ( Table 1). The contrast parents vs crosses was significant for NDM and AV. Among the lines within the 45 crosses in generation F 6:7 , there was a significant difference for NDM and PHM in 41 and 37 crosses, respectively (Table 2). In relation to the traits AV and GY, only 22 and 10 crosses, respectively, presented significant differences among their lines. This indicates a lower variability for AV and GY, and therefore, a greater difficulty to improve these traits. The estimated variation coefficients (VC) in both generations showed that NDM and AV presented the best experimental precision; PHM attained intermediate values; and GY presented the highest VC. The VC value in the planting hills trial was superior for GY. Garland and Fehr (1981) found similar results. Regarding the general means, the populations were earlier, higher, and had a higher agronomic value and yield in generation F 6:7 . All parents and crosses proved to be earlier in generation F 6:7 , due to the effect of the sowing periods (06/11/91 vs 04/12/92) in a photoperiodsensitive species like soybean. In the population sown in November as well as the one sown in December, flower induction occurred in the time of reduced photoperiod, in other words, after the 23 rd of December (southern hemisphere), except for those genotypes that own genes for a long juvenile period. Garland and Fehr (1981) also observed an earlier cycle in inbred lines of row plots, compared to the planting hills. In generation F 6 , parents and crosses had shorter plants than in F 6:7 . The reduction in PHM was associated to a greater amount of branches, on account of the lower competition degree in the planting hill system, where the 50 cm spacing between the plant hills in a row was considerably greater than the spacing in rows, where plants grew approximately 5 cm apart. As expected, the grain yield in parents and lines per area unit was lower in planting hills (F 6 ), owing to the lower plant density in the plots; similar observations were made by Garland and Fehr (1981).
The estimates of the genotypic correlation coefficients (r G ) were similar between generations F 6 and F 6:7 , based on parents and crosses (Table 3). On the other hand, the estimated correlations based on the F 6:7 lines were different, most likely due to the absence of replications in the evaluation of the lines.
Correlations between GY and NDM were positive, with a high magnitude (> 0.70) in the parent and crosses groups, in both studied crops. These results agree with those observed by Johnson et al. (1955), Shimoya (1990), and Santos et al. (1995). One of the crucial traits for the improvement of grain size and yield in soybean, for Saka et al. (1996), is the NDM. The strong association between GY and NDM complicates the achievement of productive and early inbred lines. This relation underpins the theory of Johnson and Bernard (1963), which claim that many of the high and most consistent associations must have surged because the traits are affected by the same fundamental physiological plant processes. Shukla and Pushpendra (1998), on the other hand, estimated a positive correlation of low magnitude (r G = 0.03) among these traits. Table 2. Mean squares (analysis in augmented blocks), using the effective error, with a partition of the sum of squares of F 6:7 lines under the effect of crosses, and F 6:7 progenies/crosses, for number of days to maturity (NDM, in days), plant height at maturity (PHM, in cm), agronomic value (AV, score) and grain yield (GY, in kg ha -1 ), in semi-late soybean As expected, correlations between GY and AV were positive and high (r G of 0.77 to 0.92), in parents as well as in the F 6 and F 6:7 crosses. These associations show that the AV, although a complex trait for the evaluation in a grading system with visual scores, might be useful for the process of grain yield evaluation. Similar results were obtained by Yokomizo et al. (2000) and Pandini et al. (2001). Lopes et al. (2002) estimated positive and high genotypic correlations in generation F 2 as well as in the parents. Freire Filho (1988) obtained positive correlations in the parents groups and generation F 2 , however of small magnitude in the parents, and suggested the use of more than one evaluator to increase the efficiency of AV. The positive and moderate association between GY, NDM, and PHM in soybean complicates the achievement of early high yield inbred lines of mean plant height.
As expected, heritability coefficient estimates (h 2 ) presented a broad variation in all traits and different crosses (Table 4), since heritability varies on account of the employed population, mainly due to the genetic diversity among parents and the higher or lower sensitivity of the parents to environmental variations (Vello et al. 1988). Some heritability estimates with value zero were observed for GY in both generations, and for NDM, PHM, and AV in generation F 6:7 . These estimates gave rise to negative values of genetic variance estimates, which can be explained by the small number of plants in some crosses. For Dudley and Moll (l969), such results have no other explanation than a sampling error.
The h 2 estimates for NDM varied from 0.37 to 0.99 among crosses, with a mean of 0.92 in generation F 6 , and from 0 to 0.93 among crosses, with a mean of 0.74 in generation F 6:7 . Most crosses presented a high h 2 estimate (> 0.70) in both generations, indicating the importance of genetic causes in the phenotypic variation of trait NDM. Similar coefficients of heritability were observed by several authors: Shimoya (1990) found values that vary from 0.92 to 0.98 in F 9 inbred lines; and Prado (1994), whose estimates oscillated from 0.47 to 0.84 in F 8 lines. Santos et al. (1995) and Hamawaki et al. (2000) reported h 2 estimates of small magnitude for NDM.
For PHM, the h 2 estimates varied from 0.37 to 0.85 among crosses, with a mean of 0.65 in generation F 6. In F 6:7 , the mean was 0.50, and estimates within the crosses oscillated from zero to 0.77. In both generations, most crosses presented estimates considered moderate (0.4 < h 2 < 0.7), suggesting that the trait is slightly affected by the environment. Highest values were found by Shimoya (l990), who obtained h 2 varying from 0.60 to 0.97, in generation F 9, and by Santos et al. (l995), who discovered a h 2 estimate of 0.98, using F 6 inbred lines.
The heritability estimate for AV in F 6 presented a mean of 0.69, with a spread of 0.45 to 0.84 between crosses, and a mean of 0.37 in F 6:7 , with a spread of zero to 0.90. Hamawaki et al. (2000) obtained lower h 2 values, in a range of zero to 0.61 and a mean of 0.51 in F 4:3 lines of octuple soybean crosses.
For GY, the mean heritability estimates were 0.62 (F 6 ) and 0.29 (F 6:7 ), and the values for the crosses varied from zero to 0.85 in F 6 , and from zero to 0.58 in F 6:7 . These values were compared to those reported in other studies: 0.22 to 0.86 for F 9 inbred lines (Shimoya l990); 0.48 to 0.61 for F 8 inbred lines (Prado 1994); and zero to 0.61 for F 4:3 lines (Hamawaki et al. 2000). Inconsistent results between the two generations were not foreseen, as we are dealing with advanced generations of inbreeding. Nevertheless, as the trait GY is strongly influenced by environmental factors, some causes can be cited which possibly contributed to these results. One was the method applied to estimate the experimental variance. In F 6, the geometric mean of environmental variances among hills of both parents involved in the cross was employed; and in F 6:7 the mean effective error, obtained by the variance analysis, according to the design in augmented blocks. Furthermore, the sowing time and kind of plot also varied from one Table 3. Estimates of the genotypic correlation coefficients (r G ) between number of days to maturity (NDM), plant height at maturity (PHM), agronomic value (AV), and grain yield (GY), based on the parents, diallel crosses, and progenies F 6 and F 6:7 , in semi-late soybean generation to the next. According to Johnson et al. (1955), variance component estimates are subjected to errors, mainly in the presence of interactions, and these affect the obtained parameters based on these estimates, such as heritability. The estimate of h 2 , ratio between the genotypic and phenotypic variance, can vary considerably on account of the selection unit, or the interaction genotypes by environments; in conclusion, any significant comparison of estimates obtained in different experimental situations must provide a careful evaluation of the employed material and methods.