USING GENEALOGY TO IMPROVE SELECTION EFFICIENCY OF PEDIGREE METHOD

In the pedigree method of conducting an autogamous population of segregating plants, the genealogy of the progenies is registered. Although labor-intensive, these data are rarely used. One possibility of exploiting this information is to improve selection efficiency using BLUP (Best Linear Unbiased Prediction). In this study BLUP with genealogy inclusion was compared to the mean in the progenies evaluation conducted by the pedigree method. Progenies of crosses of the common bean lines BRS MG Talismã and BRS Valente in F4:6 and F4:7 were used. The 256 F4:6 progenies were sown in February 2005, in southeast of Brazil, in a 16 × 16 simple lattice design. The grain yield data were subjected to BLUP analysis with inclusion of genealogy. Based on this analysis and the mean, the 30 progenies with best and worst performance were selected. These 60 F4:7 progenies were classified in relation to the origin, i.e., selected by BLUP, mean, or BLUP and mean and coincident results were obtained. In the selection for best performance, the efficiency of BLUP was 2.4% higher than the mean. In the selection for the opposite extreme, BLUP analysis was however not advantageous. The progenies × environments interaction indicates the need for an evaluation of the progenies in different environments before beginning selection.


INTRODUCTION
The success of improvement in the development of plants with higher grain yield, fruits and fiber is evident.However, the continuously increasing demand calls for further genetic progress in the future.Continuous success in selection programs depends on the use of all improvement strategies available.
In the case of autogamous plants, among the different methods of advancing segregating populations, the genealogy or pedigree method is particularly interesting.A peculiarity of this method is that the genealogy of the progenies in the selfing generations is registered.But, in spite of rather time-consuming for breeders, the compiled genealogy is practically not used at all (Ramalho et al., 2001).On this background, the mixed model analysis, as proposed by Henderson in 1959, is well-suited since this information on genetic progeny similarity is considered for selection purposes (Resende, 2002).The progenies are thus selected based on their genetic estimates that take not only the performance per se into account, but the performance of related progenies as well.These estimates represent the Best Linear Unbiased Prediction -BLUP (Henderson, 1975).
The advantageous effect of the inclusion of parentage information in plant improvement has been described elsewhere (Panter & Allen, 1995;Bromley et al., 2000).In a simulation study with F 4:5 progenies conducted by the pedigree method, Nunes (2006) evidenced that the BLUP procedure, considering the parentage, proved advantageous over selection based on the phenotypic mean, especially in conditions of low heritability.This information was however not corroborated by experimental data.
This study aimed to compare the selection efficiency of BLUP including genealogy information to the phenotypic mean of common bean progenies, conducted by the pedigree method.
F 1 seeds were obtained through artificial crosses of the above described parents, performed in a greenhouse (Peternelli & Borém, 1999).The F 1 and F 2 plants were grown under field conditions.The following generations up to the F 4:5 progenies were conducted by the pedigree method as follows: 64 F 2 plants were collected individually generating 64 F 2:3 progenies that were sown in rows in the following growing season.Two plants of each F 2:3 progeny were randomly collected, which originated the 128 F 3:4 progenies.In turn, these were sown again and two plants per row originated the 256 F 4:5 progenies.
The F 4:5 progenies were planted in a row and 256 F 4:6 progenies were bulk-harvested which were sown in February 2005 and evaluated in the dry sea-son.The experimental design was a 16 × 16 simple lattice.The experimental plots consisted of 2 m long rows, spaced 50 cm apart, with 15 seeds per meter.The other cultural treatments were the regionally applied for common bean.The evaluated trait was grain yield.
The data were analyzed in two ways: by the conventional approach with analysis of variance, using the following statistical model: , where: y ijk : observation of the plot that received progeny i in block k within replication j (i=1, 2,...,256; j=1,2; k=1,2,...,16); μ: constant associated to all observations; r j : fixed effect of replication j; b k(j) : random effect of block k within replication j; a i : random effect of progeny i; e ijk : random experimental error associated to observation y ijk .
The second approach focused on the mixed model.For this purpose, the previous statistical model was re-expressed in the matrix form by: , where G is the matrix of genetic additive covariances between the random progeny effects; e: error vector, dimensions 512 × 1, with The genetic additive matrix of covariances between the random effects of progenies (matrix G) can be determined by the matrix of genetic additive parentage between the progenies multiplied by the component of variance associated to these random effects - , 1996;Lynch & Walsh, 1998).According to the described conduction of the segregating population, each F 2 plant generated four related F 4:6 progenies, provided that the F 2 generation is assumed in equilibrium.Based on this known genealogy of the F 4:6 progenies, the coefficients of additive parentage were thus determined, as well as elements of matrix A, which correspond to twice Malecot's coancestry coefficient of the progenies.For the F 4:6 progenies, matrix A is therefore given by: where: ⊗ symbolizes the Kronecker matrix product.The statistical analyses were performed using the Mixed procedure of the SAS 8.0 software package (Littlel et al., 1996;SAS, 1999).After the data analysis of the F 4:6 progenies, 60 progenies (30 with best and 30 with worst performance) were selected by the mean and by BLUP.These 60 progenies, as well as the F 4:7 generation and four controls (BRS MG Talismã, BRS Valente, VC-3 and OP-NS 331) were evaluated again in a field experiment in the wet season sown in November 2005, in an 8 × 8 triple lattice design.The plots had two rows of two meters, spaced 50 cm apart.The management was similar to the previous and grain yield data were obtained.The mentioned model was also used in the subsequent analysis of variance.Based on the joint analysis of the F 4:6 and F 4:7 progenies, the components of the progenies ǵenerations interaction were partitioned, as shown by Cruz et al. (2004).
For the F 4:6 as well as the F 4:7 progenies the components of genetic variance were estimated based on the mean square expectations.The confidence intervals (CI) associated to the estimates of the genetic variance components were estimated based on the following expression (Ramalho et al., 2005): where: α: 0.05 level of significance; Furthermore, the heritability ( ) 2 ĥ for selection in the progeny mean was estimated based on the mean square expectations of the analysis of variance (Vencovsky & Barriga, 1992).The errors associated to the estimate were determined according to Knapp et al. (1985).

RESULTS AND DISCUSSION
Differences (P ≤ 0.01) were verified between the F 4:6 progenies regarding grain yield (Table 1).The significance of the effect of progenies was reinforced by the genetic and phenotypic parameter estimates of this generation (Table 2).The estimate of the genetic variance in F 4:6 progenies is different from zero, with a lower positive limit.The lower limit of h 2 is positive, which allowed the conclusion that it is also different from zero, with 95% probability.The h 2 estimate was higher than 47%.The heritability can be considered as in the narrow sense, since dominance variance 2 D σ is o f little relevance in autogamous crops (Van Oeveren & Stam, 1992).In the particular case of common bean, contribution of 2 D σ to the genetic variance in grain yield is low (Moreto et al., 2007).Moreover, only 31/256 of ( 2 D σ ) present in F 2 is exploited in F 4:5 progenies.Different h 2 estimates for common bean grain yield have been proposed in the literature.In a data collection (including 22 estimates) the mean estimate of this parameter was 32% (Moreto et al., 2007).A comparison of h 2 estimates is not easy, owing to variations due to the progeny type and the experimental conditions.Still, the h 2 value obtained here (47%) with F 4:6 progenies was higher than the estimated mean based on the revision (Table 2).These results evidence the possibility of success with selection in this segregating population, which was a basic condition for the conduction of this study.The BLUP method was applied together with the genealogy, in the hope of improving the selection efficiency as suggested elsewhere (Lynch & Walsh, 1998;Resende, 2002).Considering the results of BLUP as well as the means, the 30 best and 30 worst-performing progenies were identified (Table 3).Remarkably, of this total, nine of the best progenies were selected by both procedures (mean and BLUP), only eleven by the BLUP and ten by the mean.Thus, 20 best-performing progenies were selected in the BLUP and 19 with the mean.In the negative sense the proportions were similar.In this way it was possible to evaluate the efficiency of the mean and of the BLUP in the selection process under similar conditions.Furthermore, in terms of mean grain yield the progenies selected by BLUP and those by the mean did not coincide particularly well, especially regarding the worstperforming progenies for both selection criteria (Table 3).
The analysis of joint variance of the common progenies presented significant differences between progenies (Table 1).Moreover, the effect of the progenies × generations interaction was significant (P ≤ 0.01).The estimate of the genetic correlation between the progeny means in both generations (r g = 0.59) was not high, indicating that the progeny performance was not coincident in the two environments.Even in the  case of the progenies performance coincided in the selection, their classification was different (Table 4).The occurrence of progenies × environments interaction in common bean is well-documented (Carneiro et al., 2002;Pereira, 2003;Aguiar et al., 2004).
The main focus of this study was to verify whether there is any difference between the BLUP method and the progeny means.Among the 30 superior and 30 inferior progenies selected in the F 4:6 , 19 coincided in both groups in the following generation (F 4:7 ).Of the progenies identified as superior in F 4:6 , by the mean as much as by BLUP, 88.9% were also among the 30 best in F 4:7 .On the other hand, the coincidence for those identified by the BLUP or by the mean only was lower.Considering the selection of the 20 F 4:6 progenies by the BLUP, 14 coincided (70.0%).By the mean however, of the 19 progenies identified among the 30 best in F 4:6 , 13 coincided with good performance in F 4:7 (68.4%).Consequently, the BLUP presented an efficiency of only 2.4% over the mean.However, in the selection for the opposite extreme, the efficiency was the same (Table 5).
BLUP is particularly recommended when there is an imbalance and/or covariances between genotypes.In the case of the evaluations of progenies in autogamous plants the imbalance is hardly ever significant.In this situation the results of the BLUP are equivalent to the mean for non-related genotypes (Bernardo, 2002).However, since the genealogy of the progenies makes it possible to measure the parentage among the progenies in the pedigree method of conducting segregating populations, its use in the BLUP would be a possibility to increase the selection efficiency, justifying the collection of this information.
According to the simulation, the advantage in the selection accuracy of BLUP over the mean increases with the reduction of h 2 (Nunes, 2006).With a h 2 of 50%, a similar value to that of the F 4:6 progenies obtained in the present study (Table 2) and with a selection intensity of 10%, equivalent to the one used here, the selection efficiency of the BLUP compared to the mean would be 0.7 percentage points, that is, a slightly inferior value than observed here when selection was performed in the positive sense.In view of the heritabilities that were obtained in common bean improvement programs for the trait grain yield, the advantage of BLUP is probably not worth the effort of recording genealogy.A greater effort must be made in the moment of evaluating the progenies, which should be evaluated in a larger number of environments to reduce the effect of the progenies × environments interaction.

2 :
, where: y: vector of phenotypic data of the plots, in the dimensions 512 × 1; X: matrix of the model of the fixed effects β β β β β, dimensions 512 × 3; β β β β β: vector of the fixed effects, 3 × 1; Z 1 : matrix of the model of the random effects of blocks within replications b, 512 × 32; b: vector of the random effects of blocks within replications, 32 × 1matrix of the model of the random effects of progenies a, 512 × 256; a: vector of the random effects of the progenies, 256 × 1, with ( ) Sci. Agric.(Piracicaba, Braz.), v.65, n.1, p.25-30, January/February 2008 superior quantiles tabled in the 2 χ (Chi-square) distribution for V degrees of freedom.

Table 1 -
Summary of the individual analyses of variance in the F 4:6 and F 4:7 generations and the joint analysis of both generations for grain yield (g/plot), Lavras, MG.

Table 2 -
Estimates of genetic variance in progenies (

Table 3 -
Number of progenies selected by the mean, BLUP, mean/BLUP and their respective lower (L.L.) and upper limits (U.L.) of grain yield in the F 4:6 generation.

Table 4 -
Classification of the coincident progenies in the F 4:6 and F 4:7 generations and their origin in relation to the selection criterion used.1/Classification of the progenies selected in F 4:6 and evaluated in F 4:7.

Table 5 -
Expected and observed number of progenies in the F 4:7 generation by the selection based on the mean, BLUP and mean/BLUP in the F 4:6 generation, and percentage of coincidence.