Genetic parameters and simultaneous selection for root yield , adaptability and stability of cassava genotypes

The objective of this work was to estimate genetic parameters and to evaluate simultaneous selection for root yield and for adaptability and stability of cassava genotypes. The effects of genotypes were assumed as fixed and random, and the mixed model methodology (REML/Blup) was used to estimate genetic parameters and the harmonic mean of the relative performance of genotypic values (HMRPGV), for simultaneous selection purposes. Ten genotypes were analyzed in a complete randomized block design, with four replicates. The experiment was carried out in the municipalities of Altamira, Santarém, and Santa Luzia do Pará in the state of Pará, Brazil, in the growing seasons of 2009/2010, 2010/2011, and 2011/2012. Roots were harvested 12 months after planting, in all tested locations. Root yield had low coefficients of genotypic variation (4.25%) and broad-sense heritability of individual plots (0.0424), which resulted in low genetic gain. Due to the low genotypic correlation (0.15), genotype classification as to root yield varied according to the environment. Genotypes CPATU 060, CPATU 229, and CPATU 404 stood out as to their yield, adaptability, and stability.


Introduction
Cassava (Manihot esculenta Crantz) is a major source of carbohydrates for more than 800 million people, in several tropical countries (Save and grow, 2013).In 2012, Brazil was the second main world producer of cassava, with 25,744,829 tons of roots.The state of Pará is the main producer, with 17.92% of the national production in that same year (Instituto Brasileiro de Geografia e Estatística, 2013).
In genetic breeding programs, a great number of promising genotypes and clones are tested in different environments.Although studies on genotype x environment interaction are of great value for genotype selection in different climatic conditions, they do not provide detailed information on the individual performance of the genotypes in each environment.Adaptability and stability studies are needed for that (Cruz & Regazzi, 1994).
Vidigal Filho et al. (2007) reported that the methodologies proposed by Lin & Binns (1988) and Annicchiarico (1992) were similar for selecting more stable cassava genotypes.According to Kvitschal et al. (2009), the methodologies recommended by Eskridge (1990), Annicchiarico (1992), and Lin & Binns (1988) are more suitable for situations of low genotype x environment interaction, whereas the additive main effect and multiplicative interaction (AMMI) methodology and the one of Toler & Burrows (1998) provide better details for specific adaptations of genotypes to environments.
The harmonic mean of the relative performance of genotypic values (HMRPGV), presented by Resende (2002), allows selecting simultaneously for yield, adaptability, and stability, and can be performed using the same Blup predictors and mixed model equations.
Colombari Filho et al. (2013) used this methodology to perform a global analysis of 26 years of rice genetic breeding in Brazil.It has been used also for other species, such as sugarcane (Zeni-Neto et al., 2008), rubber tree (Arantes et al., 2013), rice (Reginato Neto et al., 2013), and common bean (Carbonell et al., 2007).For cassava, there are no know reports on the use of HMRPGV.
The objective of this work was to estimate genetic parameters and to evaluate simultaneous selection for root yield and for adaptability and stability of cassava genotypes.

Materials and Methods
Ten cassava genotypes ( All trials were established in a randomized complete block design, with four replicates.The plots had 25 plants each, distributed in five lines of five plants.Roots were harvested from nine plants located within the central lines.The soil was tilled and planting was done with a 1.0x1.0m spacing.One single application of the NPK 10-28-20 was done, 35 days after the planting of the stakes, using 40 g of fertilizer per planting spot.No irrigation was performed. Evaluations were done 12 months after sowing.Root yield of each replicate was corrected using the covariance method (Vencovsky & Barriga, 1992), according to the final stand, considering nine plants.Root yield was evaluated in kg ha -1 .The evaluated genotypes belong to the Germplasm Bank of Embrapa Amazônia Oriental, located at Belém, state of Pará, Brazil: CPATU 444, CPATU 404, CPATU 060, CPATU 229, CPATU 013, CPATU 402, CPATU 302, CPATU 058, BRS Poti, and BRS Kiriris.The two last ones are commercial cultivars tolerant to root rot, a disease caused by Phytophthora sp. and Fusarium sp.
The matrix form of this model, considering one observation per plot, is represented by: y = Xb + Zg + Wc + e, in which: y, b, g, c, and e are, respectively, vectors of data, fixed effects of blocks over the locations, genotypic effects of genotypes (random), effect of genotype x environment effects (1) According to information given by producers at the sampling location.
(random), and random errors; and X, Z, and W are the matrices of incidence of b, g, and ge, respectively, as described by Resende (2007a).The authors have shown statistically that, when using mixed models, the medium quadratic error is minimized in the prediction of true genetic values if the effects of genotypes are considered random and the number of treatments is ten or more.
The distribution and structure of means and variances are the following: The equations of mixed models are: in which: In this case, is the broad-sense heritability at the individual plot level in the block; is the determination coefficient of effects of genotype x environment interaction; s 2 g is the genotypic variance among genotypes; s 2 ge is the variance of genotype x environment interaction; s 2 e is the residual variance among plots; and is the genotypic correlation of genotypes among environments.
The estimators of components of variance using REML, with the EM algorithm, are: e tr C 22 ]/q, and ŝ2 ge = [g ê' g ê + ŝ2 e tr C 33 ]/s, in which, C 22 and C 33 come from, in which: C is the coefficient matrix of the mixed model equations; tr is the trace operator matrix; r(x) is the rank of the matrix X; N, q, and s are the total number of data, number of genotypes, and number of genotype x environment combinations, respectively.
In this model, the predicted genotypic values free of interaction, considering all locations, are measured by μ + g, in which μ is the mean of all locations.For each j location, genotypic values are predicted by μ j + g + ge, in which μ j is the mean for location j.
In the model in which genotypic effects were considered fixed, the g vector was adjusted as a fixed effect and the b vector was adjusted as a random effect.
The estimates of components of variance and genetic parameters were obtained with the linear mixed model methodology, in the statisticalgenetics software SelegenREML/Blup (Resende, 2007b).
The analysis of stability and adaptability was carried out with the HMRPGV method, calculated as: in which: n is the number of locations; V Ḡij = u j + g i + ge ij represents the genotypic value of genotype i in the specific location j, in which the mean for location j and gi and ge ij are the Blups of genotype i and of the interaction between genotype i and location j, respectively; and V Ḡ.j is the mean for V Ḡij in location j.

Results and Discussion
The effects of genotypes, free of interaction, were not significant, which is normal in joint analyses considering contrasting environments.However, the effects of interaction were highly significant, and a study of genotype stability and adaptability is needed for selection (Table 2).
Root yield showed low levels of genotypic variation (4.25%).The broad-sense individual heritability, related to genotypic effects, free of the interaction with environments, was 0.0424 (Table 3), configuring a genetic gain of low magnitude (Resende, 2002).Average root yield in each location was: 28.21 Mg ha -1 in Altamira, 17.59 Mg ha -1 in Santarém, 19.25 Mg ha -1 in Santa Luzia do Pará; and the general mean was 23.32 Mg ha -1 (Table 4).These results agree with the quantitative and polygenic nature of this trait and are similar to the estimates obtained by Barreto & Resende (2010).
The square root of heritability resulted in a selective accuracy of moderate magnitude (52.55%), which guarantees security in the selection of superior genotypes (Resende, 2004).However, the adoption of an adequate number of replicates is essential in trials aiming for efficient and high accuracy selection.With a heritability of 20%, the use of five replicates leads to a selective accuracy of 74.56%, which is adequate.The coefficient of variation showed a moderate value of 20.93%, confirming the good precision of the trials.The genotype x environment interaction was high, and the genotypic correlation for the behavior in different environments (genotypic correlation of genotypes   The method also contemplates the specific adaptation of a genotype to an environment, using = u j + g i + ge ij , which is the genotypic value of genotype i in the specific location j.Groups of varieties can be formed according to the specific adaptability to each environment, using the magnitude and signal of the estimate of interactions.The genotypes CPATU 404, CPATU 013, and CPATU 060 showed higher synergy with Altamira (Table 4).

Conclusions
1. Cassava genotypes highly interact with the environment as to root yield, which results in low genotypic correlation between environments.
2. The selected genotypes do no vary when genetic effects are used as random or fixed.
3. The genotypes CPATU 060, CPATU 229, and CPATU 404 stood out with the best yield, adaptability, and stability, and should be recommended for breeding programs.

Table 1 .
Description of the cassava (Manihot esculenta) accessions from the Germplasm Bank of Embrapa Amazônia Oriental, Brazil.

Table 4 .
Estimate of predicted genetic gain for cassava (Manihot esculenta) root yield (Mg ha -1 ) in three locations in the state of Pará, Brazil.done by the HMRPGV method.In the present work, the three best genotypes based on RPGV, HMGV, and HMRPGV were the same as the best ones based on average yield.The best genotypes to be selected based on HMRPGV were: CPATU 060, CPATU 229, and CPATU 404.This selection would generate a genetic gain of 6.0% over the general mean.