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J.T. de Farias Neto et al.

Genetic parameters and simultaneous selection for root yield, adaptability and stability of cassava genotypes João Tomé de Farias Neto(1), Elisa Ferreira Moura(1), Marcos Deon Vilela de Resende(2), Pedro Celestino Filho(3) and Sebastião Geraldo Augusto(4) (1) Embrapa Amazônia Oriental, Travessa Dr. Enéas Pinheiro, s/no, CEP 66095100 Belém, PA, Brazil. Email: [email protected], [email protected] (2)Embrapa Florestas, Estrada da Ribeira, Km 111, Caixa Postal 319, CEP 83411000 Colombo, PR, Brazil. Email: [email protected] (3)Embrapa Amazônia Oriental, Núcleo de Apoio à Pesquisa e Transferência de Tecnologia, Transamazônica, Travessa Comandante Castilho, no 190, Centro, CEP 68371150 Altamira, PA, Brazil. Email: [email protected] (4) Universidade Federal do Pará, Campus Universitário de Altamira, Avenida Coronel José Porfírio, s/no, São Sebastião, CEP 68370000 Altamira, PA, Brazil. Email: [email protected]

Abstract – 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. Index terms: Manihot esculenta, genotype x environment interaction, HMRPGV, REML/Blup.

Parâmetros genéticos e seleção simultânea quanto à produtividade de raízes, adaptabilidade e estabilidade de genótipos de mandioca Resumo – O objetivo deste trabalho foi estimar parâmetros genéticos e avaliar a seleção simultânea quanto à produtividade de raízes e à adaptabilidade e estabilidade de genótipos de mandioca. Os efeitos dos genótipos foram considerados como fixos e aleatórios, e a metodologia de modelos mistos (REML/Blup) foi utilizada para estimar os parâmetros genéticos e a média harmônica do desempenho relativo dos valores genotípicos (MHPRVG), para seleção simultânea. Dez genótipos foram avaliados em delineamento de blocos ao acaso, com quatro repetições. O experimento foi realizado nos municípios de Altamira, Santarém e Santa Luzia do Pará, PA, nos anos agrícolas de 2009/2010, 2010/2011 e 2011/2012. As raízes foram colhidas 12 meses após o plantio, em todos os locais testados. A  produtividade de raízes apresentou baixo coeficiente de variação genotípica (4,25%) e herdabilidade de parcelas individuais no sentido amplo (0,0424), o que resultou em baixo ganho genético. Em razão da baixa correlação genotípica (0,15), a classificação dos genótipos quanto à produtividade de raízes variou de acordo com o ambiente. Os genótipos CPATU 060, CPATU 229 e CPATU 404 destacaram-se quanto à produtividade, adaptabilidade e estabilidade. Termos para indexação: Manihot esculenta, interação genótipo x ambiente, MHPRVG, REML/Blup.

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% Pesq. agropec. bras., Brasília, v.48, n.12, p.1562-1568, dez. 2013 DOI: 10.1590/S0100-204X2013001200005

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

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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.

February to April. Santa Luzia do Pará has a hot and humid weather, with an average rainfall of 2,300 mm per year and an average temperature of 28oC. 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 1.0x1.0 m 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

Materials and Methods

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

Ten cassava genotypes (Table 1) were used in trials established in the municipalities of Santa Luzia do Pará (01o27'06"S, 46o57'35"W), Santarém (2o24'54"S, 54o24'36"), and Altamira (3o12'12"S, 52o12'13"W), in the state of Pará, Brazil. The trials were carried out in the growing seasons of 2009/2010, 2010/2011, and 2011/2012. Santarém has an Ami climate type, according to Köppen’s classification, with humid and hot weather and an average temperature of 27oC. The average rainfall is about 2,000 mm, with two distinct periods of rain and most rainy days concentrated from December to June. Altamira has both Am and Aw climate types. The average temperature is of 27oC and precipitation is of 2,100 mm, concentrated mostly from

Accession Sampling location in Brazil Year CPATU 013 Belém, PA 1947 CPATU 058

Unknown

1970

CPATU 060 CPATU 229 CPATU 302 CPATU 402 CPATU 404 CPATU 444

Unknown Nova Timboteua, PA Castanhal, PA Castanhal, PA Santa Maria do Pará, PA Terra Alta, PA

1970 1998 2000 2005 2005 2008

BRS Kiriris

-

BRS Poti

-

(1)

Main traits

Used for tapioca flour(1) Used for tapioca flour(1)

Yellow pulp root Tolerant to root rot, low 2006 hydrogen cyanide content Tolerant to root rot, 2007 erect growing

According to information given by producers at the sampling location.

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(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; s2g is the genotypic variance among genotypes; s2ge is the variance of genotype x environment interaction; s2e 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: s ˆ 2e = [y'y - bˆ ' y - gˆ ' Z' y - cˆ ' W' y]/[N - r(x)], s ˆ 2g = [gˆ ' gˆ + s ˆ 2e tr C22]/q, and s ˆ 2ge = [geˆ ' geˆ + s ˆ 2e tr C33]/s, in which, C22 and C33 come from, Pesq. agropec. bras., Brasília, v.48, n.12, p.1562-1568, dez. 2013 DOI: 10.1590/S0100-204X2013001200005

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 μj + g + ge, in which μj 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:

¯ ij = uj + gi + geij in which: n is the number of locations; VG represents the genotypic value of genotype i in the specific location j, in which the mean for location j and gi and geij are the Blups of genotype i and of the interaction between genotype i and location j, ¯ ij in location j. ¯ .j is the mean for VG respectively; and VG

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

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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

Table 2. Analysis of deviance for cassava (Manihot esculenta) root production.

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.

Effect Genotypes Genotype x environment interaction Residual Complete model

Deviance(1) 1,310.66 1,331.4

LRT (Chi-square) 0.28ns 21.02**

-

-

1,310.38

Deviance of adjusted model without the cited effects; distribution for 1 degree of freedom. LRT, likelihood; chi-square, 3.84 and 6.63 at 5 and 1% probability, respectively. (1)

Table 3. Estimate of components of means and variance for root yield (Mg ha-1) of cassava (Manihot esculenta) genotypes(1). Genotypes

Genotype

g + ge

CPATU 404 CPATU 013 CPATU 060 CPATU 229 CPATU 402 CPATU 302 CPATU 444 BRS Kiriris CPATU 058 BRS Poti Mean

5.2957 3.3707 2.5484 1.8113 1.5533 0.4562 3.0979 3.1434 3.3423 5.4519

μ + g + ge

Genetic Genetic values gain Altamira 33.5101 29.4774 5.2957 31.5851 27.5309 4.3332 30.7629 26.8235 3.7383 30.0257 26.0546 3.2565 29.7677 25.6031 2.9159 28.6706 24.4210 2.5059 25.1165 20.6824 1.7054 25.0710 20.7663 1.0993 24.8722 20.4359 0.6058 22.7625 18.2069 0.000 28.21 Mg ha-1 Santarém 19.2081 24.7283 1.6141 18.8438 24.2353 1.4320 18.3570 24.0591 1.2090 17.9688 22.5071 1.0004 17.3559 21.4132 0.7527 17.3309 21.7379 0.5834 17.2700 22.3890 0.4538 16.9342 22.3152 0.3146 16.6105 21.5026 0.1704 16.0607 20.35744 0.000 17.59 Mg ha-1 Santa Luzia do Pará 20.3144 24.3731 4.0568 20.1098 24.0432 0.9545 19.7936 23.8122 0.8150 19.6353 22.6222 0.7057 19.6100 23.1553 0.6350 19.4748 23.1961 0.5654 19.2186 22.2979 0.4790 18.2810 21.2097 0.2971 18.2782 22.4361 0.1552 17.8604 20.4108 0.000 19.25 Mg ha-1

New mean

33.5101 32.5476 31.9527 31.4709 31.1303 30.7204 29.9198 29.3137 28.8202 28.2144

Genotypic μ + g Genetic gain New mean μ + g + ge effect CPATU 404 0.5917 23.912 0.5917 23.9118 25.0136 CPATU 060 0.5473 23.867 0.5695 23.8896 24.8867 CPATU 229 0.4558 23.776 0.5316 23.8517 24.6248 CPATU 013 0.4389 23.759 0.5084 23.8286 24.5763 CPATU 402 0.1685 23.488 0.4404 23.7606 23.8024 CPATU 302 0.0204 23.299 0.3636 23.6838 23.2618 BRS Kiriris 0.3271 22.993 0.2650 23.5851 22.3840 CPATU 444 0.5053 22.815 0.1687 23.4888 21.8739 CPATU 058 0.5239 22.796 0.0917 23.4119 21.8205 BRS Poti 0.8256 22.495 0.0000 23.3201 20.9572 Genotypic variance 0.9815 Variance of genotype x environment interaction 5.4835 Residual variance 23.8238 Phenotypic variance 30.2889 Broad-sense individual heritability free of interaction 0.0424 Average heritability 0.2762 Selective accuracy 52.55% R2 of genotype x environment interaction 0.1811 Genotypic correlation of behavior in different environments 0.1518 Coefficient of genotypic variation (%) 4.2484 Coefficient of residual variation (%) 20.9303 23.32 General mean (Mg ha-1)

CPATU 060 CPATU 229 CPATU 404 BRS Kiriris BRS Poti CPATU 444 CPATU 402 CPATU 013 CPATU 302 CPATU 058 Mean

1.6141 1.2498 0.7630 0.3748 0.2381 0.2631 0.3240 0.6598 0.9835 1.5333

CPATU 013 CPATU 229 CPATU 060 CPATU 058 CPATU 302 CPATU 402 BRS Kiriris CPATU 444 CPATU 404 BRS Poti Mean

1.0568 0.8521 0.5360 0.3777 0.3524 0.2172 0.0390 0.9766 0.9794 1.3972

μ + g, predicted genotypic values (free of interaction); μ + g + ge, average genotypic value in the environments.

g + ge, genotypic effect per environment; μ + g + ge, predicted genotypic value capitalizing the interaction with the environments.

19.2081 19.0260 18.8030 18.5944 18.3467 18.1774 18.0478 17.9086 17.7644 17.5940

20.3144 20.2121 20.0726 19.9633 19.8926 19.8230 19.7367 19.5547 19.4129 19.2576

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with locations) was low (0.1518). This indicates that this interaction is complex, resulting in changes in genotype classification (productivity rank) between locations. The genotypic values free of interaction (μ + g) for the average location indicate that the three best genotypes were: CPATU  404, CPATU  060, and CPATU  229. In this case, the average genetic gain obtained with the selection of the three genotypes was 2.28%. The estimate of genotypic values, considering the average interaction among genotypes and environments (μ  +  g +  ge), indicated the same genotypes previously selected for use in areas with similar patterns of genotype x environment interaction. Although both methodologies selected the same genotypes, the predictions of genotypic values in the second case (μ + g + ge) were superior. Bastos et al. (2007) found that the prediction of genotypic values, considering interaction, can only be superior when the selected genotypes are grown in a location with the same pattern of genotype x environment interaction, as the one where the original trials were executed. However, inferences on genotypic means based on the first case are more secure (Table 3). The statistics of the genetic mean per location (μ + g + ge) showed that the three best genotypes in each location were: CPATU  404, CPATU  013, and CPATU  060 in Altamira; CPATU  060, CPATU  229, and CPATU  404 in Santarém; and CPATU  013, CPATU 229, and CPATU 060 in Santa Luzia do Pará (Table  4). The genetic gain with the selection of the three most productive genotypes was more expressive in Altamira (13.36%), followed by Santa Luzia do Pará

(5.82%), and Santarém (4.25%). The genetic gains in each environment (Table 4) were superior to the other estimates, considering the average of environments based on the selection according to average (Table 3). This genetic mean is the parameter that least affects the predicted genotypic values, since it considers the effects of the interaction of each environment in the selection per environment, compared with the selection for all environments based on genetic value (Rosado et al., 2012). The negative values of g + ge show that the genotypes CPATU  302, BRS  Kiriris, CPATU  444, CPATU 058, and BRS Poti are above the general mean (23.32 Mg ha-1) (Table 4). The genotypes CPATU 444, BRS Kiriris, CPATU 058, and BRS Poti were the least productive in all locations. Thus, since the selection carried out in this study considered root yield alone, these genotypes should be discarded. The genotypes CPATU 060 and CPATU 229 were among the most productive, in all locations. Therefore, these genotypes did not interact significantly with the environment. The expected reduction or increase in root yield varied according to genotype performance related to stability (HMGV), adaptability (RPGV), and both simultaneously (HMRPGV) for all environments (Table 5). There was total agreement between the three most productive genotypes based on HMGV, RPGV, HMRPGV, and average yield. These results indicate that secure predictions about genetic values can be made based on a single standard contemplating yield, stability, and adaptability (Verardi et al., 2009). The HMRPGV method selects genotypes based on their adaptability and stability, which is important

Table 5. Stability of genotypic values (HMGV), adaptability of genotypic values (RPGV), and stability and adaptability of genotypic values (HMRPGV) for cassava (Manihot esculenta) genotypes root yield. Genotype(1) 08 02 10 05 01 06 03 07 09 04

HMGV 22.2075 22.0427 21.5786 21.4380 21.0017 20.5373 20.3291 19.7088 19.5570 19.0429

Genotype 08 10 02 05 01 06 03 07 09 04

RPGV 1.0701 1.0601 1.0598 1.0456 1.0160 0.9929 0.9693 0.9415 0.9380 0.9069

RPGV × GM(2) 24.9518 24.7209 24.7153 24.3838 23.6926 23.1535 22.6039 21.9562 21.8743 21.1489

Genotype 08 02 10 05 01 06 03 07 09 04

HMRPGV 1.0691 1.0597 1.0512 1.0416 1.0151 0.9916 0.9657 0.9399 0.9344 0.9005

HMRPGV × GM 24.9320 24.7124 24.5132 24.2899 23.6718 23.1249 22.5203 21.9178 21.7904 20.9999

01, CPATU 402; 02, CPATU 229; 03, BRS Kiriris; 04, BRS Poti; 05, CPATU 013; 06, CPATU 302; 07, CPATU 444; 08, CPATU 060; 09, CPATU 058; 10, CPATU 404. (2)GM, general mean. (1)

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Genetic parameters and simultaneous selection for root yield

to direct controlled crossings in evaluation phases of genetic breeding programs and to recommend superior genotypes for commercial use. Generally, a univariate model of repeatability, considering all locations simultaneously, is suitable for selection, focusing on the average yield in all locations. However, a more complete model may allow additional inferences, such as specific genotypes for each location, selection of stable genotypes, selection of responsive genotypes (high adaptability) to environmental improvements, and selection considering the three aspects simultaneously (Sturion & Resende, 2005). Resende (2004) demonstrated that the simultaneous selection for yield, stability, and adaptability using mixed models can be 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. The method also contemplates the specific adaptation of a genotype to an environment, using  = uj + gi + geij, 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.

Acknowledgements To Fundação Amazônia Paraense de Amparo à Pesquisa (Fapespa) and to Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), for financial support and grant given, respectively.

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Received on June 29, 2013 and accepted on November 29, 2013

Pesq. agropec. bras., Brasília, v.48, n.12, p.1562-1568, dez. 2013 DOI: 10.1590/S0100-204X2013001200005

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