360570

Research ArticleSelection Index in the Study of Adaptability andStability in Maize

Rogeacuterio Lunezzo de Oliveira1 Renzo Garcia Von Pinho2 Daniel Furtado Ferreira3

Luiz Paulo Miranda Pires4 and Wagner Mateus Costa Melo5

1 Engenheiro Agronomo Mestre em Genetica e Melhoramento de Plantas DuPont do Brasil SA Divisao Pioneer SementesRodovia GO 210 km 04 Fazenda Santa Maria de Baixo Zona Rural Caixa Postal 1014 75503-970 Itumbiara GO Brazil

2 Engenheiro Agronomo Doutor em Genetica e Melhoramento de Plantas Departamento de AgriculturaDAGUniversidade Federal de Lavras (UFLA) Lavras MG Brazil

3 Engenheiro Agronomo Pos-Doutor em Estatıstica e Experimentacao AgronomicaDepartamento de Ciencias Exatas (DEX) Universidade Federal de Lavras (UFLA) Lavras MG Brazil

4 Engenheiro Agronomo Mestre em Genetica e Melhoramento de Plantas Departamento de BiologiaDBIUniversidade Federal de Lavras (UFLA) Lavras MG Brazil

5 Engenheiro Agronomo Doutor AgronomiaFitotecnia Advanta Comercio de Sementes Ltda Florianopolis SC Brazil

Correspondence should be addressed to Rogerio Lunezzo de Oliveira rogeriooliveirapioneercom

Received 10 November 2013 Accepted 29 December 2013 Published 13 February 2014

Academic Editors B Chen and W Ma

Copyright copy 2014 Rogerio Lunezzo de Oliveira et al This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

This paper proposes an alternative method for evaluating the stability and adaptability of maize hybrids using a genotype-ideotypedistance index (GIDI) for selection Data from seven variables were used obtained through evaluation of 25 maize hybrids atsix sites in southern Brazil The GIDI was estimated by means of the generalized Mahalanobis distance for each plot of the testWe then proceeded to GGE biplot analysis in order to compare the predictive accuracy of the GGE models and the grouping ofenvironments and to select the best five hybrids The G times E interaction was significant for both variables assessed The GGEmodelwith two principal components obtained a predictive accuracy (PRECORR) of 08913 for the GIDI and 08709 for yield (t haminus1)Two groups of environments were obtained upon analyzing the GIDI whereas all the environments remained in the same groupupon analyzing yield Coincidence occurred in only two hybrids considering evaluation of the two features The GIDI assessmentprovided for selection of hybrids that combine adaptability and stability in most of the variables assessed making its use morehighly recommended than analyzing each variable separately Not all the higher-yielding hybrids were the best in the other variablesassessed

1 Introduction

In breeding programs it is often necessary to obtainmeasuresof various traits to select them simultaneously This need ledto the development of selection indices allowing selectionto be performed using a single value The application ofselection indices was initially proposed by Smith [1] throughthe optimized indexThis index was later modified andmostof these modifications were also based on linear combina-tions of the phenotypic values observed The most commonmodifications are those of Brim et al [2] Kempthorne and

Nordskog [3] Pesek and Baker [4] and Tai [5] and Smith etal [6]

Other authors presented nonparametric indices appliedfor the purpose of classifying genotypes Elston [7] proposeda multiplicative index which considers all the traits with thesame economic weight Wricke and Weber [8] suggested theuse of the Euclidean andMahalanobis distances to classify thegenotypes for various traits simultaneously based on theirdistance from an ideal genotype (ideotype) defined by theresearcher Mulamba and Mock [9] developed a quite simpleindex which uses the sum of the number of order that the

Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 360570 6 pageshttpdxdoiorg1011552014360570

2 The Scientific World Journal

genotype presents for each trait the lower the value obtainedin this sum the better the classification

There are various methodologies for evaluation of theG times E interaction Crossa [10] suggests that the applicationof multivariate methods may be useful to better exploit theinformation contained in the data Recently amodification ofthe conventional AMMI analysis proposed by Yan et al [11]called the GGE biplot has been used for study of the G times Einteraction GGE analysis groups the genotype effect whichis an additive effect in the AMMI analysis with the G times Einteraction which is a multiplicative effect subjecting theseeffects to a multiplicative model of regression for sites (SREG- Site Regression) The main advantage of this technique inrelation to AMMI analysis resides in the fact that the GGEbiplot method always explains an intermediate portion of thesum of squares of genotypes (G) + interaction (G times E) inrelation to the AMMI1 (with one principal component) andAMMI2 (with two principal components) models Yan et al[12]

Garcia and Junior [13] and Farshadfar [14] incorporatedstability and adaptability parameters in selection indices toselect individuals of greatest stability and best performanceNevertheless these studies that applied nonparametric selec-tion indices as parameters of incorporated stability did it withthe mean values of the cultivars in all the environments

It is difficult to find studies in the literature that have ana-lyzed these selection indices at plot level and have analyzedthe use of these indices for adaptability and stability analysesby multivariate methods such as the GGE biplot so that theapplicability of a nonparametric selection indexmay be betterevaluated and utilized For that reason the aim of this studywas to evaluate the adaptability and stability of the genotype-ideotype distance index and selection of the best hybrids bymeans of this alternative

2 Materials and Methods

Assessment data were composed of seven traits from 25maize hybrids subjected to performance evaluation trials insix locations of the south of Brazil (Vacaria RS AbelardoLuz SC Candoi PR Canoinhas SC Castro PR and PontaGrossa PR) during the 20102011 crop year The trials wereprepared in a completely randomized block design with tworeplications The plots were composed of four five-meterrows with a spacing of 70 cm between rows Fertilizationswere carried out following the recommendations made foreach location by means of soil analysis Crop treatmentsnecessary for control of army worm (Spodoptera frugiperda)corn earworm (Helicoverpa zea) and weeds were carried out

The traits assessed were grain yieldmdashkg haminus1 percentageof damaged grains percentage of lodging percentage ofbreakage percentage of fallen plants common rust (Pucciniasorghi) score and gray leaf spot (Cercospora zeae-maydis)score

The percentage of damaged grains was determinedthrough the proportion of grains with symptoms of rotting ina 1000 grain sampleThe percentage of lodgingwas calculatedthrough the proportion of plants at an inclination of more

than 30∘ due to weakening of the roots in relation to the totalnumber of plants in the plot The percentage of fallen plantsfor its part corresponded to the proportion of plants at aninclination of more than 30∘ due to weakening of the base ofthe stalk in relation to the total number of plants in the plotThe disease severity score was based on the diagrammaticscale proposed by Agroceres [15] which ranges from 1 to 9 inwhich score 1 represents a leaf without symptoms and score9 corresponds to the material with more than 80 of the leafarea affected

The ideotype for yield (kg haminus1) was determined seekingthe value of the highest yielding plot of all the trails and usingthe next thousand value above that As the highest yieldingplot was 16959 kg haminus1 the ideotype was 17000 kg haminus1 Forthe traits of percentage of damaged grains percentage oflodging percentage of fallen plants and percentage of break-age the ideotypewas 0 For common rust and grey leaf spotthe ideotype was score 1

To obtain the matrix of variances and covariancesamong the traits assessed multivariate analysis of variance(MANOVA) was performed using the data from all thehybrids traits and locations For that purpose the modelaccording to Ferreira [16] was used expressed in the vectorialform in the following expression

119884119894119895119896

= 120583 + 120572119894

+ 120573119894

+ 120575119894119895

+ 120576119894119895119896

(1)

in which the vector 119884119894119895119896

= [1198841198941198951198961

1198841198941198951198962

119884119894119895119896119901

] refers tothe multivariate observations associated with the 119894th hybrid(119894 = 1 2 25) at the jth location (119895 = 1 2 6)

in the kth replication of this combination of the 119894 and 119895

levels of the two factors 120583 is the vector of constants of themultivariate linear model given by 120583

119894

= [1205831198941

1205831198942

120583119894119901

]120572119894

is the vector of effects of the 119894th hybrid given by 120572119894

=

[1205721198941

1205721198942

120572119894119901

] 120573119895

is the vector of effects of the jth locationgiven by 120573

119895

= [1205731198951

1205731198952

120573119895119901

] 120575119894119895

is the vector of effects ofthe interaction between the 119894th hybrid and the jth locationgiven by 120575

119894119895

= [1205751198941

1205751198942

120575119894119901

] and 120576119894119895119896

is the vector of effectsof the nonobservable experimental error corresponding toobservation 119884

119894119895119896

The manova package of the software R v 30[17] was used for MANOVA

The genotype-ideotype distance index (GIDI) for selec-tion was obtained using the data at the plot level of the seventraits assessed in the 25 hybrids Thus for each plot underassessment an index was obtained based on the generalizedMahalanobis distance using the matrix model according tothe following expression

1198632

119866119897

= diag (119868119878minus11198681015840) (2)

where the term 119868119878minus1

1198681015840 is written in the following manner

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(1198841111

minus 1198841ℓ

) sdot sdot sdot (119884119899111

minus 119884119899ℓ

)

d

(1198841her minus 1198841ℓ) sdot sdot sdot (119884

119899her minus 119884119899ℓ)

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816(119873times119899)

The Scientific World Journal 3

times

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1198811

sdot sdot sdot COV1119899

d

COV1198991

sdot sdot sdot 119881119899

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

minus1

(119899times119899)

times

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(1198841111

minus 1198841ℓ

) sdot sdot sdot (1198841her minus 119884119899ℓ)

d

(119884119899111

minus 1198841ℓ


10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816(119899times119873)

(3)

in which 1198632

119866ℓ

is the matrix of the distances of ℎ (ℎ =

1 2 25) hybrids in relation to the ideotype ℓ 119884119894119895119896119897

is theobservation of trait 119894 (119894 = 1 2 119899) where 119899 = 7 of hybrid119895 (119895 = 1 2 ℎ) at location 119896 (119896 = 1 2 119890) where 119890 = 6in replication 119897 (119897 = 1 2) 119881

1

1198812

119881119899

are the variances ofthe residues (QMerro of themultivariate analysis of variance)of the 119899 traits assessed and COV

12

COV2119899

COV(119899minus1)119899

arethe covariances among the residues of these traits

After obtaining the GIDI for each plot joint analysis ofvariance was performed to verify the presence of the G times

E interaction for the GIDI and for grain yield Once thepresence of the G times E interaction (F test significant) wasobserved analysis of adaptability and stability was performedfor the two variables which allowed the adaptation andstability of each hybrid under testing to be measured forthe GIDI and for yield This evaluation was made usingthe GGE biplot method As the interpretation of the GIDIis the opposite of yield that is the lower the value of theindex the better the performance the value of each plotwas subtracted from 2000 This value was determined usingthe same principle used in the determination of ideotype ofyield that is using the next thousand value above the greatestvalue of the index considering all the plots of all the trailsGraph interpretation was thereby able to be performed in thesamemanner as yield GGE biplot analysis was performed bymeans of the package GGEBiplotGUI of the software R v 30[17]

Analysis by means of the GGE biplot method was per-formed as presented by de Oliveira et al [18] considering thesimplified model for two principal components

119884119894119895

minus 120583119895

= 1205821

1205741198941

1205721198951

+ 1205822

1205741198942

1205721198952

+ 120588119894119895

+ 120576119894119895

(4)

in which 119884119894119895

is the mean value of hybrid 119894 in location jfor the GIDI or yield 120583

119895

is the mean value of the locationj 1205821

1205741198941

1205721198951

is the first principal component (PCA 1) of theeffect of genotypes (G) + interaction (G times A) 120582

2

1205741198942

1205721198952

isthe second principal component (PCA 2) of the effect ofgenotypes (G) + interaction (G times A) 120582

1

and 1205822

are theeigenvalues associated with the PCA 1 and with the PCA 21205741198941

and 1205741198942

are the scores of the PCA 1 and of the PCA 2respectively for genotypes 120572

1198951

and 1205721198952

are the scores of thePCA 1 and of the PCA 2 respectively for environments 120588

119894119895

isthe residue of the genotype times environment interaction alsoknown as ldquonoiserdquo corresponding to the principal componentsnot retained in the model 120576

119894119895

is the residual of the modelwith normal distribution mean value zero and variance 1205902119903(where 1205902 is the variance of the error between plots for eachenvironment and 119903 is the number of replications)

Table 1 Classification in decreasing order of the hybrids in regardto their mean grain yield (kg haminus1) and their respective mean valuesof the GIDI considering the six assessment locations

Hybrids Yield (kg haminus1) GIDI21 1471384 17845523 1392310 15303624 1390324 15762622 1384471 17020912 1316687 18264825 1314649 16057118 1258940 1706147 1244818 13317119 1234706 1733433 1163713 10673620 1161262 1534228 1121067 1654614 1101332 997001 1099973 11594611 1098410 16329416 1095694 15289513 1087005 1630955 1085068 10499615 1063655 1621162 1060371 1118829 1056395 1519586 1055886 11929917 1033476 15329910 1028067 15103814 1005997 125874

The graph accuracy of the identification methods ofmegaenvironments and winning genotypes was tested by thecross validation procedure proposed by Gabriel [19] Forthat purpose the PRESSm and PRESScorr statistics wereused to measure the discrepancy between the observed andpredicted values and the predictive correlation [20] Thiscross validation analysis was performed by means of PROCIML of the statistical package of the software SAS v 90 [21]

The GGE biplot graph was constructed as of the datafrom breakdown of the empirical mean values graphicallypresenting the hybrid with the best development as detailedby de Oliveira et al [18] The environments were grouped bymeans of the graphic approach called ldquoWhich Won Whererdquoby Yan et al [11] Thus the environments that share the samewinning genotype remain in the same group

Thefive hybrids with greatest adaptability and stability forthe GIDI and yield were identified and selected by means oftheir distance in relation to the ldquoideal genotyperdquo which wasplotted in the center of a ldquotargetrdquo in the biplot That way thehybrids plotted nearer the center of this ldquotargetrdquo are those thathave the best combination between adaptability and stabilityas presented by Balestre et al [22]


Table 2 Estimates obtained for PRESSm (sum of squared prediction error) and PRECORR(m) (predictive accuracy) in cross validation of theGGE1 and GGE2 models (biplot with 1 and 2 principal components resp) for the GIDI and for yield (ton haminus1)

Model GIDI YieldPRESSm PRECORR(m) PRESSm PRECORR(m)

GGE1 36324678 08086993 10547498 08656868GGE2 21597326 08913184 10179156 08708956

1000

500

0

minus500

5000minus500minus1000minus1500

minus1000

1557

7657

G1E1

E2

E3

E6

E4

E5

G2G3

G4 G5G6

G7

G8G9G10

G11 G12

I

II

G13

G14

G15

G16

G17

G18

G19G20 G21

G22

G23G24

G25

PCA

2

PCA 1

Figure 1 GGE biplot graph evaluating the GIDI with the groupingof the six locations (Vacaria RS Abelardo Luz SC Candoi PRCanoinhas SC Castro PR and PontaGrossa PR) identified fromE1to E6 respectively with the groups of environments being identifiedby the Roman numerals I and II the gray line represents the polygonformed by genotypes evaluated

3 Results and Discussion

The G times E interaction was significant (119875 le 001) showingthat the performance of the hybrids was not consistent inthe different assessment environments in regard to the GIDI(data not shown)The results of analysis of variance for grainyield were similar to those obtained in the GIDI analysisThe genotype and environment sources of variation and theirinteraction were significant (119875 le 001) The coefficientof variation was very low (33) which shows the highexperimental precision of the trails

The mean value of the hybrids for grain yield (kg haminus1)and for the GIDI (already subtracted from 2000 to makeits interpretation similar to that of yield) involving the sixlocations are shown in Table 1

As may be observed the highest yielding hybrids are notnecessarily those that have the greatest values of the GIDIThis is due to the fact that the highest yielding hybrids are notalways the best in the other traits assessed and considered inthe GIDI

The results of cross validation of the GGE biplot modelfor the GIDI and for grain yield are shown in Table 2

1000

500

0

minus500

minus1000

E1

E2

E3

E4

E5

E6

G1

G2G3

G4 G5G6

G7

G8G9G10

G11 G12G13

G14

G15

G16

G17

G18

G19G20 G21

G22

G23G24

G25PCA

21557


7657PCA 1

Figure 2 GGE biplot graph with the distance of the 25 hybrids(identified from G1 to G25) from the ldquoideal genotyperdquo in regard tothe GIDI Concentric circles facilitate the exploratory analysis of thedistances between the genotypes evaluated and the ideal genotyperepresented by the green arrow

In this study only the results of cross validation forthe first two principal components were presented since thereduced model was chosen due to the difficulty of evaluatingthe biplot in more than two dimensions

It may be seen that for the GGE2 model the predictiveaccuracy (PRECORR

(m)) was high for the two variablesanalyzed In addition the values were close when the twovariables are compared de Oliveira et al [18] and Balestre etal [22] evaluating the stability and adaptability of grain yieldin maize and rice obtained a PRECORR of 08617 and 090respectivelyThese values are very near those obtained in thisstudy The GGE2 model was therefore accurate for the twovariables

Subsequently the biplot was obtained and the ldquoWhichWon Whererdquo approach was carried out to identify theenvironments or megaenvironments evaluating the GIDI(Figure 1) In this figure the hybrids were identified from G1to G25

The first result to be highlighted is the high explanatorypower of the sum of squares of G + G times E presented by thetwo principal components of the biplot (PCA 1 and PCA 2)The two components added together accounted for 9214showing that the analysis was very efficient In regard togrouping two groups were obtained identified on the graph


4

2

0

minus2

minus4


E1

E2

E3

E4

E5

E6

G1G2

G3

G4

G5 G6

G7

G8G9

G10G11

G12 G13G14

G15

G16 G17G18 G19

G20

G21 G22

G23G24

G25PCA

2

PCA 1

1106

7618

Figure 3 GGE biplot graph evaluating grain yield (t haminus1) with thegrouping of the six locations (Vacaria RS Abelardo Luz SC CandoiPR Canoinhas SC Castro PR and Ponta Grossa PR) identifiedfrom E1 to E6 respectively the gray line represents the polygonformed by genotypes evaluated

by the Roman numerals I and II Group I was composed onlyof locations 2 3 4 and 6 (Abelardo Luz SC Candoi PRCanoinhas SC and Ponta Grossa PR resp) in which hybrid12 was the winner Group II was composed of locations 1 and5 (Vacaria RS and Castro PR resp) in which hybrid 24 wasthe winner In this analysis we can also observe that location6 (Ponta Grossa PR) was that which presented the greatestability for discriminating genotypes due to its high score inthe first principal component Evaluation of adaptability andstability of the hybrids by means of the approach of distancefrom the ldquoideal genotyperdquo was also performed (Figure 2)

It may be observed that hybrids 12 21 19 8 and 22 are thenearest to the ldquoideal genotyperdquo in that order Therefore theyare the five best hybrids combining adaptability and stability

GGE biplot analysis was also performed for the yielddata transformed into ton haminus1 to improve the scale of theprincipal components of the biplot In relation to the portionof the sum of squares of G + G times E explained by the twoprincipal components (Figure 3) this also was high (8724)however a little less than that found in the analysis using theGIDI (9214) Likewise the ldquoWhich WonWhererdquo approachwas performed by means of which it was seen that all thelocations were in the same group (Figure 3)

Nevertheless in analysis with the GIDI two groups wereidentified This difference is due to the fact of the GIDIaggregating other variables not only grain yield whichmakesthe G times E interaction more complex when compared to theanalysis only with yield such that the use of the GIDI ingrouping of environments becomes more informative

Subsequently evaluation of the adaptability and stabilityof the hybrids for grain yield was performed bymeans of theirdistances from the ldquoideal genotyperdquo (Figure 4)

4

2

0

minus2

minus4


E1

E2

E3

E4

E5

E6

G1G2

G3

G4

G5 G6

G7

G8G9

G10G11

G12 G13G14

G15

G16 G17G18 G19

G20

G21 G22

G23G24

G25PCA

2

PCA 1

1106

7618

Figure 4 GGE biplot graph with the distance of the 25 hybrids(numbered from G1 to G25) from the ldquoideal genotyperdquo in regardto grain yield (t haminus1) Concentric circles facilitate the exploratoryanalysis of the distances between the genotypes evaluated and theideal genotype represented by the green arrow

The five hybrids nearest to the ldquoideal genotyperdquo werehybrids 21 23 24 22 and 25 in that order Comparing thisselection with that obtained by the analysis with the GIDI(hybrids 12 21 19 8 and 22) it may be seen that only hybrids21 and 22 were common to the two selections There was alsoa change in the position of hybrids 21 and 22 comparing thetwo selections To diagnose the reason for this difference themeasurements of each hybrid were obtained for each one ofthe seven variables assessed considering the six locations

Garcia and Junior [13] also used the GIDI estimated bymeans of the Euclideandistance for selection ofmaize hybridsand to this they incorporated the parameters of adaptabilityand stability 119887 and 1198772 respectively This procedure led to theselection of stable and adapted hybrids only for year yield(kg haminus1) Euclidean distance may only be applied to traitswhich are mutually independent which was not the case ofthe traits used by the authors with a negative effect on theselection obtained by them For that reason these authorsrecommended that the correlation between the variablesassessed must be considered in the selection index Thiscorrection was performed in this study since the GIDI wasestimated by means of the Mahalanobis distance which isweighted by the matrix of variances and covariances Inaddition the evaluation of adaptability and stability wasperformed with the GIDI estimated at the plot level allowingthe selection of adapted and stable hybrids for all the variablesanalyzed

4 Conclusion

The evaluation of adaptability and stability of the GIDI ledto the selection of hybrids that combine adaptability and


stability for most of the traits assessed Use of it is morepractical than analyzing each trait separately

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] H F Smith ldquoA discriminant function for plant selectionrdquoAnnals Eugenics vol 7 no 3 pp 240ndash250 1936

[2] C A Brim H W Johnson and C C Cockerham ldquoMultipleselection criteria in soybeansrdquo Agronomy Journal vol 51 no 1pp 42ndash46 1959

[3] O Kempthorne and A W Nordskog ldquoRestricted selectionindicesrdquo Biometrics vol 15 no 1 pp 10ndash19 1959

[4] J Pesek and R J Baker ldquoDesired improvement in relation toselection indicesrdquoCanadian Journal of Plant Science vol 49 no6 pp 803ndash804 1969

[5] G C C Tai ldquoIndex selection with desired gainsrdquo Crop Sciencevol 17 no 1 pp 182ndash183 1977

[6] O S Smith A R Hallauer and W A Russell ldquoUse of indexselection in recurrent selection programs in maizerdquo Euphyticavol 30 no 3 pp 611ndash618 1981

[7] R C Elston ldquoA weight free index for the purpose of ranking ofselection with respect to several traits at a timerdquo Biometrics vol19 no 1 pp 85ndash97 1963

[8] G Wricke andW E WeberQuantitative Genetics and Selectionin Plant Breeding Walter de Gruyter New York NY USA 1986

[9] N N Mulamba and J J Mock ldquoImprovement of yield potentialof the Eto Blanco maize (Zea mays L) population by breedingfor plant traitsrdquo Egyptian Journal of Genetic and Cytology vol 7no 1 pp 40ndash51 1978

[10] J Crossa ldquoStatistical analyses of multilocation trialsrdquo Advancesin Agronomy vol 44 no 1 pp 55ndash85 1990

[11] W Yan L A Hunt Q Sheng and Z Szlavnics ldquoCultivarevaluation and mega-environment investigation based on theGGE biplotrdquo Crop Science vol 40 no 3 pp 597ndash605 2000

[12] W Yan M S Kang B Ma S Woods and P L Cornelius ldquoGGEbiplot vs AMMI analysis of genotype-by-environment datardquoCrop Science vol 47 no 2 pp 643ndash655 2007

[13] A A F Garcia and C L S Junior ldquoComparacao de ındicesde selecao nao parametricos para a selecao de cultivaresrdquoBragantia vol 58 no 2 pp 253ndash267 1999

[14] E Farshadfar ldquoIncorporation of AMMI stability value and grainyield in a single non-parametric index (GSI) in bread wheatrdquoPakistan Journal of Biological Sciences vol 11 no 14 pp 1791ndash1796 2008

[15] Agroceres Guia Agroceres de Sanidade Sementes AgroceresSao Paulo Brazil 1996

[16] D F Ferreira ldquoAnalise de variancia multivariadardquo in EstatısticaMultivariada pp 329ndash331 UFLA Lavras Brazil 2nd edition2011

[17] RDevelopment Core Team R A Language and Environment forStatistical Computing R Foundation for Statistical ComputingVienna Austria 2011

[18] R L de Oliveira R G von Pinho M Balestre and DV Ferreira ldquoEvaluation of maize hybrids and environmentalstratification by the methods AMMI and GGE biplotrdquo Crop

Breeding and Applied Biotechnology vol 10 no 3 pp 247ndash2532010

[19] K R Gabriel ldquoLe biplot-outil drsquoexploration de donnees multi-dimensionnellesrdquo Journal de la Societe Francaise de Statistiquevol 143 no 3-4 pp 5ndash55 2002

[20] C T S Dias and W J Krzanowski ldquoModel selection and crossvalidation in additive main effect and multiplicative interactionmodelsrdquo Crop Science vol 43 no 3 pp 865ndash873 2003

[21] SAS Institute SASSTAT Usersquos Guide SAS Institute Cary NCUSA 2000

[22] M Balestre V B dos Santos A A Soares and M S ReisldquoStability and adaptability of upland rice genotypesrdquo CropBreeding and Applied Biotechnology vol 10 no 4 pp 357ndash3632010

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genotype presents for each trait the lower the value obtainedin this sum the better the classification

There are various methodologies for evaluation of theG times E interaction Crossa [10] suggests that the applicationof multivariate methods may be useful to better exploit theinformation contained in the data Recently amodification ofthe conventional AMMI analysis proposed by Yan et al [11]called the GGE biplot has been used for study of the G times Einteraction GGE analysis groups the genotype effect whichis an additive effect in the AMMI analysis with the G times Einteraction which is a multiplicative effect subjecting theseeffects to a multiplicative model of regression for sites (SREG- Site Regression) The main advantage of this technique inrelation to AMMI analysis resides in the fact that the GGEbiplot method always explains an intermediate portion of thesum of squares of genotypes (G) + interaction (G times E) inrelation to the AMMI1 (with one principal component) andAMMI2 (with two principal components) models Yan et al[12]

Garcia and Junior [13] and Farshadfar [14] incorporatedstability and adaptability parameters in selection indices toselect individuals of greatest stability and best performanceNevertheless these studies that applied nonparametric selec-tion indices as parameters of incorporated stability did it withthe mean values of the cultivars in all the environments

It is difficult to find studies in the literature that have ana-lyzed these selection indices at plot level and have analyzedthe use of these indices for adaptability and stability analysesby multivariate methods such as the GGE biplot so that theapplicability of a nonparametric selection indexmay be betterevaluated and utilized For that reason the aim of this studywas to evaluate the adaptability and stability of the genotype-ideotype distance index and selection of the best hybrids bymeans of this alternative

2 Materials and Methods

Assessment data were composed of seven traits from 25maize hybrids subjected to performance evaluation trials insix locations of the south of Brazil (Vacaria RS AbelardoLuz SC Candoi PR Canoinhas SC Castro PR and PontaGrossa PR) during the 20102011 crop year The trials wereprepared in a completely randomized block design with tworeplications The plots were composed of four five-meterrows with a spacing of 70 cm between rows Fertilizationswere carried out following the recommendations made foreach location by means of soil analysis Crop treatmentsnecessary for control of army worm (Spodoptera frugiperda)corn earworm (Helicoverpa zea) and weeds were carried out

The traits assessed were grain yieldmdashkg haminus1 percentageof damaged grains percentage of lodging percentage ofbreakage percentage of fallen plants common rust (Pucciniasorghi) score and gray leaf spot (Cercospora zeae-maydis)score

The percentage of damaged grains was determinedthrough the proportion of grains with symptoms of rotting ina 1000 grain sampleThe percentage of lodgingwas calculatedthrough the proportion of plants at an inclination of more

than 30∘ due to weakening of the roots in relation to the totalnumber of plants in the plot The percentage of fallen plantsfor its part corresponded to the proportion of plants at aninclination of more than 30∘ due to weakening of the base ofthe stalk in relation to the total number of plants in the plotThe disease severity score was based on the diagrammaticscale proposed by Agroceres [15] which ranges from 1 to 9 inwhich score 1 represents a leaf without symptoms and score9 corresponds to the material with more than 80 of the leafarea affected

The ideotype for yield (kg haminus1) was determined seekingthe value of the highest yielding plot of all the trails and usingthe next thousand value above that As the highest yieldingplot was 16959 kg haminus1 the ideotype was 17000 kg haminus1 Forthe traits of percentage of damaged grains percentage oflodging percentage of fallen plants and percentage of break-age the ideotypewas 0 For common rust and grey leaf spotthe ideotype was score 1

To obtain the matrix of variances and covariancesamong the traits assessed multivariate analysis of variance(MANOVA) was performed using the data from all thehybrids traits and locations For that purpose the modelaccording to Ferreira [16] was used expressed in the vectorialform in the following expression

119884119894119895119896

= 120583 + 120572119894

+ 120573119894

+ 120575119894119895

+ 120576119894119895119896

(1)

in which the vector 119884119894119895119896

= [1198841198941198951198961

1198841198941198951198962

119884119894119895119896119901

] refers tothe multivariate observations associated with the 119894th hybrid(119894 = 1 2 25) at the jth location (119895 = 1 2 6)

in the kth replication of this combination of the 119894 and 119895

levels of the two factors 120583 is the vector of constants of themultivariate linear model given by 120583

119894

= [1205831198941

1205831198942

120583119894119901

]120572119894

is the vector of effects of the 119894th hybrid given by 120572119894

=

[1205721198941

1205721198942

120572119894119901

] 120573119895

is the vector of effects of the jth locationgiven by 120573

119895

= [1205731198951

1205731198952

120573119895119901

] 120575119894119895

is the vector of effects ofthe interaction between the 119894th hybrid and the jth locationgiven by 120575

119894119895

= [1205751198941

1205751198942

120575119894119901

] and 120576119894119895119896

is the vector of effectsof the nonobservable experimental error corresponding toobservation 119884

119894119895119896

The manova package of the software R v 30[17] was used for MANOVA

The genotype-ideotype distance index (GIDI) for selec-tion was obtained using the data at the plot level of the seventraits assessed in the 25 hybrids Thus for each plot underassessment an index was obtained based on the generalizedMahalanobis distance using the matrix model according tothe following expression

1198632

119866119897

= diag (119868119878minus11198681015840) (2)

where the term 119868119878minus1

1198681015840 is written in the following manner

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(1198841111

minus 1198841ℓ

) sdot sdot sdot (119884119899111

minus 119884119899ℓ

)

d

(1198841her minus 1198841ℓ) sdot sdot sdot (119884

119899her minus 119884119899ℓ)

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816(119873times119899)


times

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1198811


d

COV1198991


10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

minus1

(119899times119899)

times

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(1198841111

minus 1198841ℓ


d

(119884119899111

minus 1198841ℓ


10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816(119899times119873)

(3)

in which 1198632

119866ℓ




1

1198812

119881119899


12

COV2119899

COV(119899minus1)119899





119884119894119895

minus 120583119895

= 1205821

1205741198941

1205721198951

+ 1205822

1205741198942

1205721198952

+ 120588119894119895

+ 120576119894119895

(4)

in which 119884119894119895


119895


1205741198941

1205721198951


2

1205741198942

1205721198952


1

and 1205822


and 1205741198942


1198951

and 1205721198952


119894119895


119894119895










GGE1 36324678 08086993 10547498 08656868GGE2 21597326 08913184 10179156 08708956

1000

500

0

minus500


minus1000

1557

7657

G1E1

E2

E3

E6

E4

E5

G2G3

G4 G5G6

G7

G8G9G10

G11 G12

I

II

G13

G14

G15

G16

G17

G18

G19G20 G21

G22

G23G24

G25

PCA

2

PCA 1







1000

500

0

minus500

minus1000

E1

E2

E3

E4

E5

E6

G1

G2G3

G4 G5G6

G7

G8G9G10

G11 G12G13

G14

G15

G16

G17

G18

G19G20 G21

G22

G23G24

G25PCA

21557


7657PCA 1








4

2

0

minus2

minus4


E1

E2

E3

E4

E5

E6

G1G2

G3

G4

G5 G6

G7

G8G9

G10G11

G12 G13G14

G15

G16 G17G18 G19

G20

G21 G22

G23G24

G25PCA

2

PCA 1

1106

7618







4

2

0

minus2

minus4


E1

E2

E3

E4

E5

E6

G1G2

G3

G4

G5 G6

G7

G8G9

G10G11

G12 G13G14

G15

G16 G17G18 G19

G20

G21 G22

G23G24

G25PCA

2

PCA 1

1106

7618




4 Conclusion






References































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology


times

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1198811


d

COV1198991


10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

minus1

(119899times119899)

times

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(1198841111

minus 1198841ℓ


d

(119884119899111

minus 1198841ℓ


10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816(119899times119873)

(3)

in which 1198632

119866ℓ




1

1198812

119881119899


12

COV2119899

COV(119899minus1)119899





119884119894119895

minus 120583119895

= 1205821

1205741198941

1205721198951

+ 1205822

1205741198942

1205721198952

+ 120588119894119895

+ 120576119894119895

(4)

in which 119884119894119895


119895


1205741198941

1205721198951


2

1205741198942

1205721198952


1

and 1205822


and 1205741198942


1198951

and 1205721198952


119894119895


119894119895










GGE1 36324678 08086993 10547498 08656868GGE2 21597326 08913184 10179156 08708956

1000

500

0

minus500


minus1000

1557

7657

G1E1

E2

E3

E6

E4

E5

G2G3

G4 G5G6

G7

G8G9G10

G11 G12

I

II

G13

G14

G15

G16

G17

G18

G19G20 G21

G22

G23G24

G25

PCA

2

PCA 1







1000

500

0

minus500

minus1000

E1

E2

E3

E4

E5

E6

G1

G2G3

G4 G5G6

G7

G8G9G10

G11 G12G13

G14

G15

G16

G17

G18

G19G20 G21

G22

G23G24

G25PCA

21557


7657PCA 1








4

2

0

minus2

minus4


E1

E2

E3

E4

E5

E6

G1G2

G3

G4

G5 G6

G7

G8G9

G10G11

G12 G13G14

G15

G16 G17G18 G19

G20

G21 G22

G23G24

G25PCA

2

PCA 1

1106

7618







4

2

0

minus2

minus4


E1

E2

E3

E4

E5

E6

G1G2

G3

G4

G5 G6

G7

G8G9

G10G11

G12 G13G14

G15

G16 G17G18 G19

G20

G21 G22

G23G24

G25PCA

2

PCA 1

1106

7618




4 Conclusion






References































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology




GGE1 36324678 08086993 10547498 08656868GGE2 21597326 08913184 10179156 08708956

1000

500

0

minus500


minus1000

1557

7657

G1E1

E2

E3

E6

E4

E5

G2G3

G4 G5G6

G7

G8G9G10

G11 G12

I

II

G13

G14

G15

G16

G17

G18

G19G20 G21

G22

G23G24

G25

PCA

2

PCA 1







1000

500

0

minus500

minus1000

E1

E2

E3

E4

E5

E6

G1

G2G3

G4 G5G6

G7

G8G9G10

G11 G12G13

G14

G15

G16

G17

G18

G19G20 G21

G22

G23G24

G25PCA

21557


7657PCA 1








4

2

0

minus2

minus4


E1

E2

E3

E4

E5

E6

G1G2

G3

G4

G5 G6

G7

G8G9

G10G11

G12 G13G14

G15

G16 G17G18 G19

G20

G21 G22

G23G24

G25PCA

2

PCA 1

1106

7618







4

2

0

minus2

minus4


E1

E2

E3

E4

E5

E6

G1G2

G3

G4

G5 G6

G7

G8G9

G10G11

G12 G13G14

G15

G16 G17G18 G19

G20

G21 G22

G23G24

G25PCA

2

PCA 1

1106

7618




4 Conclusion






References































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology


4

2

0

minus2

minus4


E1

E2

E3

E4

E5

E6

G1G2

G3

G4

G5 G6

G7

G8G9

G10G11

G12 G13G14

G15

G16 G17G18 G19

G20

G21 G22

G23G24

G25PCA

2

PCA 1

1106

7618







4

2

0

minus2

minus4


E1

E2

E3

E4

E5

E6

G1G2

G3

G4

G5 G6

G7

G8G9

G10G11

G12 G13G14

G15

G16 G17G18 G19

G20

G21 G22

G23G24

G25PCA

2

PCA 1

1106

7618




4 Conclusion






References































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology





References































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology








Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology

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