Comparison of shifted multiplicative model, rankcorrelation, and biplot analysis for clustering winter wheatproduction environments

Subas Malla • Amir M. H. Ibrahim • Rich Little •

Steve Kalsbeck • Karl D. Glover • Cuirong Ren

Received: 9 January 2009 / Accepted: 12 January 2010 / Published online: 27 January 2010

� Springer Science+Business Media B.V. 2010

Abstract Categorization of locations with similar

environments helps breeders to efficiently utilize

resources and effectively target germplasm. This

study was conducted to determine the relationship

among winter wheat (Triticum aestivum L.) yield

testing locations in South Dakota. Yield trial data

containing 14 locations and 38 genotypes from 8 year

were analyzed for crossover genotype (G) 9 envi-

ronment (E) interactions according to the Azzalini-

Cox test. G 9 E was significant (P \ 0.05) and

contributed a small proportion of variation over the

total phenotypic variation. This suggested that for

efficient resource utilization, locations should be

clustered. The data were further analyzed using the

Shifted Multiplicative Model (SHMM), Spearman’s

rank correlation and GGE biplot to group testing

locations based on yield. SHMM analysis revealed

four major cluster groups in which the first and third

had three locations, with four locations in each of the

second and fourth groups. Spearman rank correlations

between locations within groups were significant and

positive. GGE biplot analysis revealed two major

mega-environments of winter wheat testing locations

in South Dakota. Oelrichs was the best testing

location and XH1888 was the highest yielding

genotype. SHMM, rank correlation and GGE biplot

analyses showed that the locations of Martin and

Winner in the second group and Highmore, Oelrichs

and Wall in the third group were similar. This

indicated that the number of testing locations could

be reduced without much loss of grain yield infor-

mation. GGE biplot provided additional information

on the performance of entries and locations. SHMM

clustered locations with reduced cross-over interac-

tion of genotype 9 location. The combined methods

used in this study provided valuable information on

categorization of locations with similar environments

for efficient resource allocation. This information

should facilitate efficient targeting of breeding and

testing efforts, especially in large breeding programs.

Keywords Genotype 9 environment interaction �SHMM � GGE biplot � Triticum aestivum

Introduction

In South Dakota, winter wheat is grown under diverse

conditions of abiotic and biotic stresses. These

environmental conditions vary not only from location

to location in the same year, but also from year to year

S. Malla � R. Little � S. Kalsbeck � K. D. Glover � C. Ren

Plant Science Department, South Dakota State University,

Brookings, SD 57007, USA

A. M. H. Ibrahim (&)

Department of Soil and Crop Sciences, Texas A&M

University, 2474 TAMU, College Station,

TX 77843, USA

e-mail: aibrahim@ag.tamu.edu

123

Euphytica (2010) 174:357–370

DOI 10.1007/s10681-010-0130-2

at the same location (Miller et al. 1959). The main

goal of the South Dakota Winter Wheat Breeding

Project is to develop high yielding winter wheat

cultivars that are widely adapted across the state and

in adjacent states. However, genotype 9 environment

(G 9 E) interactions, which are defined as the failure

of genotypes to perform consistently relative to each

other under different environments (Ghaderi et al.

1980), might be a major concern.

Of the two types of G 9 E interactions (crossover

and non-crossover), crossover interactions (changes

of genotype rank across environments) have been

described as the most important in plant breeding

(Baker 1988). One method used by breeders to reduce

the effect of G 9 E interactions is to combine

environments or genotypes into homogeneous groups

and then breed for each group (Abdalla et al. 1997;

Ramey and Rosielle 1983; Yau et al. 1991).

Several statistical methods have been proposed to

subdivide environments or genotypes into more

homogeneous groups. Horner and Frey (1957) used

classical variety 9 location interaction mean squares

to group locations based on locations that had

minimum interactions. Jones et al. (1960) used

variance component estimates to determine the opti-

mum numbers of plots, locations, and years in tobacco

(Nicotiana tobacum L.) cultivar testing. Guitard

(1960) used correlation of yield at pairs of locations

as means of grouping locations. A two—way pattern

analysis method was used by Byth et al. (1976) to

group lines, cultivars and environments based on

similarities in yield performance of wheat cultivars.

The most widely used technique for stratifying

environments or genotypes into groups has been

cluster analysis (Ramey and Rosielle 1983; Yau et al.

1991). Cluster analysis technique was first applied by

Abou-El-Fittouh et al. (1969) to classify cotton

(Gossipium hirsutum L.) testing regions of the Cotton

Belt (southern region of the US) and it was defined as

a tool to classify locations in order to minimize the

within-cluster genotype 9 location interactions.

Since then, the technique has been widely used by

other researchers (Campbell and Lafever 1977;

Ghaderi et al. 1980; Ramey and Rosielle 1983).

The shifted multiplication model (SHMM) was

used to analyze interaction between and among

genotypes, locations and years in multi-environment

trial (MET) data. The shifted multiplicative model

was developed by Seyedsadr and Cornelius (1992)

and utilized by Cornelius et al. (1992, 1993) and

Crossa et al. (1993) in MET data. The model

clustered genotypes or locations in such a way that

there would be statistically negligible interaction

within the group. The basis of SHMM clustering was

the measure of distance or dissimilarity between site

pairs. The dissimilarity between a pair of sites was

the residual sum of square (RSS) after fitting SHMM.

The SHMM predicted non-crossover interaction, if

the primary effects of the sites, cj1, were either all

non-positive or all non-negative. When the primary

effects did not have the same sign, a constrained

SHMM solution would be calculated. The con-

strained least squares SHMM solution assured that

the site primary effects were either all non-positive or

all non-negative.

The biplot is a graphical display of principal

component analysis (Gabriel 1971). Yan et al. (2000)

developed ‘‘GGE (Genotype (G) Genotype-by-Envi-

ronment (GE)) biplot’’ based on SREG model for

MET data. In the GGE biplot, a plot of genotype and

environment was displayed by plotting the first two

principal components (PC1—primary effects, and

PC2—secondary effects) from the data. The GGE

biplot is used to (1) identify the best performing

cultivar in a given environment, (2) identify the most

suitable environment for a given cultivar, (3) compare

any pair of cultivars across environments, (4) deter-

mine average yield and stability of the genotypes, and

(5) determine discriminating ability and representa-

tiveness of environments.

The objectives of this study were to examine

genotype 9 environment interactions and the magni-

tude of variance components estimates and then use

cluster analysis, correlation coefficients and GGE

biplot analysis to divide South Dakota winter wheat

testing environments into more homogeneous groups

based on yield data of varieties adapted to the Great

Plains for efficient resource allocation.

Materials and methods

Plant materials

An unbalanced grain yield dataset composed of 38

entries grown in the South Dakota Crop Performance

Testing (CPT) Variety Trial during 1998–2005

(8 years) was used for analysis. The set of entries

358 Euphytica (2010) 174:357–370

123

varied from year to year as newly developed germ-

plasm replaced old entries. Thirty-eight entries were

selected as they were evaluated for multiple years in

the CPT trial. Data were obtained from 14 locations:

Brookings (BRK; latitude = 44.3�N, longitude =

96.8�W), Watertown (WTN; latitude = 45.1�N,

longitude = 97.1�W), Highmore (HIM; latitude =

44.5�N, longitude = 99.5�W), Wall (WAL; lati-

tude = 44.1�N, longitude = 102.3�W), Bison (BIS;

latitude = 45.3�N, longitude = 102.3�W), Hayes

(HAY; latitude = 44.6�N, longitude = 100.9�W),

Martin (MAT; latitude = 45.2�N, longitude =

102.4�W), Selby (SEL; latitude = 45.5�N, longi-

tude = 100.0�W), Platte (PLA; latitude = 43.4�N,

longitude = 98.8�W), Sturgis (STS; latitude =

44.4�N, longitude = 103.5�W), Oelrichs (OEL;

latitude = 43.2�N, longitude = 103.2�W), Dakota

Lakes—Dry (DLD; latitude = 44.3�N, longitude =

100.0�W), Dakota Lakes—Spring Wheat Stubble

(DLS; latitude = 44.3�N, longitude = 100.0�W) and

Winner (WNR; latitude = 43.6�N, longitude =

99.9�W) (Fig. 1). Winter wheat was grown on pea

stubble and spring wheat stubble at Dakota Lakes,

which were named as Dakota Lakes—Dry and Spring

Wheat Stubble locations, respectively. Entries and

locations are listed in Table 1. Experiments were

constructed as randomized complete blocks composed

of four replications. Each plot consisted of seven rows

3.7 m long and 30 cm apart. All seven rows of each

plot were harvested and the grain yield data was

subjected to statistical analysis.

Analysis of variance

A combined analysis of variance across locations and

years was conducted for yield to test the significance

of G 9 L interaction and the estimated variance

components were calculated. Locations and entries

were considered random as they were representative

samples of winter wheat growing locations in South

Dakota and entries evaluated from 1998 to 2005,

respectively. Proc Generalized Linear Model (GLM)

of SAS (SAS Institute Inc. 2008) was used to analyze

the mixed model and unbalanced data.

Azzalini–Cox test

The Azzalini–Cox test (Azzalini and Cox 1984) was

used to identify significant G 9 E crossover

interactions. The difference between all pairs (i,j) of

genotypes in all possible pairs of locations (k,l)

(quadruple) was calculated. The null hypothesis

of non-significant G 9 E crossover interaction was

rejected if the smallest difference between the

quadruple was larger than tarffiffiffi

2p

and smaller than

�tarffiffiffi

2p

. The critical multiplier ta was calculated as:

ta ¼ �U�1

�

f�2 log 1� að Þ=�

m1 m1 � 1ð Þ

� m2 m2 � 1ð Þ�

g0:5

�

where, m1 = number of locations (14), m2 = number

of genotypes (38), a = 0.1. The standard error (r)

was the genotype 9 location 9 year mean square

(Baker 1988).

Shifted multiplicative model

The shifted multiplicative model (SHMM) was used

to group locations with reduced crossover interac-

tions. The SHMM model for the mean of the ith

genotype (i = 1, 2, 3,…, g) in the jth location (j = 1,

2, 3,…, ‘) is given by:

yij ¼ bþX

t

k¼1

kkaikcjk þ eij

where, yij = mean of the ith genotype in the jth

location for g genotypes and ‘ locations; b = shift

parameter; kk (k1 C k2 C _ C kt) are the scale

parameters (singular values) that allow imposition

of orthogonality constraints on the singular vectors

for cultivars, ak = (aik,…,agk), and locations, ck =

(cjk,…, c‘k), such thatP

i a2ik ¼

P

j c2jk ¼ 1 and

P

i aikajk0 ¼P

j cjkcjk0 ¼ 0 for k = k0; aik for k = 1,

2, 3,…, is primary, secondary, tertiary,…, effects of

the ith genotype; cjk for k = 1, 2, 3,…, is primary,

secondary, tertiary,…, effects of the jth location; eij is

the residual error; the number of multiplicative terms

t B min (g, ‘). Clustering of locations based on the

shifted multiplicative model was done following the

constrained least squares solution SAS� program, as

described by Crossa et al. (1993), to group the sites.

Spearman’s rank correlation

Spearman’s rank correlation was computed to test the

association between locations using Proc Corr of SAS

Euphytica (2010) 174:357–370 359

123

(SAS Institute Inc. 2008). The standard error was

calculated according to Fisher (1925) as follows:

SE rð Þ ¼ 1� r2� �

=n1=2

GGE biplot

The GGE biplot software (Yan and Kang 2003) was

used to generate a polygon view biplot to identify

mega-environments in South Dakota. A two-way

matrix of entries and locations was generated by

averaging over years, where rows were entries and

columns were locations. The biplot model is written

as:

Yij � bj ¼ k1ni1gj1 þ k2ni2gj2 þ eij

where Yij is the mean yield of genotype i in location

j; bj is the mean yield of all genotypes in location j; k1

and k2 are the singular values for PC1 and PC2,

respectively; ni1 and ni2 are the PC1 and PC2

eigenvectors, respectively, for genotype i; gj1 and

gj2 are the PC1 and PC2 eigenvectors, respectively,

for location j; and eij is the residual of the model

associated with the combination of genotype i in

location j.

The software was then used to generate average

environment coordinate (AEC) polygon view figures.

We interpreted the MET data based on these two

biplots as explained by Yan and Kang (2003). In the

AEC view, the average environment is marked with a

small circle. A horizontal line passing through both

the biplot origin and average tester circle is called

average environment axis or AEC abscissa and

represents the mean performance of genotypes. A

line perpendicular to the AEC abscissa which passes

through the origin is called average environment

ordinate or AEC ordinate. The AEC ordinate depicts

genotype stability. The larger the distance of a

genotype from the origin on either direction of the

AEC ordinate, the larger is the instability of that

genotype. The cosine of the angle between two

location vectors approximates the correlation of yield

performance among two locations. When 0 B h[90, two locations were positively correlated. The

correlation would be 0 when h = 90� (or -90�).

When the angle (h) was between 90� and 180�, the

correlation was negative.

The polygon view biplot describes the interaction

between genotypes and locations. The polygon was

drawn by joining the outermost genotypes, which

become the vertices of the polygon, from the origin.

Perpendicular lines drawn from the origin to the sides

of the polygon divide it into different genotype

sectors. If any location(s) falls in such a sector, the

vertex genotype will produce superior yield in the

location.

Results and discussion

Genotype and location yield are shown in Table 1,

which also displays the rankings of genotypes at

different locations. Genotypes with a ranking of 1

constituted the lowest yielding genotype at a given

location, whereas a genotype with a ranking of 38 was

Fig. 1 Fourteen crop

performance testing (CPT)

nursery locations in South

Dakota during 1998–2005

360 Euphytica (2010) 174:357–370

123

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Euphytica (2010) 174:357–370 361

123

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0)

3.1 (1

9)

5.9

(38

)4

.9(3

5)

3.5

(17

)3

.9 (35

)

3.7

TA

M1

07

(22

)3

.9(1

1)

2.3

(3)

3.6

(14

)2

.8 (10

)

4.1 (2

4)

4.2 (3

2)

4.3 (3

1)

3.0 (1

2)

2.9 (1

2)

3.9 (3

3)

5.0

(28

)5

.1(3

8)

3.8

(29

)3

.6 (29

)

3.7

SD

93

26

7(2

3)

3.9

(9)

3.5

(32

)4

.2(3

3)

3.1 (2

1)

4.1 (2

3)

4.0 (2

7)

4.3 (2

9)

3.4 (2

5)

2.8 (1

1)

3.4 (2

7)

4.9

(27

)4

.0(2

0)

3.6

(21

)3

.3 (18

)

3.7

SD

95

21

8(2

4)

3.6

(6)

4.0

(38

)4

.2(3

2)

3.4 (3

1)

4.0 (1

5)

3.9 (2

4)

4.6 (3

5)

3.7 (3

5)

2.5

(4)

2.6

(2)

5.2

(31

)4

.1(2

2)

3.2

(13

)3

.6 (31

)

3.8

BE

TT

Y(2

5)

4.3

(16

)2

.3(4

)4

.0(2

9)

3.2 (2

4)

4.0 (1

7)

3.5 (1

3)

4.1 (2

5)

3.6 (3

3)

2.9 (1

4)

3.0 (1

0)

5.8

(37

)4

.3(2

6)

3.8

(28

)4

.1 (39

)

3.8

21

37

(26

)3

.8(8

)2

.7(8

)3

.7(1

5)

3.0 (1

7)

4.4 (3

2)

3.7 (1

7)

4.0 (1

9)

3.0 (1

1)

3.2 (2

4)

4.0 (3

6)

4.6

(22

)5

.6(4

0)

4.1

(37

)3

.5 (26

)

3.8

AL

LIA

NC

E(2

7)

4.4

(24

)3

.1(1

9)

3.9

(26

)3

.2 (27

)

4.1 (2

0)

3.9 (2

3)

4.3 (3

0)

3.5 (3

1)

3.5 (3

6)

3.3 (2

4)

4.6

(21

)3

.9(1

6)

3.9

(32

)3

.5 (27

)

3.8

CU

LV

ER

(28

)4

.2(1

4)

3.5

(31

)4

.0(3

0)

3.2 (2

5)

4.1 (2

1)

4.1 (2

8)

4.1 (2

2)

3.4 (2

4)

3.1 (1

9)

3.7 (3

1)

5.1

(29

)4

.5(2

8)

3.3

(14

)3

.8 (34

)

3.9

SIO

UX

LA

ND

(29

)2

.7(1

)3

.6(3

6)

4.1

(31

)3

.5 (34

)

4.1 (2

2)

4.3 (3

6)

4.5 (3

3)

3.9 (3

7)

2.7

(8)

2.8

(6)

5.5

(35

)4

.5(3

0)

3.7

(25

)4

.0 (38

)

3.9

NE

94

65

4(3

0)

4.8

(33

)2

.2(2

)3

.4(8

)3

.8 (39

)

4.8 (3

9)

4.6 (3

8)

3.6

(4)

3.1 (1

6)

3.2 (2

1)

4.7 (4

0)

4.8

(24

)4

.7(3

2)

3.0

(10

)3

.7 (33

)

3.9

SD

95

20

3(3

1)

3.7

(7)

3.2

(23

)4

.5(3

7)

3.6 (3

5)

4.7 (3

6)

4.2 (3

3)

4.8 (3

8)

4.2 (3

9)

3.2 (2

0)

2.5

(1)

5.4

(32

)4

.2(2

5)

3.4

(16

)3

.9 (36

)

4.0

WIN

DS

TA

R(3

2)

5.0

(36

)4

.3(4

0)

3.9

(24

)3

.5 (33

)

4.3 (3

1)

4.3 (3

4)

4.0 (2

0)

2.9

(7)

3.0 (1

5)

3.9 (3

4)

4.9

(26

)4

.5(2

9)

3.8

(30

)3

.5 (23

)

4.0

SD

94

24

1(3

3)

5.6

(40

)3

.4(2

7)

4.5

(38

)2

.3(1

)4

.2 (30

)

4.3 (3

5)

4.6 (3

6)

3.5 (3

0)

2.5

(5)

4.2 (3

9)

5.5

(36

)4

.1(2

3)

4.2

(38

)3

.3 (20

)

4.0

VIS

TA

(34

)4

.8(3

2)

3.6

(35

)4

.3(3

5)

3.6 (3

6)

4.5 (3

4)

4.7 (3

9)

4.2 (2

7)

3.2 (1

7)

3.1 (1

8)

4.0 (3

7)

4.8

(25

)4

.4(2

7)

3.7

(26

)3

.5 (28

)

4.0

362 Euphytica (2010) 174:357–370

123

the highest yielder at a given location. The genotype

‘XH1888’ produced the highest yield when averaged

across the state and ‘Roughrider’ was the lowest

yielder in the state. Among locations, Watertown,

Wall and Platte were the lowest yielding (3.1 t/ha)

locations. Genotypes at Oelrichs produced the highest

average yield of 4.7 t/ha with a range of 3.7–7.3 t/ha.

The main effects and interactions of locations,

years and genotypes were significant (P \ 0.01)

(Table 2). The G 9 L interaction and G 9 Y inter-

action sources of variation contributed 1.5 and 3.0%,

respectively, to the total variation. Genotypes

accounted for 3.6% and locations accounted for

4.0% of the total variation. The Y 9 L interaction

variation accounted for 42.2% of the total variation.

This demonstrated that mean yield was very dissim-

ilar in different years across locations. Due to the

high magnitude of Y 9 L interaction, both G 9 L

and G 9 Y interactions were small. The G 9 L

interaction variance contributed 41.3% to the pheno-

typic variance.

The mean sum of squares of G 9 L 9 Y interac-

tion was used to calculate the standard error (r) for

the Azzalini-Cox test. The standard error wasffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

0:46r¼4ð Þ y¼8ð Þ

q

¼ 0:12. Grain yield of genotypes at

locations in Table 1 was the average of replications

and years, hence the standard error was also averaged

over replications and years. To calculate the critical

multiplier ta, Baker (1988) suggested use of a = 0.10

Table 2 Analysis of variance of mean grain yield (t/ha) for 38

wheat entries across 14 South Dakota locations of the crop

performance testing (CPT) nursery during 1998–2005

Source df MS r2 %a

Year (Yr) 7 169.15** 0.06 8.7

Location (Loc) 13 76.38** 0.03 4.0

Loc X Yr 65 43.58** 0.28 42.2

Reps within Loc X Yr 252

Genotype (Gen) 37 12.65** 0.02 3.6

Gen X Loc 481 0.78** 0.01 1.5 (41.3)b

Gen X Yr 116 1.58** 0.02 3.0

Gen X Loc X Yr 1073 0.46** 0.07 10.4

Residual 5029 0.18 26.8

Phenotypic variance 6.0

** Indicates significance at P = 0.01a Percentage of total variabilityb Number in parenthesis is percentage of genotype 9 location

variance component compared to phenotypic varianceTa

ble

1co

nti

nu

ed

Gen

oty

pe

Lo

cati

on

Bro

ok

ing

sW

ater

tow

nH

igh

mo

reW

all

Bis

on

Hay

esM

arti

nS

elb

yP

latt

eS

turg

isO

elri

chs

DL

akes

dry

DL

akes

SW

S

Win

ner

Mea

n

yie

ld

QT

74

06

(35

)4

.4(2

5)

3.2

(22

)4

.0(2

8)

3.4 (3

0)

4.6 (3

5)

3.9 (2

1)

5.0 (3

9)

3.4 (2

6)

3.7 (3

8)

3.4 (2

8)

5.5

(34

)5

.0(3

7)

3.5

(18

)3

.6 (30

)

4.0

SD

94

14

9(3

6)

5.4

(39

)3

.1(1

7)

5.0

(39

)3

.8 (38

)

4.1 (2

7)

4.0 (2

6)

4.6 (3

4)

3.7 (3

6)

3.2 (2

2)

4.0 (3

8)

5.5

(33

)4

.7(3

1)

4.0

(36

)3

.7 (32

)

4.2

NE

93

61

3(3

7)

4.9

(34

)3

.5(3

0)

4.5

(36

)3

.7 (37

)

4.7 (3

8)

4.2 (2

9)

4.7 (3

7)

4.0 (3

8)

3.2 (2

5)

3.2 (2

1)

6.3

(39

)4

.8(3

3)

3.6

(22

)4

.0 (37

)

4.2

XH

18

88

(38

)4

.4(2

1)

3.8

(37

)5

.4(4

0)

4.1 (4

0)

5.3 (4

0)

5.1 (4

0)

5.2 (4

0)

4.9 (4

0)

3.5 (3

4)

2.8

(5)

7.3

(40

)4

.9(3

6)

3.8

(31

)4

.9 (40

)

4.7

ME

AN

4.3

3.1

3.9

3.1

4.1

3.8

4.1

3.3

3.1

3.3

4.7

4.2

3.5

3.4

3.7

MIN

IMU

M2

.72

.12

.92

.33

.42

.93

.42

.42

.12

.53

.73

.12

.42

.43

.0

MA

XIM

UM

5.6

4.3

5.4

4.1

5.3

5.1

5.2

4.9

3.9

4.7

7.3

5.6

4.3

4.9

4.7

Val

ue

inth

ep

aren

thes

isis

the

ran

ko

fth

eg

eno

typ

ein

the

test

edlo

cati

on

(co

lum

nh

ead

ing

)

Euphytica (2010) 174:357–370 363

123

to compensate for conservativeness of the test. The

value of ta was 3.12. To test for G 9 E interaction

according to the Azzalini–Cox method, two geno-

types with large rank change at two locations were

identified. For example, high rank change occurred

between Roughrider and ‘Scout 66’ at Bison and

Sturgis (Table 1). At Sturgis, the difference between

the two genotypes was 0.7 while the difference

between the two genotypes was also 0.7 at Bison.

The difference between the genotypes exceeded

t0:1rffiffiffi

2p¼ 0:53. Thus the null hypothesis of no

G 9 E interaction was rejected.

Due to significant crossover interaction, as ana-

lyzed through partitioning of variance and Azzalini–

Cox methods, locations were clustered into groups

with reduced crossover interaction by SHMM and

GGE biplot analysis. Lillemo et al. (2004) and

Roozeboom et al. (2008) used SHMM and GGE

biplot, respectively, to group locations from data

consisting of variable numbers of genotypes evalu-

ated in multi-years and locations. A least square mean

of genotypes over years was used in the analysis of

SHMM, GGE biplot and rank correlation.

The SHMM clustered locations into different

groups (Fig. 2). The method divided the locations

into two major groups consisting of eastern, central

and western locations in one group and central and

western locations in the other group. An arbitrary cut-

off value of 1.4 in the Y-axis was used to cluster the

locations. The SHMM formed four clusters Brook-

ings, Selby and Sturgis (Cluster I), Watertown, Platte,

Martin and Winner (Cluster II), Highmore, Oelrichs

and Wall (Cluster III) and Hayes, Dakota Lakes—

SWS, Bison and Dakota Lakes—Dry (Cluster IV).

The first and second clusters consisted of locations

from eastern, central and western South Dakota,

whereas the third and fourth clusters consisted of

locations from central and western South Dakota. The

Missouri river divides the state into two parts, with

the eastern parts being mainly flat and the western

parts being mainly hilly. The average rainfall pattern

in the state over the last 30 years indicated that there

was more rain in the eastern parts, followed by the

central parts with the least rain being in the western

parts of the state (http://climate.sdstate.edu/climate_

site/climate_page.htm#). The clustering of the loca-

tions did not match the climatic (rainfall) and topo-

graphic conditions of the state.

In the GGE biplot, the polygon view showed that

there were two mega-environments displayed by the

XH1888 (38) sector and Jagger (16) sector (Fig. 3).

The XH1888 (38) mega-environment consisted of

Watertown, Brookings, Platte, Selby, Highmore,

Martin, Wall, Bison, Winner, Hayes and Oelrichs,

whereas the Jagger (16) mega-environment consisted

of Sturgis, Dakota Lakes—Dry and Dakota Lakes—

SWS. The polygon view also provided information

on the performance of the genotypes. XH1888 (38),

for instance, produced the highest yield at Water-

town, Brookings, Platte, Selby, Highmore, Wall,

Bison, Winner, Hayes and Oelrichs (Fig. 3). Jagger

(16) produced the highest yield at Sturgis, Dakota

Fig. 2 Dendrogram from

clustering 14 locations of

the crop performance

testing nursery during

1998–2005 for mean

grain yield

364 Euphytica (2010) 174:357–370

123

Lakes—Dry and Dakota Lakes—SWS. The Rough-

rider (1), Scout 66 (2), Ransom (4) and SD92107-5

(10) sectors did not contain any locations indicating

that these genotypes were among the worst perform-

ers across locations.

Figure 4 provides information on discriminating

ability and representativeness of locations. The vector

length of each location approximates its discriminat-

ing ability. The location with the longest vector

length was the most discriminating. Oelrichs had the

longest vector length and was, therefore, the most

discriminating location. The location closest to the

AEC abscissa was the most representative of the

mega-environment. In that same figure, Winner was

the most representative location. Sturgis, Dakota

Lakes—Dry, Dakota Lakes—SWS and Watertown

projected higher on the AEC abscissa and were,

therefore, least representative. An ‘‘ideal’’ location as

described by Yan (2001) was the one with the most

discriminating and representative abilities. The best

location was Oelrichs as it was closest to the ideal

location, the centre of the concentric circle. Locations

tightly clustered within a mega-environment should

be similar with regard to genotypic performance.

Such locations could be removed without much loss

of information. This would help to optimize resources

and improve program efficiency. Highmore, Wall,

Bison, Hayes, Martin, Selby, Oelrichs and Winner

were closer to each other and formed small angles

with the AEC abscissa. To optimize resource alloca-

tion, Oelrichs and Winner could easily replace other

locations in their respective groups.

Performance of entries based on the mean and

stability is shown in Fig. 5. Average Environment

Coordinate (AEC) abscissa ranked the genotypes for

mean yield. The genotype farthest from the origin

would have either the highest (on the positive side of

AEC abscissa) or lowest (on the negative side of AEC

abscissa) mean yield. The genotype XH1888 (38) was

the farthest from the origin on the positive end of the

AEC abscissa and had the highest mean yield

followed by ‘NE93613’ (37). Scout 66 (2) was the

farthest on the negative side of the AEC abscissa and

was the lowest yielding genotype. When comparing

biplot results with the mean yield of genotypes in

Table 1, the biplot approximated the ranking of

genotypes very well. Projection of the genotypes on

the AEC ordinate approximated their stability. The

higher the projection of the genotype on the AEC

ordinate, the more unstable it was. Jagger (16),

‘2137’ (26) and ‘TAM 107’ (22) were projected high

on the AEC ordinate, and were, therefore, among the

most unstable genotypes across test locations. The

genotypes Scout 66 (2), ‘Wendy’ (5), ‘Nuplains’ (8),

Fig. 3 Polygon view of the

GGE biplot based on mean

grain yield of 38 genotypes

tested in 14 year-location

combinations during 1998–

2005 in the crop

performance testing nursery

in South Dakota

Euphytica (2010) 174:357–370 365

123

‘SD93267’ (23), and ‘Windstar’ (32) were stable as

they were closer to AEC abscissa. The biplot ranked

the genotypes similar to the ranking of the testers and

identified the best genotype in the set. The genotype

at the centre of the concentric circle represents the

ideal genotype. According to Yan (2001), the ideal

Fig. 4 GGE biplot

comparing locations

(testers) for discriminating

ability and

representativeness

Fig. 5 Average

environment coordinate

view of GGE biplot

366 Euphytica (2010) 174:357–370

123

genotype should have a high mean and also be stable.

XH1888 (38) was the closest to the ideal genotype

and, therefore, was the highest yielding in the set.

Rank correlations between locations and their

respective standard errors are shown in Table 3.

The correlation between Highmore and Martin was

the highest (r = 0.86 ± 0.04, P \ 0.01) followed by

that between Highmore and Selby (r = 0.83 ± 0.05,

P \ 0.01). No correlation was observed between

Brookings and Hayes. Brookings, Platte and Sturgis

had negative but non-significant correlations with

some locations. The highest correlated location ratio

(10/13) was observed for Highmore, Hayes, and

Martin. The lowest correlated location ratios were

observed for Platte, Brookings and Sturgis. The

results indicated that Highmore, Hayes and Martin

were the most representative, whereas Platte is the

least representative.

The SHMM-formed first cluster consisted of

Brookings, Selby and Sturgis (Fig. 2). Rank correla-

tion between Brookings and Sturgis was significant

(r = 0.32, P \ 0.05), whereas Selby was not signif-

icantly correlated to either Brookings or Sturgis

(Table 3). Brookings and Sturgis both had high

moisture regimes, which might be a factor for the

positive correlation between the locations. Biplot

analysis shows that Brookings and Selby were

different from Sturgis as the former locations fell in

a different mega-environment (Fig. 3). Figure 4

shows that Brookings and Selby formed acute angles

and the approximated correlations were positive,

meaning that they had similar locations.

SHMM clustered Watertown, Platte, Martin and

Winner into one group (Fig. 2). The rank correlation

between Watertown and Platte was not significant

(Table 3). Martin and Winner are geographically

close to each other and all lie west of Missouri River.

A significant and high correlation was observed

between Martin and Winner (r = 0.67, P \ 0.01)

(Table 3). Both Watertown and Platte were not

significantly correlated with either Martin or Winner

(Table 3). Biplot results showed that all four loca-

tions were in the same mega-environment (Fig. 3).

Although the SHMM method grouped Watertown

and Platte in the same cluster, lack of a significant

association between these two locations could be

attributed to different biotic stresses at each one. High

weed pressure was a major limiting factor at Water-

town, whereas diseases were constraining factors in

Platte. Although both locations had the lowest mean

yields and grouped into the same cluster, environ-

ments at the locations were not similar.

The third group of the dendrogram contained

Highmore, Oelrichs and Wall (Fig. 2). All three

locations were significantly correlated with each other.

Table 3 shows that significant and positive correlations

between Highmore and Oelrichs (r = 0.77, P \ 0.01),

Highmore and Wall (r = 0.57, P \ 0.01) and Oelrichs

and Wall (r = 0.47, P \0.01). Biplot results showed

that all three locations were in the same mega-

environment (Fig. 3). Approximated correlations were

positive among these locations as indicated by the

acute angles among them (Fig. 4). The GGE biplot also

showed that Oelrichs was the best location (Fig. 4).

Hence, based on the results of three tests, all three

locations were similar environments with Oelrichs

being the best location in the group.

Hayes, Dakota Lakes—SWS, Bison and Dakota

Lakes—Dry represent the fourth group in the den-

drogram (Fig. 2). These locations represent the

dry environments. In some years, Bison and Dakota

Lakes—SWS became very dry. Hayes and Dakota

Lakes—SWS were significantly and positively cor-

related (r = 0.42, P \ 0.01) (Table 3). Dakota

Lakes—Dry was moderately correlated with Bison,

Hayes and Dakota Lakes—SWS with correlation

coefficients of 0.45 (P \ 0.01), 0.55 (P \ 0.01), and

0.52 (P \ 0.01), respectively (Table 3). A significant

correlation was observed between Hayes and Bison

(r = 0.64, P \ 0.01) (Table 3). In contrast to the

dendrogram and rank correlations, the biplot sug-

gested that environments Bison and Hayes were in a

different mega-environment than Dakota Lakes—Dry

and Dakota Lakes—SWS.

In breeding programs, significant G 9 E interac-

tion restricts progress in variety development. Since

the G 9 L interaction was significant, CPT nursery

locations could be divided into more homogenous

sub-regions. The SHMM, rank correlation and GGE

biplots were used to group the CPT nursery locations

based on grain yield. Clustering of locations in the

dendrogram was not similar to geographical locations

or precipitation patterns in South Dakota. Cluster I

consisted of locations having a moderate to high

moisture regime (0.53–0.64 m year-1). Most loca-

tions in clusters II, III and IV had variable

(0.41–0.53 m year-1) moisture regimes. The cluster

II sub-group contained locations having biotic

Euphytica (2010) 174:357–370 367

123

Ta

ble

3S

pea

rman

’sra

nk

corr

elat

ion

s(b

elo

wth

ed

iag

on

al)

and

stan

dar

der

rors

(ab

ov

eth

ed

iag

on

al)

amo

ng

loca

tio

ns

inth

ecr

op

per

form

ance

test

ing

nu

rser

yd

uri

ng

19

98

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00

5

inS

ou

thD

ako

ta

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ok

ing

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ater

tow

nH

igh

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reW

all

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on

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arti

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chs

DL

akes

dry

DL

akes

SW

S

Win

ner

Bro

ok

ing

s0

.15

0.1

50

.15

0.1

50

.16

0.1

50

.15

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20

.14

0.1

60

.16

0.1

60

.16

Wat

erto

wn

0.1

5N

S–

0.1

40

.14

0.1

50

.14

0.1

40

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0.1

60

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ore

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0.1

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0.1

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8

Wal

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368 Euphytica (2010) 174:357–370

123

stresses (i.e., weed and disease pressure) in Water-

town and Platte, respectively. Clustering of locations

in South Dakota might be due to environmental

factors other than moisture regime.

The results suggested that the CPT nursery loca-

tions can be divided into homogenous groups. Wide

variety adaptability and testing procedures are also

important considerations in breeding programs. For

wide adaptability, genotypes should be evaluated in

representative locations. Information obtained from

this study should be helpful in optimizing resources.

Oelrichs was the best location for testing winter wheat

in group III. If one location is to be dropped from this

group, a choice should be made between Highmore

and Wall. Due to environmental similarities, and the

fact that Highmore was more representative (Fig. 4),

Highmore rather than Wall should be used for

genotype evaluations. Similarly, Winner and Hays

could replace Martin and Bison in groups II and III,

respectively, based on Figs. 2 and 4. Thus, to optimize

resource allocation, Wall, Martin and Bison could be

abandoned without much loss of information.

Besides grouping of locations, GGE biplot pro-

vided additional information on variety performance.

XH1888 was the best genotype with the highest mean

yield, and was the highest yielder at 11 locations.

Jagger, which does not have a good level of winter

hardiness in South Dakota, was not only the highest

yielding genotype at three locations, but was also

among the least stable genotypes. If genotype stabil-

ity is the focus in the breeding program, then a

genotype like Jagger should not be selected. Instead,

genotypes such as SD93267 should be selected. Scout

66 and Ransom, which have good winter hardiness

but unstable yield performance in South Dakota, did

not perform well across the state. It is noteworthy that

genotypes at the extremes of winter hardiness were

not stable.

The GGE biplot and SHMM both effectively

grouped the locations into different mega-environ-

ments. The GGE biplot and the SHMM resulted in

two and four cluster models, respectively. Both

methods enabled reduction of genotype 9 location

variance component estimates and COI compared to

the state-wide genotype 9 location variance compo-

nent and COI. The two-cluster model led to the

ranking of the top yielding varieties. The four-cluster

model led to the grouping of locations based on

similarity of climatic conditions, or biotic stresses. A

caution should be taken as the analysis was done

using only 8 years of data.

The methods used in this study provided valuable

information on similarities among testing locations in

a large wheat breeding program in South Dakota.

Such information should be useful to breeders for

optimizing resource allocation, especially in large

breeding programs, regardless of crop species.

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