Compar/ison of regression and AMMI analyses i for...
Compar/ison of regression and AMMI analyses
i
for assessing yield stability
of maire inbred lines
A. Ndia/ya’, S. K. VasaI*, S. Mclean*, and J. Crossa
‘/%?A. CNRA BP : 53 Bambey - (Senega!)
1
2CIMM\\T, Apdo Posfal6-641, C.P. 06600, D. F., México
/
Abstrxt
i
Several shatistical techniques have been developed for the
arralysis sf’the interaction of genotypes with environments (Ci x
E), One method that has been used extensively is regression
analysis.1 The objectives of this study were to i) compare the
soIme of/ tne methods available for assessing yield stability in
the hop!e of identifying genotypes with wide stability of
petform&ce as well as good rnean performance and ii)
quantify / the probability of successful selection of a genotype
when using the additive main effect and multiplicative
interactic CI (AMMI) technique compared with the regression
techniqu , The regression technique used in this study is
particularl,y effective in emphasising the actual trend of variety
yitsld re/ponses to a range of natural environments. The results
of AMMI( method agreed with the modified regression method
analysisiE0 and 95% of the time for white and yellow lines,
respect-i ~s.ly for selecting the best lines adapted to favorable
rnvironr~ents. T
h
e
two techniques pcr:!\\; agi& :v!;z::
1
selectiort was for genotypes adapted to poor environments.
Howeve; AMMI method was more effective in detecting
specific adaptability for specitk environments.
Résumé
j
Plusieur’; techniques statistiques ont été développées dans le
cadre c’e l’étude de l’interaction génotype x milieu et lâ
méthod:i de régression linéaire a été largement utilisée.
L’object/if de cette étude est de comparer les résultats obtenus
à partir] de quelques méthodes dans l’espoir d’identifier des
gknotyp/e» performants et à large adaptabilité et ii) de
quantifi:r la probabilité de sélectionner un génotype en
u:ilisant1 les valeurs prédites par la méthode AMMI comparée à
celle obtenue par les techniques de régression. La technique
de régression est particulièrement efficace pour mettre !‘rrcent
sur la tendance du rendement d’une variété dans piusieurs
environnements. Les résultats obtenus par la méthode AMMI
concorcent presque avec ceux de la méthode de régression
modifiée (dans 80 et 95% des cas pour 1e.s lignées blanches et
jaunes riespectivement) quand il s’agi; de sélectionner 12s
meilleures lignks adaptées 3 des environnements favorables
et seulement de façon partielle pour celles adaptées à des
milieux défavorables. Cependant, la méthode AMMI paraît plus
efficace dans l’identification d’une adaptabilité spécifique et
pour un environnement spécifique.
Intmduckion
Over the last decade, CIMMYT Lowland Tropical Maizc Subprogram
has developed several productive maize (Zea YYU~~ L.) inbred lines with
good combining ability. Sources of the lines include original populations,
mbreeding tolerant populations, recycled elite lines, and recycled early
generation lines reconstituted through the forward and reverse
inbreeding procedure (FRIP). Inbred lines are evaluated for combining
ability as from the ç3 or SA sta,ge and are also tested per se in line
evaluation trials (LETs) across many locations in collaboration with
national programs in developing countries. Yicld data bave been used to
examine many approaches to the analysis of stability.
Of the numerous statistical techniques developed to analyse thc
interaction of genotypes with environments (G x E), the regression
analysis has been extensively uscd. This was first introduced by Mooers
(1921) and was given prominence by Yates and Co&ran (1938) who used
the mean performance of ail genotypes grown in an environment as a
suitable index of productivity of the envirorunent. The performance of
i
each genotype was plotted against this index for each environment, and
simple rcgression was fitted by least squares to sumtnarise the
genotype’s response.
t,.. ’
Finlay and Wlkinson (1963) used the regression trt’chni~llle to exantiw
the yield stability of various bar+; (Hordeurn vrtZgare L.) gcnotypes. TheJ.
considered regression slopes anti overall yield level of genotypes as
important stability criteria.
Rberhart and Russe1 (1966) also used a linear regression approach to
determine yield stability in maize. Lu addition to the regression slopes (b-
values) and mean yield, thcy considered deviations from the regression
line as another important component of varietal stability. A variety is
considered stable when ils b-value is close to 1.0 with a minimum sum of
squared deviations. Varieties witln b-values significantly different from
unity are not stable; thovc with high b-values are considcred to be
responsive to high-yield environuents and vice versa for those with low
b-values.
Multivariate methods 1,JL < ;:,c :,.:Gi\\ u~t.d ir, ~n;!y~ing stability in plant
breeding. Crossa et al. (1988a) applied thc principal coordinate analysis,
proposed by Wcscott (1%7), to determiue varietal stability in two
international triais (EVT 12 ‘ind EVT 13) evaluated over 1979 - 1983. The
results showcd that four <lnd threc stable varielies had been dcrived
from CIMML’T Popul,l tien 22 ad Population 43., respectively. Also
116
i
cleven selectîons derived from Population 28 showed good levels of
stability in bath ktigh and low yiclding c?n\\iir(\\lllllcnts. Crossa ef a/. (1990)
also usetl thc Additive Main Effect and Multiplicative Interactioll
(AMMI) metho& with additive effect for genotypes and environulents
and the u:ultiplm~tEve tcrms for genotype x environment interaction, for
analysing data Ii-om international maize cultivar tri&. Resul’ts showed
that AMMI inxcascd the precision of yicld estimates I:O a level
quivalent 10 inmasing thc number of replicalions by a factor of 2.6.
Considerable confmion hns arisen from the fact that the V~~OUS methods
of stability analysis havc engendered many differmt mcasures of
slability. Son~? cf the studics reported in thc literature showed that
diffcrent nmsur,es; of stahility arc similar but no1 idcntical in c%ssifying
lcsl gt~nolypcs Jtï;id/or cnvironments. In sotnc othcr (‘ases; thc test
~;t’notylx?s and Ç17~vironments <lrc classifier1 differcntly by tliP diffc~rcnt
slability Ill~lilSllWS.
.
compare thc rc!sults of three niethods of asscst;ing yicld s!ùbility in
an attcmpt tc i:&ntify widc stability of performance as well as pod
mean performance;
?
quantif,y thc 1 xobability of successful seicction of a genotype when
using AMMI pdictive values, comparcd with the probability of
selcction baa.d on thr predictive values of regrcssion techniques
and/ OI trcatuia?nt ~ncans.
Materials and ~~w~bods
was analysed for onc whitt? and one
(LETs) testcd at ten loc,ations in 199-l.
a at comtx locations, data for 9 and 8 lnc‘ations wer~l
white (LETW940-2) and tht‘ ~cllow
perfOrn~al~~~
Of fie genotype is tvtter tlta tt tlte mean performance Of dl
gcnotypes evaluated.
The A~$MI analysis. AMMI was pcrforntcd using MATMODEL (Gauch,
19s7; Crossa (1990). This mode1 first fils addit:iv+> effects for genotypes
((;) and environments (E) by d:.e usual addilive analysis of variancc
procedure, Thereafter, it fils multiplicative effects for geitotypc-
env~onment (G x E) interaction by principal components analysis @‘CA).
The 1inea.r regression approach. Environments were subdivided,
accord@ to AMMI method, into two major groups: tltose with positive
G x E interaction and those that had negative G x E interaction. Thc
sbability Itarameters proposed by Eht+art and Russell1 (‘1965) wcre thon
c6tlculated for each line in eaclt group. Lines that had across location
iilectrt yicld qua1 to or larecr Iltan il?? $t.dItcl ~illt?dll Wt’W sclected.
Geitotypes were then classified b,ts~d on thcir ref,rcssion coc~fficients.
Results
Whitc lines. For the white inbred lino tri,Js, ,AkIIMI analysis sltowed tltat
environments, genotypes, and G x E inhraction were highly significant
(P < 0.001) and accounted for 46, 24, and 30% of the trcatment sum of
syuares respectively (Table 1). In 11rc~ biplol. (Fig.1 ) t’tc principal
componont axis 1 (PCAl) geItotypes (crl;iirolr~nenls) that alrpear ahnos!
on a pcqtendicular Iine ltave sintil~ mteraction patterm.. Genotypes
(cnvironments) with large positive or itc@ive PCAl scores bave large
interacUons whereas gcnotypes (cnvin\\!-fil~~l:ts)
\\-vit11 PC:AI scores clow
to WY !?avc smala interactions. Croct.: rf 2. (70X!) pnin:ed out tha:
~;woLY~~?s aud environments with PC.41 scorcls oI Ihe same jiglt producc
positive interaction effects, whereas coiubiitatiort of PC41 scores witlt
opyosite signs have negative speçific iittcractions
Table 1. Additive main effects ;md multiplicative interaction aualysis of
variante for grain yield (kg ha 10*) of 119 white inbred lines of ma&,
including the first two interaction principal component axes (PC41 and
PCA2).
-.
--.-- .--_ I - -___---__- I_~
hm-e of variation
df
5:l~~~s f:f squares (x 106)
h1rw-t squarc3
---1 ___ --j-_
YZlt combinations
1070
1262.-M
1.17
-
Genotype (G)
118
3OO:~i
7 7.4**
-.-
hvironnwnt (E)
8
;79.iL?
72.w*
G x El
91;
x!.9-1
o.w*
interaction PCAl
122
12;’ 2-l
: Il’**
i
interaction PCA2
123
77.1-I
0.62**
_
Rcsidual
696
1721.77
@.30
-.ll---..---.-_-
** Pa.001
/
l
Figl: Biplot ofthe yield means andthe
k principal
componentaxis olthe
119whiie lines - 9 locations
100 -
_._... --_-- --
euA
50 i
l
2409
2 9 0 0
3400
3900
Table 2. Mean gr;h yield (kg/ha) of the top 20 white inbred lines adapted to
favorable env: rotments
/
- __-
-
01 / l?all
Entrics na
II .t?;ln
Mean yicI&
Guakmala
Salvador
1
_-__
- -
1
t
?iY.Lii
3668.4
5967.1
2181.3
POL%~~$
-
-1023.1
Oîïi.ii
319fi 9
3699.6
422'7.8
5631.1
3134.0
3912.3
4277.1
ÇPo4.0
3815.6
3211.7
3271.5
5532.4
3714.4
3567.6
5123.1
6517.0
5155.8
389h.s
4703.9
6632.9
3734.6
3738.2
3669.3
4715.2
2310.7
3982.1
4306.9
5776.2
3352.0
3792.6
2899.'1
4257.3
1872.6
2567.A
41w ti
53X7.1
2961.8
4316.8
3898.2
-La.8
3617.9
3746.Q
3010 Y
3816.5
230x.9
2707.4
3883.4
43hs.4
3570.7
371.4 (‘
37,%.X
4x00.3
3210.4
33-13.h
2937.8
3572.5
229-M
z46.2
3734.1
5601.9
3781.A
7x10 (;
.idS. 2
48î7.2
3121.0
2"4m-1
-i301.3
ÇhlÇ.7
3329.1
??fj(.J.!~
.
119
: Grolcp 3 consists Of genotypes with high positive interaction. These are
welI adapted to favorable environments such as Guatemela, Salvador
and Poza Rica 1 (PORl). Table 2 gives the mean yield of the top 20 wkte
bes adapted to favorable environments. The overall mcan yield varied
korn 17’86 kg/ha for line 92 to 3625 kg/ha for line 20 whereas the mean
yield ovcr favorable environments varied from 2899 kg/ha for l.ine 33 to
5123 kg/ha for line 20. Only lines 28, 33, 53, 92 ad 99 had overd ~QÜLI
yield lower than the grand mean (2230 kg/ha). These lines were
predominanlly derîved from Population 21 and from rec.ycled lines.,
Grotip 2 includes genotypes and ~environments with near-zero interaction
(Table 3). Included in this group were the more stable lines and they
performed well at the Honduras site. Chly five of them had mean yiel&
Iarger than the grand mean. About 25% of the lincs were seiections frcw~
Popula tien 21.
Grou)t 3 consists of genotypes and environments with higher negativt:
interactions (Table 4). They are adapted to unfavorable cuviromnents
like Costa Rica, Nicaragua, ThaGsnd, Colombia and Poza l&:a 2 (POR2 ),
The AMMI 2 mode1 captured 86% of the treatment combination sum of
squares. PCAl and PCA2 explained 33.2 and 20.1% of the G x E
interaction, respectively.
Table 3. Mean grain yield (kg/ha) of the 20 most .stabk white inbred lines in
Honduras.
----
Entries no
Overall mear.
Honduras
-
-
2
2190.0
2272.b
15
2493.0
22j(j. 7
18
2077.3
2304.4
26
2163.3
1811.2
40
1661.5
1054.7
47
2482.6
2704.3
6.3
1793.8
1913.9
68
1923.7
2101.6
70
1972.4
976.4
72
2069.3
1752.7
70
2266.3
X75.3
7’4
2236.1
2142.7
K-1
2303.9
2385.1)
89
1519.9
1988.2
92
1932.7
960.2
9h
1968.1
:207s. 1
701
2130.7
7113
.-
7
_L.
103
1995.1
^2b3.7
11:)
1852.4
1729.4
116
1971.9
7 ?90.,7
-
-
-
-
-
ain :yieid (kgha) of the 20 white lines adapted to unfavorable
1068.8
22641.9
4 3
1949.:!
1859.6
1746.2
1851 1
533.0
2630.5
2507.3
44
1677.17
15X1.9
1942.1
573,‘s
1699.2
934.8
2554.6
4 6
2372.‘,
2176.6
2862.2
312.5
2052.4
2712.9
29X.9
4 8
16lh:l
15q;. 9
2220.9
419.:)
2153.8
942.3
2247.7
5 8
2335.1
2-4-45.9
2267.4
639.5
3065.1
2066.3
-1171.3
60
1369. $
1232.5
1211.4
558.0
314.7
1532.9
2545.5
64
1629.5
1461.5
1469.2
424.0
627.0
1527.5
3259.7
80
175-l. 3
1 i;CX~.-i
13HO.6
1104.3
1737.1
1494.1
X70.5
8 2
19YZ. 3
i 33s
2323.1
131.4
ix-i.7
1572.5
311: -
--L, .3
8 3
19 10. 3
1 !:;,$j, 0
21196.1
455.0
860.0
2160.8
2833.2
8 3
2071,~
7O?p;
2ml.6
1722,;
1x1.3
17O-i.9
3343.0
87
960 : I
I:l2 1 3
1.187.3
D52. ~?S
39i.l
1172.3
lG98.5
P S
7 660. 3
1 3s 1 8
‘7311 --. . . . 267.1
1933.4
1233.3
-J7J?
i-.
-. j
105
204-I. 1
I:)ls.!
2314.1
I.W.?
i ihS.9
216.7
37lh.l.
107
1 Y97.2
I E 15,s
2bH.9
I~Wf?~
12.523
1278
- ?
.-
2137. 3
111
117id
1 1 7.1."'
17.43.4
100“.,
0.1)
827.4
3?91.?
113
3010.3
2;Kw,o
3 806.3
1029.3
736.8
32-I-1.5
3332.7
115
327b?
.?h:lS,G
1 W.8
1417.4
x79.4
5535.3
5462.6
119
1741 .jK
290(‘~:4
i 001.3
425.1
3966.7
5498.7
3010.1
Rcpblic and Poza Rica1 ~(PORI). The mean yielti ovt?r these
e~lviron~~~e& varied ~~OUI 2773 kg/ha for line 97 to 5777 kg/ha for L[>e
12. Thcsc lines wcre derived mainly from Population 24 (46X) and
population 36. 0111~ lincs 24, 79 nnd 97 yieldcd helow thc grand mean.
~,&le 6. Mean grain yield (kgha) of the top 20 yellow lines adayted to
favorable environments.
-E~S Overa~~ mcan
Mcan
G u a t e m a l a Rep. Don~. Pozii Rica 1
11°
y icldl
- - - - Y - -
3538.8
5039.i
4239.8
6435.0
4444.3
9
3712.8
4802.4
4826.8
5233.1 4345.2
12
4074.3
5774.4
5698.5
6424.1 5209.6
!4
2434.6
303-4.8
1995.5
4069.
?
Lws.9
19
2427.7
3181.6
2522.5
3886.2 3136.2
24
2133.5
2830.5
2248.4
3622.!) 2391.2
33
2622.9
34hfi.c)
1888.8
3878
s
4033.2
-41
2390.1
3374.9
3104.3
4097.fl
2027.7
4-4
4024.5
5438.5
4515.7
6073.7
573i.l
46
2280.4
3236.0
2870.7
3730.n
31Ob.G
47
3703.5
3445.5
2672.1
4292.0 3371.4
48
2398.5
3436.7
3383.7
3921.7
3W4.6
:,-JL,
2283.3
3130.9
2308.7
4627.8 2456.1
(12
3874.3
5067.1
4178.3
6401.4 4561.6
M!l
2752.1
3737.5
3850.3
3407.b 3954.6
77
2517.0
3x4.7
3156.4
4057.9 3299.7
78
2559.2
3440.5
3322.4
4470.7
2538.5
79
2080.0
2925.3
2156.0
4150.2
2469.7
92
2745.4
3607.6
2047.3
5569.2
320ii.2
97
2003.5
2773.4
1880.1
3384.7 3055.3
- -
-
‘Mean ucross thr thrrc sclected sites in the goup.
i;ror~p ;! ti~iudeti thc yellow lines with near-zero inter‘titim. The mm
yield rcspnnsr varicd froc 1644 kg/ha for line 83 tu 3011 I;g/h~ for line
3 (Table 7). AL Poza Rica 2, 50% of these lines had an ovcr~ll IIUWII yicld
bolow the grand mean (2252 kg,‘hti)
Gmrp ;3 consists of 20 yellow lines adapted to unfavor~~hlt~ sites likc
Cuba, Thaïland and Colfnnbia (Table 8). The mean yicld rt+p~nçc over
thcsc? locations varied from 1160 kg/ha for line 86 to 2211 kg/ha for Iinc
112.
122
For the yellow lines 1111~ two groups were identified (Fig. 2). Group 1
included Cuba, Tha nd and Pananm’While Group 2 had Guatemala,
Poza Rical, Po2a Rit 2, Colombia and Dominic Republic.
Table 7. Mean gra.
pield (kg/ha) of 20 stable yellow lines at Poza Rica 2
_-I
Entrie?
Overall nwan
Poza Rica 2
- -
5
-
3021.6
4307.1
7
2829.7
3960.4
13
2321.1
3269.8
26
2219.7
3073.5
28'
1989.7
2926.8
29
2482.4
2707.2
31
2061.7
4297.1
34
2508.3
4598.9
3b
2117.7
3610.1
36;
24d8.8
3690.4
4:’
2430.2
4165.8
50
2185.9
3220.4
51
1928.5
2653.6
6s:
1796.7
3409.0
74,
2586.9
3179.2
76
1879.8
2059.7
83
16G.8
2393.5
85
1955.7
2708.7
95
1822.7
2448.1
1011
2018.4
2367.0
. - -
-
-
Table 8. Mean grail yield (kgha) of 20 ycllow inbred lines adapted to
unfavorable envh xinents
Entry Owrall
no
mm7
2 0
2143.7
21
1596.5
1609.1
1237.3
58-i.2
2050.3
2564.4
27 :
428.6
1398.0
1372.9
621.C
1024.2
1773.9
35
775.3
1410.4
3481.6
523.ci
1313.8
2323.2
52
574.7
1440.8
1675.7
206.1
1660.1
2221.4
53
528.8
1379.9
1896.1
783.11
1308.3
1531.6
56
647.5
1.554.x
1‘454.0
779.1
2167.4
1818.7
60
914.7
1601.8
1558.8
788.6
1799.9
2259.9
69
518.8
1332.9
1493.5
58-4.h
43-l.Q
2818.6
81
16t?O. 5
3713.5
1-M. 1
413..\\
2ow.;
2865.9
84
2222.2
~803.7
16X1.3
544.:
2872.1
2116.9
86
16X1
1160.0
1223.1
601. fi
1399.1
1416.4
88
2445.5
?!039.2
1657.1
7',9...*
2105.0
3595.4
96
18Z5.6
1.681.7
1638.2
201. f)
2177.7
2709.4
100
1751.1
1.524.2
1891.7
338.1
1317.2
2549.9
110
1932.4
T.538.0
1502.6 5P9.ci L
1357.3
2702.7
111
1992.6
1.898.5
18821.2
90-1.1
2493.3
2312.3
112
2487.9
2211.8
2015.2
488.0
‘123-4.0
5109.9
113
19i.8.9
I649.3
1066.5
3X9.6
2419.3
2721.9
114
2005.6
1~678.8
1924.9
0.0
1765.1
3025.0
----~
‘Mean across the four GTKII sites in tho goup
123
Fig.2 : B~~plot of tha yleld means and the
fkst principal component axis of the
119 yellow linas - 8 locations
FoT both whitc and yeUow line trials, environu~ental effect dominated
the analysis. The G x E interaction SUI\\ of squares was about 1.4 times
larger than thc genotype sum of squares. The importance, of thc
environmental effect is illustrated by partitioning the locations as shown
in Figs. 1 and 2. Clearly, the triais involved a wide range of environments
that need to bc characterized in tems of climatic fac(ors as well as biotic
and or abiotic constraints for a biological explanation of the genotype x
environment interaction.
Regression analysis
Thc regrtssion approach makes it possible to classify genotypes, on thc
basis !jf t?tcir b-~lucs, as rmponding or adaFted to high yil:lding sites
~&PIS) or to bw yielding sites (tms). Site means for grain yield ranged
from 1076 kg/ha at Nicaragua to ?+IO2 kg/ha at Guatemala fer the white
lines. Mean grain yields of the yellow lines varied from 546 kg/ha in
Cuba to 3141 kg/ha in Poza Rica 2. According 10 the b-values, 58% of thc
white lines and 49% of the yellow .ines had slopes larger than 1.0 in high
yielding sites md cannot be considcred as ideal genotypes.
For thc \\vhitc lines, 28% are idml lines (ID) with mean yield over
loc~ations ~:aryin!: h-cm 2236 to 330 kg/ha; 32% are bcst for the ltjgh
yiclding sites (I-IYS) with across-Ior.dticln mcan yicld ranging from 2236
to 3442 kg/ha. The remaining 40 Y1 ‘ire best for low yielding sites (LYS);
across-loz;itiorl IIIC~II yield vdriod 11.om 2212 to 440s kg/ha.
224
Although white lines
114 and 25, and yellow linos 3,13,15,23,33,34,
and 39 were clssifiel
no high-yield envioumeuts, we do not Comider
them as ideal gcnot
es in spite of their high across locations mean
yield . This indica tes
:at. good avcrage performance does not sigùfy
good adaptability an
cice-versa.
Furthermore, 30% o
II~ white lines are selcctions from Population 21
and 22% came from
iyçled lines; 24% of the ycllow fines were derived
from Population 24,
IV, were from recycled lincs and 18.5% from Sint-
Amarillo TSR.
Figures 3 and 4 1
vide the relationship of ~cnotypc adaptation
(regression coefficiel
and genotype mean yield for thc white and the
ycllow Lues, reqect
ly. Using thc gcneralisecl intcqm?tation of G x E
analysis as reported
Finlay and Wilkinson (1963L cach group of lines
ma y be classified as
~11 in Table 9. Thc proportion of lines that werc
adaptcd to the high
‘avorable cnvironmc~~~ts ~.V,IS grciitcr than 50% in
each go-OU~. Similat
t17c pcrccntngc of cnvirc~ntitcnts in Which the
pcrfomance of mach
notype was better thm thc mean performance of
a11 genolypes varied
ND -24 to 100% and 38 tc lOi)X for the white and
thc yellow lines, req
tively.
Table 9. PercenMge i
ranges of grain yield (kg/ha) of lines specifically
adapted to high
favorable (b>l.O), a11 (b=l.O), and unfavorable
(b4.0) environme
- - -
-_--
_--.--
IV,
AIl env.
Unfavoral-rle env.
(b=l.O)
(lsl.0)
_ _ _ _ - _-_---~.-
_-.----
C;roup
x
Yielc
-
-
w
Y0
Yield
rmp
%
Yield range -
_ _ .-.._..-
- Whitc
5 2
2 2 3 6
7 7
24
2 2 3 2 - 3 6 2 5
2-1 2 2 3 6 4 4 0 8
Ycllow 6 5
2 2 8 0
77
2 7
2 2 3 3 - 2 9 9 7
X 7 2 9 9 - 2 8 2 7
--.-----~ _-.-...
-.... _.----.--
Fi& Biplot of the mean yield snd the coefficients
regrenion bi for fhe lt9wbiC lines RWOW 9 locntionr
125
Discussion
G x E interactions linlit thc accur&:y of yit>ld estiu~;lt.es ami complicate
the identification genotypcs for gencral adaptation 10 a large munber of
environmcnts. Maizc brcedcrs a~-c thcrcforc conccrned about t h e
accuracy with which C x E is quml.ified. The mcthods evalualed in our
study yielded similar but net identical rcsults.
Resulls of AMMI analysis rjf triaI,- invol~+ng bath whitc ar,d yellow
endospcrm lines allowcd thc Grouping o
f
genotypcs and/or
ènvironments bascd on their interactions. The first two principal
components accountcd for 51.3 nnd 56.9% of the interaction sums of
CCpiWS for Ihe Fcklitt- cliId iht ),,>!Ia ~ti li:3?3, ; ~3p:fi~:~,~lJi.
Environmental effects dominnterl the per~omance of the lines in this
study thus highlighting tho import+lcc of location variability as a
principal factor in the tria1 network. 11 is thereforc necessary to find a
good approach to sclect homogeneous locations for international trials.
AM?I method could bc used for th:is purlxm~. The principlc underlying
this approach would be to decide which locations, rather than how
ntany, are cssentinl to ~lcarl\\~ rc\\:c<ll thc ::! xx-turc of G x 1: interaction
truly prcscnl anto:lg thc s.!:~iplc c)f ~!WS r~i:.l c~nvironmcnls in~;olvecl in
the triaLs.
study, it seems that genotypes with b< 1.0 usually
over locations below the grand mean. Eberhart and
:;ed that in situations where there are no surplus
,can be stored, or where long-term stqrage is not
ieties may be the most desirable. For the developed
er, the breeder usually wants varieties that produce
in ali environments. Hence, he desires varieties with
unit regression coefficient (b = 1) and small (near
Analysis other than regression is
n overall picture of how stability and mean yield are
to be traded off.
$MI analysis agreed well with the modified regression
“mg the best white (ahout 80%) and yellow lines (about
favorable environments, and only partial@ for those
d to poor environments. However, the AMMI mcthod
t in detecting adaptability to specific environments. As
sa et aI. (1990), in plant breeding, the appropriate gain
eved with AMMJ provides a tool for selecting better
therefore achieving higher realized progress from
gested the need for research
AMMI mode1 for analysing
In the method:; lx-oposcd by Finlay and Wilkinson (1963) and St-Pierre ef
al. (196;‘), tht! /.average yield asross a11 gcnotypcs in an environment is
used as an ;lsu;essmelG
i
of that environment etcept that the latter
approach is e:l:lxxssed in termi of percentage. St-Pierre ef al.‘s approach
agrees with f/hte modifïed regression method only in dctecting high
yielding geno y1x.s (overall mean yieid superior i!* L;I to pnd iil?xl) ??ut
does net prc’wide the keys for distributing gc?notypes inlo type:; of
apptability. 1
Conclu.sion
127
.fie aueors are grateful to thc numrous collaborators in national maiz(-,
research programs that cxricd out the linc! evaluation tr*al.s (LETs)
presented in this payer.
crossa, J., H.G. Gauch, Jr., and R. Zobel, 1990. Additive Mi~in Xects ‘md
Multiplicative Interaction Analysis 0T t w o lnlerm tioml Maizcl
Cultivar Tri&. Cmp Sci. 30: 493 - 500.
crossa, J., 1988. A con~parix~n of rcsults obtained l,viih twc, ~ycthods for
asscssing yield st&ility. 771evr: Appl. Genet. 75: -kO- 467.
Denis, J.B. and P. Vincourl, 1952. Pr~nordma des mtiLhodc:s statistiyuns
d’analyse des interactions gi’notypc 1 - milieu. Agronomie 2(3): 219 -
230.
Eberhart, S . A . , and W.A. Ruswll, 1 9 6 6 . Stability prmwters lor
compasing varieties. Crop Sca. 6(l): 36- 40.
Fiday, KW., and G.N. Wilkilxon, 1963. The analysis of adaptation in a
plant breeding programme. Arts. /. Apic. Res., 31: 742-754.
Gauch, H.G., 1987. MATMODEI hlicrocoaqwfev Poser. ithac<i, NY.
Hugh, G., and H.G. Gauch, Jr., 19X8. Modo1 selcction and Vahdation for
yicld Triais with Inlt?rxtion. Riometrics 44: 705 - 715.
Lin, C.S., and G. Butlcr, 19%. .A data-base approach for selecting
locations for regional triills. (-/~II. I. PZlzrrt. Sci. 68: 651- 659.
Saint-Pierre, C.A., H.R. Klini,k, dnd F.M. Gauthier, 1967. Early generation
selection under different c>nvironnrents as it influences eidaptation of
barley. CRII. j. ofPlnrrt Scierrce 47: 507- 517,
sinuons, N.W., 1991. Selcciion for local addptation in a plan!. breeding
progr~nune. 7’lzeor. A{qll. Gar&. 82: 363-367.
bd, S.K., and S. hklcm (rd~), l99-4. 77le i.ozdmd Tmpid h-lnize
f'rogrnrn Specinl Rcporf. bit>\\ ic o, D. F., ClMhfYT.
Westcott, B., 1986. Son~ m~:h& ior analysing ~:~~~otypC-.C~l~~ir~~~u~îC”t
interaction. Heredifj 56: 233-233.
Witcmhe, J.R., 1988. Estiwtt>l;
i-If sLibilily for c-ompmn~~ varieties.
&dyticn 39: 11-1s
i
for assessing yield stability
of maire inbred lines
A. Ndia/ya’, S. K. VasaI*, S. Mclean*, and J. Crossa
‘/%?A. CNRA BP : 53 Bambey - (Senega!)
1
2CIMM\\T, Apdo Posfal6-641, C.P. 06600, D. F., México
/
Abstrxt
i
Several shatistical techniques have been developed for the
arralysis sf’the interaction of genotypes with environments (Ci x
E), One method that has been used extensively is regression
analysis.1 The objectives of this study were to i) compare the
soIme of/ tne methods available for assessing yield stability in
the hop!e of identifying genotypes with wide stability of
petform&ce as well as good rnean performance and ii)
quantify / the probability of successful selection of a genotype
when using the additive main effect and multiplicative
interactic CI (AMMI) technique compared with the regression
techniqu , The regression technique used in this study is
particularl,y effective in emphasising the actual trend of variety
yitsld re/ponses to a range of natural environments. The results
of AMMI( method agreed with the modified regression method
analysisiE0 and 95% of the time for white and yellow lines,
respect-i ~s.ly for selecting the best lines adapted to favorable
rnvironr~ents. T
h
e
two techniques pcr:!\\; agi& :v!;z::
1
selectiort was for genotypes adapted to poor environments.
Howeve; AMMI method was more effective in detecting
specific adaptability for specitk environments.
Résumé
j
Plusieur’; techniques statistiques ont été développées dans le
cadre c’e l’étude de l’interaction génotype x milieu et lâ
méthod:i de régression linéaire a été largement utilisée.
L’object/if de cette étude est de comparer les résultats obtenus
à partir] de quelques méthodes dans l’espoir d’identifier des
gknotyp/e» performants et à large adaptabilité et ii) de
quantifi:r la probabilité de sélectionner un génotype en
u:ilisant1 les valeurs prédites par la méthode AMMI comparée à
celle obtenue par les techniques de régression. La technique
de régression est particulièrement efficace pour mettre !‘rrcent
sur la tendance du rendement d’une variété dans piusieurs
environnements. Les résultats obtenus par la méthode AMMI
concorcent presque avec ceux de la méthode de régression
modifiée (dans 80 et 95% des cas pour 1e.s lignées blanches et
jaunes riespectivement) quand il s’agi; de sélectionner 12s
meilleures lignks adaptées 3 des environnements favorables
et seulement de façon partielle pour celles adaptées à des
milieux défavorables. Cependant, la méthode AMMI paraît plus
efficace dans l’identification d’une adaptabilité spécifique et
pour un environnement spécifique.
Intmduckion
Over the last decade, CIMMYT Lowland Tropical Maizc Subprogram
has developed several productive maize (Zea YYU~~ L.) inbred lines with
good combining ability. Sources of the lines include original populations,
mbreeding tolerant populations, recycled elite lines, and recycled early
generation lines reconstituted through the forward and reverse
inbreeding procedure (FRIP). Inbred lines are evaluated for combining
ability as from the ç3 or SA sta,ge and are also tested per se in line
evaluation trials (LETs) across many locations in collaboration with
national programs in developing countries. Yicld data bave been used to
examine many approaches to the analysis of stability.
Of the numerous statistical techniques developed to analyse thc
interaction of genotypes with environments (G x E), the regression
analysis has been extensively uscd. This was first introduced by Mooers
(1921) and was given prominence by Yates and Co&ran (1938) who used
the mean performance of ail genotypes grown in an environment as a
suitable index of productivity of the envirorunent. The performance of
i
each genotype was plotted against this index for each environment, and
simple rcgression was fitted by least squares to sumtnarise the
genotype’s response.
t,.. ’
Finlay and Wlkinson (1963) used the regression trt’chni~llle to exantiw
the yield stability of various bar+; (Hordeurn vrtZgare L.) gcnotypes. TheJ.
considered regression slopes anti overall yield level of genotypes as
important stability criteria.
Rberhart and Russe1 (1966) also used a linear regression approach to
determine yield stability in maize. Lu addition to the regression slopes (b-
values) and mean yield, thcy considered deviations from the regression
line as another important component of varietal stability. A variety is
considered stable when ils b-value is close to 1.0 with a minimum sum of
squared deviations. Varieties witln b-values significantly different from
unity are not stable; thovc with high b-values are considcred to be
responsive to high-yield environuents and vice versa for those with low
b-values.
Multivariate methods 1,JL < ;:,c :,.:Gi\\ u~t.d ir, ~n;!y~ing stability in plant
breeding. Crossa et al. (1988a) applied thc principal coordinate analysis,
proposed by Wcscott (1%7), to determiue varietal stability in two
international triais (EVT 12 ‘ind EVT 13) evaluated over 1979 - 1983. The
results showcd that four <lnd threc stable varielies had been dcrived
from CIMML’T Popul,l tien 22 ad Population 43., respectively. Also
116
i
cleven selectîons derived from Population 28 showed good levels of
stability in bath ktigh and low yiclding c?n\\iir(\\lllllcnts. Crossa ef a/. (1990)
also usetl thc Additive Main Effect and Multiplicative Interactioll
(AMMI) metho& with additive effect for genotypes and environulents
and the u:ultiplm~tEve tcrms for genotype x environment interaction, for
analysing data Ii-om international maize cultivar tri&. Resul’ts showed
that AMMI inxcascd the precision of yicld estimates I:O a level
quivalent 10 inmasing thc number of replicalions by a factor of 2.6.
Considerable confmion hns arisen from the fact that the V~~OUS methods
of stability analysis havc engendered many differmt mcasures of
slability. Son~? cf the studics reported in thc literature showed that
diffcrent nmsur,es; of stahility arc similar but no1 idcntical in c%ssifying
lcsl gt~nolypcs Jtï;id/or cnvironments. In sotnc othcr (‘ases; thc test
~;t’notylx?s and Ç17~vironments <lrc classifier1 differcntly by tliP diffc~rcnt
slability Ill~lilSllWS.
.
compare thc rc!sults of three niethods of asscst;ing yicld s!ùbility in
an attcmpt tc i:&ntify widc stability of performance as well as pod
mean performance;
?
quantif,y thc 1 xobability of successful seicction of a genotype when
using AMMI pdictive values, comparcd with the probability of
selcction baa.d on thr predictive values of regrcssion techniques
and/ OI trcatuia?nt ~ncans.
Materials and ~~w~bods
was analysed for onc whitt? and one
(LETs) testcd at ten loc,ations in 199-l.
a at comtx locations, data for 9 and 8 lnc‘ations wer~l
white (LETW940-2) and tht‘ ~cllow
perfOrn~al~~~
Of fie genotype is tvtter tlta tt tlte mean performance Of dl
gcnotypes evaluated.
The A~$MI analysis. AMMI was pcrforntcd using MATMODEL (Gauch,
19s7; Crossa (1990). This mode1 first fils addit:iv+> effects for genotypes
((;) and environments (E) by d:.e usual addilive analysis of variancc
procedure, Thereafter, it fils multiplicative effects for geitotypc-
env~onment (G x E) interaction by principal components analysis @‘CA).
The 1inea.r regression approach. Environments were subdivided,
accord@ to AMMI method, into two major groups: tltose with positive
G x E interaction and those that had negative G x E interaction. Thc
sbability Itarameters proposed by Eht+art and Russell1 (‘1965) wcre thon
c6tlculated for each line in eaclt group. Lines that had across location
iilectrt yicld qua1 to or larecr Iltan il?? $t.dItcl ~illt?dll Wt’W sclected.
Geitotypes were then classified b,ts~d on thcir ref,rcssion coc~fficients.
Results
Whitc lines. For the white inbred lino tri,Js, ,AkIIMI analysis sltowed tltat
environments, genotypes, and G x E inhraction were highly significant
(P < 0.001) and accounted for 46, 24, and 30% of the trcatment sum of
syuares respectively (Table 1). In 11rc~ biplol. (Fig.1 ) t’tc principal
componont axis 1 (PCAl) geItotypes (crl;iirolr~nenls) that alrpear ahnos!
on a pcqtendicular Iine ltave sintil~ mteraction patterm.. Genotypes
(cnvironments) with large positive or itc@ive PCAl scores bave large
interacUons whereas gcnotypes (cnvin\\!-fil~~l:ts)
\\-vit11 PC:AI scores clow
to WY !?avc smala interactions. Croct.: rf 2. (70X!) pnin:ed out tha:
~;woLY~~?s aud environments with PC.41 scorcls oI Ihe same jiglt producc
positive interaction effects, whereas coiubiitatiort of PC41 scores witlt
opyosite signs have negative speçific iittcractions
Table 1. Additive main effects ;md multiplicative interaction aualysis of
variante for grain yield (kg ha 10*) of 119 white inbred lines of ma&,
including the first two interaction principal component axes (PC41 and
PCA2).
-.
--.-- .--_ I - -___---__- I_~
hm-e of variation
df
5:l~~~s f:f squares (x 106)
h1rw-t squarc3
---1 ___ --j-_
YZlt combinations
1070
1262.-M
1.17
-
Genotype (G)
118
3OO:~i
7 7.4**
-.-
hvironnwnt (E)
8
;79.iL?
72.w*
G x El
91;
x!.9-1
o.w*
interaction PCAl
122
12;’ 2-l
: Il’**
i
interaction PCA2
123
77.1-I
0.62**
_
Rcsidual
696
1721.77
@.30
-.ll---..---.-_-
** Pa.001
/
l
Figl: Biplot ofthe yield means andthe
k principal
componentaxis olthe
119whiie lines - 9 locations
100 -
_._... --_-- --
euA
50 i
l
2409
2 9 0 0
3400
3900
Table 2. Mean gr;h yield (kg/ha) of the top 20 white inbred lines adapted to
favorable env: rotments
/
- __-
-
01 / l?all
Entrics na
II .t?;ln
Mean yicI&
Guakmala
Salvador
1
_-__
- -
1
t
?iY.Lii
3668.4
5967.1
2181.3
POL%~~$
-
-1023.1
Oîïi.ii
319fi 9
3699.6
422'7.8
5631.1
3134.0
3912.3
4277.1
ÇPo4.0
3815.6
3211.7
3271.5
5532.4
3714.4
3567.6
5123.1
6517.0
5155.8
389h.s
4703.9
6632.9
3734.6
3738.2
3669.3
4715.2
2310.7
3982.1
4306.9
5776.2
3352.0
3792.6
2899.'1
4257.3
1872.6
2567.A
41w ti
53X7.1
2961.8
4316.8
3898.2
-La.8
3617.9
3746.Q
3010 Y
3816.5
230x.9
2707.4
3883.4
43hs.4
3570.7
371.4 (‘
37,%.X
4x00.3
3210.4
33-13.h
2937.8
3572.5
229-M
z46.2
3734.1
5601.9
3781.A
7x10 (;
.idS. 2
48î7.2
3121.0
2"4m-1
-i301.3
ÇhlÇ.7
3329.1
??fj(.J.!~
.
119
: Grolcp 3 consists Of genotypes with high positive interaction. These are
welI adapted to favorable environments such as Guatemela, Salvador
and Poza Rica 1 (PORl). Table 2 gives the mean yield of the top 20 wkte
bes adapted to favorable environments. The overall mcan yield varied
korn 17’86 kg/ha for line 92 to 3625 kg/ha for line 20 whereas the mean
yield ovcr favorable environments varied from 2899 kg/ha for l.ine 33 to
5123 kg/ha for line 20. Only lines 28, 33, 53, 92 ad 99 had overd ~QÜLI
yield lower than the grand mean (2230 kg/ha). These lines were
predominanlly derîved from Population 21 and from rec.ycled lines.,
Grotip 2 includes genotypes and ~environments with near-zero interaction
(Table 3). Included in this group were the more stable lines and they
performed well at the Honduras site. Chly five of them had mean yiel&
Iarger than the grand mean. About 25% of the lincs were seiections frcw~
Popula tien 21.
Grou)t 3 consists of genotypes and environments with higher negativt:
interactions (Table 4). They are adapted to unfavorable cuviromnents
like Costa Rica, Nicaragua, ThaGsnd, Colombia and Poza l&:a 2 (POR2 ),
The AMMI 2 mode1 captured 86% of the treatment combination sum of
squares. PCAl and PCA2 explained 33.2 and 20.1% of the G x E
interaction, respectively.
Table 3. Mean grain yield (kg/ha) of the 20 most .stabk white inbred lines in
Honduras.
----
Entries no
Overall mear.
Honduras
-
-
2
2190.0
2272.b
15
2493.0
22j(j. 7
18
2077.3
2304.4
26
2163.3
1811.2
40
1661.5
1054.7
47
2482.6
2704.3
6.3
1793.8
1913.9
68
1923.7
2101.6
70
1972.4
976.4
72
2069.3
1752.7
70
2266.3
X75.3
7’4
2236.1
2142.7
K-1
2303.9
2385.1)
89
1519.9
1988.2
92
1932.7
960.2
9h
1968.1
:207s. 1
701
2130.7
7113
.-
7
_L.
103
1995.1
^2b3.7
11:)
1852.4
1729.4
116
1971.9
7 ?90.,7
-
-
-
-
-
ain :yieid (kgha) of the 20 white lines adapted to unfavorable
1068.8
22641.9
4 3
1949.:!
1859.6
1746.2
1851 1
533.0
2630.5
2507.3
44
1677.17
15X1.9
1942.1
573,‘s
1699.2
934.8
2554.6
4 6
2372.‘,
2176.6
2862.2
312.5
2052.4
2712.9
29X.9
4 8
16lh:l
15q;. 9
2220.9
419.:)
2153.8
942.3
2247.7
5 8
2335.1
2-4-45.9
2267.4
639.5
3065.1
2066.3
-1171.3
60
1369. $
1232.5
1211.4
558.0
314.7
1532.9
2545.5
64
1629.5
1461.5
1469.2
424.0
627.0
1527.5
3259.7
80
175-l. 3
1 i;CX~.-i
13HO.6
1104.3
1737.1
1494.1
X70.5
8 2
19YZ. 3
i 33s
2323.1
131.4
ix-i.7
1572.5
311: -
--L, .3
8 3
19 10. 3
1 !:;,$j, 0
21196.1
455.0
860.0
2160.8
2833.2
8 3
2071,~
7O?p;
2ml.6
1722,;
1x1.3
17O-i.9
3343.0
87
960 : I
I:l2 1 3
1.187.3
D52. ~?S
39i.l
1172.3
lG98.5
P S
7 660. 3
1 3s 1 8
‘7311 --. . . . 267.1
1933.4
1233.3
-J7J?
i-.
-. j
105
204-I. 1
I:)ls.!
2314.1
I.W.?
i ihS.9
216.7
37lh.l.
107
1 Y97.2
I E 15,s
2bH.9
I~Wf?~
12.523
1278
- ?
.-
2137. 3
111
117id
1 1 7.1."'
17.43.4
100“.,
0.1)
827.4
3?91.?
113
3010.3
2;Kw,o
3 806.3
1029.3
736.8
32-I-1.5
3332.7
115
327b?
.?h:lS,G
1 W.8
1417.4
x79.4
5535.3
5462.6
119
1741 .jK
290(‘~:4
i 001.3
425.1
3966.7
5498.7
3010.1
Rcpblic and Poza Rica1 ~(PORI). The mean yielti ovt?r these
e~lviron~~~e& varied ~~OUI 2773 kg/ha for line 97 to 5777 kg/ha for L[>e
12. Thcsc lines wcre derived mainly from Population 24 (46X) and
population 36. 0111~ lincs 24, 79 nnd 97 yieldcd helow thc grand mean.
~,&le 6. Mean grain yield (kgha) of the top 20 yellow lines adayted to
favorable environments.
-E~S Overa~~ mcan
Mcan
G u a t e m a l a Rep. Don~. Pozii Rica 1
11°
y icldl
- - - - Y - -
3538.8
5039.i
4239.8
6435.0
4444.3
9
3712.8
4802.4
4826.8
5233.1 4345.2
12
4074.3
5774.4
5698.5
6424.1 5209.6
!4
2434.6
303-4.8
1995.5
4069.
?
Lws.9
19
2427.7
3181.6
2522.5
3886.2 3136.2
24
2133.5
2830.5
2248.4
3622.!) 2391.2
33
2622.9
34hfi.c)
1888.8
3878
s
4033.2
-41
2390.1
3374.9
3104.3
4097.fl
2027.7
4-4
4024.5
5438.5
4515.7
6073.7
573i.l
46
2280.4
3236.0
2870.7
3730.n
31Ob.G
47
3703.5
3445.5
2672.1
4292.0 3371.4
48
2398.5
3436.7
3383.7
3921.7
3W4.6
:,-JL,
2283.3
3130.9
2308.7
4627.8 2456.1
(12
3874.3
5067.1
4178.3
6401.4 4561.6
M!l
2752.1
3737.5
3850.3
3407.b 3954.6
77
2517.0
3x4.7
3156.4
4057.9 3299.7
78
2559.2
3440.5
3322.4
4470.7
2538.5
79
2080.0
2925.3
2156.0
4150.2
2469.7
92
2745.4
3607.6
2047.3
5569.2
320ii.2
97
2003.5
2773.4
1880.1
3384.7 3055.3
- -
-
‘Mean ucross thr thrrc sclected sites in the goup.
i;ror~p ;! ti~iudeti thc yellow lines with near-zero inter‘titim. The mm
yield rcspnnsr varicd froc 1644 kg/ha for line 83 tu 3011 I;g/h~ for line
3 (Table 7). AL Poza Rica 2, 50% of these lines had an ovcr~ll IIUWII yicld
bolow the grand mean (2252 kg,‘hti)
Gmrp ;3 consists of 20 yellow lines adapted to unfavor~~hlt~ sites likc
Cuba, Thaïland and Colfnnbia (Table 8). The mean yicld rt+p~nçc over
thcsc? locations varied from 1160 kg/ha for line 86 to 2211 kg/ha for Iinc
112.
122
For the yellow lines 1111~ two groups were identified (Fig. 2). Group 1
included Cuba, Tha nd and Pananm’While Group 2 had Guatemala,
Poza Rical, Po2a Rit 2, Colombia and Dominic Republic.
Table 7. Mean gra.
pield (kg/ha) of 20 stable yellow lines at Poza Rica 2
_-I
Entrie?
Overall nwan
Poza Rica 2
- -
5
-
3021.6
4307.1
7
2829.7
3960.4
13
2321.1
3269.8
26
2219.7
3073.5
28'
1989.7
2926.8
29
2482.4
2707.2
31
2061.7
4297.1
34
2508.3
4598.9
3b
2117.7
3610.1
36;
24d8.8
3690.4
4:’
2430.2
4165.8
50
2185.9
3220.4
51
1928.5
2653.6
6s:
1796.7
3409.0
74,
2586.9
3179.2
76
1879.8
2059.7
83
16G.8
2393.5
85
1955.7
2708.7
95
1822.7
2448.1
1011
2018.4
2367.0
. - -
-
-
Table 8. Mean grail yield (kgha) of 20 ycllow inbred lines adapted to
unfavorable envh xinents
Entry Owrall
no
mm7
2 0
2143.7
21
1596.5
1609.1
1237.3
58-i.2
2050.3
2564.4
27 :
428.6
1398.0
1372.9
621.C
1024.2
1773.9
35
775.3
1410.4
3481.6
523.ci
1313.8
2323.2
52
574.7
1440.8
1675.7
206.1
1660.1
2221.4
53
528.8
1379.9
1896.1
783.11
1308.3
1531.6
56
647.5
1.554.x
1‘454.0
779.1
2167.4
1818.7
60
914.7
1601.8
1558.8
788.6
1799.9
2259.9
69
518.8
1332.9
1493.5
58-4.h
43-l.Q
2818.6
81
16t?O. 5
3713.5
1-M. 1
413..\\
2ow.;
2865.9
84
2222.2
~803.7
16X1.3
544.:
2872.1
2116.9
86
16X1
1160.0
1223.1
601. fi
1399.1
1416.4
88
2445.5
?!039.2
1657.1
7',9...*
2105.0
3595.4
96
18Z5.6
1.681.7
1638.2
201. f)
2177.7
2709.4
100
1751.1
1.524.2
1891.7
338.1
1317.2
2549.9
110
1932.4
T.538.0
1502.6 5P9.ci L
1357.3
2702.7
111
1992.6
1.898.5
18821.2
90-1.1
2493.3
2312.3
112
2487.9
2211.8
2015.2
488.0
‘123-4.0
5109.9
113
19i.8.9
I649.3
1066.5
3X9.6
2419.3
2721.9
114
2005.6
1~678.8
1924.9
0.0
1765.1
3025.0
----~
‘Mean across the four GTKII sites in tho goup
123
Fig.2 : B~~plot of tha yleld means and the
fkst principal component axis of the
119 yellow linas - 8 locations
FoT both whitc and yeUow line trials, environu~ental effect dominated
the analysis. The G x E interaction SUI\\ of squares was about 1.4 times
larger than thc genotype sum of squares. The importance, of thc
environmental effect is illustrated by partitioning the locations as shown
in Figs. 1 and 2. Clearly, the triais involved a wide range of environments
that need to bc characterized in tems of climatic fac(ors as well as biotic
and or abiotic constraints for a biological explanation of the genotype x
environment interaction.
Regression analysis
Thc regrtssion approach makes it possible to classify genotypes, on thc
basis !jf t?tcir b-~lucs, as rmponding or adaFted to high yil:lding sites
~&PIS) or to bw yielding sites (tms). Site means for grain yield ranged
from 1076 kg/ha at Nicaragua to ?+IO2 kg/ha at Guatemala fer the white
lines. Mean grain yields of the yellow lines varied from 546 kg/ha in
Cuba to 3141 kg/ha in Poza Rica 2. According 10 the b-values, 58% of thc
white lines and 49% of the yellow .ines had slopes larger than 1.0 in high
yielding sites md cannot be considcred as ideal genotypes.
For thc \\vhitc lines, 28% are idml lines (ID) with mean yield over
loc~ations ~:aryin!: h-cm 2236 to 330 kg/ha; 32% are bcst for the ltjgh
yiclding sites (I-IYS) with across-Ior.dticln mcan yicld ranging from 2236
to 3442 kg/ha. The remaining 40 Y1 ‘ire best for low yielding sites (LYS);
across-loz;itiorl IIIC~II yield vdriod 11.om 2212 to 440s kg/ha.
224
Although white lines
114 and 25, and yellow linos 3,13,15,23,33,34,
and 39 were clssifiel
no high-yield envioumeuts, we do not Comider
them as ideal gcnot
es in spite of their high across locations mean
yield . This indica tes
:at. good avcrage performance does not sigùfy
good adaptability an
cice-versa.
Furthermore, 30% o
II~ white lines are selcctions from Population 21
and 22% came from
iyçled lines; 24% of the ycllow fines were derived
from Population 24,
IV, were from recycled lincs and 18.5% from Sint-
Amarillo TSR.
Figures 3 and 4 1
vide the relationship of ~cnotypc adaptation
(regression coefficiel
and genotype mean yield for thc white and the
ycllow Lues, reqect
ly. Using thc gcneralisecl intcqm?tation of G x E
analysis as reported
Finlay and Wilkinson (1963L cach group of lines
ma y be classified as
~11 in Table 9. Thc proportion of lines that werc
adaptcd to the high
‘avorable cnvironmc~~~ts ~.V,IS grciitcr than 50% in
each go-OU~. Similat
t17c pcrccntngc of cnvirc~ntitcnts in Which the
pcrfomance of mach
notype was better thm thc mean performance of
a11 genolypes varied
ND -24 to 100% and 38 tc lOi)X for the white and
thc yellow lines, req
tively.
Table 9. PercenMge i
ranges of grain yield (kg/ha) of lines specifically
adapted to high
favorable (b>l.O), a11 (b=l.O), and unfavorable
(b4.0) environme
- - -
-_--
_--.--
IV,
AIl env.
Unfavoral-rle env.
(b=l.O)
(lsl.0)
_ _ _ _ - _-_---~.-
_-.----
C;roup
x
Yielc
-
-
w
Y0
Yield
rmp
%
Yield range -
_ _ .-.._..-
- Whitc
5 2
2 2 3 6
7 7
24
2 2 3 2 - 3 6 2 5
2-1 2 2 3 6 4 4 0 8
Ycllow 6 5
2 2 8 0
77
2 7
2 2 3 3 - 2 9 9 7
X 7 2 9 9 - 2 8 2 7
--.-----~ _-.-...
-.... _.----.--
Fi& Biplot of the mean yield snd the coefficients
regrenion bi for fhe lt9wbiC lines RWOW 9 locntionr
125
Discussion
G x E interactions linlit thc accur&:y of yit>ld estiu~;lt.es ami complicate
the identification genotypcs for gencral adaptation 10 a large munber of
environmcnts. Maizc brcedcrs a~-c thcrcforc conccrned about t h e
accuracy with which C x E is quml.ified. The mcthods evalualed in our
study yielded similar but net identical rcsults.
Resulls of AMMI analysis rjf triaI,- invol~+ng bath whitc ar,d yellow
endospcrm lines allowcd thc Grouping o
f
genotypcs and/or
ènvironments bascd on their interactions. The first two principal
components accountcd for 51.3 nnd 56.9% of the interaction sums of
CCpiWS for Ihe Fcklitt- cliId iht ),,>!Ia ~ti li:3?3, ; ~3p:fi~:~,~lJi.
Environmental effects dominnterl the per~omance of the lines in this
study thus highlighting tho import+lcc of location variability as a
principal factor in the tria1 network. 11 is thereforc necessary to find a
good approach to sclect homogeneous locations for international trials.
AM?I method could bc used for th:is purlxm~. The principlc underlying
this approach would be to decide which locations, rather than how
ntany, are cssentinl to ~lcarl\\~ rc\\:c<ll thc ::! xx-turc of G x 1: interaction
truly prcscnl anto:lg thc s.!:~iplc c)f ~!WS r~i:.l c~nvironmcnls in~;olvecl in
the triaLs.
study, it seems that genotypes with b< 1.0 usually
over locations below the grand mean. Eberhart and
:;ed that in situations where there are no surplus
,can be stored, or where long-term stqrage is not
ieties may be the most desirable. For the developed
er, the breeder usually wants varieties that produce
in ali environments. Hence, he desires varieties with
unit regression coefficient (b = 1) and small (near
Analysis other than regression is
n overall picture of how stability and mean yield are
to be traded off.
$MI analysis agreed well with the modified regression
“mg the best white (ahout 80%) and yellow lines (about
favorable environments, and only partial@ for those
d to poor environments. However, the AMMI mcthod
t in detecting adaptability to specific environments. As
sa et aI. (1990), in plant breeding, the appropriate gain
eved with AMMJ provides a tool for selecting better
therefore achieving higher realized progress from
gested the need for research
AMMI mode1 for analysing
In the method:; lx-oposcd by Finlay and Wilkinson (1963) and St-Pierre ef
al. (196;‘), tht! /.average yield asross a11 gcnotypcs in an environment is
used as an ;lsu;essmelG
i
of that environment etcept that the latter
approach is e:l:lxxssed in termi of percentage. St-Pierre ef al.‘s approach
agrees with f/hte modifïed regression method only in dctecting high
yielding geno y1x.s (overall mean yieid superior i!* L;I to pnd iil?xl) ??ut
does net prc’wide the keys for distributing gc?notypes inlo type:; of
apptability. 1
Conclu.sion
127
.fie aueors are grateful to thc numrous collaborators in national maiz(-,
research programs that cxricd out the linc! evaluation tr*al.s (LETs)
presented in this payer.
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Multiplicative Interaction Analysis 0T t w o lnlerm tioml Maizcl
Cultivar Tri&. Cmp Sci. 30: 493 - 500.
crossa, J., 1988. A con~parix~n of rcsults obtained l,viih twc, ~ycthods for
asscssing yield st&ility. 771evr: Appl. Genet. 75: -kO- 467.
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d’analyse des interactions gi’notypc 1 - milieu. Agronomie 2(3): 219 -
230.
Eberhart, S . A . , and W.A. Ruswll, 1 9 6 6 . Stability prmwters lor
compasing varieties. Crop Sca. 6(l): 36- 40.
Fiday, KW., and G.N. Wilkilxon, 1963. The analysis of adaptation in a
plant breeding programme. Arts. /. Apic. Res., 31: 742-754.
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Hugh, G., and H.G. Gauch, Jr., 19X8. Modo1 selcction and Vahdation for
yicld Triais with Inlt?rxtion. Riometrics 44: 705 - 715.
Lin, C.S., and G. Butlcr, 19%. .A data-base approach for selecting
locations for regional triills. (-/~II. I. PZlzrrt. Sci. 68: 651- 659.
Saint-Pierre, C.A., H.R. Klini,k, dnd F.M. Gauthier, 1967. Early generation
selection under different c>nvironnrents as it influences eidaptation of
barley. CRII. j. ofPlnrrt Scierrce 47: 507- 517,
sinuons, N.W., 1991. Selcciion for local addptation in a plan!. breeding
progr~nune. 7’lzeor. A{qll. Gar&. 82: 363-367.
bd, S.K., and S. hklcm (rd~), l99-4. 77le i.ozdmd Tmpid h-lnize
f'rogrnrn Specinl Rcporf. bit>\\ ic o, D. F., ClMhfYT.
Westcott, B., 1986. Son~ m~:h& ior analysing ~:~~~otypC-.C~l~~ir~~~u~îC”t
interaction. Heredifj 56: 233-233.
Witcmhe, J.R., 1988. Estiwtt>l;
i-If sLibilily for c-ompmn~~ varieties.
&dyticn 39: 11-1s