
African Crop Science Journal
African Crop Science Society
ISSN: 10219730
Vol. 11, Num. 2, 2003, pp. 6573

African Crop Science Journal, Vol. 11. No. 2, 2003, pp. 6573
YIELD STABILITY OF SORGHUM HYBRIDS AND PARENTAL LINES
R. Kenga, S. O. Alabi^{1} andGupta^{2 }
Institute of Agronomic Research (IRAD) P. O. Box 33 Maroua, Cameroon
^{1}Department of Plant Science IAR/Ahmadu Bello University, Zaria, Nigeria
^{2}ICRISAT, NASC complex, Pusa, New Delhi 110 012, India
(Received 26 November, 2001; accepted 31 March, 2003)
Code Number: cs03009
ABSTRACT
Seventyfive sorghum hybrids and twenty parental lines were evaluated for two
consecutive years at two locations. Our objective was to compare relative stability
of grain yields among hybrids and parental lines. Mean grain yields and stability
analysis of variance, which included linear regression coefficient (bi) and
deviation from regression (S^{2}d) were used to determine relative
stability. Genotypes x environment interactions were significant. Significant
hybrids x environment interactions were also detected. Hybrids and parental
lines had significantly different regression coefficients, as indicated by
hybridenvironment (linear) mean squares. Hybrids showed significantly higher
mean yield compared with parental lines and the yield advantage generally increased
with increasing environmental yield potential. Hybrids bi values were significantly higher (0.02  2.14) than for parental line (0.82  1.52). Deviations from regression for hybrids were higher than those of parental line. Crosses between hybrids ICSA 38 x Damougari, and ICSA 39 x Damougari produced the highest grain yields. Their bi
values were not significantly different from unity, but S^{2}d estimates
were significantly greater than zero. Thirteen hybrids recorded bi values
close to unity, small S^{2}d and grain yields higher than the mean
of all the hybrids. Based on our findings it is apparent that in the dry land agriculture of west Africa, selection of hybrids for superior yields across
environments should be emphasized first, and then the relative stability of
these hybrids over environment should be determined.
Key Words: Genotype x environment interaction, regression coefficeints, sorghum bicolor, West Africa
RÉSUMÉ
Soixante quinze hybrides du sorgho et vingt lignées parentales ont été évaluées pendant deux années dans deux localités formant ainsi quatre environnements. L'objectif était de comparer la stabilité des hybrides et des lignées parentales. La moyennes des rendements grain et l'analyse de la variance de la stabilité qui comprend le coefficient de régression linaire (bi) et la déviation des moyennes des sommes de carrés
(S^{2}d) ont été utilisées comme indice de stabilité. Les interactions génotypes x environnement étaient significatif. L'interaction hybrides x environnement était également significatif. Les coefficients de régression (bi) des hybrides et des lignées parentales étaient significativement différents. Les hybrides étaient plus productif et répondirent mieux aux conditions favorables. Les coefficients de régression (bi) des hybrides (0.02  2.14) étaient significativement supérieur a ceux des lignées parentales (0.821.52). Les déviations des moyennes des sommes des carrées
(S^{2}d) des hybrides étaient plus élevées que celle des lignées parentales. Les hybrides ICSA 38 x Damougari et ICSA 39 x Damougari ont donné les meilleurs rendements. Leurs coefficients de régression étaient significativement différents de l'unité, mais les déviations
S^{2}d étaient supérieur a zéros. Il ressort de cette étude que dans les régions chaudes de l'Afrique de l'Ouest, l'accent devrait être mis d'abord a la sélection des hybrides a haut rendement et ensuite on pourra déterminer la stabilité relative des meilleurs hybrides.
Mots Clés: Interaction génotype x environnent, hybrides du sorgho, stabilité, Afrique de
l'Ouest
INTRODUCTION
Sorghum (Sorghum bicolor (L.) Moench) is a major crop of the semiarid tropics of Africa (Axtell et al.,
1999). However, with regard to its production, not only do the conditions for
the crop vary greatly between the different areas of the region but also growing
seasons differ from each other considerably. This in part explains the observed
variations in the development and growth of sorghum as well as in grain yield
attained. In the dry land agriculture of West Africa, abiotic and biotic stresses
limit potential grain yields. Local farmers are usually completely reliant
on yield stability of their rainfed crops. Even though several improved varieties
have been developed and released, the yield gains have been insignificant at
farmers' level such that the average yields are approximately 800 kg ha ^{1 }(FAO, 1997). The demand for cereals in West Africa calls for an increase in production of sorghum, one of the major cereals grown in the continent.
Developing high yielding and adaption of sorghum
hybrids is one approach to resolving cereal grain deficits. The success of
a hybrid depends as much on its stable performance over varied environments
as well as on its inherent yielding ability. The desired hybrid is one that
would be adapted to a wide range of growing conditions in a given production
area, with above average yields and below average variances across environment.
That is to say, sorghum growers need cultivars that are dependable and consistent
across a wide array of stress conditions and yet have high yield potential
that may be expressed when production conditions become more favorable. In
this respect, Allard and Bradshaw (1964) suggested that, while developing cultivars
with specific adaptation to predictable specific environments, plant breeders
should aim to produce cultivars that are adapted to withstand unpredictable
transient environmental variations. In addition, evidence for enhanced hybrid
stability would facilitate wider acceptance of sorghum hybrids by growers throughout
the region.
One of the early attempts to obtain measurement of the stability of individual
lines was made by Plaised and Peterson (1959) who estimated the variance component
of cultivars x location interaction for each of the possible pairs of cultivars
tested. The average of the estimates of all combinations using a common cultivars
was considered paramount for stability measurements. This method becomes cumbersome
when a large number of genotypes are tested. Furthermore, this model lacks
a dynamic estimate of stability and adaptability. A different model was developed
by Finlay and Wilkinson (1963). This model is based on linear regression; for
each variety a linear regression of individual yields on the mean of all varieties
for each environment is computed. The main feature of this model is the use
of average yields of all varieties to describe the environment, so that the
complexities of defining the interacting edaphic and seasonal factors are avoided.
It provides two measures of the genotypic changes to environment: the regression
coefficient (bi) and the variety mean. In the experiment upon which this model
was developed, it was found that 70% of the genotype x environment (G x E)
was attributed to linear regression. However, this model does not take into
account the nonlinear component. To address this limitation, Eberhart and
Russell (1966) developed a stability model based on computing two stability
parameters: linear regression and deviation from regression. In effect, this
model divides the genotype x environment interaction into two aspects: (i)
deviation due to the response of the variety to varying environmental indexes
(linear) and (ii) the unexplained deviations from the regression on the environmental
index (non  linear). These estimates of linear and non  linear parameters
provide an adequate account of the dynamic response of genotypes to changing
environment and are used with mean performance to assess the potentialities
of different genotypes. This approach has been extensively used by plant breeders
on various crops (Virk et al.,
1985; Becker and Leon, 1988; Gupta and Ndoye, 1991; Pettonee  saino et al.,
1993). In West Africa, however, no such studies have been conducted to establish
the stability of sorghum lines.
This study was thus, conducted with a view to compare the grain yield and
relative stability of sorghum hybrids and their parental lines in West Africa
dry land
condition. The three evaluation traits used were grain yields, regression
response to changing environments, and the stability of production estimated
as deviation
from regression.
MATERIALS AND METHODS
Parental lines and hybrids of sorghum. Five cytoplamic genetic malesterile
sorghum lines (ATX 623, ICSA 38, ICSA 39, ICSA 41 and ICSA 902 NG) were crossed on to each of 15 pollen
restorer male fertile parents to produce 75 F1 hybrids. The 15 male parents were selected from different origins and representing the types of elite varieties commonly grown in West Africa region. The checks were openpollinated released varieties and landraces from various breeding programs of the West Africa region. The male sterile lines were kafirmilo derivatives and have the same cytosterile mechanism.
Site characteristics. Trials consisted of 100 sorghums entries, including
the 75 F1ybrids, 20 parental lines, and 5 checks were conducted in four environments
made up of two years (1998 and 1999 rainy season) and two locations. The first
location was at the Institute of Agricultural Research for Development (IRAD)
research farm (Lat. 11° 30'N, Long 15° 30 'E, Alt. 300 m) at Maroua
in Cameroon. The vegetation in the area around Maroua is typical of Sudan sahelien
zone (Windmeiger and Adrienne, 1993). Mean total annual rainfall is approximately
750 mm and the length of the growing period is 110  140 days with frequent
drought. Soil at Maroua is sandy, silicious reddish colored, low in fertility
and organic matter. The second location was at ICRISAT Research farm (Lat.
11°53' N, Long. 8° 14'E,
Alt. 440 m) at Bagauda in Nigeria, with average annual rainfall of 900 mm and
the length of growing period is 140  160 days. The landscape is flat and dissected
by low to medium density of in land valleys typical of the Sudan savanna zone
on plintic luvisol with average depth of 90 cm.
Field experiments. Planting was done immediately after the first good rain (25 mm),and the planting dates are presentd in Table 1. The 100 entries were arranged in 10 x 10 triple lattice design. The experiment was replicated three times in each environment. Each plot consisted of four rows of 5 m length with a spacing of 80 cm between rows, resulting in total plot size of 16 m^{2}. All rows were thinned to a distance of 20 cm between plants at two per hill, resulting in a population of about 125 000 plants per hectare. The experiments carried out in all environments were rainfed. Standard cultural practices for optimum sorghum production were carried out. The same dose of fertiliser (60 kg N, 40 kg P2 O5 , and 30 kg K2 O) ha^{1} was applied as a basal dose in each experiment. Forty kg of nitrogen in the form of urea (100 kg ha^{1}) was topdressed five weeks after planting and then incorporated into the soil. When mature, the panicles from the two central rows, leaving the border plants of each plot were harvested, air dried, threshed and weighed to estimate grain yield.
TABLE 1. Description of environment with year wise, location wise, total rainfall in crop season, planting date and environmental mean for grain yield average over hundred genotypes grown in each environment
Environment  Year  Location  Planting date  Rainfall(mm)  Environmental mean yields (t ha^{1}) 
1  1998  Maroua  05 July  672  2.43 
2  1998  Bagauda  18 June  930  3.10 
3  1999  Maroua  12 July  805  1.54 
4  1999  Bagauda  12 June  985  3.60 
Statistical procedure. All statistical analyses were performed using the general linear model (GLM) procedures, (SAS Institute, 1989). The data were analyzed in two ways. First lattice designs were analysed separately for each environment and then a combined analysis over environments was performed. Data used for statistical analyses consisted of entry mean yields at each environment. Environments were considered as random effects in the linear model. Hybrids and parental lines were considered as random, representing the current pool of elite hybrids and varieties in the region. Stability parameters were estimated for grain yields by using the model described by Eberhart and Russell (1966). This model utilizes the deviations from the grand mean of the yield over the various environments as production indexes of the environments. It provides regression response indexes (b values) and means squares for deviations from regressions minus pooled error (S^{2}d values) as indexes of production response and stability, respectively. The performance of a variety is then defined by the equation:
Yij = µi +
b_{i} I_{j} +d_{ij }
Where Y_{ij} is the mean grain yield of the i^{th} genotype in the j^{th} environment, µi is the mean of the i^{th} genotype,
bi the coefficient which measures the regression of the i^{th} genotype on different environments (linear response predictive), dij is the deviation from regression of the genotype in the j^{th} environment, and I_{j} is the environmental index calculated as the mean of all genotype at the j^{th} environment less the grand mean over all environments.
Since the sum of I_{j} over all environments is zero, the yield of a variety in a given environment can be predicted as follows: Y_{ij} = x_{i} + b_{i}I_{j}. Where xi and bi are estimates of µ_{i} and b_{i},
respectively. The mean squares due to deviations from regression (S^{2}d)
indicate the degree of reliance that can be placed upon linear regression.
In fact, S^{2}d reveals a nonlinear response of varieties (nonpredictive).
When the deviations are significant, the genotype stability is specified
by a joint consideration of both µ and b.
The significance of means squares was tested against the pooled error.
The ttest based on the standard error of regression value was used to test
the significant deviation of b from 1.0. To determine whether deviations
from regression were significantly different from zero, the Ftest was employed
(i.e., comparing the mean squares due to deviations from regression with
pooled error mean squares). In addition, a separate analysis for hybrids
and parental lines were conducted to test for heterogeneity of the slopes
among entries of the two genotypic groups. The entries x environment (linear)
mean square estimates were tested separately for hybrids and parental lines
using the respective deviation mean squares.
RESULTS AND DISCUSSION
The environments used in this study provided a wide array of sorghum production
conditions and grain yield potentials. Rainfall in the four environments
was irregular, Rainfall during the cropping season, dates of sowing, environmental mean are presented in Table 1. Lattice
design did not show considerable advantage over randomised complete block
design. The efficiency of lattice was less than 8%. This might be due to
homogeneity of the fields used for the experiment. This suggests that randomised
complete block design may easily be employed where the experiment site is
observed to be homogenous and experiment well replicated (Duley and Moll,
1969). Bartlett's test (Steel and Torrie, 1980) failed to reject the hypothesis
that variances attributable to genotype performance across environments
were of similar magnitude.
Environment mean squares were highly significant (Table 2). The genotype
mean squares were highly significant (P < 0.01), indicating that the genotypes differed in yield performances. The mean squares due to G x E interaction effects also showed significant differences, indicating that the genotypes responded differently relative to each other to a change in environment. This permitted the partition of environment and G x E sources of variation into environment (linear), G x E (linear) interaction effects (sum of squares due to regression, bi) and unexplainable deviation from linear regression (pooled deviation mean squares, S^{2}d)
(Table 2).
TABLE 2. Pooled analysis of variance for stability of grain yield (t ha^{1}) over environments
Source of variation  Df  Means squares  
Genotypes (G)  99  3.4234202** 
Environment (Env)  3  237.7880721** 
Genotypes x Env  297  1.4091254** 
Env + (Genotype x Env)  300  3.772914 
Environments (linear)  1  713.363363** 
Genotype x Env (linear)  99  1.4996487* 
Pooled deviation from regression  200  1.350229** 
Pooled error  800  0.921216 
*, ** Significant at 5% and 1% probability levels, respectively The mean square due to environment (linear) was significant, indicating
that differences existed between environments. The G x E (linear) interaction
was significant, indicating that the stability parameter "b" estimated by linear response to change in environment was not the same for all genotypes. The nonlinear responses as measured by pooled deviations from regressions were highly significant, indicating that differences in linear response among genotypes across environments did not account for all the G x E interaction effects, and therefore, the fluctuation in performance of genotypes grown in various environments was not fully predictable. A large portion of the sum of squares of G x E effects (64.5%) was accounted for by the deviations from regression. Only 35.5% was accounted for by the linear regression on the means in different environmental situations. These results suggest that the magnitudes of G x E interaction effects in this set of materials are largely due to differential nonlinear responses of genotypes to varying environment; thus S^{2}d
parameters become important. These results are in agreement with earlier
findings by Eberhart and Russell (1966), Eagles et al., (1977) and
Witcombe (1988). The grain yields of hybrids ranged from 1789 kg ha^{1} to 4189 kg ha^{1} with an average of 2823 kg ha^{1}.
The mean grain yields of parental lines ranged from 1516 kg ha^{1} to 3284 kg ha^{1}.
The best check yielded 2647 kg ha^{1} (Table 3)
TABLE 3. Mean grain yields (t ha^{1}), regression response indexes (b) and deviation from regression (S^{2}d) for sorghum hybrids, parental lines and checks
Genotypes 
Mean grain yields 
b  SE(b)^{1}  S^{2}d 

Hybrids 
ATX 623 
x NR 711761  3.142  1.29  ±0.36  0.02 
x NR 711762  3.293  0.98  ±0.16  0.82 
x NR 711822  2.553  0.68  ±0.40  0.22 
x NR 711823  2.922  1.42  ±0.41  0.35 
x NR 711681  3.164  1.06  ±0.25  0.52 
x NR 711683  2.042  0.72  ±0.36  0.01 
x KSV 41  2.955  1.50  ±0.36  0.03 
x KSV 42  3.042  1.38  ±0.33  0.16 
x S 35  2.308  0.74  ±0.41  0.31 
x CS 54  3.253  1.22  ±0.37  0.04 
x CS 61  2.865  1.26  ±0.35  0.05 
x CS 95  2.871  1.20  ±0.24  0.53 
x CS 141  2.852  1.06  ±0.30  0.31 
x CS 144  2.899  0.81  0.45  0.58 
x Damougari  3.924  1.2  ±0.39  0.17 
ICSA 38 
x NR 711761  2.477  0.74  ±0.34  0.07 
x NR 711762  3.216  0.77  ±0.34  0.13 
x NR 711822  2.765  0.02*  ±0.36  0.03 
x NR 711823  3.422  1.17  ±0.24  0.56 
x NR 711681  2.510  0.48  ±0.34  0.09 
x NR 711683  2.660  0.68  ±0.41  0.37 
x KSV 41  2.834  1.19  ±0.29  0.36 
x KSV 42  3.204  2.14*  ±0.33  0.16 
x S 35  2.434  1.08  ±0.45  0.56 
x CS 54  3.196  1.28  ±0.42  0.40 
x CS 61  2.893  1.57  ±0.38  0.15 
x CS 95  2.131  0.52  ±0.29  0.33 
x CS 141  1.840  0.38*  ±0.15  0.85 
x CS 144  1.875  0.59  ±0.37  0.05 
x Damougari  4.189  1.18  ±0.51  1.06* 

ICSA 39   
x NR 711761  2.297  0.35*  ±0.20  0.70 
x NR 711762  2.859  0.59  ±0.37  0.02 
x NR 711822  2.479  0.55  ±0.51  1.05* 
x NR 711823  2.671  0.47  ±0.51  1.07** 
x NR 711681  2.531  0.38*  ±0.29  0.37 
x NR 711683  2.535  0.26**  ±0.20  0.71 
x KSV 41  2.728  1.96*  ±0.47  0.70 
x KSV 42  2.456  1.33  ±0.32  0.22  
x S 35  2.706  0.84  ±0.37  0.05 
x CS 54  2.980  1.45  ±0.32  0.23 
x CS 61  2.650  0.81  ±0.27  0.44 
x CS 95  2.723  0.49  ±0.35  0.07 
x CS 141  2.722  0.94  ±0.42  0.35 
x CS 144  1.789  0.28  ±0.39  0.19 
x Damougari  4.175  0.94  ±0.57  1.52** 
ICSA 41 
x NR 711761  2.459  1.24  ±0.24  0.58  
x NR 711762  3.003  0.43*  ±0.26  0.49 
x NR 711822  2.633  0.95  ±0.27  0.44 
x NR 711823  2.651  0.46  ±0.32  0.20 
x NR 711681  2.483  0.36  ±0.35  0.07 
x NR 711683  2.768  1.02  ±0.33  0.17 
x KSV 41  2.525  1.39  ±0.32  0.23 
x KSV 42  2.713  1.38  ±0.31  0.28 
x S 35  3.046  1.08  ±0.43  0.47 
x CS 54  2.998  1.16  ±0.41  0.30 
x CS 61  2.633  1.10  ±0.37  0.09 
x CS 95  2.425  0.88  ±0.34  0.11 
CS 141  2.974  1.17  ±0.47  0.72 
x CS 144  3.007  1.50  ±0.41  0.30 
x Damougari  3.104  0.67  ±0.50  1.02** 
Genotypes  Mean grain yields  b  SE(b)1  S2d  
ICSA 902 
x NR 711761  3.058  1.67*  ±0.29  0.33  
x NR 711762  3.318  1.48  ±0.40  0.26 
x NR 711822  2.504  1.07  ±0.42  0.35 
x NR 711823  2.977  1.00  ±0.25  0.51 
x NR 711681  2.751  1.31  ±0.44  0.71 
x NR 711683  2.765  0.79  ±0.45  0.57 
x KSV 41  3.045  1.55*  ±0.29  1.02  
x KSV 42  3.546  1.65*  ±0.34  0.09 
x S 35  2.617  0.75  ±0.35  0.04 
x CS 54  2.963  1.41  ±0.37  0.05 
x CS 61  2.649  0.81  ±0.39  0.19 
x CS 95  2.793  1.34  ±0.54  1.34* 
x CS 141  2.284  1.35  ±0.33  0.16 
x CS 144  3.087  1.12  ±0.51  1.08* 
x Damougari  3.964  1.44  ±0.34  0.12 
Parental lines 
NR 711761  1.635  0.46*  ±0.29  0.16 
NR 711762  1.608  0.30**  ±0.32  0.08 
NR 711822  1.708  0.52**  ±0.27  0.22 
NR 711823  1.516  0.50**  ±0.30  0.13 
NR 711681  1.702  0.31*  ±0.36  0.07 
NR 711683  1.543  0.92  ±0.35  0.01 
KSV 41  1.869  1.21  ±0.28  0.20 
KSV 42  2.100  1.74**  ±0.16  0.46 
S 35  2.266  1.09  ±0.27  0.22 
CS 54  1.735  1.32  ±0.32  0.09 
CS 61  1.837  1.37  ±0.29  0.16 
CS 95  2.450  1.08  ±0.40  0.23 
CS 141  2.275  1.02  ±0.43  0.35 
CS 144  2.483  0.87  ±0.54  0.90** 
Damougari  2.901  1.88  ±0.50  0.65* 
BTX 623  3.284  0.84  ±0.36  0.06 
ICSB 38  2.890  0.94  ±0.35  0.04 
ICSB 39  2.386  1.29  ±0.51  0.70* 
ICSB 41  2.479  1.66  ±0.41  0.27 
ICSB 902 NG  2.373  0.66  ±0.44  0.37 
Checks 
Zouaye  2.409  0.27*  ±0.29  0.04 
CS 210  2.646  1.08  ±0.18  0.44 
CS 154  2.335  0.97  ±0.27  0.06 
CS 133  2.647  1.07  ±0.36  0.43 
Djigari  2.048  1.61  ±0.30  0.06 
Mean  2.669 
SE”  0.257 
LSD at 5%  0.714 
CV%  33.37 
*, ** b values significantly different from unity at 5% and 1% level, and S^{2}d
significantly different from zero at 5% and 1% levels, respectively
^{1}SE (b) = Standard error of b
Large disparity in regression coefficients occurred between hybrids and
parental lines. The estimates of regression coefficient (b), the mean squares
due to deviation from regression (S^{2}d) and the mean grain yield
are presented in Table 3. On the average, hybrids consistently had larger
b values, which ranged from 0.01 to 2.14 and deviations from regression
(S^{2}d), which ranged from  0.82 to 1.52, while the regression
coefficient for parental lines ranged from 0.30 to 1.88 and the deviation
from regression ranged from 0.22 to 0.90. Even though parental lines showed
slightly lower S^{2}d compared to hybrids, there was no evidence
that parental lines provided an additional component of yield stability
in terms of reduced deviation from regression; the mean grain yield was
very low. However, parents such as ICSB 902 NG, ICSB 38, ICSB 41, S 35,
and CS 141 were more stable and could be useful in hybrid breeding programs.
The hybrids ICSA 38 x Damougari and ICSA 39 x Damougari produced the highest
grain yields of 4189 kg ha^{1} and 4175 kg ha^{1},
respectively and were significantly superior to the best check. However, their mean squares due to deviation from regression (S^{2}d)
were significantly greater than zero. Thirteen hybrids recorded significantly
higher yield than the mean of all the hybrids. These hybrids were: ICSA
902 x Damougari, ICSA 902 x KSV41, ICSA 902 x NR 711762, ICSA 41 x CS
144, ICSA 41 x S 35, ICSA 38 x NR 711823, ICSA 38 x NR 711762, ATX 623
x Damougari, ATX 623 x CS 54, ATX 623 x KSV 42, ATX 623 x NR 711681, ATX
623 x KSV42 and ATX 623 x NR 711762. All these thirteen hybrids combined high yield with bi were not significantly different from unity and had S^{2}d
values that were not significantly different from zero. That is, although
the sorghum hybrids differed in yield stability across changing environments,
high yielding potential and stability were not mutually exclusive. These results are in agreement with previous findings of Heinrich et al.
(1983). Deviation mean squares were significant for only seven hybrids (Table
3). This suggests general adaptability of most of the high yielding hybrids.
On the other hand, eleven hybrids had linear regression values (bi) significantly
different from unity. Of these, ICSA 902 x NR 711761, ICSA 902 x KSV 42, ICSA 902 x KSV41, ICSA38 x KSV42 and ICSA 39 x KSV42 had above average linear response (b>1) and above average yields, indicating the ability of these hybrids to respond to more favourable growing condition. Six hybrids had regression coefficients significantly less than unity and nonsignificant deviatio from regression, indicating its suitability under less favourable environmental condition.
A study of genotype x environment interaction can lead to a successful
evaluation of stable genotypes, which could be released to farmers and/or
used in future
breeding programs. The model elaborated by Eberhart and Russell (1966) defined
the stable variety as having unit regression (b = 1), with a minimum deviation
from regression (S^{2}d = 0). They also added that a variety must
have high mean performance.
The hybrids ICSA 38 x Damougari and ICSA 39 x Damougari produced the highest
grain yields, had "b" values that were not significantly different from unity but with S^{2}d
significantly different from zero, implying that these hybrids were highly
responsive to environmental changes. On the other hand, the thirteen hybrids,
which very closely followed the two top yielders in mean performance, had
high stability and gave superior grain yields, which confers general adaptability.
The seven hybrids, which had superior yields, but significant deviations from regression, could be defined as unstable. Their performance over environments cannot be predicted. However, high and positive deviations from regression at some environments may also reveal that the genotype has higher adaptability to these specific growing conditions than the average of the whole material. This is often the case with resistance to edaphic factors (Nurminiemi and Rognili, 1996).
The mean squares for hybrid x environment interaction effects were highly
significant (Table 4). Pooled deviation mean squares were also highly significant,
indicating that the differences in linear response among hybrids across
environments did not account for the entire hybrid x environment interactions.
A large portion of sums of squares of hybrids x environment interaction
(63.8%) was accounted for by the deviation from regression, only 36.2% was
accounted for by the linear regression.
TABLE 4. Meansquares from regression of hybrids and parents grain yields of sorghum on an environmental index over environments
Sources of variation  Degree of freedom  Mean squares  
All entries genotypes  99  3.423**  
Environments (Env)(linear)  1  713.363** 
Genotypes x Env (linear)  99  1.499*+ 
Pooled deviation from regression  200  1.350** 
Hybrids  74  2.533** 
Environments (Env)(linear)  1  592.930** 
Hybrids x Env (linear)  74  1.545**+ 
Pooled deviation from regression  150  1.344** 
   
Parental  19  3.106** 
Environments (Env)(linear)  1  100.289** 
Parental x Env (linear)  19  1.072**+ 
Pooled deviation from regression  40  1.073** 
** Significant at the 1% level when tested against pooled error
+ non significant when tested against pooled deviations
The parental lines also showed significantly different responses to environmental
variation (Table 4). A significant portion of the interaction was attributed
to the linear change in genotype mean per unit change in environment mean.
However, the linear model was not entirely satisfactory because the pooled
deviations source of variation was also significant and explained 67.8%
of parent x environment interaction.
In general, for both the hybrids and the parental lines, when the regression
mean squares were tested against pooled error, the level of significance
was very high (P < 0.001), and the regression mean squares against the deviation mean squares demonstrated that the nonlinear regression explained the genotype x environment interaction effects.
In the present study, the deviation mean squares were significant in all
instances, indicating non  linear response or specific interactions with
environments. The large G x E interactions observed provide two important
suggestions. First a genotype should be designated as stable on the basis
of the importance of the components of variation of G x E interaction effects
found in the study, and secondly that the region may be subdivided into
zones of similar environments for which suitable sorghum varieties and hybrids
would be developed. In general, the major sorghum growing areas vary relatively
little in altitudes, but variation may be considerable with the rainfall
pattern. Therefore, subdivision of the environments according to annual
rainfall distribution may be considered. However, Eberhart and Russell (1966)
pointed out that interaction due to seasonal and other types of environmental
variations classified by Allard and Bradshaw (1964) as "unpredictable" are not effectively reduced by subdivision. Consequently, the aim of breeding for widely adapted genotypes is not hampered by subdivisions.
Hybrids were the top yielding entries in each environment; a greater responsiveness
to increasingly favorable environments was indicated by a large b value.
Response pattern showing significant S^{2}d were not adequately
described by the linear regression. These results suggested therefore,
that appropriate hybrid selection strategies in the region should emphasise
selection
for yield and the evaluation of stability of the high  yielding hybrids
to determine if differences occur in stability among the elite hybrids
being developed. This process would provide sorghum growers with high
probability
of enhanced yields combined with yield stability.
ACKNOWLEDGEMENTS
The authors are grateful to Dr S.G. Ado, Department of Plant Science, ABU/IAR Zaria, Nigeria for useful suggestions.
REFERENCES
 Allard, R. W. and Bradshaw, A. D. 1964. Implications of
genotype x environment interactions in plant breeding. Crop Science 4:503507.
 Axtell, J., Kapran, I., Ibrahim, Y., Ejeta, G. and Andrews, D.J. 1999. Heterosis in sorghum and pearl millet. In: Proceedings of the genetic and exploitation of heterosis in crops. ASACSSASSSA, 677 South Segoe Road, Madison, WI. 53711, USA. pp.
375386.
 Becker, H. C. and Leon, J. 1988. Stability analysis in plant breeding. Plant Breeding 101:123.
 Duley, I. W. and Moll, R.H. 1969. Interpretation and use of estimates
of heritability and genetic variances in plant breeding. Crop Science 9:257262.
 Eagles, H. A., Hinz, P. N. and Frey, K. J. 1977.
Selection of superior cultivars of oats (Avena sativa L.)
by using regression coefficients. Crop Science 17:101105.
 Eberhart, S. A. and Russell, W. A. 1966. Stability parameters for comparing
varieties. Crop Science 6:3640.
 Finlay, K. W. and Wilkinson, G. N. 1963. The analysis of adaptation
in a plant breeding program. Australian Journal Agricultural Research 15:742754.
 Food and Agriculture Organization of the United Nation, Rome, 1997. FAO Year Book. Statistics Series No.
135.
 Gupta, S. C. and Ndoye, S.C. 1991. Yield stability of promising
pearl millet genotypes in Senegal. Maydica 36:8386.
 Heinrich, G. M., Francis, C. A. and Eastin, J.D. 1983. Stability
of grain sorghum yield components across diverse environments. Crop Science 23:210212.
 Nurminiemi, M. and Rognili, O. A. 1996. Regression analysis
of yield stability is strongly affected by companion test varieties and
location:
examples from a study of Nordic barley lines. Theoretical and Applied Genetics 93:468476.
 PettoneeSaino, P., Moore, K. and Pehu, E. 1993. Phenotypic stability
of oats measured with different stability analyses. Journal of Agricultural Science, Cambridge.
121:1319.
 Plaisted, R. L. and Peterson, L.C. 1959. A technique for evaluating
the ability of selections to yield consistently in different locations
or seasons. American Potato Journal 36:381385.
 SAS Institute. 1989. SAS/Stat users guide, Ver. 6, 4^{th} ed.,
vol. 2. SAS Inst., Inc., Cary, NC.
 Steel, R.G.D. and Torrie, J.H. 1980. Principles and Procedures of Statistics
2^{nd} ed.
McGrawHill Book Co. New York. 663pp.
 Virk, D.S., Chahal, S. S. and Pooni, H.S. 1985. Repeatability of stability
estimators for downy mildew incidence in pearl millet. Theoretical and Applied Genetics 70:102106.
 Witcombe, J. R. 1988. Estimates of stability for comparing varieties. Euphytica 39:1118.
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African Crop Science Society
