African Crop Science Journal
African Crop Science Society
ISSN: 1021-9730
Vol. 11, Num. 2, 2003, pp. 65-73

African Crop Science Journal, Vol. 11. No. 2, 2003,  pp. 65-73


R. Kenga, S. O. Alabi1 andGupta2  

Institute of Agronomic Research (IRAD) P. O. Box 33 Maroua, Cameroon  
1Department of Plant Science IAR/Ahmadu Bello University, Zaria, Nigeria
2ICRISAT, NASC complex, Pusa, New Delhi 110 012, India

(Received 26 November, 2001; accepted 31 March, 2003)

Code Number: cs03009


Seventy-five 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 (S2d) 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 hybrid-environment (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 S2d estimates were significantly greater than zero. Thirteen hybrids recorded bi values close to unity, small S2d 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


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 (S2d) 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 (-0.82-1.52). Les déviations des moyennes des sommes des carrées (S2d) 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 S2d 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


Sorghum (Sorghum bicolor (L.) Moench) is a major crop of the semi-arid 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 non-linear 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.


Parental lines and hybrids of sorghum. Five cytoplamic -genetic male-sterile 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 open-pollinated released varieties and landraces from various breeding programs of the West Africa region. The male sterile lines were kafir-milo 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 m2.  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 top-dressed 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 (S2d values) as indexes of production response and stability, respectively. The performance of a variety is then defined by the equation:

Yij = µi + bi Ij +dij 

Where Yij is the mean grain yield of the ith genotype in the jth environment, µi is the mean of the ith genotype, bi the coefficient which measures the regression of the ith genotype on different environments (linear response -predictive), dij is the deviation from regression of the genotype in the jth environment, and Ij is the environmental index calculated as the mean of all genotype at the jth environment less the grand mean over all environments.

Since the sum of Ij over all environments is zero, the yield of a variety in a given environment can be predicted as follows: Yij = xi + biIj.  Where xi and bi are estimates of µi and bi, respectively. The mean squares due to deviations from regression (S2d) indicate the degree of reliance that can be placed upon linear regression. In fact, S2d reveals a non-linear response of varieties (non-predictive). 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 t-test 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 F-test 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.


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, S2d) (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 non-linear 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 non-linear responses of genotypes to varying environment; thus S2d 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 (S2d) for sorghum hybrids, parental lines and checks
Genotypes Mean grain yields b SE(b)1 S2d
ATX 623
x NR 71176-1 3.142 1.29 ±0.36 0.02
x NR 71176-2 3.293 0.98 ±0.16 -0.82
x NR 71182-2 2.553 0.68 ±0.40 0.22
x NR 71182-3 2.922 1.42 ±0.41 0.35
x NR 71168-1 3.164 1.06 ±0.25 -0.52
x NR 71168-3 2.042 0.72 ±0.36 -0.01
x KSV 4-1 2.955 1.50 ±0.36 0.03
x KSV 4-2 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
x NR 71176-1 2.477 0.74 ±0.34 -0.07
x NR 71176-2 3.216 0.77 ±0.34 -0.13
x NR 71182-2 2.765 0.02* ±0.36 0.03
x NR 71182-3 3.422 1.17 ±0.24 -0.56
x NR 71168-1 2.510 0.48 ±0.34 -0.09
x NR 71168-3 2.660 0.68 ±0.41 0.37
x KSV 4-1 2.834 1.19 ±0.29 -0.36
x KSV 4-2 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*
x NR 71176-1 2.297 0.35* ±0.20 -0.70
x NR 71176-2 2.859 0.59 ±0.37 -0.02
x NR 71182-2 2.479 0.55 ±0.51 1.05*
x NR 71182-3 2.671 0.47 ±0.51 1.07**
x NR 71168-1 2.531 0.38* ±0.29 -0.37
x NR 71168-3 2.535 0.26** ±0.20 -0.71
x KSV 4-1 2.728 1.96* ±0.47 0.70
x KSV 4-2 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**
x NR 71176-1 2.459 1.24 ±0.24 -0.58
x NR 71176-2 3.003 0.43* ±0.26 -0.49
x NR 71182-2 2.633 0.95 ±0.27 -0.44
x NR 71182-3 2.651 0.46 ±0.32 -0.20
x NR 71168-1 2.483 0.36 ±0.35 -0.07
x NR 71168-3 2.768 1.02 ±0.33 -0.17
x KSV 4-1 2.525 1.39 ±0.32 -0.23
x KSV 4-2 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 71176-1 3.058 1.67* ±0.29 -0.33
x NR 71176-2 3.318 1.48 ±0.40 0.26
x NR 71182-2 2.504 1.07 ±0.42 0.35
x NR 71182-3 2.977 1.00 ±0.25 -0.51
x NR 71168-1 2.751 1.31 ±0.44 0.71
x NR 71168-3 2.765 0.79 ±0.45 0.57
x KSV 4-1 3.045 1.55* ±0.29 1.02
x KSV 4-2 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 71176-1 1.635 0.46* ±0.29 -0.16
NR 71176-2 1.608 0.30** ±0.32 -0.08
NR 71182-2 1.708 0.52** ±0.27 -0.22
NR 71182-3 1.516 0.50** ±0.30 -0.13
NR 71168-1 1.702 0.31* ±0.36 0.07
NR 71168-3 1.543 0.92 ±0.35 0.01
KSV 4-1 1.869 1.21 ±0.28 -0.20
KSV 4-2 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
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 S2d significantly different from zero at 5% and 1% levels, respectively
1SE (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 (S2d) 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 (S2d), 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 S2d 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 (S2d) 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 KSV4-1, ICSA 902 x NR 71176-2, ICSA 41 x CS 144, ICSA 41 x S 35, ICSA 38 x NR 71182-3, ICSA 38 x NR 71176-2, ATX 623 x Damougari, ATX 623 x CS 54, ATX 623 x KSV 4-2, ATX 623 x NR 71168-1, ATX 623 x KSV4-2 and ATX 623 x NR 71176-2.  All these thirteen hybrids combined high yield with bi were not  significantly different from unity and had S2d 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 71176-1, ICSA 902  x KSV 4-2, ICSA 902 x KSV4-1, ICSA38 x KSV4-2 and ICSA 39 x KSV4-2 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 non-significant 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 (S2d = 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 S2d 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 non-linear 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 S2d 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.


The authors are grateful to Dr S.G. Ado, Department of Plant Science, ABU/IAR Zaria, Nigeria for useful suggestions.


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