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Additive Main Effects and Multiplicative Interaction and Genotype Main Effect and Genotype by Environment Interaction Effects-Biplot Analysis of Sorghum Grain Yield in Uganda

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Journal of Agricultural Science
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Genotype-by-environment interaction analysis is vital for cultivar release, and to identify suitable crop production sites. The current study aimed to determine sorghum grain yield stability and adaptability and to identify the most informative and representative environments for sorghum grain yield performance in Uganda. Sorghum grain yield data of eight (08) genotypes; ICSR 160, IS8193, IESV92043DL, IESV92172DL, GE17/1/2013A, GE35/1/2013A, SESO1, and SESO3 tested across eight (08) major sorghum production area in Uganda for two consecutive seasons of 2017 using randomised complete block design with 2 replications were analysed via Additive Main effects and Multiplicative Interaction (AMMI) and Genotype Main Effect and Genotype by Environment interaction effects (GGE) using PB tools. Genotype IESV92043DL was the ideal genotype in the entire test environments with mean grain yield of 2783 kg ha-1 however genotype ICSR 160 had the highest grain yield of 2823 kg ha-1 across all the test environment. On the other hand, GE17/1/2013A was the most stable and adapted genotype across all the test environment. Of the eight (08) environments tested, biplot analysis precisely grouped the test environments into two presumed mega-environments with the best genotype being IS8193 and ICSR 160. Out of eight (08) trial sites, two (02) environments; Abi and Mayuge were the most representative and informative environment for sorghum grain yield performance in Uganda.
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Journal of Agricultural Science; Vol. 12, No. 6; 2020
ISSN 1916-9752 E-ISSN 1916-9760
Published by Canadian Center of Science and Education
98
Additive Main Effects and Multiplicative Interaction and Genotype
Main Effect and Genotype by Environment Interaction Effects-Biplot
Analysis of Sorghum Grain Yield in Uganda
Charles Andiku
1
, Geofrey Lubadde
2
, Charles J. Aru
1
, Michael A. Ugen
1
& Johnie Ebiyau
1
1
National Semi Arid Resources Research Institute, Soroti, Uganda
2
Department of Crop Production and Management, Faculty of Agriculture and Animal Sciences, Busitema
University, Tororo, Uganda
Correspondence: Charles Andiku, National Semi Arid Resources Research Institute, P.O. Box 56, Soroti, Uganda.
E-mail: andikuc@gmail.com
Received: March 8, 2020 Accepted: April 14, 2020 Online Published: May 15, 2020
doi:10.5539/jas.v12n6p98 URL: https://doi.org/10.5539/jas.v12n6p98
Abstract
Genotype-by-environment interaction analysis is vital for cultivar release, and to identify suitable crop
production sites. The current study aimed to determine sorghum grain yield stability and adaptability and to
identify the most informative and representative environments for sorghum grain yield performance in Uganda.
Sorghum grain yield data of eight (08) genotypes; ICSR 160, IS8193, IESV92043DL, IESV92172DL,
GE17/1/2013A, GE35/1/2013A, SESO1, and SESO3 tested across eight (08) major sorghum production area in
Uganda for two consecutive seasons of 2017 using randomised complete block design with 2 replications were
analysed via Additive Main effects and Multiplicative Interaction (AMMI) and Genotype Main Effect and
Genotype by Environment interaction effects (GGE) using PB tools. Genotype IESV92043DL was the ideal
genotype in the entire test environments with mean grain yield of 2783 kg ha
-1
however genotype ICSR 160 had
the highest grain yield of 2823 kg ha
-1
across all the test environment. On the other hand, GE17/1/2013A was the
most stable and adapted genotype across all the test environment. Of the eight (08) environments tested, biplot
analysis precisely grouped the test environments into two presumed mega-environments with the best genotype
being IS8193 and ICSR 160. Out of eight (08) trial sites, two (02) environments; Abi and Mayuge were the most
representative and informative environment for sorghum grain yield performance in Uganda.
Keywords: sorghum (Sorghum bicolor), multiplicative models, genotype, and yield stability
1. Introduction
Environment is important in determining the performance of crop genotypes especially for quantitative variables.
Likewise the multiplicative effect of the genotype by environment [genotype by environment interaction (GEI)]
further complicates the expressivity of the variables resulting in selection. This directs plant breeders to select
genotypes that are suitable for certain environment. It is important to study genotypes response to different
environments and henceforth select cultivars suitable for specific or diverse environments. However, cultivars
that are adapted to diverse environments are the most desirable in breeding therefore understanding genotype by
environment (GxE) interaction is very key in a plant breeding program before the variety is released to the
uptake pathway. The yield potential of a variety is controlled by both the genetic and various environmental
factors that vary over the years and locations. The study of quantitative traits like grain yield is further
convoluted by GxE interaction; especially across many trial locations (Kaya et al., 2002). Therefore, evaluation
of newly developed varieties across several environments is fundamental to estimate the magnitude of GEI, and
for cultivar recommendation. Several statistical approaches have been used to analyse GE1 for recommending
specific or general selection in plant breeding. As noted by Lubadde et al. (2017), more than one method should
be used for better comparison. In this study the Additive Main effects and Multiplicative Interaction (AMMI)
and the Genotype Main Effect and Genotype by Environment interaction effects (GGE) models was adopted.
Nyaligwa et al. (2018) acknowledged that AMMI and GGE models have been used by many breeders to analyse
GE1. AMMI employs both analysis of variance (ANOVA) and principle component analysis (PCA) (Zobel et al.,
1988) to analyse the main effects (additive effect) and the non-additive residual effect (Akter et al., 2014)
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respectively to ascertain GEI for trait of interest such as sorghum grain yield in this current study. While GGE
biplots on the other hand display both genotype and genotype by environment disparity for traits (Crossa et al.,
2002). In this current study, both AMMI and GGE biplot was used for estimating yield stability and adaptability
of improved sorghum genotype over the major sorghum production areas in Uganda as excellent tools for visual
display and interpretation of multi environments data (Rakshit et al., 2017). Therefore, the objectives of this
study were to (i) determine sorghum grain yield stability and adaptability, (ii) identify the most discriminating
(informative) and representative environments for sorghum grain yield performance in Uganda and (iii)
determine the presence of sorghum production mega environments in Uganda.
2. Materials and Methods
2.1 Trial Sites
The trial was conducted at eight (08) different sites namely Arua, Iganga, Mayuge, Namutumba, Pallisa, Serere,
Oyam and Kitgum (Table 1 and Figure 1) that represent the major sorghum production areas in Uganda for two
consecutive seasons (first and second seasons) of 2017. Each site and two consecutive seasons formed the eight
(08) environment in which sorghum grain yield data were collected for AMMI and GGE biplot analysis.
2.2 Experimental Materials and Design
Eight (08) genotypes including two checks (SESO1 and SESO3) (Table 2) were used in this study. The trials were
arranged in randomised complete block design with two replications per location. Each genotype was planted in
a plot with 4 rows at spacing of 60 cm apart and 20 cm between plants within the row and each plot was
measuring 4 m long.
Table 1. Characteristics of the locations used in the study
Code Location Geographical position Elevation Mean Temp Annual
Rainfall Agro-ecologies
Latitude Longitude m °C mm
E1 Arua 3°19N 30°55'51E 1215 23.9 1404 West Nile farmlands
E2 Iganga 0°3633N 33°287"E 1120 23.3 1313 Lake Victoria Crescent
E3 Kitgum 3°1642N 32°5312E 760 24.1 1125 North Eastern Central Grass Bush farmlands
E4 Mayuge 0°2735N 33°2849E 1,190 22.3 979 Lake Victoria Crescent
E5 Namutumba 0°5010N 33°4110E 1,080 22.0 1322 Lake Kyoga Basin
E6 Oyam 2°2624N 32°2322E 900 21.6 1500 Northern moist farmlands
E7 Pallisa 1°842N 33°4234E 1,070 23.4 1353 Lake Kyoga Basin
E8 Serere 1°2939N 33°2719E 1140 23.8 1362 Lake Kyoga Basin
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Figure 1. Map of Uganda showing the locations (marked in yellow) used in the study
The trials were weeded manually thrice for good crop establishment and no fertilizer was applied during the crop
growing cycle however they were sprayed with cypermethrin to control pests at four weeks after crop emergence,
then at intervals of two weeks for 6 weeks.
Table 2. List of sorghum genotype used in this study
Code Genotypes Source Pedigree or Origin Variety status Special attributes
G1 GE17/1/2013A (GE17) USA, Perdue University Pure line Resistant to Smut and Striga, and early maturity
G2 GE35/1/2013A (GE35) Texas Pure line Sweet stalk and seed, and resistant to striga
G3 ICSR 160 [(IS 12622Cx555)
× (IS 3612Cx2219B)-5-1
× E 35-1], ICRISAT
Pure line Suitable for lager beer production and drought
tolerant/stay green trait.
G4 IESV 92043DL KARI Mtama 1 × Seredo, ICRISAT Pure line Resistant to midge, drought tolerant, juicy sweet stalk
suitable for forage.
G5 IESV92172DL ICRISAT Pure line Short height and medium maturity with high
threshability
G6 IS8193 Land Race from East Africa, ICRISAT Pure line Resistant to bird damage, drought and Striga tolerant.
G7 SESO1 (M91057)-Check 1 [GPR 148 x E35-1] × CS 3541) Released variety
in Uganda
White seeded, early maturity and good for brewing.
G8 SESO3 (SRN 39)-Check2 Sudan Released variety
in Uganda
Early maturing, high yielding, good for food and
tolerant to striga, drought and bird damage.
2.3 Data Collection and Analysis
Grain yield data were collected on sorghum genotypes per the (IBPGR, 1993) descriptors. Harvesting was done
manually at physiological maturity at all the trial sites. The grain yield data were analysed using combined
analysis of AMMI and GGE biplot using PB tools (Version 1.4, http://bbi.irri.org/products) and the models were:
Y
ij
= μ + δ
i
+ β
j
+
k
δ
ik
β
jk
+ ε
ij
(for AMMI) (1)
Y
ij
= μ + β
j
+
k
δ
ik
β
jk
+ ε
ij
(for GGE Biplot) (2)
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Where, Y
ij
is the mean yield of i
th
genotype in j
th
environment, μ is the overall mean, δ
i
is the genotypic effect, β
j
is the environment effect, λ
k
is the singular value for PC axis k, δ
ik
is the genotype eigen vector value for PC axis
n, β
jk
is the environment eigen vector value for PC axis k and ε
ij
is the residual error assumed to be normally and
independently distributed (0, σ
2
/r), where σ
2
is the pooled error variance, and r is the number of replicates
(Crossa et al., 2002; Gauch et al., 2008). The mean sorghum grain yield was separated by the least significant
difference (LSD) test.
3. Results and Discussions
The sorghum grain yield results of the eight (08) sorghum genotypes across the eight (08) environments showed
that genotype ICSR 160 had the highest mean grain yield of 2823 Kg per ha
-1
, superseded by IESV92043DL, and
IS8193 with grain yield of 2783 Kg ha
-1
and 2740 Kg ha
-1
respectively (Table 3). These genotypes consistently
and significantly performed better than the checks across the environments. The combined analysis of variance
across the environment for grain yield of eight (08) sorghum genotypes showed that the treatment, genotypes and
environment components were significantly different (P < 0.001) unlike G×E interactions at 0.05 level. Our data
therefore showed that genotypes and environments used during the study were different. Therefore, there was
great diversity between the genotypes. The absence of GEI in this current study clearly indicates breeding for
specific adaptability for the targeted trait. According to Andiku et al. (2019), presence of low or no GxE
interactions in any study shows that screening programs for such important trait could be conducted centrally at
one or two locations to minimise breeding costs.
Table 3. Grain yield of eight sorghum genotypes across the environments
Environment Abi Iganga Kitgum Mayuge Namutumba Oyam Pallisa Serere
Genotype
means
Genotype ------------------------------ Grain sorghum yield (Kg ha
-1
) -------------------------------
GE17/1/2013A 1808 2441 2031 3702 2862 3376 2024 2104 2544
GE35/1/2013A 1532 2694 2014 3278 2512 3334 1948 2124 2430
ICSR 160 1710 2985 2122 4091 3264 3610 2167 2637 2823
IESV92043DL 1856 2977 2127 3859 3224 3566 2082 2576 2783
IESV92172DL 1739 2488 1987 3208 2882 2837 1967 1647 2344
IS8193 2126 3077 2239 3563 2864 3382 2199 2471 2740
SESO1 (Check1) 1576 2507 2067 3596 2634 3426 2023 2016 2481
SESO3 (Check2) 1524 2599 2001 3752 3100 3156 1999 2097 2529
Mean 1734 2721 2074 3631 2918 3336 2051 2209 2584
LSD (0.05) 538.7ns
C.V % 18.4
Note. ns: not significant at level 0.05.
According to Akter et al. (2014), a genotype or an environment is assumed to have small interaction (stable)
when the first Interaction Principal Component Axis (IPCA1) score is almost to zero or equivalent to zero. More
still, the horizontal line (y-ordinate) is the IPCA1 value of zero while the vertical line represents the grand mean
for grain yield (Figure 2) where a genotype or environment on the right side of the vertical line are high yielding
unlike their counter parts on the left hand side of the vertical line. However, genotypes and environments that
appear on perpendicular and horizontal lines have similar mean and interaction patterns respectively (Akter et al.,
2019). Consequently, our study provided a visual expression of the relationships between the IPCA1 and means
of genotypes and environments as shown in Figure 2. The AMMI biplot showed four groupings of genotypes;
IESV92172DL (G5) generally low yielding and unstable, GE17/1/2013A (G1), GE35/1/2013A (G2), SESO1
(G7), and SESO3 (G8), low yielding and moderately stable, IESV92043DL (G4) high yielding and the
moderately stable while ICSR 160 (G3) and IS8193 (G6) are high yielding but unstable.
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Figure 2. AMMI biplot (genotypes and environments plotted against their IPCA1 scores) for sorghum grain yield
in Kg per hectare
Out of the eight (08) environments, half of the environments; Iganga (E2), Mayuge (E4), Namutumba (E5) and
Oyam (E6) were high yielding since they were positioned on the right side of the vertical line with Iganga (E2)
being the most stable environment since its Interaction Principal Component Axis (IPCA) scores was close to
zero than other environments while the low yielding environments were positioned at the left side of the vertical
line [Arua (E1), Kitgum (E3), Pallisa (E7) and Serere (E8)]. The genotype or environment IPCA scores (either
positive or negative) displays their stability in the AMMI biplot. The more the IPCA score is close to zero (low
interaction), the more stable the genotype or environment as opposed to environments (or genotypes) with large
first IPCA scores (high interactions).
The pattern of GEI was cross-validated from distribution of eight sorghum genotypes over eight environments on
the AMMI display of the first and second IPCA of genotypes and the environment (AMMI 2 model) as proposed
by Vargas et al. (2001). This second model of AMMI helps to further examine adaptation of the genotypes across
the environment (Figure 3). More still, (Purchase, 1997) explained the stability pattern of genotype display in
AMMI 2 model where he emphasised that the stable genotypes are closer to the centric ring of the biplot. Based
on this argument, Figure 3 results further showed that, GE17/1/2013A (G1) and SESO1 (G7) being more stable
based on their closeness to the centric ring of the biplot. Conversely, ICSR 160 (G3) and IESV92172DL (G5)
had diffused position therefore they were considered unstable across the study environment. The AMMI 2 model
biplot further showed that genotypes ICSR 160 (G3) and IESV92172DL (G5) and environments Abi (E1),
Mayuge (E4) and Namutumba (E5) contributed more to the GE interaction effect.
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Figure 3. AMMI 2 biplot (IPCA2 scores plotted against IPCA1 scores) for sorghum grain yield in Kg per hectare
SESO3 (G8) and ICSR 160 (G3) were specifically adapted to Namutumba (E5) and Mayuge (E4) respectively.
On contrary, GE35/1/2013A (G2) and IS8193 (G6) were specifically adapted to Iganga (E2). The observed
results can be attributed to fundamental GEI (Wallace et al., 1995). More still, the GGE biplot informative and
representativeness is of great significant measure of testing environments. The visual length of the environment
vectors which is proportional to the standard deviation within the respective environments determines the
environmental discriminatory ability. Superior environmental discriminating ability is displayed by the
extensiveness of the environment vector. Consequently, in this study, the environmental vector biplot identified
Abi (E1), Mayuge (E4) and Namutumba (E5) as favourably informative (discriminating) for the trial genotypes,
as revealed by the extensive environment vectors (Figure 3) therefore exert strong interaction with genotype.
Informative test environments precisely fix differences among the genotype accordingly inform breeders on
selection decision. Iganga (E2) was non informative (least discriminating) of the eight (08) environments
followed by Pallisa (E7), as revealed by the minuscule environment vector. The non-informative trial
environments like Iganga (E2) and Pallisa (E7) tends to furnish little information on the genotypes therefore
should not be used as trial environments. More still, a trial environment with smaller Average-Environment Axis
(AEA) angle is more representative than their counter parts. The AEA (the line that passes through the average
environment and the biplot origin) measures the representativeness of the average environment. Trial
environments that are both informative and representative are superior environments for selecting overall
genotype with good adaptability. Therefore, testing sorghum genotype for grain yield solely in Abi (E1) and
Mayuge (E4) is adequate based on their representative and informative ability for sorghum grain yield in the
study. Namutumba (E5) is informative but not representative due to its dispersed position; hence such
environment can be used for rapid elimination of unstable genotypes during the selection process (Tukamuhabwa
et al., 2012) under a single mega-environment or for selecting genotypes under mega-environments for specific
adaptability. Use of those particular environments with non-informative and representative ability for assessing
sorghum grain yield may give ambiguous results due to their low informative and representative ability. Yan and
Rajcan (2002) defined the superior environment as the environment with substantial PC1 scores (informative)
and small PC2 scores (representative) as observed for Abi (E1).
GGE biplot for the environment vector view for the stability study of genotypes for sorghum grain yield over the
eight (08) environments identified the genotype IESV92043DL (G4) as the stable genotypes with fairly high
sorghum grain yield mean performance (Figure 4). The biplot origin represents a stable genotype with grand
mean value and thus zero contribution of the additive effect of genotype and multiplicative interactions shows
the stability of the genotype. However, based on the same principle, SESO1 (G7) was identified as stable
genotype but with low sorghum grain yield mean performance. This result was not surprising since SESO1 (G7)
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was a released registered commercial cultivar which has already adapted in these environments. The distance
between two genotypes estimates the Euclidean distance between them consequently measuring the dissimilarity
between the genotypes. In this study, all the used genotypes are quite different in their genetic make-up with
respect to sorghum grain yield due to their diffuse position (Figure 4). Out of the eight (08) environments,
Mayuge (E4) was found to be the most superior environment in terms of sorghum grain yield performance and
genotype, ICSR 160 (G3) was best adapted to Mayuge (E4) and Namutumba (E5) while IESV92043DL (G4)
was specifically best adapted to Oyam (E6). Therefore, ICSR 160 (G3) and IESV92043DL (G4) with a particular
adaptation to environments; Mayuge (E4)/Namutumba (E5) and Oyam (E6) respectively could be selected and
recommended for specific adaptability as observed in this study.
Figure 4. GGE biplot for the environment vector view to show similarities among the environments
On contrary, genotype focused biplot (Figure 5) conveyed that IESV92043DL (G4) is the most stable genotype
for sorghum grain yield in the entire study environment while ICSR 160 (G3) is the superior genotype,
succeeded by IESV92043DL (G4) and IS8193 (G6) respectively. However, IESV92043DL (G4) was depicted as
superior genotype in the entire study environments due to its outstanding relative stability and adaptability
couple with moderate sorghum grain yield from AMMI and GGE biplots display. This is a desirable plant
breeding trait consequently such genotype can be recommended for possible release as a variety to up take
pathway. The genotypic stability displayed in the study indicated that it performs well regardless of the GxE
interaction thus wide adaptability of the genotype.
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Figure 5. GGE biplot for the genotype view to show genotype ranking relative to an ideal genotype
The dynamic stability displayed by the genotypes calls for specific selection of genotypes suitable for particular
environments (Andiku et al., 2019). However, genotypes; GE17/1/2013A (G1), GE35/1/2013A (G2),
IESV92172D (G5), SESO1 (G7), and SESO3 (G8) recorded low yield unlike their counter parts [ICSR 160 (G3),
IESV92043DL (G4) and IS8193 (G6)] that had high yields as evidenced by their positioning on the right side of
the AEC abscissa (single-arrowed line (Figure 5). These high yielding genotypes could be selected for possible
release as a variety. On the other hand, genotypes with below-average mean (left side of the AEC abscissa);
SESO1 (G7) and GE17/1/2013A (G1) which are stable could be selected. The extensiveness of the non-arrowed
line to the AEC regardless of the direction, indicates that genotype is unstable (high level of GEI) in the entire
test environments. Conversely, genotypes IESV92043DL (G4)/SESO1 (G7) and GE17/1/2013A (G1) were fairly
stable as well as high and low yielding respectively in terms of grain yield performance.
Physical envision of the which-won-where pattern of Multi Environment Yield Trials (METs) data is very crucial
for understanding possible existence of different mega-environments (ME) in the production area as cited by
Singh et al. (2019). The display of GGE-biplot clearly shows which-won-where pattern, as such it concisely
summarises the GEI pattern of a trial as displayed for sorghum grain yield data in Figure 6. In the current study,
there are four sectors with two mega environments namely Mega Environment I consisting of Abi (E1), Iganga
(E2), Kitgum (E3), and Pallisa (E7) with the best genotype being IS8193 (G6). Mega environment II had the
environments; Mayuge (E4), Namutumba (E5), Oyam (E6) and Serere (E8) with the best genotype being ICSR
160 (G3). These results suggested that genotypes with high grain yield for these two mega environments were
ICSR 160 (G3) and IS8193 (G6) as observed under AMMI biplot (Figure 2). However Mega Environment II
also had IESV92043DL (G4) with specific adaptability to Oyam (E6). These Mega Environment suggests
feasible existence of different mega environments for sorghum production across the country. According to Oral
et al. (2018), environments that are positioned within the same sector have strong correlations, and GEI
suggesting effect of the environment on the genotypes and the presence of mega environment which is observed
in this current study.
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Figure 6. IPCA2 scores plotted against IPCA1 scores based on sorghum grain yield across eight environments to
show the which-won-where pattern
The fascinating point from this GGE biplot view is that the genotypes [ICSR 160 (G3), IESV92043DL (G4), and
IS8193 (G6)] that fall within the two mega environments were genotypes that out-performed the registered
commercial released cultivar [(SESO1(G7) and SESO3 (G8)]. No environments fell into sectors with genotypes;
GE17/1/2013A (G1), GE35/1/2013A (G2), IESV92172DL (G5), SESO1(G7) and SESO3 (G8) as vertices,
suggesting that these genotypes did not perform well in any of the eight (08) environments. However, this Mega
Environment pattern needs further verifying through setting repeated seasonal trials across the study location
since this Mega Environment pattern was solely deduced from two seasons data of 2017 without considering
subsequent years.
4. Conclusion
In this study, both the AMMI and GGE models identified IESV92043DL (G4) as the ideal genotype as it was
stable and high yielding across the entire study environments. Using the same data, the three (03) promising
sorghum genotypes [ICSR 160 (G3), IESV92043DL (G4) and IS8193 (G6)] with grain yield gain of 11.6%,
10.0% and 8.3% over the check (SESO3) respectively were identified and released as varities in Uganda;
NAROSORG1, NAROSORG3, and NAROSORG2 respectively. On the other hand, stable genotype
GE17/1/2013A (G1) with below-average yield mean of 2544 Kg ha
-1
was released as NAROSORG4 because of
being resistant to covered kernel smut.
Abi (low yielding) and Mayuge (high yielding) were the most representative and informative environment in the
country for sorghum grain yield performance and only testing sorghum genotypes for grain yield performance in
these two environments can be enough. Namutumba can be used for rapid elimination of unstable genotypes
during the selection process since it was informative but not representative.
The test environments for sorghum grain yield performance were delineated into two presumed
mega-environments but this Mega Environment pattern needs further verifying through setting repeated seasonal
trials across the study location since this Mega Environment pattern was solely deduced from two seasons data
of 2017 without considering subsequent years.
Acknowledgements
This publication is an output from research projects funded by Alliance for a Green Revolution in Africa
(AGRA), Harnessing Opportunities for Productivity Enhancement (HOPE II) project funded by Bill Melinda
Gate foundation and the Ugandan National Agricultural Research Organisation (NARO). We thank Dr. Eric
Manyasa of ICRISAT and Dr. Gichuru Lillian of AGRA for their technical input. We would also like to thank Mr.
Amayo Robert of Busitema University for editing the work.
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References
Akter, A., Hasan, M., & Kulsum, M. (2019). Stability and adaptability of promising hybrid rice genotypes in
different locations of Bangladesh. Adv. Plants Agric. Res., 9(1), 35-39. https://doi.org/10.15406/apar.2019.
09.00407
Akter, A., Jamil, H., Umma, K., Islam, M., Hossain, K., & Mamunur, R. (2014). AMMI biplot analysis for
stability of grain yield in hybrid rice (Oryza sativa L.). J. Rice Res., 2(2), 126. https://doi.org/10.4172/
jrr.1000126
Andiku, C., Tukamuhabwa, P., Ssebuliba, J. M., Talwana, H., Tumwegamire, S., & Gruneberg, W. (2019).
Evaluation of the American yam bean (Pachyrhizus spp.) for storage root yield across varying
eco-geographic conditions in Uganda. Journal of Agricultural Science, 11(8), 100. https://doi.org/10.5539/
jas.v11n8p100
Crossa, J., Cornelius, P. L., & Yan, W. J. C. S. (2002). Biplots of linear-bilinear models for studying crossover
genotype × environment interaction. Crop Science, 42(2), 619-633. https://doi.org/10.2135/
cropsci2002.6190
Gauch, H. G., Piepho, H.-P., & Annicchiarico, P. J. C. S. (2008). Statistical analysis of yield trials by AMMI and
GGE: Further considerations. Crop Science, 48(3), 866-889. https://doi.org/10.2135/cropsci2007.09.0513
IBPGR (International Board for Plant Genetic Resources). (1993). Descriptors for sorghum [Sorghum bicolor
(L.) Moench]. International Board for Plant Genetic Resources, Rome, Italy.
Kaya, Y., Palta, C., & Taner, S. (2002). Additive main effects and multiplicative interactions analysis of yield
performances in bread wheat genotypes across environments. Turkish Journal of Agriculture and Forestry,
26(5), 275-279.
Lubadde, G., Tongoona, P., Derera, J., & Sibiya, J. (2017). Analysis of Genotype by Environment Interaction of
Improved Pearl Millet for Grain Yield and Rust Resistance. Journal of Agricultural Science, 9(2), 188-195.
https://doi.org/10.4314/ujas.v17i1.6
Nyaligwa, L. M., Shimelis, H., Mwadzingeni, L., & Laing, M. D. (2018). Genotype-by-environment interaction
analysis of maize hybrids for grain yield and maize streak virus severity in the mid-altitude agro-ecologies.
Australian Journal of Crop Science, 12(8), 1304. https://doi.org/10.21475/ajcs.18.12.08.PNE1108
Oral, E., Kendal, E., & Dogan, Y. J. F. E. B. (2018). Selection the best barley genotypes to multi and special
environments by AMMI and GGE biplot models. Fresenius Environmental Bulletin, 27(7), 5179-5187.
Purchase, J. L. (1997). Parametric analysis to describe genotype × environment interaction and yield stability in
winter wheat (PhD thesis, University of the Orange Free State, South Africa).
Rakshit, S., Ganapathy, K., Gomashe, S., Dhandapani, A., Swapna, M., Mehtre, S., … Jadhav, B. J. T. J. O. A. S.
(2017). Analysis of Indian post-rainy sorghum multi-location trial data reveals complexity of genotype×
environment interaction. The Journal of Agricultural Science, 155(1), 44-59. https://doi.org/10.1017/
S0021859616000137
Singh, C., Gupta, A., Gupta, V., Kumar, P., Sendhil, R., Tyagi, B., Singh, G., Chatrath, R., Singh, G. J. C. B., &
Biotechnology, A. (2019). Genotype × environment interaction analysis of multi-environment wheat trials
in India using AMMI and GGE biplot models. Crop Breeding and Applied Biotechnology, 19(3), 309-318.
https://doi.org/10.1590/1984-70332019v19n3a43
Tukamuhabwa, P., Asiimwe, M., Nabasirye, M., Kabayi, P., & Maphosa, M. (2012). Genotype by environment
interaction of advanced generation soybean lines for grain yield in Uganda. African Crop Science Journal,
20(2), 107-116. https://doi.org/10.1007/s10681-011-0404-3
Vargas, M., Crossa, J., van Eeuwijk, F., Sayre, K. D., & Reynolds, M. P. (2001). Interpreting treatment ×
environment interaction in agronomy trials. Agronomy Journal, 93(4), 949-960. https://doi.org/10.2134/
agronj2001.934949x
Wallace, D., Yourstone, K., Baudoin, J.-P., Beaver, J. S., Coyne, D. P., White, J. W., & Zobel, R. (1995).
Photoperiod × temperature interaction effects on the days to flowering of bean (Phaseolus vulgaris L.). In
M. Pessarakli (Ed.), Handbook of plant and crop physiology.
Yan, W., & Rajcan, I. (2002). Biplot analysis of test sites and trait relations of soybean in Ontario. Crop Science,
42(1), 11-20. https://doi.org/10.2135/cropsci2002.1100
jas.ccsenet.org Journal of Agricultural Science Vol. 12, No. 6; 2020
108
Zobel, R. W., Wright, M. J., & Gauch, H. G. (1988). Statistical analysis of a yield trial. Agronomy journal, 80(3),
388-393. https://doi.org/10.2134/agronj1988.00021962008000030002x
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... AMMI model is useful for selecting the best-performing genotypes with specific and wide adaptation (Andiku et al., 2020;Seyoum et al., 2020;Enyew et al., 2021;Worede et al., 2021). ...
Thesis
Sorghum (Sorghum bicolor [L.] Moench) is the foundation crop in the world's dry regions, for food, feed, and bioenergy feedstock. There has not been a systematic breeding program and farmers-preferred varieties of the crop in Namibia due to several constraints. There is a need to develop high-yielding and farmer-preferred sorghum varieties with drought-adaptive traits to boost sorghum productivity in the country. The overall goal of this study was to contribute to the national sorghum breeding program aimed at improving sorghum production and productivity through the development and deployment of climate-smart cultivars preferred by farmers and markets in Namibia via induced mutagenesis. The specific objectives of the study were: (1) to assess the present state of sorghum production in northern Namibia and document farmers’ perceived production constraints and trait preferences in new varieties to guide drought-tolerance breeding; (2) to determine the optimum doses of a single and combined use of gamma radiation and ethyl methanesulfonate (EMS) for effective mutation breeding in sorghum; (3) to determine the genetic profile of elite sorghum lines developed via gamma radiation using diagnostic simple sequence repeat (SSR) markers and phenotypic traits for selection; and (4) to determine the Genotype by environment interaction (GEI) of newly-developed mutant and traditional sorghum lines for grain yield and yield related traits for drought-prone areas of Namibia. In the first study, a survey was conducted using a participatory rural appraisal in the following six selected sorghum-growing constituencies: Kapako and Mpungu (Kavango West Region), Eenhana and Endola (Ohangwena Region), and Katima Mulilo Rural and Kongola (Zambezi Region). Data were collected using a structured questionnaire involving 198 farmers in 14 sampled villages across the regions. An equal proportion of male and female respondent farmers cultivate sorghum, suggesting the value of the crop to both genders in Namibia. Most respondent farmers (63.6%) were in productive age groups of <40 years old. In the study areas, low-yielding landrace varieties, namely Ekoko, Okambete, Makonga, Kamburo, Nkutji, Katoma, Fuba, Dommy, Kawumbe, and Okatombo, were widely cultivated, and most of the farmers did not use chemical fertilizers to cultivate sorghum. Farmers’ perceived sorghum production constraints in the study areas included recurrent drought, declining soil fertility, insect pest damage, high cost of production inputs, unavailability of improved seed, lack of alternative improved varieties with farmers’ preferred traits, lack of organic manure, limited access to market and limited extension service. The key farmers’ preferred traits in a new sorghum variety included high grain yield, early maturity, and tolerance to drought and storage pests. The study recommends genetic improvement and new variety deployment of sorghum with the described farmers-preferred traits to increase the sustainable production of the crop in Namibia. In the second study, two concurrent experiments were conducted as follows: in experiment I, the seeds of four sorghum genotypes (Parbhani Moti, Parbhani Shakti, ICSV 15013, and Macia) were treated using five gamma radiation doses (0, 300, 400, 500 and 600 Gray [Gy]), and three EMS doses (0, 0.5 and 1.0%), and gamma radiation followed by EMS (0 and 300 Gy and 0.1% EMS; 400 Gy and 0.05% EMS). In experiment II, the seeds of two sorghum genotypes (Macia and Red sorghum) were treated with only seven doses of gamma radiation (0, 100, 200, 300, 400, 500 and 600 Gy). The combined applied doses of gamma radiation and EMS are not recommended due to poor seedling emergence and seedling survival rate below LD50. The best dosage of gamma radiation for genotypes Red sorghum, Parbhani Moti, Macia, ICSV 15013 and Parbhani Shakti ranged between 392 and 419 Gy, 311 and 354 Gy, 256 and 355 Gy, 273 and 304 Gy, and 266 and 297 Gy, respectively. The optimum dosage ranges of EMS for genotypes Parbhani Shakti, ICSV 15013, Parbhani Moti and Macia were between 0.41% and 0.60%, 0.48% and 0.58%, 0.46% and 0.51%, and 0.36% and 0.45%, respectively. The above dose rates are useful for induced mutagenesis and creating genetic variation in the tested sorghum genotypes for breeding programs. In the third study, 20 mutant lines (which were at mutation generation 7 [M7]) were developed using gamma-irradiation at 350 Gy from the seed of the variety Macia (SDS 3220). Also, five check varieties were used for the comparative study. DNA extraction was carried out on young and fresh leaves samples per test line 20 days after sowing. Seventeen SSR markers amplified a total of 50 alleles, which varied from 2 to 5 (mean = 2.94). The number of effective alleles per locus varied from 1.08 to 2.53, with a mean of 1.96. The observed heterozygosity ranged from 0.00 to 0.21 (mean = 0.09). The mean expected heterozygosity value was 0.45 indicating moderate genetic differentiation of the tested lines for selection and hybridization. Cluster analysis classified the genotypes into three main groups. Moderate to high genetic distance (≥ 0.50) was displayed between drought-tolerant and high-yielding genotypes that aided in selecting mutant lines such as ‘ML2, ML3, ML4, ML7 and ML14’ compared with the check varieties ‘Macia, Kotovara, ICSR 137, and ICSV 17004’. The selected lines are a useful source of genetic variation for breeding high-yielding and drought-tolerant varieties suited for the drought-prone environments of Namibia. In the fourth study, 50 sorghum genotypes, including 10 newly-developed mutant lines (M9), 33 landraces, two sorghum varieties widely grown in Namibia, and five standard check varieties were evaluated under field conditions using a 10 x 5 alpha lattice design with three replications. The experiments were carried out in four environments with two growing seasons in Namibia. Data were collected on grain yield and related traits and subjected to the Additive Main Effects and Multiplicative Interaction (AMMI) model. The AMMI model showed that 93.9% of the total genetic variation was attributed to days to 50% flowering (DF), while 94.04% of the variation was due to plant height (PH), 86.52% to panicle weight (PW), 70.67% to thousand-grain weight (TGW), and 90.68% to grain yield (GY). The larger variations attributed to genotypic effects for PL (36.3%), TGW (33.2%) and PH (20.7%) are useful for genotype selection for yield-related traits. Based on a multi-trait biplot and Best Linear Unbiased Prediction (BLUPs) analyses of the GEI data across all drought-prone testing environments, the medium maturity mutant line designated as L7P9-13 was selected as the best yielding (2 tons/ha) and recommended for the drought-prone areas of Namibia. In summary, the study identified sorghum production systems, key farmers’ perceived production constraints and trait preferences in new varieties in Namibia. Also, the best dosage of gamma radiation and EMS were determined for increasing the genetic diversity in sorghum for genetic enhancement. Newly developed mutant lines ML2, ML3, ML4, ML7 and ML14 displayed moderate to high genetic distance useful for breeding high-yielding and drought-tolerant varieties suited for the drought-prone environments of Namibia. The medium maturity and drought-tolerant mutant line designated as L7P9-13 was the best yielding (2 tons/ha) and recommended for large-scale production in the country. https://researchspace.ukzn.ac.za/handle/10413/21554
... To analyse GEI, various statistic models such as the Additive Main Effects and Multiplicative Interaction (AMMI) has been widely used (Yan and Kang 2002;Gauch 2006;Gauch et al. 2008). AMMI model is useful for selecting the best-performing genotypes with specific and wide adaptation (Andiku et al. 2020;Seyoum et al. 2020;Enyew et al. 2021;Worede et al. 2021). ...
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