Parametric and Non-Parametric Measures to Identify Stable and Adaptable Cotton (Gossypium Hirsutum L.) Genotypes

ABSTRACT

The study, comprised seventeen genotypes, was conducted during 2016 to 2019 growing seasons. The design was Randomized Complete Block Design (RCBD) with three replications to identify adaptable cotton genotypes. Parametric and non-parametric measures, principal component analysis (PCA) and correlation among the ranks of the parameters computed using R software. The environment, genotype and genotype-environment interaction contributed 79.58, 3.2 and 15.46% of the variation, respectively, and were significant (p < 0.001). The highest (1510.7 kg/ha) and lowest (1080.1 kg/ha) seed cotton yield was recorded from G12 and G8 genotypes respectively. Coefficients of determination (R²) and superiority index (P_i) recognized G13, G11, G10 and G11, G12, G7 as the top three stable genotypes correspondingly. G10 was selected three times as superior by stability variance (σ²), wricke’s ecovalence (W_i) and deviation from regression (S²d_i). Seed cotton yield positively correlated with GAI, Kang’s rank-sum (KRS), Huhn and Nassar S⁽¹⁾, S⁽⁶⁾ S⁽³⁾ while negatively correlated with Thennarasu stability measures NP⁽²⁾, NP⁽³⁾ and NP⁽⁴ . The first, second and third clusters of the PCA biplot comprised, 4, 4 and 10 parameters respectively. G12, with highest seed cotton yield and good stability, was the best genotype and recommended for variety verification.

摘要

这项研究包括17种基因型，在2016年至2019年的生长季节进行. 该设计采用随机完全块设计（RCBD），进行三次重复，以鉴定适应性棉花基因型. 参数和非参数测量，主成分分析（PCA）和使用R软件计算的参数等级之间的相关性. 环境、基因型和基因型-环境相互作用分别贡献了79.58%、3.2和15.46%的变异，具有显著性（p＜0.001）. G12和G8基因型的籽棉产量最高（1510.7公斤/公顷），最低（1080.1公斤/ha）. 决定系数（R2）和优势指数（Pi）分别认定G13、G11、G10和G11、G12、G7为前三个稳定基因型. G10被稳定性方差选为三倍优 (σ²)，wricke的生态价（Wi）和回归偏差（S2di）. 籽棉产量与GAI、Kang秩和（KRS）、Huhn和Nassar s（1）、s（6）s（3）呈正相关，而与Thennarasu稳定性指标NP（2）、NP（3）和NP（4）负相关. PCA双图的第一、第二和第三聚类分别包括4个、4个和10个参数. G12是棉花产量最高、稳定性好的最佳基因型，推荐用于品种验证.

KEYWORDS:

• Cotton
• genotype
• genotype-environment interaction
• parametric and non-parametric
• seed cotton yield
• stability

关键词:

• 棉
• 基因型
• 基因型环境相互作用
• 参数化和非参数化
• 籽棉产量
• 稳定性

Introduction

Cotton (Gossypium hirsutum L.) belongs to the family Malvaceae, and the genus Gossypium comprised about 50 species of which only four (G. hirsutum, G. herbaceum, G. barbadense, and G. arboreum) are cultivated while the remaining 46 are wild growing in the tropics and sub-tropics (Gotmare, Singh, and Tule 2000). The upland cotton (Gossypium hirsutum) is the most popular under cultivation more than any other of the cultivated species (Liu et al. 2013). Moreover, the tetraploid Gossypium hirsutum and Gossypium barbadense are the most widely cultivated cotton species nowadays (Deng et al. 2018). A total of 52 flavonoids, that play a role in cotton fiber quality and color, from cotton, Gossypium hirsutum (Nix, Paull, and Colgrave 2017). Asia (68.7%), America (21.1%) and Africa (6.3%) are the largest seed cotton producing continents and China, India, United States of America, Pakistan and Brazil are the top seed cotton yield producing countries in the world (Faostat 2021). In terms of cotton production area, 87% of the world’s coverage occurs in developing countries (Nix, Paull, and Colgrave 2017). Cotton is currently growing worldwide in approximately 75 countries mainly in the warmer and hotter dry areas of the tropics subtropics and temperate regions (Ayana et al. 2016). Cotton is the most important source of fiber and edible oil covering 40% of the global textile need and 3.3% of edible oil and its seed contains 16% to 24% oil (Khan et al. 2010). Cotton is among the most important seed fiber crops in the world using as a raw material in many spinning and weaving industries, where the fibers from cotton covers 85–90% of the total fibers production and it contains 18–26% oil of the weight of the seeds (Al-Obaidi and Al-Jubouri 2023). As a result, it is called the king of natural fiber crops (Saleem et al. 2009).

Environmental variations among growing environments result in poor yield performance in cotton (Boyer 1982). According to Allard and Bradshaw (1964) environmental variation can be divided into two components as predictable and unpredictable. The former one includes, cropping system, management, long-term climatic condition and others. The latter includes like amount and distribution of rainfall, temperature, established population and others. The lint quality and the seed cotton yield particularly is highly sensitive to agro-climatic conditions (Abro, Rizwan, Deho, et al. 2022) indicating the execution of Multi-Environment Trial (MET) in cotton to identify adaptable genotypes is vital. The presence of a significant genotype-environment interaction (GEI) in yield and yield components and lint quality of seed cotton yield is a common phenomenon (Abro, Rizwan, Rajput, et al. 2022; De Assis Machado et al. 2002; Peixoto et al. 2021; Riaz et al. 2019; Sadabadi et al. 2018; Satish, Jain, and Chhabra 2009; Shahzad et al. 2019; Teodoro et al. 2019). Hence, it is important to conduct a MET to develop stable and high yielding varieties. The existence of significant GEI interaction is both a good opportunity and a challenge for plant breeders (Baraki, Tsehaye, and Abay 2014) and in such situations it is important to combine the yield performance and stability (M. S. Kang and Magari 1995). To identify the stable ones three different methods, viz. parametric univariate, non-parametric univariate, and multivariate methods, can be used (Flores, Moreno, and Cubero 1998). As a result, most breeders and agronomists faced a problem in selecting the most suitable measures to identify desirable genotype and it seems about the breeders’ choice to select the appropriate methods based on different aspects. In this study, different parametric and non-parametric stability measures are used and similarly, Kamali et al., (2009);Kamali et al., (2011) on seed cotton yield and Ahmadi et al., (2018);Cenci and Saavedra (2019);Kılıç (2012) on other crops used parametric and non-parametric stability statistics to identify desirable genotypes.

It is widely cultivated because of it is important raw material for a different products, like textiles, paper, livestock feed, edible oil, medicinal products and many others and hence, the world production is increasing from time to time reached about 41.3 million tons in 2020 (FAOSTAT 2021). Cotton is a good source of cash for the producers in addition to its role as an export item in the national economic development of the country. Furthermore, it offers considerable employment opportunity on farms, industry, and commercial trade, input and service sectors. However, the productivity especially in developing countries is very low (Ayana et al. 2016). Gebregergis et al., (2020) reported that the seed cotton yield in Northern Ethiopia is very low ranging from 1720–2610 kg/ha because of different intermingled constraints. The absence of high yielding varieties is among the most important constraints in Ethiopia that resulted in low productivity and production. Such problems can be solved and desired varieties can be investigated by executing MET using many genotypes. Hence, the objective of this study is to identify high seed cotton yielding and stable cotton genotypes to boost productivity in the growing areas of western Tigray, Ethiopia.

Materials and methods

Description of the material and designs

The present experiment was conducted in the Western Tigray, Northern Ethiopia, during the 2016–2019 cropping seasons under rainfed conditions in 8 environments and 17 cotton genotypes, obtained from breeding program in werer agricultural research center, were used in the trial (Table 1). The design was randomized complete block design (RCBD) with three replications and each plot consisted of 5 meter long five rows with 90 cm and 20 cm spacing between rows and plants respectively. Data on seed cotton yield were taken from the middle rows of each plot and total seed cotton yield (kg/ha) was calculated for each genotype at each test environment.

Table 1. Genotype designation, growing environment and testing sites description.

Genotype designation								Environment description
Gen code	Pedigree	Source	Gen code	Pedigree			Source	Location	Year	Env
G1	Arbominehfromno.3–209-90f1288	WARC	G10	Cucurova1518 × lg-450 35–4			WARC	Humera	2016	E1
G2	DP-90 cucurova 151,837–7	WARC	G11	Delcero x DP-90 f5-5-4-72			WARC	Kebabo	2016	E2
G3	Eurobperv x stam 59A 04–5	WARC	G12	Delcero x DP-90 f5-5-4-2-2			WARC	Humera	2017	E3
G4	Hs-46 × Stoneville 453-19-2	WARC	G13	Delcero x DP-90 f5-5-2-2-1			WARC	Kebabo	2017	E4
G5	Hto 052 × DP-9012-7	WARC	G14	Delcero x DP-90 f5-5-4-3-2			WARC	Banat	2018	E5
G6	Isa 205 h x stam 59A a 11–4	WARC	G15	Delcero x gl-7-8-2			WARC	kebabo	2018	E6
G7	Stam 59A x cucurova 151,830–2	WARC	G16	Delcero x krishna 16–2			WARC	Humera	2019	E7
G8	Stam 59A x cucurova 151,830–6	WARC	G17	DP-90/Standard Check			WARC	Kebabo	2019	E8
G9	Stam 59A x gedera 236–1	WARC
Description of the Testing sites
Climatic and edaphic description			Geographic position of the test sites
			Banat		Humera	Kebabo
Latitude (^oN)			13 ° 48’		14°15’	13°36’
Longitude (^oE)			36 °30’		36°37’	36°41’
Altitude (masl)			619		609	696
Annual rainfall (mm)			501		576.4	888.4
Temp (^oc)		Min	NA		18.9	18.7
		Max	NA		37.6	36.4
		Ave	27–30		28.25	27.55
Soil Texture (%)		Clay	56		35.66	57
		Silt	26		25.66	28
		Sand	18		38.66	15

WARC: Werer Agricultural Research Center of the Ethiopian Institute of Agricultural Research based in Afar regional state, Ethiopia.

Statistical analysis

AMMI Analysis of variance

The seed cotton yield was subjected to a combined analysis of variance for seed yield and AMMI model, which combines the conventional ANOVA and PCA (Zobel 1990). This was used to determine the Genotype (G), environment and genotype by environment interaction (GEI) as well as to further partition the GEI into interaction principal components (IPCs). Tukey HSD was performed to explain the significant differences among mean seed cotton yields of the 17 cotton genotypes. The AMMI model for the yield of the i^th genotype in the j^th environment is computed as:

${\mathrm{Y}}_{\mathrm{ij}}=\mathit{\mu }+{\mathrm{g}}_{\mathrm{i}}+{\mathrm{e}}_{\mathrm{j}}+\sum _{\mathrm{n}=1}^{\mathrm{N}}{\mathit{\lambda }}_{\mathrm{n}}{\mathit{\gamma }}_{\mathrm{in}}{\mathit{\delta }}_{\mathrm{jn}}+{\mathit{\rho }}_{\mathrm{ij}}+{\mathit{\epsilon }}_{\mathrm{ij}}$; Where: Y_ij: the observed mean yield of i^th genotype in the j^th

environment; µ: the grand mean; gi: the i^th genotypic effect (G); e_j: the j^th environment effect (Kaiser); $\sum _{\mathit{n}=1}^N{\lambda }_n{\gamma }_{\mathit{in}}{\delta }_{\mathit{jn}}+{\rho }_{\mathit{ij}}+{\epsilon }_{\mathit{ij}}$ is the GEI; ${\mathit{\lambda }}_n:$ the eigenvector for the i^th genotype from n^th IPCA; ${\mathit{\delta }}_{\mathit{jn}}:$ the eigen vector for the j^th environment from the n^th IPCA; ${\rho }_{\mathit{ij}}:$ the GE interaction; N: the number of IPCA retained in the model; and ${\epsilon }_{\mathit{ij}}:\mathit{\hspace{0.17em}}$the random error term.

Moreover, different parametric and non-parametric stability measures described in (Table 2) were also computed.

Table 2. Parametric and non-parametric stability measures and their descriptions.

Parametric stability measures and their descriptions
Stability measures	Formula	Description
Wricke’s Ecovalence (Wi) (Wricke 1962)	${\mathrm{W}}_i^2={\sum }^{{\left({\mathit{X}}_{\mathit{ij}}-{\bar{X}}_{\mathit{i}}-{\bar{X}}_{\mathit{j}}+\bar{X}\right)}^2}$ Where; Xij is the seed yield of genotype i in environment j; ${\bar{X}}_{\mathit{i}}$: the average yield of genotype i; and, ${\bar{X}}_{\mathit{j}}$: the average seed yield of the environment j; $\bar{X}$: the overall mean and E is the number of environments.	Genotypes with low Wi values are stable
Shukla stability variance (σ^2) (Shukla 1972)	${\sigma }_i^2=\left[\frac{p}{\left(\mathit{p}-2\right)\left(\mathit{q}-1\right)}\right]W_i^2-\left[\frac{\underset{\mathit{i}}{\overset{2}{{{\displaystyle \sum }}^W}}}{\left(\mathit{p}-1\right)\left(\mathit{p}-2\right)\left(\mathit{q}-1\right)}\right]$ Where; Wi: is wricke’s ecovalence; p and q: the numbers of genotypes and environments, respectively	Genotypes with lower values are stable
Coefficient of Variation (CVi) (Francis and Kannenberg 1978)	$\mathit{C}{V}_i=\frac{S{D}_x}{\mathit{X}}\times 100$ Where; SDx: the standard deviation of a genotype mean across environments	Genotypes with low CVi, are stable
Coefficients of determination (R^2) (Pinthus 1973)	$R_i^2=\frac{b_i{\sum }^{{\left({\bar{X}}_{\mathit{j}}-\bar{X}\right)}^2}}{{\sum }^{{\left({\bar{X}}_{\mathit{j}}-\bar{X}\right)}^2}}$ Abbreviations as mentioned above	Genotypes with lowest Ri2 are stable
Geometric Adaptability Index (GAI) (Mohammadi and Amri 2008)	$\mathit{GAI}=\sqrt[\mathit{E}]{\left({\bar{X}}_1\right)({\bar{X}}_2)\dots \left({\bar{X}}_{\mathit{l}}\right)}$ Where; ${\bar{X}}_1,{\bar{X}}_2,{\bar{X}}_1$ are the mean yields of the 1^st, 2^nd and l^th genotypes across the environments; E: number of environments	Genotypes with high GAI are stable
Superiority index (Pi) (Lin and Binns 1988)	$P_i=\frac{{\sum }^{{({\mathit{X}}_{\mathit{ij}}-M_j)}^2}}{2\mathit{E}}$ Where; Xij: is the average seed yield of genotype i in environment j; Mj:is the seed yield of the genotype with maximum performance among all genotypes in the j^th environment and E: is the number of environments	Genotypes with lowest Pi are stable
Eberhart and Russel regression coefficient (bi) and deviation from regression (S^2di) (Eberhart and Russell 1966)	$b_i=1+\frac{{\sum }_i\left(X_{\mathit{ij}}-{\bar{X}}_{\mathit{i}}-{\bar{X}}_{\mathit{j}}+\bar{X}\right)\left({\bar{X}}_{\mathit{j}}-\bar{X}\right)}{{\sum }_j\left({\bar{X}}_{\mathit{j}}-\bar{X}\right)}$	The genotypes with bi = 1 are stable
	$S^2{d}_i=\frac{1}{\mathit{E}-2}\mathit{\hspace{0.17em}}\left[\sum _i\left(X_{\mathit{ij}}-{\bar{X}}_{\mathit{i}}-{\bar{X}}_{\mathit{j}}+\bar{X}\right)\left(X_j-\bar{X}\right)\right]-{\left(b_i-2\right)}^2\sum _j{\left({\bar{X}}_{\mathit{j}}-\bar{X}\right)}^2$ Where; Xij: yield of genotype i in environment j; ${\bar{X}}_{\mathit{i}}$: the average seed yield of genotype I; ${\bar{X}}_{\mathit{j}}$: average yield of the environment j;$\bar{X}$: the overall mean; E is the number of environments	The genotypes with S^2di = 0 are stable
Non-parametric stability measures and their descriptions
Stability Measures	Formula	Description
Kang’s rank-sum (KRS) (M. Kang 1988)	$\mathit{KRS}=R_{\mathit{yield}}$ + R${\sigma }_i^2$ Where; Ryield: rank of yield; R${\sigma }_i^2$: rank of shukla stability measure	The genotypes with lowest KRS are stable
Average rank differences in different environments (S i^(1)) (Hühn and Nassar 1989)	$S_i^{\left(1\right)}=2\sum _j^{\mathit{m}-1}\sum _{j^{\prime }=\mathit{j}+1}^{\mathit{m}}\frac{\left|{\mathit{r}}_{\mathit{ij}}-r_{i{j}^{\prime }}\right|}{\mathit{m}\left(\mathit{m}-1\right)}$	The lowest value for each of these statistics reveals high stability for a certain genotype
The variance among the ranks in different environments (S i^(2))	$S_i^{\left(2\right)}=\sum _{\mathit{j}=1}^m\frac{{({\mathit{r}}_{\mathit{ij}}-{\bar{r}}_{\mathit{i}})}^2}{\left(\mathit{m}-1\right)}$
The sum of squares of rank for each genotype relative to the mean of ranks (S i^(3))	$S_i^{\left(3\right)}=\sum _{\mathit{j}=1}^m\frac{{({\mathit{r}}_{\mathit{ij}}-{\bar{r}}_{\mathit{i}})}^2}{r_i}$
The sum of the absolute deviations for each genotype relative to the mean of ranks (S i^(6))	$S_i^{\left(6\right)}=\sum _{\mathit{j}=1}^m\frac{\left|{\mathit{r}}_{\mathit{ij}}-{\bar{r}}_{\mathit{i}}\right|}{r_i}$
Thennarasu stability measures of NPi^(1), NPi^(2), NPi^(3), and NPi^(4) (Thennarasu 1995)	$\mathit{N}{P}_i^{\left(1\right)}=\frac{1}{m}\sum _{\mathit{j}=1}^m\left|r_{ij}^{\ast }-M_{di}^{\ast }\right|$	Genotypes with Low values of each of these statistic are highly stabile
	$\mathit{N}{P}_i^{\left(2\right)}=\frac{1}{m}\left[\sum _{\mathit{j}=1}^m\frac{\left|r_{ij}^{\ast }-M_{di}^{\ast }\right|}{M_{\mathit{di}}}\right]$
	$\mathit{N}{P}_i^{\left(3\right)}=\sqrt{{\sum }^{\frac{{\left(r_{ij}^{\ast }-{\bar{r}}_{\mathit{i}}^{\ast }\right)}^2/\mathit{m}}{{\bar{r}}_{\mathit{i}}}}}$
	$\mathit{N}{P}_i^{\left(4\right)}=\frac{2}{\mathit{m}\left(\mathit{m}-1\right)}\left[\sum _j^{\mathit{m}-1}\sum _{j^{\prime }=\mathit{j}+1}^{\mathit{m}}\frac{\left|r_{ij}^{\ast }-r_{i{j}^{\prime }}^{\ast }\right|}{{\bar{r}}_{\mathit{i}}}\right]$ Where; rij: rank of i^th genotype in the j^th environment based on adjusted data; $r_{ij}^{\ast }$: mean ranks for adjusted data; $M_{di}^{\ast }:$ median ranks for adjusted data; while ${\bar{r}}_{\mathit{i}}$: and Mdi are mean and median ranks of the unadjusted data respectively: N also represents for NP in some cases.

Principal Component Analysis and Association of the Stability Measures

Finally based on the ranks of genotypes in the different environments spearman’s rank correlation analysis (Piepho and Lotito 1992) was undertaken to estimate the correlation among the different stability statistics. For better visualization of the association of the stability measures PCA was computed to detect interrelationships among the stability statistics using the “factoextra” package (Kassambara and Mundt 2020) of R software 4.2.2. While all other data were analyzed with the assistance of R statistical environment version 4.2.2 (R Core Team 2022) using “metan” package (Olivoto, Lúcio, and Jarman 2020).

Results

Combined AMMI Analysis of Variance and genotypic performance

The seed cotton yield data were subjected to AMMI analysis, which combines analysis of variance (ANOVA) with additive and multiplicative parameters in to a single model (Gauch 2013). The results of the combined ANOVA for seed cotton yield showed that the genotypes (G), environments and GEI were significant (p < 0.001). This confirms the genotypes were different in their genetic potential and the environments in which the genotypes were grown were different. The E, GEI and G effects contributed 79.58%, 15.46%, and 3.2% of the total variation respectively and the GEI was partitioned further to seven statistically significant PCA with 35.8 and 27.9% of PCA1 and PCA2 respectively (Table 3). The E effect was more than five times of the GEI effect and more than 28 time of the G effect. There was statistical significant difference in seed cotton yield among the cotton genotypes and the highest seed cotton yield was recorded from G12 and G11 with 1510.75 and 1474.9 kg/ha respectively while the lowest seed cotton yield (1080.14 kg/ha) was recorded from G8 and the grand mean seed cotton yield was 1325.28 kg/ha. Regarding to the locations and growing environments, there was a statistically significant difference among the environments and locations (Table 4). The highest (2320.5 kg/ha) and the lowest (602.5 kg/ha) seed cotton yield were recorded from E1 and E6 correspondingly.

Table 3. Combined AMMI ANOVA of 17 cotton genotypes.

Source	DF	SS	MS	% SS	% GEI	GEI Accumulation (%)
REP(ENV)	16	175095	10943		.	.
ENV	7	147253217	21036174***	79.58	.	.
GEN	16	5929475	370592***	3.2	.	.
ENV:GEN	112	28603510	255388***	15.46	.	.
PC1	22	10234889	465222***	5.53	35.8	35.8
PC2	20	7991077	399554***	4.32	27.9	63.7
PC3	18	5670604	315034***	3.06	19.8	83.5
PC4	16	1809854	113116***	0.98	6.3	89.9
PC5	14	1440971	102927***	0.78	5	94.9
PC6	12	1085381	90448***	0.59	3.8	98.7
PC7	10	370733	37073***	0.2	1.3	100
Residuals	256	3068071	11985	1.66	.	.
Total	407	185029369	454618		.	.

Table 4. Seed cotton yield (Kg/ha) across the growing environments and locations.

Gen code	Environments (E)								Gen Mean
	E1	E2	E3	E4	E5	E6	E7	E8
G1	2440.7	812.1	1194.6	1191.9	1130.7	455.3	2531.1	1079.2	1354.5^efg
G2	1938.4	989.9	757.3	677	914.6	602.9	2180	994.4	1131.8^jk
G3	1997.3	1110.3	736.6	485.9	1201.6	627.1	2597.7	551.7	1163.5^ij
G4	2647.6	1677.9	1018.6	1076.5	1184.3	504.4	1530.1	924.6	1320.5^fg
G5	2821.7	392.5	1097.5	967.5	1261.9	729.3	2704.9	889.7	1358.1^efg
G6	2281.7	1144.2	1106.7	1352	850.7	390.1	2134.4	1127	1298.4^g
G7	2073.7	1569.3	1099	1082.8	1093.6	739	2701.1	1327.3	1460.7^abc
G8	1970.3	1063.1	630	665.6	294.3	743.5	2512.6	761.8	1080.1^k
G9	2036.6	1716.2	360.1	917.6	1435.5	714.6	2242.7	248.7	1209.0^hi
G10	2358.3	1124.1	1231.2	1198.5	1168	661.9	2148.8	946.1	1354.6^efg
G11	2757.6	1462.8	965	1185.2	1521.9	615.8	2598.4	692.6	1474.9^ab
G12	2179.8	1747.7	1120	1506.5	954.9	758.4	2528.4	1290.3	1510.8^a
G13	2380.7	1268.2	1114.3	1157.2	1313.7	352.1	2481.7	879.4	1368.4^def
G14	2162.8	1972.9	982.6	851.1	1181	454.2	2645.1	1001.4	1406.4^cde
G15	2595.7	1172.5	1078.9	1057.4	1401.4	509.7	2242.4	1044.4	1387.8^de
G16	2159.3	1548.2	1320	864.7	1064	563.9	1347.7	957.5	1228.1^h
G17	2647	658.9	1080.2	1349.4	1623.6	820.9	2254.2	943.6	1422.2^bcd
EnvMean	2320.5^a	1260.6^b	993.7^d	1034.5^d	1152.7^c	602.5^f	2316.5^a	921.2^e	1325.28
MSD (<0.005)									62.04
CV (%)									10.7
Mean of the genotypes across the Three locations
Location	Humera			Kebabo			Banat
Yield	1876.9a			954.7c			1152.6b

Parametric Stability Measures

Since the effect of genotypes on seed cotton yield was found highly significant, mean of the seed cotton yield was taken into account and for this reason a total of 17 parametric and non-parametric stability measures and seed cotton yield rank were calculated to identify the stable genotypes. According to the seed cotton yield rank (Yld) G12, G11 and G7 were the top three high yielding and G8, G2 and G3 were the low yielding cotton genotypes (Table 4). According to Eberhart and Russell (1966), regression coefficients (b_i) genotypic values near to unity (b_i = 1) lowest deviation from regression (S²d_i = 0) is considered as the most stable. Accordingly, b_i and S²d_i identified G9, G17, G15, and G10, G13 and G15 as the most stable genotypes respectively (Table 5). The coefficients of determination (R²) (Pinthus 1973) and Superiority index (P_i) (Lin and Binns 1988) recognized G13, G11, G10 and G11, G12 and G7 as the top three stable genotypes correspondingly while coefficient of variation (Francis and Kannenberg 1978) identified genotypes G16, G12, G10 as the top three stable genotypes. G10 was selected more than any other genotype (three times) as the most stable one by Shukla stability variance (σ²) (Shukla 1972), Ecovalence (W_i) (Wricke 1962) and the Eberhart and Russell (Eberhart and Russell 1966) deviation from regression (S²d_i). Exceptionally, geometric adaptability index (GAI) (Mohammadi and Amri 2008), Superiority index (P_i) (Lin and Binns 1988) and seed cotton yield rank selected three genotypes viz. G7, G11 and G12 as the top three stable ones and these genotypes are statistically non-significant and are the high yielding genotypes (Table 4). Both the seed cotton yield rank and GAI are the only stability measures which identified G12 as the most stable one ranked first.

Table 5. Values and ranks of parametric stability measures for 17 cotton genotypes.

Gen	Yld	CV	σ^2	Wi	bi	S^2 di	R^2	Pi	GAI
G1	1354.5	54.7	53760	67.1	1.1	52154.5	0.91	129720	1188
G2	1131.8	52.4	24153	62.6	0.89	21355.2	0.94	230478	1020
G3	1163.5	65.5	75823	46.8	1.12	73442.1	0.89	227150	981
G4	1320.5	49	142053	68.3	0.85	137033.8	0.71	139299	1193
G5	1358.1	66.6	187190	51.2	1.29	155046.9	0.83	198020	1127
G6	1298.3	48.6	48521	60.6	0.92	49024.7	0.89	137271	1153
G7	1460.7	43.9	52260	84.5	0.94	53647.2	0.88	77396	1353
G8	1080.1	70.4	118971	30.6	1.07	122076.5	0.81	304100	882
G9	1209	62.8	179757	24.1	1	186891.1	0.72	210884	950
G10	1354.6	43.3	15216	85.7	0.9	12248.4	0.96	107835	1255
G11	1474.9	55	50100	80.4	1.24	26250.5	0.96	60013	1292
G12	1510.7	40.5	69628	81	0.87	65690.4	0.84	61638	1405
G13	1368.4	52.8	16358	70.5	1.11	12863.4	0.97	88855	1187
G14	1406.4	54	99654	63.1	1.09	100837.5	0.84	88608	1225
G15	1387.8	49.7	18803	84	1.05	19980.7	0.96	86982	1246
G16	1228.1	39.7	175318	59.6	0.59	103333.9	0.61	211832	1145
G17	1422.2	49.9	119635	63.7	0.98	124747	0.78	136851	1280
Rank
G1	10	12	8	8	8	7	6	8	9
G2	16	9	4	11	10	4	5	16	14
G3	15	15	10	15	12	10	8	15	15
G4	11	6	14	7	14	15	16	11	8
G5	8	16	17	14	16	16	12	12	13
G6	12	5	5	12	6	6	7	10	11
G7	3	4	7	2	4	8	9	3	2
G8	17	17	12	16	5	13	13	17	17
G9	14	14	16	17	1	17	15	13	16
G10	9	3	1	1	9	1	3	7	5
G11	2	13	6	5	15	5	2	1	3
G12	1	2	9	4	13	9	11	2	1
G13	7	10	2	6	11	2	1	6	10
G14	5	11	11	10	7	11	10	5	7
G15	6	7	3	3	3	3	4	4	6
G16	13	1	15	13	17	12	17	14	12
G17	4	8	13	9	2	14	14	9	4

Non-parametric stability measures

Nassar and Huehn’s (Hühn and Nassar 1989) statistics, Thennarasu’s (Thennarasu 1995) statistics and Kang’s (M. Kang 1988) rank-sum and ranks for seed cotton yield of 17 cotton genotypes are depicted in (Table 6). Based on the Nassar and Huehn stability measures of S⁽¹⁾, identified G1, G17, G7, G10 and G15 as the most stable while G3, G16, G6, G5 and G11 as unstable genotypes. G15 had the lowest values of S⁽²⁾, S⁽³⁾ and S⁽⁶⁾ stability measures and as a result was selected as the most stable genotype and the latter two stability measures also ranked G10 as the second stable genotype. Generally, S⁽²⁾, S⁽³⁾ and S⁽⁶⁾ stability measures also recognized for G10, G13 and G15 as the most stable (with in top five) genotypes and for genotypes G3, G6, G8 and G9 as unstable genotypes. Based on the second non-parametric stability statistics (Thennarasu’s stability) it is clear from the (Table 6) that genotypes with the lowest values are recognized as more stable while those with highest value as unstable. The lowest value of NP⁽¹⁾ was recorded from G15 followed by G13, G4, G2 and G1 and so that these genotypes are the most stable ones respectively according to this stability statistics. NP⁽²⁾ selected G2, G15, G4, G8 and G15 as stable ones in that order and G12, G17 and G7 as unstable ones. Similar to NP⁽²⁾, NP⁽³⁾ also selected G2 as the top stable genotype followed by G15, G8 and G4. G1 had the lowest NP⁽⁴⁾ and as a result selected as the most stable while G12 with the highest value was selected as the unstable genotype ranked in the 17^th. G11, G13, G15, G7 and G10 had the lowest values of Kang’s rank-sum stability statistics and hence, are the most stable genotypes and these genotypes had greater than the average seed cotton yield. On the other hand, G9, G8 and G16 had the highest value of this stability statistics and declared as the unstable genotypes while G11, G13 and G15 with smallest value as the highly stable.

Table 6. Values and ranks of non-parametric stability measures for 17 cotton genotypes.

Gen	Yld	S^(1)	S^(2)	S^(3)	S^(6)	NP^(1)	NP^(2)	NP^(3)	NP^(4)	KRS
G1	1354.5	0.00	20.8	15.2	3.20	3.38	.56	.53	.000	18
G2	1131.8	0.25	22.3	14.5	3.85	3.25	.23	.34	.019	20
G3	1163.5	0.50	35.1	24.3	5.10	5.00	.37	.47	.042	25
G4	1320.5	0.25	19.6	15.5	3.13	3.13	.31	.44	.027	25
G5	1358.1	0.32	29.3	20.8	3.37	4.13	.59	.66	.042	25
G6	1298.3	0.36	31.7	27.0	4.42	4.75	.50	.55	.037	17
G7	1460.7	0.11	28.1	11.7	2.43	4.13	.69	.76	.017	10
G8	1080.1	0.18	35.1	33.0	5.76	4.88	.33	.43	.014	29
G9	1209.0	0.25	43.8	30.4	5.02	5.38	.47	.60	.024	30
G10	1354.6	0.14	20.3	10.4	2.33	3.50	.41	.52	.018	10
G11	1474.9	0.32	26.9	15.2	2.84	4.00	.62	.67	.044	8
G12	1510.7	0.25	28.6	12.0	2.39	4.25	1.42	.95	.048	10
G13	1368.4	0.21	18.4	13.2	2.71	3.13	.42	.45	.024	9
G14	1406.4	0.18	30.1	20.0	3.64	3.88	.39	.58	.020	16
G15	1387.8	0.14	10.8	7.7	2.31	2.75	.29	.37	.017	9
G16	1228.1	0.43	24.3	22.0	3.90	3.75	.33	.46	.042	28
G17	1422.2	0.04	30.2	17.7	3.20	4.75	.73	.76	.005	17
Ranks
G1	10	1	5	7	8.5	5	12	9	1	10
G2	16	10.5	6	6	12	4	1	1	7	11
G3	15	17	16	14	16	16	6	7	13	12
G4	11	10.5	3	9	7	2.5	3	4	11	13
G5	8	13.5	11	12	10	1.5	13	13	14	14
G6	12	15	14	15	14	13.5	11	10	12	8
G7	3	3	9	3	4	1.5	15	16	4	4
G8	17	6.5	15	17	17	15	4	3	3	16
G9	14	10.5	17	16	15	17	10	12	9.5	17
G10	9	4.5	4	2	2	6	8	8	6	5
G11	2	13.5	8	8	6	9	14	14	16	1
G12	1	10.5	10	4	3	12	17	17	17	6
G13	7	8	2	5	5	2.5	9	5	9.5	2
G14	5	6.5	12	11	11	8	7	11	8	7
G15	6	4.5	1	1	1	1	2	2	5	3
G16	13	16	7	13	13	7	5	6	15	15
G17	4	2	13	10	8.5	13.5	16	15	2	9

Correlation among stability parameters

The mean seed cotton yield was positively and significantly correlated with GAI, KRS, Pi and S⁽⁶⁾ (p < 0.001), with W_i (p < 0.01) and with S⁽³⁾ (p < 0.05) but it was negatively and significantly (p < 0.005) correlated with NP⁽²⁾ and NP⁽³⁾ (Figure 1). The seed cotton yield rank also had negative and positive, but non-significant, correlation with NP⁽⁴⁾ and NP⁽¹⁾ respectively. S² d_i and b_i had non-significant correlation among each other and GAI had a positive and significant correlation with Yld, W_i, P_i, KRS, and S⁽⁶⁾ (p < 0.001), S⁽³⁾ (p < 0.005), with S⁽³⁾ (p < 0.005) and CV (p < 0.05) while significantly negative (p < 0.05) correlation with NP⁽²⁾ and NP⁽³⁾. Most of the Nassar and Huehn stability measures had a positive and significant correlation among each other except that of S⁽¹⁾ which showed non-significant but positive correlation with S⁽²⁾ and S⁽⁶⁾. Among the Thennarasu’s stability measures only NP⁽³⁾ had a positive and significant correlation with NP⁽¹⁾ and NP⁽²⁾ and all the others had a positive but non-significant correlation to each other. Exceptionally, all of these Thennarasu’s stability parameters had non-significant correlation with the Kankg’s rank sum. Kang’s rank sum had a positive and significant correlation with Yld, σ² (Sh), W_i, R², P_i, GAI, S⁽³⁾ and S⁽⁶⁾ (p < 0.001), with S² d_i (p < 0.005) and with S⁽²⁾ (p < 0.05) while it was negatively but non-significantly correlated with NP⁽²⁾, NP⁽³⁾ and b_i.

Figure 1. Spearman’s correlation for the ranks of parametric and nonparametric stability measures.

Principal component analysis

Based on the rank correlation matrix a principal component analysis was executed. The first five PCs accounted 92.38% of the total variation of the stability parameters. The first PC accounted 44.9% of the total variation and it was significantly associated with KRS, S⁶, S3, S², GAI, Pi, S²di, Wi, Sh, and Yld. PC2 (20.3%) was mainly influenced by NP³, NP² and NP¹. PC3 (13.8%) was associated with NP⁴, bi, S¹ and R². PC5 that accounted only 5.9% of the total variation was associated only with CVP while there was no considerable correlation between PC4 (7.3%) and the stability statistics (Figure 2). PC1 and PC2 revealed the highest (65.3%) percent of variance and hence, these two PCs were used to create a PCA-based biplot. In the biplot the stability statistics and the seed cotton yield clustered in to three clusters: cluster I comprised of NP¹, NP², NP³ and S²; cluster II consisted of NP⁴, S¹, R² and bi; and cluster III included Yld, GAI, Pi, KRS, CV, Wi, S⁶, S³, Sh, S²di. Seed cotton yield showed strong positive correlation with the stability statistics in cluster II and cluster III.

Figure 2. PCA showing the contribution of the stability statistics on extracted principal components based on square cosine and squared coordinates.

Discussion

There is a high possibility of the occurrence of significant GEI in many MET which can be occurred if the different genotypes performed differently across the given environments and it is familiar to most researches (Allard and Bradshaw 1964). Such interactions may be with no interaction, quantitative interaction or qualitative interaction (Ceccarelli 2015). The combined ANOVA of the AMMI model in this study demonstrated that, both the environment, genotype (G) and genotype x environment interaction (GEI) were significant with 79.58%, 3.2% and 15.46% of the total variation correspondingly (Table 3). This corroborates with the findings of Farias et al., (2016);Maleia et al., (2010);Shahzad et al., (2019) who found a significant E, G and GEI using AMMI model ANOVA. Campbell and Jones (2005);Killi and Harem (2006);Riaz et al., (2019);Unay et al., (2004) also conducted studies in cotton genotypes and found a significance of E, G and GEI. Specifically, the former three authors also reported that the significant variation was because of E, GEI and G accordingly. There was statistical significant difference among the genotypes evaluated across the eight environments in their seed cotton yield (Table 4). Ten cotton genotypes viz. G12, G11, G7, G17, G14, G15, G13, G5, G10 and G1 are high yielding genotypes with above the average mean seed cotton yield while the remaining seven genotypes yielded lower than the grand mean (Table 4). G12, G11 and G7 genotypes with mean seed cotton yield of 1510.75, 1474.9 and 1460.73 kg/ha were the high yielding genotypes respectively while G8 was the lowest yielding genotype. The productivity of seed cotton yield varies from 1855–3174 kg/ha (Ali, Aslam, and Hussain 2005), 1445–2877 kg/ha (Riaz et al. 2019), 1720–2612 kg/ha (Gebregergis et al. 2020) and 1960–3096 kg/ha (Shahzad et al. 2019). However, the productivity obtained in this study is lower than earlier reports which may be due to genetic variability of the study materials and the environments under which the experiments were conducted. However, Zeng et al., (2014) and Vineeth et al., (2022) reported a seed cotton yield of lower than 1275.5 kg/ha and 1100 kg/ha respectively which is lower than the average seed cotton yield of genotypes in this study.

Yield stability refers to a genotype’s capability to perform consistently across a wide range of environments (Annicchiarico 2002). Regarding to the stability, genotypes with the smallest variance for a studied trait across the growing environments are considered stable, considered as a biological or static concept of stability (Becker and Leon 1988). Based on the second concept of stability, the dynamic or agronomic concept of stability, a given genotype is recognized as stable if its response to the growing environments is parallel to the average response of all genotypes in the trial (Becker and Leon 1988). The former stability concept is not acceptable by most agronomists and breeders, since they desire genotypes having higher under favorable conditions or improved agronomic practices (Robert, 2002). On the other hand, Simmonds (1991) reflected that the static stability may be more important than the dynamic stability in different situations especially in agricultural production with limited agronomic practices. Both parametric and non-parametric stability statistics have their own strengths and limitations (Delic, Stankovic, and Konstantinov 2009) and hence, most breeders are integrating both parametric and non-parametric stability measures. Furthermore, some others are also integrating different multivariate analyses in addition to these stability measures. As a result, Heravani et al., (2005);Kamali et al., (2009) used different parametric and non-parametric stability measures in their study in cotton crop.

The variability in seed yield of genotype may be predictable (regression) and unpredictable (variance deviation) (Eberhart and Russell 1966). As a result, regression method was executed for the stability analysis of the genotypes. Accordingly, G9 with the b_i value equal to unity (b_i = 1) is the most stable one and hence this b_i can be considered as biological or static concept of stability (Eberhart and Russell 1966). Riaz et al., (2019) used b_i to identify stable and adapted cotton for its seed cotton yield and suggested the importance of using this stability measure. Although this G9 was selected as the stable genotype by b_i this genotype was low yielder (1209 kg/ha) which is below the average seed cotton yield. The high seed cotton yielder genotype G12 (1510.7 kg/ha) was identified among the unstable genotypes together with G4, G5, G11 and G16 since their b_i values had larger variation from unity. On the other hand, this G12 was recognized as it is among the top four stable ones according to CV, W_i, P_i, GAI, S⁽³⁾ and S⁽⁶⁾ indicating there is a bit controversy with the b_i. Similar result was also reported by Vaezi et al., (2019) in selection of stable barley genotypes while this is in contradiction to the findings of Temesgen et al., (2015) in faba bean where this b_i could recognized for the high yielding genotypes as the stable ones. Furthermore, Shahbazi (2019) also reported that, CV, P_i and GAI are the stability measures used to choose the high yielding genotype. According to the deviation from regression, G10, G13 and G15 with the lowest values of S² d_i are considered as the most stable genotypes and all produced above the average mean yield (Table 5). Kang’s, 1988 (KRS), considers the seed cotton yield rank and the Shukla stability variance (σ²) rank so as to recognize genotypes with lowest value as stable while those with highest value as unstable. Accordingly, G11, G13 and G15 are declared as the most stable while G9, G8 and G16 declared as unstable. The stable genotypes according to this parameter had a seed cotton yield above the average mean and those declared as unstable had below the average seed cotton yield and accordingly this study suggest that KRS may be among the important parameters to select desirable genotypes which is similar to the findings of (Farshadfar, Sabaghpour, and Zali 2012).

Non parametric stability measures of Thennarasu (N⁽ⁱ⁾) and Huhn stability statistics of S_i⁽¹⁾, S_i⁽²⁾, S_i⁽³⁾ and S_i⁽⁶⁾ computed based on the genotype rankings in the different environments (Table 6) distinguishing genotypes with minimum change of rank across environments are known as stable genotypes while those of with higher changes of ranks as unstable. The Huhn stability statistics of S_i⁽¹⁾, S_i⁽²⁾, S_i⁽³⁾ and S_i⁽⁶⁾ identified genotypes G6, G8 and G9 among the unstable genotypes while G10 and G15 among the most stable genotypes. This is in contrast to the findings of Kilic et al., (2010);Temesgen et al., (2015) who reported these parameters were able to recognize for high yielding genotypes as unstable while for low yielding genotypes as stable. Similar to the b_i, Thennarasu’s stability of N⁽²⁾, N⁽³⁾ and N⁽⁴⁾ selected G12, with the highest values of these statistics, as most unstable genotype. This is because of the performance of this genotype highly varies across environments ranging from 758.4–2528.4 kg/ha in E6 and E7 respectively (Table 4) confirming there was high variability among the growing environments and this is in line with the findings of Kaya and Taner (2003).

Among the parametric stability measures, GAI, P_i and W_i had positive and significant correlation with seed cotton yield while the remaining had non-significant correlation. Hence, GAI, P_i and W_i are among the best parametric measures to identify superior genotypes and this is in accordance with Kaya and Taner (2003). Related to the Huehn stability measures S_i⁽³⁾ and S_i⁽⁶⁾ had a positive and significant correlation with the seed cotton yield rank and these parameters are associated with the agronomic stability. According to Hühn and Nassar (1989) these stability measures combines mean yield and stability based on stability ranks in the growing environments. S_i⁽²⁾ had a positive and significant (p < 0.001) correlation with S_i⁽³⁾ and S_i⁽⁶⁾ which is in line with the findings of Farshadfar et al., (2012), Furthermore, S_i⁽¹⁾ had significant correlation with S_i⁽³⁾ and similarly Scapim et al., (2000) also reported a significant correlation among S_i⁽¹⁾ and S_i⁽³⁾. N⁽¹⁾ had significant correlation with S_i⁽²⁾, S_i⁽³⁾ and S_i⁽⁶⁾. Similarly, Abdulahi et al., (2008);Farshadfar et al., (2012) also found significant correlation of N⁽¹⁾ with S_i⁽²⁾ and S_i⁽³⁾. NP⁽¹⁾ and NP⁽⁴⁾ had positively and negatively but non-significant correlation with the seed cotton yield rank. On the other hand, NP⁽²⁾ and NP⁽³⁾ had a negatively significant correlation with the yield rank and this study indicates they are not appropriate measures to select high yielding genotypes. Moghaddam and Pourdad (2009) also reported that both the Huehn and Thennarasu’s stability measures had a negative correlation with the seed cotton yield rank, indicating there is no complete similarity of these parameters in prioritizing the genotypes. Unlike to this study, Kadhem et al., (2010) reported that all of these parameters showed negative correlation with the seed cotton yield rank suggesting these are not important to select stable rice genotypes. However, in contrast to this, Vaezi et al., (2018) reported that all of these stability measures showed positive correlation with seed cotton yield rank suggesting as they are important to select stable barley genotypes. Among the Thennarasu’s stability measures it was only NP⁽³ which had highly and positively correlation with NP⁽¹⁾ and NP⁽²⁾.which is different from the findings of Vaezi et al., (2018) who reported all of these parameters had a positive and significant correlation among each other. KRS had a positive and significant correlation with Yld, σ², W_i, R², P_i, S⁽³⁾, S⁽⁶⁾, S² d_i and S⁽²⁾ indicating it is important to incorporate KRS with these stability measures to select a desirable genotype. However, Khalili and Pour (2016) reported that this Kang’s rank sum had a negative and significant correlation with seed cotton yield rank, S⁽³⁾, and all the Thennarasu’s stability measures. Generally, the seed cotton yield was positively and significantly correlated with GAI, KRS, Pi, S⁽⁶⁾, W_i, and S⁽³⁾, S⁽⁶⁾ and this study suggests these parameters may be important in selecting high yielding and stable genotype. The different stability measures used in this study are not consistent in identifying the stability of the genotypes since some genotypes become stable according to some parameters while unstable according to other parameters. Such phenomenon is a common challenge in GEI studies and similar suggestions were forwarded by Khalili and Pour (2016);Vaezi et al., (2018).

A PCA biplot using the rank correlation matrix of 17 parametric and non-parametric stability measures in seed cotton yield was executed. Kaiser (1960) suggested that PCs greater than a unity is considered as significant and accordingly five PCs. The first five PCs accounted 92.38% of the total variation of the stability statistics. The first PC accounted for 44.9% of the total variation and it was significantly correlated with KRS, S⁶, S3, S², GAI, Pi, S²di, Wi, Sh, and Yld. The second PC contributed 20.3% of the total variation and it was mainly influenced by NP³, NP² and NP¹. PC3 explained 13.8% of the total variation and it was associated with NP⁴, bi, S¹ and R². PC5 that accounted only 5.9% of the total variation was associated only with CV while there was no considerable correlation between PC4, which accounted 7.3%, and the stability statistics (Figure 2). This corroborates with the findings of Pour-Aboughadareh et al., (2023) who reported that most of the stability statistics were associated with the first six PCs and similarly, Pour-Aboughadareh et al., (2021) also reported that most of the physiological traits were associated with the first five PCs.

PC1 and PC2 were used to create a PCA-based biplot, which is vital to investigate the relationships between seed cotton yield and stability statistics; and the association between the stability statistics. In the biplot, a cosine angle between two statistics vectors shows a strong positive correlation; where as a large cosine angle between the statistics shows a weak correlation. On the other hand, no correlations and strong negative correlations were displayed at cosine 90° and 180° respectively. Accordingly, seed cotton yield showed strong positive correlation with the stability statistics in cluster II and cluster III (Figure 3). Hence, these stability statistics express a dynamic concept of stability due to their close correlation with the seed cotton yield. Similarly, Moghaddam and Pourdad (2009) also clustered the seed cotton yield with the likes of P_i, KRS and b_i while this is in contrast to the results of Kadhem et al., (2010);Temesgen et al., (2015) who reported seed yield was negatively correlated with these parameters. On the other hand, it was not correlated with NP¹ and S² while it was strongly and negatively correlated with NP² and NP³. According to the biplot the stability statistics and the seed cotton yield grouped in to three clusters (I-III). Cluster I comprised of four statistics viz. NP¹, NP², NP³ and S²; cluster II consisted of four parameters namely NP⁴, S¹, R² and bi; and cluster III included Yld and other nine stability parameters viz., GAI, Pi, KRS, CV, Wi, S⁶, S³, Sh and S²di. Seed cotton yield (Yld) belongs to the third cluster confirming it had positive association with the stability statistics in this cluster. This result corroborates with the findings of Pour-Aboughadareh et al., (2023) and Verma et al., (2018).

Figure 3. PCA showing the grouping of the stability statistics in the first two principal components.

Conclusion and recommendation

In the current study, a significant GEI was found confirming there was a variation among the genetic potential of the genotypes, the environments and their interaction confirming the seed cotton yield rank variation across environments. In such situations, selecting desirable genotypes, integrating parametric, non-parametric and other graphical measures in a given study seems ideal for agronomists and plant breeders. Seed cotton yield was positively associated with nine stability parameters viz., GAI, Pi, KRS, CV, Wi, S⁶, S³, Sh and S²di indicating these stability statistics express a dynamic concept of stability because of their positive association with the seed cotton yield. Both the seed cotton yield rank, GAI, P_i and W_i identified G12 (the high yielder genotype) as most stable genotype ranked first and this genotype was also moderately stable according to some other stability parameters. Hence, this genotype considered as superior genotype and recommended for variety verification to get recognition from the Ministry of Agriculture of the country and to be used as improved variety in the country. Finally, this study recommends to developing a new cotton variety in the study areas, it is crucial to evaluate a range of genotypes across years and locations to see the spatial, temporal and their interaction, which enables to evaluate their performances and stabilities simultaneously.

Highlight

• Genotype “Delcero x dellopile 90 f5-5-4-z-2” (G12) is the high yielder and moderately stable genotype and hence, this genotype is recommended in the region and the country as well to be used as new variety.

• Cotton seed is positively associated with nine stability parameters viz., GAI, Pi, KRS, CV, Wi, S⁶, S³, Sh and S²di indicating these stability statistics express a dynamic concept of stability.

• This study recommends to develop a new variety it is crucial to evaluate genotypes across years and locations to see the spatial, temporal and their interaction.

• This study suggests integrating parametric, non-parametric and other graphical measures is vital to select stable and high yielding genotype.

Authors’ contributions

FB and ZG designed the study; FB, YB, ZG, GT, ZG, AA, AA and WN conducted the study at field level and collected the required data. FB analyzed the data and wrote the initial draft of the manuscript. ZG, YB and GT further developed the manuscript and all authors read and approved the final manuscript.

Acknowledgments

The authors would like to sincerely acknowledge to Tigray Agricultural Research Institute for the financial support, and they would like to extend their special thanks to all Humera Agricultural Research Center researchers for their commitment during conducting the present study.

Disclosure statement

No potential conflict of interest was reported by the author(s).