Designing an Index for Multi-location Yield Stability Analysis Involving Univariate and Multivariate Methods in Rice (Oryza sativa L.)

Abstract

Under different environmental conditions, crop yields differ primarily due to G and E interactions. The Global Rice Array (GRA-IV) is IRRI's fourth flagship project to identify climate-resilient rice genotypes. Use of Several univariate and multivariate methods can differentiate genotypes based on their behaviour under different environmental conditions. Since genotypes were ranked differently across models, ASR and Yield Stability Index (YSI) were combined in this study. It included 15 rice genotypes (from a collection of global rice arrays IV called the "Antenna Panel"). Experimentation done in five diverse environments in the Northern Tarai region of India. Grain yield over five diverse environments was significantly influenced by genotypes, G (24.51%), environments, E (40.79%), and genotype and environment effects combined (34.69%). G2, G5, G8, G15 and G10 exhibited lowest ASR values. G2 is the most stable high-yielder, concluded on the basis of new stability index calculated by combining the ASR's and YSI values; these superior genotypes can benefit breeding programs in the future. A stable-high yielder can be more accurately predicted with the new stability index.

Keywords:
AMMI, Rice-yield; Multi-environment evaluation; Stability; Non-Parametric; Parametric

HIGHLIGHTS

"Antenna Panels" characterize the changing climate dynamics through the crop’s eye.

New stability index can decipher stability more accurately.

INTRODUCTION

A majority of Asia's staple food requirements are met by rice, which feeds more than three billion mouths worldwide [¹,²]. The massive increase in population over the next few decades will necessitate a 50% increase in rice production [³,⁴]. A majority of Indians rely on rice directly or indirectly to meet their calorie needs [⁵]. On a global scale, China is ranked first producing 148.99 million metric tons and India is ranked second among all countries producing 129.47 million metric tons of rice [¹]. Recent years have seen the Indian subcontinent's rice production face several challenges, mainly due to degrading crop-environments and changing climate conditions [⁶,⁷]. Most Indian varieties has already reached a yield-plateau, leading to a decline in factor productivity as well as a stagnation in yields [⁸]. Globally, climate variability accounts for 1/3rd of rice yield fluctuations [⁹]. A diverse panel of heterogeneous genotypes containing beneficial genes called “Antenna Panel” - is developed by the Global Rice Array-IV (GRA-IV), has been launched by IRRI. It enables researchers to better understand G ˟ E interactions and stay ahead of climate change. GRA-IV aims to accelerate genetic gain by identifying environmental factors that influence adaptive traits. An enormous project such as this can help accelerate the development of better adapted varieties of rice across the globe. Genetic interactions play significant role in the variation of varieties' stability across various environments. It has been shown that the majority of polygenic traits in rice, such as grain yield, are highly affected by various sorts of environmental conditions [¹⁰]. There is also evidence to suggest that grain yields in crops are not always determined by the same set of genetic systems across diverse environmental conditions [¹¹]. The development of genotypes tailored to a particular environment complex is therefore often desirable [¹²]. In multi-location trials (MLTs), genotypes were found to differ either due to a change in rank or by their exact differences without any changes in ranks [¹³]. Selection of superior stable genotypes well suited to Himalayan foothills (tarai) and Indo-gangetic plains, from this global collection of genotypes can help break yield plateau. Spatially and temporally spread trials can identify stable and superior varieties [¹⁴]. Yield stability analysis models, both parametric and non-parametric, have their own advantages and disadvantages. These models are used to assess the stability of crop yields over different environments and years. Parametric models suffer from issues like assumption sensitivity, limited flexibility, requires a large amount of data to reliably estimate parameters, and obtaining such datasets can be challenging, susceptibility to outliers whereas non-parametric models, often require large amounts of data for training, which may be a limitation in agricultural contexts where data collection can be resource-intensive. So, combining multiple methods of stability analysis is highly recommended [¹⁵-¹⁸]. The average sum of Ranks is based on ranks other than raw values making it less sensitive to outliers. Moreover, ASR provides a more reliable measure of central tendency when the data distribution is not normal but skewed. Such assessment of median performance is important for stability analysis. Combination of ASR with YSI provides more holistic evaluation and comprehensive analysis of G x E as it includes yield of genotypes across environments along with stability ranks. This combination provides a nuanced understanding of stability by striking a balance between high yield and stability and henceforth increasing the accountability of selection of genotypes. Using Yield Stability Index (YSI) and Average of Stability Rankings (ASR) together identified the highest yielding and stable rice genotypes for Himalayan foothills (tarai) and Indo-gangetic plains. Based on the performance and stability of these exotic genotypes over five different testing environments, the findings of this study will help rice improvement programs start off on the right foot. This will also help identify/predict stable-high yielders more precisely using a combinatorial Index involving Univariate and Multivariate Methods for yield stability analysis over Multi-location.

MATERIAL AND METHODS

Plant materials and field evaluation

This study involved field experimentation during July to October of 2021 at the university farm of Pantnagar (E I), Rudrapur (E II), Krishi Vigyan Kendra Kashipur (E III), Krishi Vigyan Kendra Dhanauri Haridwar (E IV) and Agriculture Research Centre Majehra (E V), Uttarakhand, India. Five locations were considered for the current study. Pantnagar (E I) and Rudrapur (E II), generally experience a subtropical climate. Summers are warm, with temperatures ranging from 25 to 40 degrees Celsius. Monsoon season typically occurs from June to September, bringing rainfall to the region with an average of 250 mm to 308.8 mm per month. Maximum rainfall was observed during the month of August. The growing location at Kashipur (E III) and Haridwar (E IV) witnessed maximum rainfall during September and the temperature fell to 20 degrees Celsius towards the end of the growing season, that is November. Growing location Majhera (E V) is situated in the hills of Uttarakhand, India and thus the growing conditions were cooler than other sites with temperatures ranging from 15 to 20 degrees Celsius and witnessed erratic rainfall ranging from 30 mm during November to 461.7 mm during October. The genetic materials for this experiment were part of the Global Rice Array (GRA-IV's antenna panel) (Table 1). At all growing sites, 15 genotypes were transplanted on 22nd July and harvested between as per maturity. Every plot was transplanted with four rows of 2 m length, and the experiment was replicated thrice. In all five locations, standard agronomic practices were followed. We recorded and reported grain yields for each plot in kilograms per hectare.

Statistical analysis and procedures

With an online software program PBSTAT-GE 2.3 (www.pbstat.com) [¹⁹], parametric and non-parametric methods of stability analysis like, “Huehn” (1990), “Nassar and Huehn” (1987) (S(i)) and “Thennarasu” (1995) (NP(i)), “Wricke's (1962) ecovalence” (W2i), “Francis and Kannenberg's (1978) coefficient of variance” (CVi), regression coefficient (bi) and deviation from regression (S2di) were were calculated. In order to analyze the AMMI model and to construct biplots, we used GEA-R (2017) Version 4.1 software available at www.cimmyt.org [²⁰]. According to Purchase and coauthors (2000) and Bajpai and Prabhakaran (2000), AMMI stability values (ASV) and Yield Stability Index (YSI) were estimated [²¹, ²²].

RESULTS AND DISCUSSION

Analysis of Variance across different locations

The perusals of Table 1 indicated that grain yield ranged from 1985.56 kg/ha (G 5) to 4378.50 kg/ha (G 4) with grand mean of 3074.00 kg/ha over studied environments. The observations on grain yield recorded from the investigated environments were analyzed separately to check the genotypic significance. The ANOVA of five studied environments showed that significant genotypic differences were present and hence all of them were included for pooled analysis (Table 2). At the 1% level of significance, the pooled analysis showed highly significant mean sums of squares for all sources of variations (Table 3); this indicates the possibility of relevant crossover and non-crossover effects. Amongst tested genotypes Persistent performance in terms of yield was due to non-crossover interactions while a shifting of ranking over different growing conditions was due to crossover. It is evident that genotypes perform differentially across environments thus requiring to be tested over different seasons and across diverse locations to decipher interactive G × E effects precisely and to identify stable genotypes for future. The significant genotypic differences for grain yield indicated the preponderance of sufficient genetic variability among the genotypes. There were significant differences in conditions in the studied environments, and the prevailing climatic conditions heavily influenced grain yields. Under different environments, genotypic performance differed significantly due to the significant interactions between G and E. A number of researchers [²³, ²⁴] have previously reported the importance of genotype (G), environment (E) and interactions between genotype and environment for rice grain yield. Due to the significant interaction between G and E in the present study, the analysis was extended to decipher various stability parameters using available models.

Table 1
Yields of different rice genotypes across different environments

Coded number	Genotypes	E I	E II	E III	E IV	E V	Mean
G 1	MINGHUI 63	4383.00	4363.00	3245.83	4166.66	2100.00	3651.70
G 2	ZHENSHAN 97 B	2979.33	3875.00	2570.83	3541.66	1780.00	2949.36
G 3	IR 64	3380.00	6288.00	2100.00	4583.33	1345.00	3539.26
G 4	IRBB 66	3580.00	5200.00	3437.50	6875.00	2800.00	4378.50
G 5	IRRI 147	1735.33	3475.00	754.16	2708.33	1255.00	1985.56
G 6	SANHUANGZHAN NO 12	1616.66	3275.00	3070.83	6250.00	2555.00	3353.50
G 7	IR771286-122-2-2-3	2492.00	4788.00	1845.83	4166.66	1177.00	2893.90
G 8	IR772398-14-1-2-10	2218.66	4063.00	2587.50	2916.66	1700.00	2697.16
G 9	SAMBHA MAHSURI + SUB 1	4409.00	1900.00	3350.00	833.33	1013.00	2301.06
G 10	SUPA	2569.00	2988.00	866.66	2687.50	1625.00	2147.23
G 11	IRRI 104	4319.66	6363.00	3041.66	4583.33	2562.00	4173.93
G 12	N 22::IRGC 19379-1	4371.33	2575.00	1741.66	2500.00	1569.00	2551.40
G 13	MTU1010	2654.66	6913.00	2820.83	5000.00	2725.00	4022.70
G 14	NANHI	1313.00	5150.00	1154.16	2708.33	2345.00	2534.10
G 15	JASMINE 85	2394.66	4888.00	1895.83	3750.00	1725.00	2930.70
	Mean	2961.08	4406.93	2298.88	3818.05	1885.06	3074.00

Table 2
ANOVA of different environments for grain yield

SOV(Source of Variation)	Df degrees of freedom)	MSS (Mean Sum of Square) for grain yield
		E I	E II	E III	E IV	E V
Replication	2	174390	9946	63024	178016	499
Genotypes	14	3402324**	6302085**	2430182**	7146664**	1049214**
Error	28	577096	14223	500673	51598	2330

Table 3
Pooled ANOVA for grain yield across environments

SOV	df	MSS
Environment (E)	4	49021184**
Genotype (G)	14	8417203**
G x E	56	2978317**
Error	140	229184

• * and ** refers to significant at 0.05 and 0.01 probability levels, respectively

Stability estimation by using Non-parametric models

Crop performance including rice is mainly governed by the interaction of both the crop genetic makeups (G) as well as prevailing environmental conditions (E). Thus making the need of understanding the G×E interactions, indispensable. Simple ANOVA (Analysis of variance) is insufficient to decipher interactive G × E effects and calls for subsequent use of supplementary statistics like non-parametric and parametric methods for understanding the interactive effects in a better way. Sensitivity of non-parametric methods are less to measurements of error [²⁶, ²⁷]. Non-parametric procedures are advantageous because of the reduction of biases, simpler calculations and greater interpretability of the results. As well as, results obtained from the non-parametric methods are indifferent to the inclusion or exclusion of one or more genotypes in the study [²⁶, ²⁷]. As evident from the results above, the five growing seasons were significantly diverse due to weather fluctuations. Largely differing growing environments thus resulted in significant yield deviations among the experimental rice genotypes. As for example, in our study from a close insight of table 1 it was seen that mean grain yield ranged from 754.16 kg/h for G 5 in E III to 6913.00 kg/h for G 13 in E II. Interactive G × E effects thus can be witnessed to reduce yield performance of genotypes by minimizing their effectiveness. Thus in order to increase the reliability and heritability of such traits and to better decipher the interactive G × E effects yield stability need to be assessed with high precision [¹⁵]. Henceforth non-parametric models were used in this study to accomplish the desired objectives. Huehn (1990) and Nassar and Huehn (1987) developed four parameters for stability analysis i.e. S(1), S(2), S(3) and S(6). For each of these four statistics, the lowest value corresponds to high stability [²⁶, ²⁷, ²⁸]. The parameter S(1) considers the mean of differential absolute genotypic ranks over all test environments and it indicated that genotype G 2 [S(1) = 2.4 , rank= 1], G 15 (S(1) = 2.8 , rank= 2), G 5 (S(1) =3.8 , rank=3) were found desirable across test locations (Table 4).The parameter S(2) is based upon the rank variances over all environments in which the experiments were conducted and it indicated the genotype- G 2 (S (2) = 3.7, rank=1) as most stable genotype followed by G 15 (S (2) =5.3, rank=2), G 5 (S (2) =10.3, rank=3), G 8 (S (2)= 14.8, rank=4) and G 11 (S(2) =15.3, rank=5).

Table 4
Ranking of different genotypes of rice according to non-parametric models

Genotype	S ⁽¹⁾	S ⁽¹⁾ Rank	S ⁽²⁾	S ⁽²⁾ Rank	S ⁽³⁾	S ⁽³⁾ Rank	S ⁽⁶⁾	S ⁽⁶⁾ Rank	NP ⁽¹⁾	NP ⁽¹⁾ Rank	NP ⁽²⁾	NP ⁽²⁾ Rank	NP ⁽³⁾	NP ⁽³⁾ Rank	NP ⁽⁴⁾	NP ⁽⁴⁾ Rank
G 1	4.8	5	15.7	6	4.9412	8	2.0392	10	3	7	0.5	10	0.6949	10	0.9412	10
G 2	2.4	1	3.7	1	0.8293	2	0.6341	2	1.4	1	0.175	2	0.2098	1	0.2927	1
G 3	7.4	13	37.3	12	7.5652	10	2.087	11	4.8	13	0.8	12	0.7917	11	1.0725	11
G 4	5.0	7.5	18.7	8	6.3333	9	3.5	15	3	7	3	15	1.6116	15	2.0833	15
G 5	3.8	3	10.3	3	0.7717	1	0.4567	1	2	3	0.1538	1	0.226	2	0.2992	2
G 6	7.8	14	43.3	14	16.2222	14	3.2222	13	5	14	1.25	13	0.8174	12	1.0833	12
G 7	5.0	7.5	16.7	7	3.8969	7	1.2165	6	2.8	4	0.28	5	0.3768	6	0.5155	6
G 8	4.8	5	14.8	4	1.4043	3	0.6809	3	2.8	5	0.3111	6	0.3661	5	0.5106	5
G 9	8.4	15	49.2	15	22.8333	15	3.375	14	5.6	15	0.3733	8	0.6535	9	0.875	9
G 10	5.6	9	20.3	9	1.5932	5	0.7797	4	3.4	9	0.2615	4	0.3415	4	0.4746	4
G 11	4.8	5	15.3	5	1.5676	4	1.2973	7	3	7	0.75	11	0.9456	13	1.2973	13
G 12	6.4	10.5	27.5	11	7.6667	11	1.4444	8	4	11	0.3333	7	0.4343	7	0.5926	7
G 13	6.4	10.5	26.7	10	8.5	12	3	12	3.8	10	1.2667	14	1.1554	14	1.6	14
G 14	7.2	12	39.2	13	8.7071	13	1.9798	9	4.6	12	0.4	9	0.5657	8	0.7273	8
G 15	2.8	2	5.3	2	1.7674	6	0.8837	5	1.6	2	0.2	3	0.2394	3	0.3256	3

The parameter S(3) sums the absolute genotypic deviations from the mean of ranks and it indicated that the most stable genotype was G 5 (S (3) =0.77, rank=1) followed by G 2 (S(3)=0.8293, rank=2), G 8 (S(3)=1.40 , rank=3), G 11 (S (3) =1.56 , rank=4) and G 10 (S (3) =1.59 , rank=5). In case of stability parameters S(6) , the summation of squared genotypic ranks from the mean of ranks is considered, and it revealed that the most stable genotype was G 5 (S (6) = 0.45, rank=1), followed by G 2 (S (6) = 0.63, rank=2), G 8 (S (6) = 0.68, rank=3), G 10 (S (6) = 0.77, rank=4) and G 15 (S(6) = 0.88, rank 5). S (1-6) models showed that genotype G 2 was far more stable according to S (1) and S (2), while G 5 was most stable according to S (3) and S (6).

Thennarasu (1995) [²⁹] developed stability statistics i.e. NP (1-4), based on the adjusted genotypic mean ranks over all test environments. The lower parametric values correspond to high stability. The stability parameter NP (1) revealed G 2 (NP (1) = 1.4, rank=1), G 15 (NP (1) = 1.6, rank=2), G 5 (NP (1) = 2.00, rank=3), G 7 (NP (1) = 2.8, rank=4) and G 8 (NP (1) rank=5) as most stable genotypes. However, the stability parameter NP (2) revealed G5 (NP (2) = 0.15, rank=1), G 2 (NP (2) = 0.17, rank=2), G 15 (NP (2) = 0.2, rank=3), G 10 (NP (2) = 0.26, rank=4) and G 7 (NP (2) = 0.28, rank=5) as most stable genotypes. The stability parameter NP (3) revealed G 2 (NP (3) = 0.20, rank=1), G 5 (NP (3) = 0.22, rank=2), G 15 (NP (3) = 0.23, rank=3), G 10 (NP (3) = 0.34, rank=4) and G 8 (NP (3) = 0.36, rank=5) as most stable genotypes while the stability parameter NP (4) revealed genotype G 2 (NP (4) = 0.2927, rank=1), G 5 (NP (4) = 0.2992, rank=2), G 15 (NP (4) = 0.32, rank=3), G 10 (NP (4) = 0.47, rank=4) and G 8 (NP (4) = 0.51, rank=5) as most stable. NP (1), NP (3) and NP (4) parameters revealed G 2 as the most stable genotype whereas NP (2) stability parameter found out G 5 as the most stable genotype. Thus, it is evident from the use of above non-parametric methods that results are difficult to validate. Genotype G 2 was most stable genotype according to S (1), S (2), NP (1), NP (3) and NP (4) parameters, over all the five growing environments while G 5 was most stable genotype according to S (3), S (6) and NP (2). Non-parametric methods resulted in differential rankings, making it difficult for breeders to conclude. The differences in genotype rankings across yield stability analysis models can be attributed to a combination of model assumptions, data characteristics, and the specific features that each model emphasizes or handles differently. As evident in this study, the shift in genotypic rankings across methods suggests the need to combine these parameters with others. [³⁰].

Stability analysis by using parametric models

Amongst parametric models used in this study, Wricke’s ecovalence method and Francis and Kannenberg’s method are based upon variances whereas Eberhart-Russell’s method was based upon regression. The magnitude of interaction of different genotypes over several environments is indicated by the varying range of different variables, where those with least variances interacts less with the environment and those having greater variances are highly affected by environments [³¹]. On these lines, the ecovalence (W2i) of each genotype is estimated. This method judges performance of genotypes by considering its contribution towards interaction sum of squares. The genotypes having a low value of W2i possess low stability variance and hence are considered as stable [³²]. The W 2i indicated that genotype G 2 (W 2i = 366993.9, rank=1) was most stable followed by genotype G 5 (W 2i= 462102.4, rank=2), G 15 (W 2i = 642282, rank=3), G 8 (W 2i = 889486.9, rank=4) and G 7 (W 2i = 1031212, rank=5) (Table 5).

The coefficient of variation (CVi) identifies the desirable genotypes on basis of low CVi and high mean yield [³³]. A close perusal of Table 5 indicated that genotype G 1 (CVi= 26.97, rank=1) followed by G 2 (CVi= 27.96, rank=2), G 8 (CVi= 32.9, rank=3), G 11 (CVi= 35.66, rank=4) and G 4 (CVi= 37.74, rank=5) were most stable genotypes. The rank of the genotypes by parameter CVi is different as compared to the W2i stability parameters. The limitation of the CVi model lies in the fact that when attempting to compare genotypes all over varying yielding environments, if standard deviation and mean do not fluctuate parallely then biases occur. [³⁴]

Table 5
Ranking of different genotypes of rice according to parametric models.

Genotype	Wᵢ²	Wᵢ² Rank	σ²ᵢ	σ²ᵢ Rank	CVi	CVi Rank	bi	bi Rank	s2di	s2di Rank	Sum of ranks of parametric and non-parametric models [SR(P+NP)]	Average Sum of Ranks (ASR)
G 1	1419543	8	999349.6	8	26.97	1	0.78	4	327853.25**	9	100	7.1
G 2	366993.9	1	88489.57	1	27.96	2	0.77	5	-30960.11	2	25	1.8
G 3	3548443	9	2841667	9	55.72	13	1.88	14	-13193.73	3	153	10.9
G 4	3981939	10	3216807	10	37.74	5	1.30	9	1123348.05**	11	140.5	10.0
G 5	462102.4	2	170795	2	55.48	12	1.00	1	77617.46	5	45	3.2
G 6	9657224	14	8128112	14	51.93	10	0.78	3	3074748.82**	14.5	172	12.3
G 7	1031212	5	663293.4	5	53.02	11	1.46	11	-42732.74	1	96.5	6.9
G 8	889486.9	4	540647	4	32.9	3	0.76	6	135929.93**	7	57	4.1
G 9	16167882	15	13762335	15	67.04	15	-0.26	15	2995706.87**	14.5	190	13.6
G 10	1269612	7	869601.8	7	40.93	6	0.71	8	223639.45**	8	91	6.5
G 11	1218345	6	825235.4	6	35.66	4	1.38	10	123290.30	6	97	6.9
G 12	6126846	13	5072977	13	43.54	7	0.36	12	1377201.01**	12	145.5	10.4
G 13	4249076	11	3447984	11	47.02	9	1.65	13	718076.69**	10	160.5	11.5
G 14	4564260	12	3720739	12	63.34	14	1.16	2	1408464.83**	13	147	10.5
G 15	642282	3	326719.6	3	46.14	8	1.27	7	35247.44	4	60	4.3

A popular and widely used method given by Eberhart and Russell (1966), identifies stable genotypes on the basis of unity of regression coefficient (bi=1) and mean square deviations from regression (s2di=0) non-significantly differing from zero [³⁵]. The bi values are subjected to t-test whereas s2di to F-test respectively. When bi value is more than unity then the genotype is found to be sensitive to varying growing conditions and thus can exhibit better adaptation to that specific growing environment. Association of bi with low mean indicates towards the genotypes being poor performer across all test environments. These results indicated that only one genotype, i.e. G 5 (bi=1.00, rank=1; s2di =77617.46), performed better across all studied environments. Several other researchers also obtained the same kinds of results using the Eberhart and Russell (1966) model [³⁶,³⁷]. So, above parametric models or univariate models even after using linear and non-linear component values of G × E for assessing yield-stability showed up differential ranking of genotypes. Wricke’s ecovalence showed G 2 to be most stable, Francis and Kannenberg’s method showed G 1 as stable whereas Eberhart and Russell’s method found G 5 to be stable across all the tested environments. Shifting of ranking across methods was thus observed. A multivariate PCA was also incorporated into the study. Also, a single selection criterion needs to be developed by amalgamating various stability methods and considering genotype yield performance [¹⁵,³⁰]. Major limitation in using the parametric models is that upon violation of its prior assumptions (normality, homoscedasticity and linearity/additivity), reliable results cannot be ensured [²⁶].

AMMI biplots, ASV and YSI based analysis of Stability

AMMI based stability calculations involves the use of analysis of variance (ANOVA) and principle component analysis (PCA) multiplicative model to separate the additive portion of the G×E interaction and then analyzing the interactive G×E effects from the additive-ANOVA model [³⁸]. The AMMI-biplot can provide insight into interactive G×E effects [³⁹]. In deciphering the interactive G×E effects, the AMMI model outshines other models. In addition to identifying the most-suited genotype for a given environment, AMMI stability analyses assist in determining the most-suited environment for a given genotype [⁴⁰]. Furthermore, it provides additional information such as comparing between different genotypes based on their performance, and identifying mega-environments or favorable/unfavorable environments for different genotypes based on their performance. AMMI-based stability models are not sensitive to most critical parts of the crossover network effects and do not provide any advantage for genotypic and site evaluation when analyzing multi-location trials [⁴¹].

Stability was also analyzed using the AMMI model. As for grain yield, ANOVA of AMMI model revealed significant mean sums of squares (MSS) for all sources of variations. G × E Interaction effect being significant, suggests that the genotypes under study performed differently in different test environments. Within the G-E interaction, environmental main effects can also be observed. Although environment effects were small compared to genotype (main effect) and genotype × environment (interaction effect), they were still significant, indicating that the environment is variable. Due to genotype-environment interplay, genes respond differently to surroundings (Table 1). Researchers previously reported similar results, according to Katsenios and coauthors, their results of AMMI-ANOVA revealed that the G × E interaction effect (80.36%) explained majority of the variation. They employed AMMI model to finally identify three genotypes that were the most suitable genotypes for the three growing environments under study. Hilmarsson and coauthors, evaluated the yield and 1000-kernel weight of 32 genotypes of barley in seven different environments. They applied the AMMI model, a factorial model, and a linear mixed model methods to analyze G x E. Similarly, Nhantumbo and coauthors, conducted an experiment with maize genotypes in different environments to assess yield stability using AMMI and they found suitable genotypes for non-water limiting conditions in Mozambique. In another study conducted in Lithuania, Tarakanovas and coauthors, also used AMMI for assessing grain yield of wheat varieties. [⁴²-⁴⁵]. It has been demonstrated successfully in many previous studies that AMMI analysis can be used to identify superior and stable genotypes for a variety of growing environments [⁴⁶-⁴⁸]. An insight of Table 6 indicated that 34.69 % of total sum of square (TSS) was attributable to G × E effects, 24.51 % to genotypic effects and 40.9 % to environment effect. The significance of G × E effects was further weighted using F-statistics after partitioning them into principal components. AMMI's two principal components, IPCA I and IPCA II, accounted for 58.77% and 26.26% of genotype × environment interaction, respectively

Over 80 percent of the interaction between G × E is due to these two components. The AMMI with two principal components axis was found to be the best predictive model in the present study. It was considered that genotypes with IPCA 1 scores close to zero were the most stable [⁴⁹]. Biplots generated from AMMI are visually inspected by plotting the first multiplicative component with the trait of interest [⁵⁰]. As shown in Figure 1, AMMI I biplots plot genotype and environment IPCA I scores against mean grain yields. The genotypes that deviate further from the ordinate on the right hand side are high-yielders, while those that deviate from the ordinate on the left are low-yielders. As can be seen from table 7, G5 yields the lowest and G4 yields the highest. IPCA1 and IPCA2 scores from genotypes and environments were plotted against each other in AMMI biplot II. A genotype close to its origin is considered to be more stable, while a genotype far from its origin is considered to be less stable. AMMI stability value (ASV) can be calculated based on IPCA I and IPCA II component scores [³¹]. The AMMI biplot I and II, ASV (AMMI Stability Value), revealed that genotype G 8 (IPCA I, -0.05377; ASV rank=1) was the most stable genotype. (Table 7 and Figure 1 and Figure 2).

Stability alone does not guarantee high crop yield, so it should not be used to pick good varieties. That is stable genotypes which are poor yielders are undesirable from producers point of view. This issue is further addressed using the YSI. YSI combines both mean performance and stability into one index, and can be used to select stable and high-yielding genotypes at the same time [¹⁵,¹⁶]. An AMMI stability value (Rasv) is combined with mean grain yield (Ry) of genotypes across environments to calculate YSI. Across study environments, the genotype G 11 (YSI=7, rank=1) was the most stable and high yielding genotype. Thus, this new Index ensures Improved Decision-Making in Plant Breeding Programs using both average sum of ranks (ASR) and Yield Stability Index (YSI) , plant breeding programs can make more informed decisions about which genotypes are likely to perform well in a variety of real-world conditions. This can contribute to the development of more robust and adaptable crop varieties.

Table 6
ANOVA of AMMI model showing IPCA components along with per cent variation

Source of Variation	df	MSS	Variation explained (%)
Environment	4	49021194**	40.79055
Genotype	14	8417199**	24.51384
Genotype x Environment	56	2978317**	34.69562
IPCA I	17	5766673**	58.77807
IPCA II	15	2920382**	26.26467
IPCA III	13	1168854**	9.11055
IPCA IV	11	886498.5**	5.84671
Error	150	219583.3

• * and ** refers to significant at 0.05 and 0.01 probability levels, respectively

Table 7
Various IPCA components along with ASV and YSI values

Genotypes	Mean Yield	Yield Rank	IPCA I	IPCA II	IPCA III	ASV Value	ASV Rank	YSI Value	YSI Rank
G 1	3651.7	4	-0.27167	0.072705	0.183396	0.612304	8	12	5
G 2	2949.367	7	-0.12266	0.086202	-0.05075	0.287726	3	10	2
G 3	3539.267	5	0.27079	-0.33118	0.448299	0.690595	9	14	6
G 4	4378.5	1	0.289971	0.464898	0.264286	0.798274	11	12	4
G 5	1985.568	15	0.072448	-0.05773	-0.1237	0.172105	2	17	10
G 6	3353.5	6	0.335622	0.8603	-0.17617	1.14204	13	19	12
G 7	2893.901	9	0.205794	-0.04223	0.231212	0.462481	7	16	9
G 8	2697.167	10	-0.05377	-0.03298	-0.26989	0.124765	1	11	3
G 9	2301.067	13	-1	-0.01015	-0.11239	2.237937	15	28	15
G 10	2147.235	14	-0.1377	0.018623	-0.10335	0.308719	4	18	11
G 11	4173.934	2	0.046209	-0.3066	0.183795	0.323574	5	7	1
G 12	2551.401	11	-0.5788	0.042773	0.143056	1.296004	14	25	14
G 13	4022.701	3	0.459265	-0.27519	-0.08344	1.063997	12	15	8
G 14	2534.1	12	0.309314	-0.36513	-0.51305	0.782617	10	22	13
G 15	2930.7	8	0.175182	-0.12431	-0.0213	0.411278	6	14	7

CONCLUSIONS

In a nutshell, the results obtained through the whole study, revealed that separate application of parametric and non-parametric models results in differential ranking of genotypes which creates an ambiguity in selection of stable genotype. In case of non-parametric model the genotype G 2 was found as most stable (S (¹), S (²), NP (¹), NP (³) and NP (⁴)) however the parameter S(³) and S (⁶) gave it 2^nd rank. W² _i suggested that genotype G 2 was the most stable genotype however CV_i gives it 2^nd rank. The results of Eberhart and Russell (1966) indicated G 5 as most stable genotype. As it was difficult to identify stable genotypes on basis of a single stability parameter, hence the use of ASR (average of sum of ranks of all methods used) was recommended to select stable genotypes. The stable genotypes exhibited low ASR values. The perusal of Table 7 indicated that the genotypes G 2, G 5, G 8, G 15 and G 10 were most stable genotypes as they had lowest ASR value of 1.8, 3.2, 4.1, 4.3 and 6.5 respectively. On basis of Yield Stability Index (YSI) scores, the genotype, G 11 (YSI=7, rank=1) followed by G 2 (YSI=10, rank=2), G 8 (YSI=11, rank=3), G 4 (YSI=12, rank=4) and G 1 (YSI=12, rank=5) were identified as most stable and high yielding rice genotypes for grain yield across studied environments (Table 7 and Figure 1 and 2). The ASR method in combination with YSI revealed that G2 is the most stable genotype along with a good yield.

Figure 1
AMMI-I biplot for Grain Yield. Numbers plotted in the biplots indicates the genotypes namely, MINGHUI 63 (1), ZHENSHAN 97 B (2), IR 64 (3), IRBB 66 (4), IRRI 147 (5), SANHUANGZHAN NO 12 (6), IR771286-122-2-2-3 (7), IR772398-14-1-2-10 (8), SAMBHA MAHSURI + SUB 1 (9), SUPA (10), IRRI 104 (11), N 22::IRGC 19379-1 (12), MTU1010 (13), NANHI (14) and JASMINE 85 (15).

Figure 2
AMMI-II biplot for Grain Yield. Numbers plotted in the biplots indicates the genotypes namely, MINGHUI 63 (1), ZHENSHAN 97 B (2), IR 64 (3), IRBB 66 (4), IRRI 147 (5), SANHUANGZHAN NO 12 (6), IR771286-122-2-2-3 (7), IR772398-14-1-2-10 (8), SAMBHA MAHSURI + SUB 1 (9), SUPA (10), IRRI 104 (11), N 22::IRGC 19379-1 (12), MTU1010 (13), NANHI (14) and JASMINE 85 (15). This AMMI biplot revealed that genotype G 8 was the most stable genotype.

Acknowledgments

First author acknowledges International Rice Research Institute, Phillipines for providing the Global Rice Array genotypes for conducting the field trials. Support from Joint Director NEBCRC, Pantnagar, Resource persons of Krishi Vigyan Kendra, Resource persons of Kashipur, Krishi Vigyan Kendra, Dhanauri, Haridwar and Resource persons of Agriculture Research Centre Majehra, Uttarakhand, India is duly acknowledged by all authors. The author also acknowledges Ms. Babita Kohli, Assistant Manager, NABARD, for her assistance in drawing his attention to a number of sources. The opinions of a number of unnamed reviewers, scientists, and other departmental teachers are also greatly valued.

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• Funding:

  This research received no external funding.

Edited by

Editor-in-Chief:

Bill Jorge Costa

Associate Editor:

Bill Jorge Costa

Publication Dates

• Publication in this collection
  11 Oct 2024
• Date of issue
  2024

History

• Received
  28 Mar 2023
• Accepted
  30 July 2024