Integrating AMMI, Bayesian-AMMI, BLUP, and GGE biplot models to improve the identification of high-yielding and stable barley genotypes

Abstract

Background

The evaluation of genotype-by-environment interaction (GEI) through multi-environment trials (METs) is an essential prerequisite in breeding improvement programs targeting wide adaptation. In this study, a panel of newly developed barley genotypes was examined under field conditions at five experimental sites across Iran’s warm climatic zone during the 2023–2025 growing seasons.

Results

The pooled analysis of variance clearly demonstrated that effects of genotype (G), environment (E), and GEI influenced all measured traits, including the number of days to heading (DH), days to physiological maturity (DM), grain filling period (GFP), plant height (PH), 1000-kernel weight (TKW), and grain yield (GY). Analytical outputs obtained from the additive main effects and multiplicative interaction (AMMI) model, as well as the best linear unbiased prediction (BLUP) approach, highlighted the substantial contribution of genotype × environment interaction to variation in grain yield. Insights from genotype–trait (GT) biplot analysis indicated that TKW and GFP were positively associated with GY. When genotypes were ranked using the multi-trait stability index (MTSI), G5 (1.689), G4 (1.914), G20 (2.380), and G14 (2.508) achieved the highest scores, reflecting superior performance and stability across test environments. A comprehensive evaluation strategy integrating classical AMMI, BLUP, Bayesian AMMI, and genotype-by-environment (GGE) biplot methodologies was employed to identify genotypes that combine productivity with stability. Across all derived stability parameters, including the weighted average of absolute scores (WAAS) and its yield-weighted counterpart (WAASY), genotype G4, derived from the pedigree [Sahra/3/Bda/Rhn-03//ICB-107766], consistently outperformed other candidates. This genotype exhibited a robust yield response, high stability, and broad environmental responsiveness. Independent validation using the stability Mahalanobis distance (SM) index and Y × WAASY biplot visualization further substantiated these findings.

Conclusion

In conclusion, genotype G4 represents a strong candidate for subsequent validation trials and potential varietal release in the warm agroecological regions of Iran and other areas with comparable climatic conditions.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12870-026-09142-0.

Introduction

Barley (Hordeum vulgare) ranks among the earliest domesticated cereal crops and is currently cultivated across a broad spectrum of agroecological zones, including temperate, subarctic, and subtropical regions. Although its primary contemporary applications are as livestock feed and as a raw material for malting and brewing industries, whole-grain barley has gained increasing attention in human nutrition owing to its recognized health-promoting properties and favorable storage and processing characteristics. The extensive genetic variability and ecological plasticity of barley underline its strategic importance in diversified cropping systems, particularly in environments where other cereals exhibit limited adaptability or productivity [1]. From a nutritional perspective, barley grain serves mainly as a source of carbohydrates, also providing appreciable amounts of protein, dietary fiber, and essential micronutrients. A standard serving of cooked pearled barley supplies approximately 193 kcal, 44 g of carbohydrates, and 6 g of dietary fiber, along with minerals such as selenium, iron, and magnesium [2, 3].

Globally, barley is the fourth most widely produced cereal crop, with the bulk of production concentrated in temperate regions, particularly in Russia, the European Union countries, Australia, Canada, and the United States. Countries such as France, Germany, and Australia contribute substantially to global output. According to FAO statistics, annual barley production reaches several tens of millions of tons, positioning barley as a key coarse grain in international markets for feed, malting, and, in some regions, direct human consumption [4]. Beyond its economic relevance, barley plays a critical role in food security by maintaining productivity under marginal conditions, including drought-prone, saline, and low-fertility soils. Moreover, the availability of rich genetic resources enables the development of stress-tolerant cultivars adapted to drought, heat, and biotic stresses, which is increasingly important under climate change scenarios [5].

Crop performance is determined by the combined effects of genotype (G), environment (E), and their interaction (GEI). The presence of GEI often results in different genotype rankings across environments, complicating selection decisions and cultivar recommendations. Although GEI is frequently perceived as an undesirable source of variation, it also provides opportunities for breeders to exploit either specific adaptation to defined target regions or broad adaptation coupled with yield stability under fluctuating environmental conditions. Such interactions are commonly observed during the evaluation of advanced breeding lines in multi-environment trials (METs), particularly at the final stages of cultivar development [6]. Anticipated climate change effects are expected to intensify GEI patterns by increasing the frequency and magnitude of abiotic stresses—such as drought, heat, and cold—as well as biotic challenges, while also altering soil physical and chemical properties, including temperature regimes and nutrient dynamics. Accurate interpretation of GEI, therefore, requires analytical frameworks that extend beyond conventional analysis of variance. While univariate and multivariate empirical approaches have long been used in plant breeding, modern statistical methodologies that integrate genotypic and environmental information provide deeper insight into the biological mechanisms underlying GEI. Recent methodological advances have refined and expanded classical stability concepts developed throughout the twentieth century. Among these, the genotype plus genotype-by-environment (GGE) interaction biplot, best linear unbiased prediction (BLUP), and the additive main effects and multiplicative interaction (AMMI) model are widely recognized as powerful tools for evaluating GEI and for identifying genotypes that combine superior mean performance with stability across multi-environment trials (METs) [6–9].

The GGE biplot approach employs principal component analysis of environment-centered data to simultaneously visualize genotype main effects and GEI, thereby capturing the most relevant variation for genotype evaluation [10]. This method enables breeders to identify mega-environments, determine winning genotypes within each group, and assess the discriminating power and representativeness of test locations. By integrating performance and stability into a single graphical framework, the GGE biplot facilitates informed decision-making regarding genotype recommendation and trial optimization [11]. Complementarily, the AMMI model integrates analysis of variance to partition additive genotype and environment effects with principal component analysis to model multiplicative GEI, resulting in a more interpretable depiction of genotype responses across diverse environments. Owing to its capacity to detect stable genotypes, delineate mega-environments, and enhance the precision of cultivar recommendations, AMMI remains a cornerstone of GEI analysis in crop improvement research [12–14].

The Best Linear Unbiased Prediction (BLUP) methodology, implemented within a mixed-model framework, estimates genotypic values by accounting for both fixed and random effects, thereby producing unbiased and shrinkage-adjusted predictions that are particularly advantageous in METs with unbalanced data structures [15]. Unlike descriptive approaches, BLUP improves prediction accuracy and reduces overfitting, making it a valuable complement to AMMI and GGE analyses. In this context, AMMI characterizes interaction structure, GGE emphasizes visualization of adaptability and stability, and BLUP provides reliable predicted genotypic values, together enhancing selection efficiency and recommendation reliability [7, 16]. The Bayesian AMMI model further extends the classical AMMI framework by incorporating Bayesian inference into GEI analysis [17–19]. This approach enables the estimation of posterior distributions and credible intervals for model parameters, providing a rigorous quantification of uncertainty and allowing the integration of prior knowledge into the analytical process. Consequently, Bayesian AMMI provides a more flexible and informative assessment of genotype stability and adaptability than frequentist methods [20].

Collectively, BLUP, classical AMMI, and Bayesian AMMI can be integrated into a complementary analytical pipeline for GEI investigation in plant breeding. Within this framework, BLUP delivers robust predictions of genotypic performance, Bayesian AMMI models GEI under probabilistic assumptions, and classical AMMI ensures interpretability and structural validation of interaction patterns. The combined use of these methodologies enhances predictive accuracy, interpretability, and uncertainty assessment, thereby supporting more reliable genotype selection and environmental characterization [20, 21]. In light of these considerations, the primary objective of the present study was to identify high-yielding and stable barley genotypes adapted to the warm climatic conditions of Iran by integrating multiple stability and adaptability assessment approaches across multi-environment trials. We surmise that this study provides a significant insight into the use of various analytical methods to select the ideal genotypes and therefore identify optimal environments that could effectively support the management of breeding cycles and facilitate seed multiplication.

Materials and methods

Plant genetic materials and experimental layout

A diverse panel of barley genetic material was examined in this study, consisting of 18 elite barley genotypes and three widely grown commercial cultivars—Negin, Oxin, and Golchis—which served as performance benchmarks. The experimental material was tested under multi-environment trial (MET) conditions representative of Iran’s warm agroecological zones during two successive cropping cycles (2023–2024 and 2024–2025). All genotypes originated from national crossing and selection efforts undertaken by the Cereal Research Department (CRD) of the Seed and Plant Improvement Institute (SPII) in Karaj, Iran. Comprehensive passport descriptors for the tested genotypes are summarized in Table 1. The progression of breeding activities, from the initial hybridization phase through successive screening stages to the final MET evaluation, is outlined in the schematic diagram shown in Fig. 1. Benchmark cultivars were included for their documented yield stability and broad adaptation across Iran’s warm climatic gradient, spanning from humid northern environments to arid southern regions (Fig. 1).

Table 1.

Pedigree of investigated genotypes of barley in the present study

Code	Pedigree
G1	Negin (Reference)
G2	Oxin (Reference)
G3	Ataco/Comino//Aleli/3/Bichy2000/4/Arupo/K8755//Mora/5/Yousef
G4	Sahra/3/Bda/Rhn-03//ICB-107766
G5	Sahra/3/Bda/Rhn-03//ICB-107766
G6	CHENG DU 105/4/EGYPT4/TERAN78//P.STO/3/QUINA/5/ABETO//…/6/L.527/MB2367//(CI7117-9/Deiralla106)/3/Gorgan//Aths/BC
G7	Cheng Du 105/4/Egypt4/Teran78//P.Sto/3/Quina/5/Abeto//…/6/Schayler/3/M.Rnb86.80/Nb2905//L.527/4/Rhn-03//L.527/Nk1272
G8	L.527/MB2367//(CI7117-9/Deiralla106)/3/Gorgan//Aths/BC/4/Bda/Rhn-03//ICB-107766
G9	L.527/MB2367//(CI7117-9/Deiralla106)/3/Gorgan//Aths/BC/5/Kavir/Badia/3/Torsh/9cr.279–07/Bgs/4/Karoon/Kavi
G10	Zahak/1-BC-80012
G11	Nimrooz/4/Anoidium/Arbayan-01/3/Lignee527/Nk1272//Jlb70-63
G12	Nimrooz/6/CHENG DU 105/4/EGYPT4/TERAN78//P.STO/3/QUINA/5/ABETO//…
G13	Yousef/4/Anoidium/Arbayan-01/3/Lignee527/Nk1272//Jlb70-63
G14	Yousef/4/Anoidium/Arbayan-01/3/Lignee527/Nk1272//Jlb70-63
G15	Behrokh/Vada//Nik
G16	Nosrat/Nik*2
G17	Gob/Aleli//Canela/3/Arupo*2/Jet/4/Arupo/K8755//Mora/5/Icnb-105960/Torkman/6/Zahak
G18	Karoon/Kavir/4/Rhodes's'//Tb/Chzo/3/Gloria's'/5/Legia
G19	Karoon/Kavir/3/Rhodes's'//Tb/Chzo/4/Gloria's'/5/Nik/6/Yousef
G20	WB-00–14
G21	Golchin (Reference)

Fig. 1.

Timeline of breeding cycles of investigated barley genotypes in the present study and geographical distribution of test environments. The source of the climatic map is available at: https://commons.wikimedia.org/wiki/File:Iran-climate-map.svg

Field experiments were established at five geographically distinct research sites: Ahvaz (designated as environments E1 and E6), Darab (E2 and E7), Zabol (E3 and E8), Gonbad (E4 and E9), and Moghan (E5 and E10). At each location, trials followed a randomized complete block design with three replicates. Before planting, locally recommended agronomic practices were applied to ensure optimal crop establishment. Basal nutrient management included the incorporation of 32 kg ha^–1 of nitrogen and 100 kg ha^–1 phosphorus (P₂O₅) before sowing, followed by a supplementary nitrogen application of 40 kg ha^–1 at the onset of stem elongation (Zadoks growth stage GS = 31). Experimental units were laid out as small plots to facilitate the simultaneous assessment of multiple genotypes. Each plot comprised six rows of 5 m length, spaced 20 cm apart. A constant seeding rate of 350 seeds m^–2 was maintained across all environments to ensure comparability. Sowing operations were consistently conducted in early November across all environments in both seasons using a small-plot planter (Wintersteiger, Austria). The initial irrigation was applied immediately after sowing, whereas precipitation during the autumn and winter periods was considered sufficient for early crop development. Additional irrigations were scheduled during spring at critical developmental phases as defined by the Zadoks cereal growth scale [22], including stem elongation (GS 31), booting (GS 41), anthesis (GS 69), early milk (GS 71), and dough development (GS 83). Weed management was implemented during the tillering stage (GS 29) using selective herbicides targeting both grass and broadleaf species, Pumasuper and Granstar were applied according to manufacturer recommendations. Other crop protection measures were adopted when required, in accordance with standard regional agronomic guidelines. Throughout the growing season and before harvest, data were collected on key phenological and yield-related attributes, namely plant height (PH), 1000-kernel weight (TKW), the number of days to heading (DH), grain filling period (GFP), and the number of days to physiological maturity (DM). At harvest maturity (generally in early June), each plot was mechanically harvested using a small-plot combine (Wintersteiger, Austria), and grain yield (GY) was calculated and expressed on a hectare basis (kg ha^–1).

Statistical data analysis

All statistical procedures were implemented in the R computing environment (version 4.3.3; [23] using a combination of dedicated packages and native functions. Initially, a pooled analysis of variance (ANOVA) was conducted for all recorded traits to quantify the effects of genotype (G), environment (E), and genotype-by-environment interaction (GEI). Relationships among traits were explored using a genotype–trait (GT) biplot analysis in the “metan” package [24]. To simultaneously account for mean performance and stability across multiple traits, the multi-trait stability index (MTSI) was employed, as implemented in metan. This multivariate selection index is designed for multi-environment trials and enables the ranking of genotypes based on their proximity to a predefined ideotype. Genotypes with smaller MTSI values are considered closer to the ideal combination of high performance and stability. The MTSI was computed according to the expression proposed by Olivoto et al. [25]:

where is the score of the genotype i-th in the factor j-th and is the score of the ideal genotype in the factor j-th.

Grain yield data were subsequently subjected to an in-depth assessment of stability and adaptability. AMMI integrated the ANOVA results with singular value decomposition (SVD) to quantify and partition the GEI variance into distinct interaction principal component axes (IPCA). The classical AMMI model was first applied to partition and characterize the GEI structure. To integrate the descriptive power of AMMI with the predictive strength of mixed models, BLUP-based stability metrics were derived. Specifically, the weighted average of absolute scores (WAAS) and its yield-weighted counterpart (WAASY) were calculated following the methodology of Olivoto et al. [15]. Genotypic BLUPs were estimated as the sum of the overall mean and the corresponding genotypic effect. The WAAS based on BLUPs (WAASB) was obtained through singular value decomposition of the GEI matrix derived from BLUP estimates. The WAAS and WAASY indices were calculated using the following formulations:

where, IPCA_ik is the score of the i-th genotype in the k-th IPCA, EP_k is the explained variance of the k-th IPCA for 1, 2, …, and p, considering p the number of significant PCAs, or a declared number of IPCAs, rG_i is rescaled values (0–100) for grain yield, rW_i is rescaled values (0–100) for WAASB (BLUP-based WAAS), is weight for grain yield, is weight for WAASB index. Additionally, three BLUP-based indices proposed by Resende [26] were computed to quantify stability and adaptability further: the harmonic mean of genotypic values (HMGV), the relative performance of genotypic values (RPGV), and their combined form (HMRPGV):

where, E is the number of environments included in the analysis, G_vij is the genotypic value (BLUP) for the i-th genotype in the j-th environment. These indices were performed using ‘metan’ package.

Genotypic stability relative to an ideotype was further assessed using the stability Mahalanobis distance (SM) index, following Johnson and Wicherm [27]. In this framework, the ideotype corresponds to a hypothetical genotype located at the origin of the interaction principal component space. The SM index was computed as:

where, IPCA_i is the i-th p-dimensional vector of scores from the interaction term of the AMMI model, 0 is the p-dimensional vector of zero, which represents the ideal genotype regarding the stability (origin), and Σ is and diagonal matrix composed of the reciprocals of eigen-values from the interaction term of the AMMI model. Lower SM index values indicate greater genotypic stability. The Mahalanobis distance accounts for the importance of IPCAs through the diagonal matrix Σ. This matrix contains the reciprocals of the eigenvalues associated with each IPCA. The eigenvalues themselves represent the amount of variance explained by the corresponding IPCA from the interaction term of the AMMI model. Following the analysis, a combined plot is presented. This plot denoted by the stability Mahalanobis (SM) plot, visualizes the estimated SM index values for each genotype alongside their corresponding marginal posterior means for yield (or any trait of interest). Additionally, it presented the 95% highest posterior density (HPD) intervals for both SM and yield, providing a comprehensive view of the Bayesian model’s estimates and their uncertainty. For Bayesian inference, the Bayesian-AMMI model was fitted using the Gibbs sampler algorithm with 70,000 Markov chain Monte Carlo (MCMC) iterations, including a burn-in of 7,000 iterations and thinning every seven steps. Posterior distributions of AMMI-based indexes—namely the Bayesian weighted average of absolute scores (BWAAS), Bayesian weighted average of absolute scores incorporating yield (BWAASY), and the SM index—were directly derived from the sampled parameters λ and α. This was possible because these indices are calculated from the estimated model parameters. In each chain, the posterior means, standard deviation, 95% highest posterior density (HPD) intervals, and convergence diagnostics were evaluated following Raftery and Lewis [28]. The R scripts for implementing Bayesian AMMI analysis and the Bayesian AMMI-based indexes, including BWAAS, and BWAASY, along with the functionality to generate the SM plot, are available in ChiDO software (https://jarquinlab.shinyapps.io/chido/, [29]. Finally, the relationship between yield performance and stability, along with the identification of ideal genotypes, was evaluated using genotype-by-environment (GGE) biplot analysis, implemented via the metan package.

Results

Analysis of variance and trait variability across test environments

The combined analysis of variance demonstrated that environmental conditions, genetic background, and their interaction exerted statistically significant effects on all evaluated traits (Table 2). The coefficients of variation ranged from 1.0% to 18.63%, indicating acceptable experimental precision, with the greatest dispersion observed for thousand-kernel weight (TKW), grain yield (GY), and days to heading (DH). Phenological development showed wide plasticity across environments; DH ranged from 69 days (genotype G16 in environment E8) to 143.3 days (genotype G21 in E10), with an overall mean of 108 days (Figure S1). Similarly, days to physiological maturity (DM) ranged between 109.3 and 191.7 days, averaging 146.9 days, with minimum and maximum values observed for G2 in E8 and G10 in E10, respectively (Figure S2). The grain filling period (GFP) showed substantial variability, ranging from 24.7 to 53.3 days, with an average of 38.9 days; the shortest duration was observed in G3 in E3, whereas the longest was associated with G2 and G20 in E10 (Figure S3). Plant height (PH) ranged from 63 cm (corresponding to G3 in E8) to 131.3 cm (corresponding to G9 in E7), with an average of 98 cm (Figure S4). TKW varied from 31.8 g to 52.3 g, with an average of 39.3 g; the lower and highest values were recorded for G21 in E6 and G5 in E5, respectively (Figure S5). GY, as the primary target trait, exhibited pronounced variation across genotypes and environments, ranging from 2250 kg ha^–1 (corresponding to G3 in E1) to 8050.9 kg ha^–1 (corresponding to G7 in E3), with an overall mean of 4402.3 kg ha^–1 (Figure S6).

Table 2.

Combined analysis of variance and P-values for likelihood ratio test (LRT) for measured traits in investigated barley genotypes across 10 environments

Source of variation	df	GY	PH	DH	DM	TKW	GFP
Environment (E)	9	85026,032**	10925.9**	31248.1**	38607.1**	552.4**	1819.8**
Replication/E	20	236644	46.20	8.9	3.4**	2.5	7.2**
Genotype (G)	20	2021686**	513.4**	165.2**	57.6**	82.5**	55.7**
GE interaction	180	832274**	69.0**	29.3**	15.5**	18.2**	22.4**
Residuals	400	294403	19.8	3.8	2.0	3.1	3.9
Coefficient of variation (%)		18.63	4.54	1.82	1	4.52	5.12
G		2.75e−03	1.39e−14	1.19e−10	3.18e−06	1.26e−05	2.13e−03
GE interaction		1.03e−17	5.35e−25	3.61e−63	6.33e−63	2.23e−63	8.43e−47
Phenotypic variance		513339	51	16.90	7.95	9.63	11.2
Broad-sense heritability ()		0.07	0.29	0.26	0.17	0.19	0.098
Coefficient determination for interaction effects (r2GEI)		0.34	0.32	0.50	0.56	0.43	0.54
Heritability of genotype means (h2mg)		0.58	0.86	0.82	0.73	0.68	0.59
Genotypic coefficient of variation (CVg)		4.52	3.93	1.97	0.81	0.806	2.70

GY, PH, DH, DM, TKW, and GFP indicated grain yield, plant height, the number of days to heading, the number of days to physiological maturity, 1000-kernel weight, and grain filling period, respectively

^**Significant at 0.01 probability level

The GT biplot analysis revealed that the first and second principal components (PCs) accounted for 63.9% and 13.4% of the total phenotypic variation, respectively, and together accounted for 77.3% of the cumulative variation across environments (Fig. 2A). Consequently, most of the genotype differentiation was summarized along PC1. In this biplot, trait vectors show the directions of increasing trait values, and their relative lengths indicate how well PC represents those traits. Hence, traits with similarly oriented vectors are positively correlated, orthogonal vectors indicate little correlation, and oppositely directed vectors indicate negative association. Genotypes projecting in the same quadrant and direction as a trait vector can be interpreted as relatively superior for that trait. In contrast, genotypes near the origin are close to the multivariate mean or are poorly represented by these two components. Correlation analysis grouped the measured traits into two clusters: the first comprised GY, TKW, and GFP; the second comprised PH, DM, and DH. Genotypes G3, G4, G5, G7, and G18 exhibited the highest grain-yield values.

Fig. 2.

A The GT-plot depicts the relationships among measured traits in the investigated barley genotypes across 10 test environments in Iran’s warm climate. DH, DM, PH, TKW, GFP, and GY indicated the number of days to heading, the number of days to physiological maturity, plant height, 1000-kernel weight, grain filling period, and grain yield, respectively. B The multi-trait stability index (MTSI) for identifying the superior genotypes. The red line is cut-off line based on SI = 20%

The multi-trait stability index (MTSI) was applied to integrate performance and stability across all measured traits and environments. The Likelihood ratio test (LRT) confirmed significant genotypic and GEI effects for all traits. Two principal factors (FA1 and FA2) together explained 72.93% of the total phenotypic variance. Factor loadings indicated that DH, GFP, and TKW were predominantly associated with FA1, while GFP, GY, and DM mainly influenced FA2. Estimated selection gain (SG) ranged from − 3.62 for PH to 131.7 for GY (Table S1). Based on MTSI rankings—where lower values denote greater proximity to the ideotype—genotypes G5 (1.689), G4 (1.914), G20 (2.380), and G14 (2.508) were identified as the most desirable across the test environments (Fig. 2B).

BLUP model

The BLUP model was employed to estimate genetic-variation parameters. The LRT indicated significant G and GEI effects for all traits (Table 2). GY and PH exhibited the largest phenotypic variances. Broad-sense heritability at the individual observation level ranged from 0.07 to 0.29, whereas heritability estimated based on genotype means () was substantially higher, ranging from 0.58 to 0.86. GY and PH represented the extremes for both heritability metrics, with GY showing the lowest and PH the highest values. These two traits also displayed the greatest genotypic coefficient of variation (CVg). The coefficient determination for the interaction effect, , ranged from 0.32 to 0.56, with the largest values estimated for DM, GFP, and DH. According to the BLUP-based ranking, the highest overall performance pattern was: G4 > G15 > G20 > G13 > G21 > G14 > G6 > remaining genotypes (Fig. 3). The stability and adaptability indices HMGV, RPGV, and HMRPGV identified genotypes G4, G6, G13, G15, and G20 as the most superior genotypes (Table 3).

Fig. 3.

Estimated grain yield for the investigated barley genotypes using the BLUP model

Table 3.

Estimated values for BLUP-based stability and adaptability statistics in 21 barley genotypes across 10 test environments

Code	HMGV	RPGV	HMRPGV
G1	4132	4399	4368
G2	4125	4411	4379
G3	4024	4308	4264
G4	4466	4733	4719
G5	4221	4456	4449
G6	4346	4581	4545
G7	4206	4504	4459
G8	4143	4392	4376
G9	3862	4129	4105
G10	3526	3760	3746
G11	4078	4301	4275
G12	4052	4305	4289
G13	4310	4588	4536
G14	4297	4553	4531
G15	4444	4684	4660
G16	4283	4531	4521
G17	3996	4228	4200
G18	4146	4398	4372
G19	3742	4021	3971
G20	4377	4640	4626
G21	4246	4528	4504

HMGV harmonic mean of genotypic values, RPGV relative performance of genotypic values, HMRPGV harmonic mean of the relative performance of genotypic values

AMMI model

Results from the AMMI model indicated that GY was significantly influenced by E, G, and GEI (Table 4). The GEI component was partitioned into seven significant interaction principal component axes (IPCAs), where IPCA1–IPCA7 accounted for 23.9%, 22.2%, 16.3%, 9.8%, 8.6%, 6.8%, and 6.2% of the GEI variance, respectively. Based on the AMMI-II biplot (Fig. 4A), the first two PCs accounted for 46.10% of the total variation in the GEI. Environments E3, E4, E5, E7, and E8 which are farther from the biplot center, had a significant impact on the GEI. On the other hand, genotypes G2, G4, G8, G10, G15, G16 and G20 with the lowest IPCA scores showed broad stability in all testing environments.

Table 4.

The result of AMMI model for grain yield data of 21 investigated barley genotypes across 10 test environments

Source of variation	df	Mean	F-statistic	PV	APV
Environment (E)	9	85026032	359.3**
Replication/E	20	236644	0.8
Genotype (G)	20	2021686	6.8**
GE Interaction	180	832274	2.8**
PC1	28	1276450	4.3**	23.9	23.9
PC2	26	1279373	4.3**	22.2	46.1
PC3	24	1016579	3.4**	16.3	62.3
PC4	22	665064	2.2**	9.8	72.1
PC5	20	641739	2.2**	8.6	80.7
PC6	18	569714	1.9*	6.8	87.5
PC7	16	584995	1.9*	6.2	93.8
PC8	14	426923	1.4	4	97.8
PC9	12	279106	0.9	2.2	100
Residuals	400	294403

PV portion of variance, APV accumulated portion of variance

^* and ** indicated Significant at 0.05 and 0.01 probability levels, respectively

Fig. 4.

AMMI-II biplot rendered using classical (A) and Bayesian AMMI (B) models to show the impact of genotypes and environments on the GEI effect. E1/E6, E2/E7, E3/E8, E4/E9, and E5/E10 represented the first- and second-years experiments in the Ahvaz, Darab, Zabol, Gonbad, and Moghan locations, respectively

In the Bayesian AMMI model [B-AMMI], all sampled MCMC chains exhibited satisfactory convergence according to the applied diagnostic criteria, as the model passed diagnostic tests such as those of Rafter and Lewis (1992). The posterior means of grain yield for the 21 genotypes and 10 environments, along with their lower and upper HPD limits, are presented in Table 5. While the observed grain yields ranged from 2250 and 8050.90 kg ha⁻¹, the Bayesian posterior means estimates ranged from 3676.61 (genotype G10) to 4795.35 (genotype G4) kg ha⁻¹. Moreover, the grain yield (kg ha⁻¹) across the 10 environments presented significant variation, ranging from 3382.75 kg ha⁻¹ (environment E1) to 6917.43 kg ha⁻¹ (environment E3). Non-overlapping HPD intervals indicated statistically significant differences in grain yield among most environments. The first and second Bayesian IPCAs explained 27.59% and 23.77% of the total GEI variation, respectively. The B-AMMI-based biplot identified G2, G4, G5, G10, G11, and G15 as the most stable genotypes, while environments E4, E5, E7, and E8 showed the strongest GEI effects (Fig. 4B).

Table 5.

Mean of the marginal posterior effects (mean) of the Bayesian–AMMI model for grain yield in the 21 investigated barley genotypes and 10 test environments along with the first and second singular values (λ1, and λ2), and the lower and upper highest posterior density (HPD) regions at 95%

Code	Lower HPD	Mean	Upper HPD
G1	4374.78	4402.35	4429.78
G2	4425.15	4454.34	4481.90
G3	4281.12	4308.68	4336.02
G4	4767.98	4795.35	4823.01
G5	4431.75	4461.78	4486.65
G6	4529.18	4555.89	4584.06
G7	4515.81	4542.45	4572.56
G8	4358.67	4388.26	4416.25
G9	4097.95	4123.31	4151.85
G10	3648.82	3676.61	3704.16
G11	4218.32	4250.34	4275.32
G12	4270.20	4298.45	4324.09
G13	4565.07	4593.01	4619.99
G14	4532.67	4562.61	4588.59
G15	4662.87	4690.23	4716.47
G16	4515.83	4544.18	4571.07
G17	4151.51	4178.59	4204.87
G18	4356.71	4382.93	4410.45
G19	3959.95	3987.52	4014.83
G20	4658.16	4685.81	4713.20
G21	4545.40	4572.35	4600.01
E1	3354.89	3382.75	3409.44
E2	4008.38	4034.04	4062.07
E3	6889.50	6917.43	6944.35
E4	3335.47	3364.57	3391.18
E5	4984.35	5013.69	5041.28
E6	4163.79	4191.87	4217.88
E7	3357.43	3388.33	3414.33
E8	4789.09	4816.31	4844.06
E9	3446.94	3472.86	3500.19
E10	5417.46	5444.36	5470.07
λ1	7118.65	7561.49	7923.74
λ2	6953.36	7333.48	7710.75

Model-based stability indices

Various weighted averages of absolute scores (WAAS) and weighted averages of absolute scores and yield balance (WAASY) were computed using the AMMI, BLUP, and B-AMMI models to identify genotypes that combine high performance with stability. In general, lower WAAS values indicate greater stability, whereas higher WAASY values identify superior and high-yielding genotypes. Under the classical AMMI model, genotypes G4, G5, G8, G10, G12, and G16 were the most stable according to WAAS index (Fig. 5A), whereas G4, G5, G15, G16, and G20 were selected as superior based on WAASY (Fig. 5B). In the BLUP framework, the WAASB metric identified G5, G8, G11, G12, and G16 as the most stable genotypes (Fig. 5C), whereas WAASBY highlighted G4, G5, G8, G16, and G20 as the highest-performing and most stable genotypes (Fig. 5D). In the B-AMMI model, the BWAAS identified genotypes G4, G5, G12, G16, and G21 as the most stable (Fig. 5E), whereas BWAASY identified G4, G5, G16, G20, and G21 as the highest-performing and most stable genotypes (Fig. 5F).

Fig. 5.

Estimated values of the weighted average of absolute stability (WAAS) and mean performance (Y) (WAASY) for the genotypes considering weights of 50 and 50 for the yield and stability based on classical AMMI model (A-B), BLUP (C-D), and Bayesian AMMI (E–F) models, respectively

The stability Mahalanobis (SM) distance biplot simultaneously visualized the estimated stability values for each genotype, along with their corresponding marginal posterior means for yield. Additionally, it presented the 95% highest posterior density (HPD) intervals for both SM and yield, providing a comprehensive view of the Bayesian model’s estimates and their uncertainty. The rendered biplot using the SM index divided all genotypes into four quadrants (I–IV). Genotypes in quadrant IV (highest stability and yield) are ideal for breeding programs due to their consistent performance. While genotypes in quadrant I offer potentially high yield with lower stability. Accordingly, quadrant I consisted of genotypes G6, G7, G13, G14, and G15, whereas quadrant IV embraced genotypes G4, G5, G16, G20, and G21 (Fig. 6A).

Fig. 6.

Grouping the investigated genotypes and test environments based on the Bayesian stability Mahalanobis distance index (A) and weighted average of the absolute scores (B). E1/E6, E2/E7, E3/E8, E4/E9, and E5/E10 represented the first- and second-years experiments in the Ahvaz, Darab, Zabol, Gonbad, and Moghan locations, respectively

The Y × WAAS biplot provided a comprehensive assessment of genotype performance by simultaneously considering grain yield (GY) and stability across environments. Accordingly, all genotypes studied were clustered into four adaptation groups. Genotypes such as G7, G13, and G6 fell into the high-yield but unstable quadrant (quadrant I), suggesting strong performance but inconsistent responses across environments. In contrast, G3, G17, G18, and G19 were located in the low-yield and unstable region, indicating poor overall suitability. Several genotypes, including G8, G9, G10, G11, and G12, exhibited low WAAS values but below-average yields, reflecting high stability but limited productivity. The most desirable genotypes—characterized by high yield and high stability—contained G4, G5, G8, G15, G16, G20, and G21, which were positioned closest to the ideal point, confirming them as the top-performing and most stable genotype. Environmental vectors further revealed that sites such as E3, E5, E7, and E8 contributed strongly to genotype discrimination, whereas environments closer to the origin (e.g., E1, E2) were more representative and exerted weaker interaction effects. Overall, the biplot clearly identified G4, G5, G16, and G20 as broadly adapted, high‑performing, and stable genotypes across test environments (Fig. 6B).

Identification of ideal genotypes

Two complementary GGE biplot analyses were used to identify superior and ideal genotypes and to validate selections obtained from AMMI and BLUP models. The ‘mean performance vs stability’ biplot visualizes genotype mean performance and stability by superimposing an average environment coordinate (AEC) onto a genotype-focused biplot. The AEC is defined by the mean PC1 and PC2 scores of the environments and is indicated by a small arrow. A line drawn from the biplot origin through the AEC establishes the average reference axis; the orthogonal projections of genotype points onto this axis approximate genotype mean yield. When the AEC abscissa represents G, the AEC ordinate approximates the G × E interaction for each genotype and thus reflects its variability or instability. Larger absolute projections onto the AEC ordinate, regardless of direction, indicate greater instability. Based on the biplot, genotypes G13, G4, G20, G14, G15, G18, G6, G2, G16, G5, G21, G3, and G17 exhibited the highest average grain yields across the test environments, respectively. Among these, G2, G4, G13, G14, G15, G16, and G20 displayed greater stability, as indicated by their shorter projections onto the AEC ordinate (Fig. 7A). The 'ranking genotype' view of a biplot provides a visual comparison of various genotypes against a defined "ideal" genotype. The ideal genotype is represented by a small circle with an arrow pointing toward it, signifying its role as the benchmark for optimal performance. This benchmark is characterized by exceptional yield across all tested environments, achieving the highest average yield while demonstrating complete stability. In this biplot, the genotypes are arranged according to their distance from the ideal genotype, enabling a clear evaluation of each genotype's performance. The results indicated that G14, followed by G4, G13, G20, and G15, were closest to the central circle and therefore were identified as the ideal genotypes, exhibiting high performance and stability (Fig. 7B).

Fig. 7.

A The “means vs stability” viewpoint of GGE biplot for simultaneous selection of grain yield and stability of investigated barley genotypes across 10 test environments. B The “Ranking genotype” viewpoint of GGE biplot for selection of ideal genotypes. E1/E6, E2/E7, E3/E8, E4/E9, and E5/E10 represented the first- and second-years experiments in the Ahvaz, Darab, Zabol, Gonbad, and Moghan locations, respectively

Discussion

The development of high-yielding and environmentally resilient crop cultivars is intrinsically dependent on the breadth of genetic diversity encompassed within breeding materials. Such diversity constitutes a cornerstone of modern breeding programs, as it underpins the capacity to generate cultivars that simultaneously exhibit superior performance and yield stability across heterogeneous agroecological conditions. Adequate genetic variation facilitates the deliberate enhancement of key agronomic attributes, including nutritional value and tolerance to a wide range of abiotic and biotic constraints, while also enabling the strategic selection of parental lines possessing complementary and favorable traits for region- and management-specific cultivar development [13]. The systematic exploitation of this variability allows breeders to improve crop productivity and environmental adaptability in a structured manner, thereby contributing to the long-term sustainability of agricultural systems [30]. In this study, multiple analytical frameworks—including AMMI, Bayesian AMMI, BLUP, and GGE biplot methodologies—were applied to identify barley genotypes that combine high performance with phenotypic stability under the warm climate conditions of Iran. The results derived from combined ANOVA, AMMI, and BLUP models (Table 2) revealed highly significant effects of environment (E), genotype (G), and their interaction (GEI) for all measured traits. The persistent significance of the genotypic effect across traits and the presence of considerable genetic variability among the examined genotypes indicate substantial potential for effective selection. Moreover, the pronounced GEI underscores differential genotypic responses across environments, emphasizing the importance of selecting genotypes with either broad or specific adaptation to target environments. In breeding programs, the selection of high-yielding genotypes alone is insufficient,such genotypes must also demonstrate consistent performance across diverse environments. Therefore, stability analyses are essential for assessing the broad adaptability of genotypes ([31–35], Dalgıç et al. 2025). These findings are in strong agreement with earlier reports in barley, which consistently documented significant contributions of genotype, environment, and their interaction to phenotypic variation [16, 36–43].

Our results indicate that the substantial variation observed in phenological traits, specifically days to heading and maturity, reflects a key agronomic trade-off in warm climates: although early-flowering genotypes can escape terminal heat and drought stress, they may forgo maximum yield potential relative to later-maturing lines, which, in turn, are at greater risk of yield loss if severe heat occurs during the grain-filling period [44]. Notably, the superior and stable genotypes (G4, G5, and G20) consistently exhibited thousand-kernel weight values near the upper end of the observed range, indicating a strong positive association between kernel weight and grain yield. Under warm climatic conditions, the capacity to maintain a high thousand-kernel weight suggests efficient assimilate partitioning and resilience to terminal heat stress, a primary determinant of overall yield stability [45].

In plant breeding, reliance on single-trait selection can lead to biased or suboptimal decisions, as it does not adequately capture the complex interrelationships among multiple agronomic traits. Consequently, the application of multi-trait selection approaches has become indispensable for the effectively identifying of superior genotypes across a broad spectrum of traits. Among these approaches, the multi-trait stability index (MTSI) has gained relevance in multi-environment trials (METs), as it enables the concurrent assessment of both genotypic performance and stability across traits and environments [25]. The MTSI was explicitly designed to address major limitations of conventional linear selection indices, including multicollinearity among traits and the subjective definition of weighting coefficients. By integrating information from correlated traits together and genotype × environment responses, this index provides a robust and holistic framework for ranking genotypes based on their overall desirability, adaptability, and phenotypic stability. As a result, MTSI facilitates more efficient identification of breeding candidates with wide adaptation potential. In the present study, MTSI model indicated that the first two latent factors accounted for 72.93% of the total phenotypic variation observed across test environments (Table S1). The index imposed positive selection pressure on grain yield while concurrently favoring negative selection for plant height, the number of days to heading, and physiological maturity. This result is highly relevant from a breeding perspective. Earliness constitutes a key adaptive trait, enabling genotypes to escape the most detrimental effects of high temperatures and terminal drought that typically occur during the late grain-filling period. Moreover, selection for reduced plant height is often associated with an improved harvest index and increased lodging resistance. The ability of the MTSI to simultaneously promote high yield and these critical adaptive traits underscores its effectiveness in balancing productivity with environmental resilience, thereby facilitating the identification of truly superior genotypes for the target production system. According to the ranking illustrated in Fig. 2B, genotypes G5 (1.689), G4 (1.914), G20 (2.380), and G14 (2.508), characterized by the lowest MTSI values, were identified as the most desirable barley genotypes across test environments. The effectiveness of MTSI in selecting high-performing and stable genotypes has been consistently demonstrated in earlier studies [46, 47]. Our results regarding the agronomic characteristics of the superior genotypes (G4 and G5) are consistent with established principles of barley breeding for temperate and semi-arid environments. Phenological traits—particularly days to heading and physiological maturity—are critical for adaptation to conditions characterized by terminal drought and heat stress, where optimal flowering timing enables the crop to complete grain filling prior to the onset of severe stress [48]. Plant height remains a key trait, with intermediate stature often providing an optimal balance between adequate biomass production and reduced lodging risk, thereby directly influencing harvestable yield [49]. Furthermore, thousand-kernel weight is a major component of grain yield, and its stability across environments serves as an important indicator of broad adaptability. The superior performance of the selected genotypes reflects a favorable combination of these traits, consistent with evidence highlighting the complex interactions among yield components and phenology in determining final grain yield under diverse environmental conditions [50].

Best Linear Unbiased Prediction (BLUP) is a cornerstone statistical approach in modern breeding, providing robust estimates of genotypic merit. By integrating information from related genotypes, accounting for environmental effects, and accommodating data of heterogeneous quality, it enhances selection accuracy and increases the likelihood of identifying superior genotypes [13, 51]. Within this context, de Resende [26] introduced a set of BLUP-derived stability and adaptability metrics, namely the relative performance of genotypic values (RPGV), the harmonic mean of genotypic values (HMGV), and the harmonic mean of the relative performance of genotypic values (HMRPGV). The RPGV metric quantifies genotypic performance relative to environmental means, whereas HMGV emphasizes yield stability while simultaneously accounting for mean performance across environments. By information from both indices, HMRPGV provides a unified measure that reflects genotypic stability and relative productivity, thereby offering a comprehensive criterion for selection [52]. In the present investigation, application of these BLUP-based indices consistently ranked genotypes G4, G6, G13, G15, and G20 among the top-performing and most stable candidates (Table 3). These findings align with previous evidence demonstrating that BLUP-derived indices, due to their strong association with yield performance and stability, represent an effective dynamic stability concept and serve as powerful tools for screening superior genotypes in breeding programs [42].

The AMMI model partitions genotype-by-environment interaction (GEI) by decomposing additive main effects and multiplicative interaction components. Its Bayesian extension refines this framework by treating model parameters as random variables, thereby reducing the risk of overfitting and enabling rigorous quantification of uncertainty. Consequently, the Bayesian AMMI approach is well suited to complex datasets and to applications such as breeding programs that require informed, risk-aware decision-making [20, 53]. In the present study, both the classical and Bayesian AMMI models captured a substantial proportion of the GEI variation. The biplot representations derived from each approach highlighted genotypes and environments that contributed most strongly to the interaction structure. Notably, both modeling strategies consistently identified genotypes G2, G4, G10, and G15 as exhibiting superior stability across environments (Fig. 4).

Genotypic performance and stability were jointly assessed using the weighted average of absolute scores (WAAS) and the yield–stability weighted index (WAASY), derived from the AMMI, Bayesian AMMI, and BLUP analytical frameworks. Across all modeling approaches, genotypes G4, G5, and G16 consistently exhibited the lowest WAAS values, indicating greater stability than the remaining genotypes. When yield performance was incorporated via the WAASY criteria, these genotypes—along with G20—achieved the highest index values, reflecting their overall superiority in both productivity and stability (Fig. 5). To further discriminate genotypes based on their yield potential and stability patterns, the stability Mahalanobis distance (SM) and Y × WAAS graphical analyses were employed. The SM biplot partitions genotypes into four distinct categories: high yield with high stability (quadrant IV), high yield with low stability (quadrant I), low yield with high stability (quadrant III), and low yield with low stability (quadrant II) [54]. According to Fig. 6A, genotypes G4, G5, G20, and G21 were positioned in quadrant IV, demonstrating a favorable combination of high productivity and consistent performance across environments. These genotypes therefore represent promising candidates for further evaluation and potential deployment in targeted production environments. Genotypes G6, G7, G13, G14, and G15 were located in quadrant I, suggesting high yield potential under favorable conditions but reduced stability across environments. In contrast, genotypes G8, G10, and G12 occupied quadrant III, characterized by stable yet comparatively low yield performance, indicating their potential value as sources of resilience-related traits or for cultivation in marginal environments where yield stability is prioritized over maximum productivity. Quadrant II comprised genotypes G3, G11, G17, and G19, which exhibited both low yield and poor stability and are therefore considered unsuitable for recommendation. The SM biplot further indicated that none of the evaluated genotypes displayed complete general adaptability, as all deviated to some extent from the biplot origin. Nevertheless, genotypes G1 and G2—used as reference standards—as well as G8 and G18 were positioned relatively close to the center, suggesting moderate and balanced performance across environments. While the reference genotypes behaved as expected, G8 and G18 merit further, more detailed evaluation due to their intermediate stability profiles. Consistent with the SM analysis, the Y × WAAS plot also classified genotypes and environments into four quadrants. In this scenario, genotypes G2, G4, G5, G14, G15, and G20 were grouped in quadrant IV, reflecting their superior yield performance combined with high stability and indicating suitability for cultivation under favorable environmental conditions. Additionally, environments E3, E5, E7, and E8, located in quadrants I and II, demonstrated strong discriminative capacity, highlighting their effectiveness in differentiating genotypic performance in multi-environment trials (Fig. 6B). A particularly noteworthy finding is the co-identification of the sister lines G4 and G5 as superior and stable genotypes, a consistency that can be directly attributed to their shared pedigree (Sahra/3/Bda/Rhn-03//ICB-107766). This genetic background provides a plausible explanation for their performance in the warm agroecological zones of Iran. The maternal parent, ‘Sahra’, is a well-established Iranian barley cultivar with specific adaptation to northern regions of the country, which are characterized by humid and warm conditions,it is therefore likely to contribute favorable alleles for traits such as earliness, efficient water use, and stable grain filling under high temperatures. In contrast, the paternal lineage includes elite breeding lines, incorporating international germplasm such as Rhn-03, selected for high yield potential and robust performance under drought-prone environments.

In the GGE biplot methodology, the ideal genotype plot is a graphical tool for ranking genotypes relative to a theoretical reference genotype that combines the highest mean yield with complete stability across environments. This hypothetical genotype is located at the center of a series of concentric circles and serves as a standard against which all tested genotypes are evaluated. Genotypes positioned closer to this reference point are considered more desirable, as they simultaneously exhibit superior productivity and stable performance. In contrast, a greater distance from the center indicates lower agronomic value due to diminished yield potential, instability, or both. In parallel, the mean performance versus stability view utilizes the average environment coordination (AEC) method, in which the horizontal axis represents mean yield performance and the vertical axis reflects yield stability. Genotypes with large positive projections along the AEC abscissa and minimal dispersion along the ordinate are therefore characterized as high-yielding and stable across environments. When considered together, these complementary graphical representations provide a comprehensive basis for interpreting multi-environment trial interpretation, facilitating the identification of broadly adapted genotypes, the detection of environment-specific responses, and the prioritization of promising genetic material for cultivar release or further breeding advancement [55]. In the present study, genotypes G4, G14, G15, and G20 demonstrated superior performance, combining high mean yield with pronounced stability, and were consistently highlighted as outstanding entries in the GGE biplot analyses. Consistent with these findings, previous studies have emphasized the effectiveness of the GGE biplot approach as a reliable graphical method for discriminating superior genotypes in multi-environment trials [7, 16, 37, 43, 56].

Using multiple independent yet complementary analytical frameworks, genotypes G4 and G20 were consistently identified as superior due to their simultaneous expression of high yield potential and phenotypic stability. Genotype G5 also demonstrated a favorable combination of stability and performance across several selection indices. In contrast, genotypes G15 and G14 consistently yielded high. However, their stability was comparatively lower in some analyses, suggesting that they may be better suited to more favorable or less variable environments. Approaches incorporating uncertainty estimation and shrinkage effects, such as Bayesian-AMMI and BLUP, largely confirmed the genotype rankings obtained from conventional AMMI and GGE biplot analyses. Furthermore, the application of the MTSI index and the WAAS/WAASY metrics enhanced selection efficiency by integrating yield performance with stability while accounting for trait correlations. Finally, the SM and Y × WAAS classification schemes provided an intuitive, operational grouping of genotypes that was highly consistent with the numerical selection indices. Overall, the integration of complementary models and approaches provided a robust evaluation framework, wherein classical biplots facilitated the visualization of interactions, BLUP-based indices informed practical selection decisions, and Bayesian analyses enabled rigorous quantification of predictive uncertainty.

Conclusion

Substantial genetic variability was detected for grain yield and several key agronomic traits–including the number of days to heading, physiological maturity, grain-filling period, thousand-kernel weight, and plant height–among newly developed barley genotypes evaluated across ten warm-environment testing sites in Iran. The integration of multiple analytical models and stability metrics substantially enhanced the discrimination of genotypes exhibiting both superior yield performance and environmental stability. Based on the combined evidence, genotypes G4, G5, G14, and G20 were identified as particularly promising. Notably, genotypes G4 and G20 consistently demonstrated outstanding performance and broad adaptability. Moreover, the application of graphical decision-support tools, including the Mahalanobis distance-based index and the Y × WAAS framework, enhanced selection precision by providing complementary insights beyond conventional GGE biplot analysis. A limitation of this study is that evaluations were restricted to ten environments. Nevertheless, the concurrent use of diverse statistical approaches is strongly recommended for future multi-environment trials to comprehensive selection decisions.

Authors’ contributions

Conceptualizations, A.P.; methodology, A.P.; software, A.P., B.J. and M.D.; validation, M.D., J.B. and A.P.; formal analysis, A.P., B.J. and M.D.; investigation, H.Z., A.G., A.M., S.K., A.O., K.S., A.M. and M.K.; resource, A.P.; data curation, A.P.; writing-original draft preparation, A.P. and B.J., writing-review and editing, A.P. and J.B. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no extra funding.

Data availability

Data will be made available on request.

Declarations

Ethics approval and consent to participate

Not applicable.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.