1 Introduction

The chickpea (Cicer aeritinum) is a diploid (2n = 16) annual shrub that stands out as the sole domesticated species of Genus Cicer and ranks the third most cultivated legume globally [1]. The majority of chickpea production occurs in developing countries that consume more than 90% of their produce locally [2]. Its preference for growth in arid and semi-arid regions, often on poor soil, is attributed to its relatively low irrigation needs compared to cereals. In Pakistan, chickpea is the 2nd most important pulse crop after dry bean, best suited to a cool, dry climate. Chickpea cultivation occupies 73% of the pulse area in Pakistan with a total production of 545000 tonnes during 2019-20, which was 22% higher than the last year [3]. However, production has remained stagnant for the last couple of decades while the consumption rate increased gradually with time, and deficiency is met through imports. Additionally, chickpeas also play an important role in addressing global nutritional challenges. They provide good quality protein, essential nutrients, and dietary fibre, contributing to food security for a large world population. In developed countries, the consumption of chickpeas is increasing due to their recognised benefits, such as gluten-free grain flour, high dietary fibre, vitamins and healthy alternatives to meat products [4]. This trend emphasises the versatility and the growing importance of chickpeas in meeting the diverse nutritional needs of the population globally.

The chickpea productivity in the farmer field is very low in the region, with an average chickpea grain yield of about 670 kgha−1 (Ullah et al., 2020). The chickpea productivity is limited by several biotic and abiotic stresses like Fusarium wilt, ascochyta blight and drought [3, 5]. Most areas under chickpea cultivation are in arid regions where unfavourable weather or lack of critical moisture at the time of sowing are the main yield-limiting factors. Additionally, Chickpea genetic makeup further complicates efforts to boost yield, with less than 1% outcrossing and a narrow genetic base, resulting in a significant lack of genetic diversity posing a bottleneck in enhancing crop yield. Researchers are striving to develop climate-resilient, high-yield crop varieties suitable for consumer preference. However, the challenges extended beyond biological and environemntal factors to include social and cultural constraints. Because many farmers lack access to modern agricultural technologies, conventional farming practices are often used. Moreover, limited financial resources and a lack of extension services hinder the adoption of improved chickpea varieties. Recognising these challenges, the Chickpea Productivity Enhancement Project was launched in Pakistan through collaborative efforts between the Australian Centre for International Agricultural Research (ACIAR), Australian partners, and local research institutes. This initiative aims to address the pressing need for enhanced chickpea productivity by leveraging scientific expertise, innovative technologies, and collaborative partnerships to develop sustainable solutions tailored to the unique challenges faced by chickpea farmers in Pakistan, ultimately improving resilience in crop yield.

Local public sector research institutes have developed several genotypes suitable for their regional environment, with phenotypic plasticity, showing tolerance to local climatic conditions [6]. Despite these efforts, there has been a lack of comprehensive evaluation of these regionally confined chickpea varieties under diverse agro-climatic conditions. The performance of chickpea varieties is significantly influenced by the genotype by environmental interaction [7]. Literature showed that any particular environmental variation might induce disparity in the genotypic performance [8]. This interaction of genotypic and non-genotypic effects, instigating relative differential performances of cultivars in diverse backgrounds, depicts genotype × environment interactions. Linear mixed models, which include both fixed and random effects, are increasingly used to analyse multi-location trials [9]. These models used factor analytic structures of genetic variance and covariance, which have been reported to be more flexible and parsimonious than other structures [10]. This means that fewer parameters need to be estimated compared to the unstructured variance and covariance models. Graphical tools like heatmaps can be estimated to show genetic association across different locations resulting from the factor analytic model in order to make inferences about genotypes by environmental interaction, stability and adaptability of genotypes [11]. Additionally, environmental loadings of the factor analytic model can also be correlated to environmental covariates such as temperature, rainfall, humidity, fertiliser, wind speed and others in order to observe trends in genotypic performance across different locations based on environmental conditions [12, 13].

The present study aims to address the gap in comprehensive evaluation by assessing the yield performance of chickpea varieties collected from different research institutes across the country and contrasting environmental conditions. The objective is to use a mixed model approach to test the genotype versus environmental interactions over two years to select high-yielding and stable-performing chickpea varieties for future farming. The findings will provide valuable insights for policymakers and researchers in developing effective breeding strategies for chickpea improvement.

2 Materials and methods

A set of 14 chickpea genotypes (12 Desi type and 2 Kabuli type) were collected from different research institutes across the country (Table 1). In this study, four sites, symbolizing areas of high chickpea production (Table 2), consumption, and selling market, were selected to test the genotypes. Field experiments were conducted on farmer fields in a randomised complete block design (RCBD) with three replications from October to April for two consecutive years (2017-18 and 2018–2019) under rainfed conditions. A written consent was obtained from the farmer before the conduction of varietal trials.

Table 1 List of chickpea genotypes used in the study and their source
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Table 2 Description of trial sites for crop yield performance of chickpea genotype
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There were 16 rows in each plot with a row spacing of 30 cm. The seeds were sown using a precision dibbler, 10 cm apart in 10 m long rows. The seed of each variety was inoculated with peat-based rhizobial inoculant (N2-Biofertilizer, Ayub Agricultural Research Institute, Faisalabad) and fungicide (Thiophenate methyl at 2 g per kg seed) before sowing. The recommended protocols for chickpea crop production were used to manage each trial site [14]. During experimentation, no irrigation was applied.

2.1 Data collection

Ten plants were randomly selected from each plot's middle rows to record the phenological data for each tested variety. The recorded parameters included days to 50% flowering (DF), days to 50% maturity (DM), plant height (PH), number of pods per plant (NPP), 100-seed weight (HSW), and Grain yield (GY). The mean grain yield was estimated at each location and season for each genotype.

2.2 Statistical analysis

The analysis using a mixed model [15, 16] was carried out. The genotype by environment interactions was studied by Additive Main Effects and Multiplicative Interactions (AMMI) [17]. This model aligns the analysis of variance (Table S2) and principal component analysis (PCA) with the additive parameters in a single analysis [16] using R-studio 1.3.1093 software [18]. The AMMI model was also performed to deduce high yield specific to broadly adapted genotype. The AMMI model used was as follows;

$${{\varvec{y}}}_{{\varvec{z}}{\varvec{x}}}={\varvec{\upmu}}+{\boldsymbol{\alpha }}_{{\varvec{z}}}+{{\varvec{\beta}}}_{{\varvec{x}}}+\sum_{{\varvec{k}}=1}^{{\varvec{N}}}{{\varvec{\lambda}}}_{{\varvec{k}}}{{\varvec{\gamma}}}_{{\varvec{z}}{\varvec{k}}}{{\varvec{\delta}}}_{{\varvec{k}}{\varvec{x}}}+{{\varvec{Q}}}_{{\varvec{z}}{\varvec{x}}}$$
(1)

where y is the responsive variable like the grain yield of genotypes (z) in an environment (x). Here, α is the grand mean of the zth genotype, and β is the mean deviation of the xth environment. Whereas, N is the total number of PCA axis in the model, λ is the eigenvalues of kth IPCA, γ is the zth genotype score of eigenvectors kth, δ is the xth environment eigenvector of axis kth, Q is the residuals of zth genotype in environment xth. The value analysed was used in biplot [19] to draw a graphical representation of genotype by environment interactions.

The AMMI framework was used for fixed effect mean when genotype, environment, or both are considered reasonably as a random effect. The Eq. (1) can be rearranged into a linear mixed model to describe the methodology.

$${\varvec{y}}={{\varvec{X}}}_{{\varvec{\beta}}}+{{\varvec{Z}}}_{{\varvec{\mu}}}+\in $$
(2)

Here, X and Z are the design matrix linked with random and fixed effects, y is the responsive variables like grain yield, β and µ are the vectors of random and fixed effects, ∈ is the random error. The vector β and µ were assessed by an illustrious mixed model equation [20].

$$ \begin{array}{*{20}c} {\varvec{\beta}} \\ {\varvec{\mu}} \\ \end{array} = \left[ {\begin{array}{*{20}c} {{\varvec{X}}^{{\varvec{t}}} {\varvec{R}}^{ - 1} {\varvec{X}}} & {{\varvec{X}}^{{\varvec{t}}} {\varvec{R}}^{ - 1} {\varvec{Z}}} \\ {{\varvec{Z}}^{{\varvec{t}}} {\varvec{R}}^{ - 1} {\varvec{X}}} & {{\varvec{X}}^{{\varvec{t}}} {\varvec{R}}^{ - 1} {\varvec{Z}} + {\varvec{G}}} \\ \end{array} } \right] \left[ {\begin{array}{*{20}c} {{\varvec{X}}^{{\varvec{t}}} {\varvec{R}}^{ - 1} {\varvec{y}}} \\ {{\varvec{Z}}^{{\varvec{t}}} {\varvec{R}}^{ - 1} {\varvec{y}}} \\ \end{array} } \right] $$
(3)

The obtained G and R components of variance were estimated by Restricted Maximum Likelihood (REML) using maximum algorithm prediction [21]. Multivariate graphical representation in the form of BLUP for the genotype by environmental interactions by a weighted average of absolute score matrix (WAASB) was done using the following equation.

$$ {\varvec{WAASB}}_{{\varvec{z}}} = \mathop \sum \limits_{{{\varvec{k}} = 1}}^{{\varvec{N}}} \left| {{\varvec{IPCA}}_{{{\varvec{zk}}}} \times {\varvec{NZ}}_{{\varvec{k}}} {\varvec{A}}} \right| / \mathop \sum \limits_{{{\varvec{k}} = 1}}^{{\varvec{N}}} {\varvec{NZ}}_{{\varvec{k}}} $$
(4)

The IPCAzk is the score of zth genotype in the kth interaction of principal component analysis (IPCA), NZ is the value of the variance of kth IPCA. Therefore, the lowest WAASB value of genotype is found most stable [16].

Multi-trait stability index was also calculated based on ideotype distance using the scores obtained during factor analysis (FA). The selection difference of mean performance and WAASBY index was calculated for each trait considering 15% selection intensity, This moderate threshold helps in selecting superior genotypes while maintaing genetic diversity in the crop population [22, 23]. The selection of genotype with a mean performance of multi-trait depends on genotype and ideotype distance. This was calculated using the following equation.

$${\varvec{X}}={\varvec{\mu}}+{\varvec{L}}\mathcal{F}+\mathcal{e}$$
(5)

where X is the vector of observation, µis the mean vector, L is the factorial matrix of loadings, Ϝ is the common factor. The initial loadings were computed factors with eigenvalues greater than 1. The measure of different traits for stability index (MTSI) were calculated with the equation below.

$${{\varvec{M}}{\varvec{T}}{\varvec{S}}{\varvec{I}}}_{{\varvec{z}}}={\left[{\sum }_{{\varvec{k}}=1}^{{\varvec{N}}}\left({\mathcal{F}}_{{\varvec{z}}{\varvec{k}}}-{\mathcal{F}}_{{\varvec{k}}}\right)\right]}^{0.5}$$
(6)

where MTSI for zth genotype, Ϝzk is the kth score of zth genotype, Ϝk is the kth score of ideotype. The genotype with the lowest multi-trait stability index was considered near the ideotype that showed all the variables' high mean performance.

The selection of superior genotype with best performance and stability index is done by the WAASBY index (GY) that allows the estimation of genotypic performance and stability index (WAASB). The high value of grain yield (GY) depicting best genotypic performance and for broader stability is explained by the lowest WAASB index where WAASBY index was calculated by following equation.

$$ {\text{WAASBY}}_{{\text{n }}} { = }\frac{{\left( {{\text{r}}{\rm M}_{{\text{n}}} { } \times {\text{r}}\theta_{{\text{i}}} } \right){\text{ + (r}}{\rm N}_{{\text{n}}} { } \times \,\theta_{{\text{j}}} {)}}}{{\theta_{{\text{i}}} { + }\theta_{{\text{j}}} }} $$
(7)

Here, the WAASBYn index estimate for the performance and stability of nth genotype. The θi and θj calculate for the response variable, and the value of stability assumed for this study is 65 and 35, respectively. The value of GY and WAASB are rescaled from 0 to 100 so that comparison could be made simple and easy.

Where,

$${\varvec{r}}{{\varvec{M}}}_{{\varvec{n}}}=\frac{100-0}{{{\varvec{M}}}_{{\varvec{m}}{\varvec{a}}{\varvec{x}}}-{{\varvec{M}}}_{{\varvec{m}}{\varvec{i}}{\varvec{n}}}}\times \left({{\varvec{M}}}_{{\varvec{n}}}-{{\varvec{M}}}_{{\varvec{m}}{\varvec{a}}{\varvec{x}}}\right)+100$$

And

$${\varvec{r}}{{\varvec{N}}}_{{\varvec{n}}}=\frac{0-100}{{{\varvec{N}}}_{{\varvec{m}}{\varvec{a}}{\varvec{x}}}-{{\varvec{N}}}_{{\varvec{m}}{\varvec{i}}{\varvec{n}}}}\times \left({{\varvec{N}}}_{{\varvec{n}}}-{{\varvec{N}}}_{{\varvec{m}}{\varvec{a}}{\varvec{x}}}\right)+0$$

Here, rMn and rNn are rescaled value GY and WAASB for the nth genotypes. The Mn and Nn are the response variable of (GY) and stability for the nth genotype. Here the objective of this estimation is to analyze the genotype based on the estimated value of the response variable and genotypic stability.

Considering the mixed effect model, the WAASB and WAASBY indices analysed the genotypic categorisation with the AMMI-led stability index, including the absolute value for PCA1 and the AMMI-based stability value (ASV) [24]. Furthermore, several stability index were used in this study. These includes the sum of absolute value for PCAs (SIPC), the average value of squared eigenvector (EV), the absolute value of PCAs relative contribution (ZA). The simultaneous selection index were also calculated. Each index was derived by summing the ranks of ASV, EV, SIPC and ZA with rank of average yield [25], resulting in ssiASV, ssiEV, ssiSIPC, and ssiZA, respectively. The genotypic categorisation was calculated based on the WAASBY index and GY, which were further analysed with PCA analysis to explore the correlation among computed indexes.

3 Results

This section explains the overall genotype performance in field trials across different environments, followed by genotype by environmental interactions. The outcomes analysed are accompanied by minimal interpretation, with the explanation provided in the discussion section.

3.1 Overall performance and estimated variances

The likelihood ratio test demonstrated highly significant effects for genotypes and environments (p < 0.05) in chickpea field trials (Table 3).

Table 3 P-values for likelihood ratio test of the analysed traits
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Figure 1 indicates the qualitative interaction of genotypes due to crossovers in different locations since the rank order of genotypes continuously changes over different environments. The grand mean of grain yield (GY) was 1063 kgha−1, whereas the lowest GY mean was 893 kgha−1, and the highest mean value was 1303 kgha−1. The likelihood ratio test showed that genotype by environment interactions was significant for all the studied traits (Table S3). The impact of the environment was highly significant for all the traits, and genotypic performance was influenced strongly by the environment in which it was grown (Fig. 1b). For example, genotypes 4 and 10 exhibited a maximum yield of 1253 kgha−1 and 1247 kgha−1, respectively, in environment 1. A maximum output of 1175 kgha−1 and 1129 kgha−1, in genotypes 6 and 1, respectively, was achieved in environment 2 while environment 3 was conducive in achieving higher yields in genotypes 9 (1637 kgha−1) and 3 (1152 kgha−1). At the same time, environment 4 was the best for genotype 9 (1303 kgha−1) and 1 (1241 kgha−1), respectively (Table S4).

Fig. 1
figure 1

a Grain yield estimated from best linear unbiased prediction (BLUP) for 14 chickpea genotype. Blue and Red dots explain genotypes with BLUP above and below of BLUP means. b shows grain yield of 14 chickpea genotypes across four different environments. Red, orange, green and blue block displays the environment 1, 2,3 and 4 respectively

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The phenotypic variance (δp) observed was 68.6%, 37.6%, 26.6%, 68.1%, 73.1% and 41.5% due to residual variance for plant traits GY, DF, DM, PH, NPP and HSW respectively. Similarly, the computed genotypic variance was 5.56%, 10.5%, 0.45%, and 13.7% for GY, DF, NPP, and HSW, respectively, resulting in low estimate of narrow sense heritability. The significant difference between phenotypic and genotypic variance cannot not solely account due to heritability. Environmental factors also contribute significantly to phenotypic variance, as location-specific conditions such as soil, rainfall, and temperature can cause considerable variation. Moreover, genotype by environment interaction causes phenotypic variation under varying conditions, which increases phenotypic variation without corresponding to genotypic variation. The accuracy of selection (AS) for genotype that measures the correlation between observed and predicted value for characters DF, DM, NPP, HSW, and GY was 0.628, 0.35 × 10–5, 161, 0.695, and 0.560, respectively. The coefficient of variation for genotype (CVg) for the response variables was 6.52, 1.13, 1.34, and 3.85 was less than half of the residual coefficient of variation (CVr), 22.9 2.13, 19.6, and 6.70 for GY, DF, NPP, and HSW respectively. Moreover, high δ2GEI/ δ2g value (4.64, 4.97, 77.8) showed result of low correlation between genotypes across different environments (rge) with value 0.273, 0.580, 0.266, 0.519 for GY, DF, NPP and HSW (Table 4). Therefore, Genotypes 9, 1, and 3 had the maximum predicted means among the evaluated genotypes. Genotype 6, 5, 14, and 2 were the other varieties that performed well with minimal variance.

Table 4 Variance component and genetic parameters
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Pearson correlation coefficient showed a significant negative correlation between grain yield (GY) and both plant height (PH) and days to maturity (DM). A significant negative correlation was also observed of hundred seed weight (HSW) with days to flowering (DF) and days to maturity (DM). The total number of pods per plant (NPP) was correlated positively to days to maturity (DM) and plant height (PH) with r = 0.22 and 0.55, respectively. Plant height was associated positively with DF (r = 0.38) and DM (0.5). The days to maturity (DM) positively correlated with DF (0.92), implying that plant height will proliferate with an increase in DF and DM. Similarly, climatic parameters, including temperature, humidity, and rainfall, also influenced the performance of the seleceted traits. A strong correlation between rainfall and humidity was observed at Attock (S1), Karak (S3), and Larkana (S4) with values 0.8, 0.48, and 0.47, respectively. Both temperature and humidity exhibited a negative correlation among all the selected environments (Fig. 2). These findings provide valuable insights for informed decision making in chickpea breeding programs aimed at selecting high performing genotypes with enhanced stability across diverse environmental conditions.

Fig. 2
figure 2

Pearson correlation matrix among selected traits of 14 chickpea genotypes, DF days to 50% flowering, DM days to 50% maturity, PH plant height, NPP number of pods per plant, HSW hundred seed weight, GY grain yield

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3.2 Genotype × environmental interactions

Analysis of chickpea genotype trials revealed that the accumulated variance of the first two principal components amounted to 83.0% (Table S5), thus showing genotype by an environmental variation impacting chickpea grain yield. The angle between environments 1 and 3 was less than 90° (θ < 90°), depicting a positive correlation. Thus, suggesting the same magnitude of interactions tends to be affected independently. The vector angle more than 90° (θ > 90°) showed a negative correlation among environments 2, 3, and 4. Genotype 9 performed best in all tested environments. This genotype is illustrated by the equation y = 1303 + (−10.9x), where x is the first environment principal component axis that defines the line for genotype 9 (Fig. 3).

Fig. 3
figure 3

a AMMI biplot for year 2018. b AMMI biplot for year 2019, presenting which ranking and which won where by studying the second principal component axis (PCA2) against the first principal component axis (PCA1) of grain yield (kgha-1) for 14 chickpea genotypes evaluated in four different environments

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The grouping of traits contributing to yield for a genotype mimics the genotypic environmental interactions within the particular environment (Fig. 4). The angle and length of the vector showed the relationship between selected traits and genotype. For instance, hundred seed weight (HSW) for genotype 1 (Bhakkar-2011), 3 (Bittal-2016) and 4 (Noor-2013) performed well in environment 2 (Bhakkar). Grain yield (GY), number of pods per plant (NPP), and hundred seed weight (HSW) traits of genotype Bittal-2016 and Noor 2013 were best at Bhakkar (B) and Attock (F). Plant height (PH) for genotypes KK-1 and KK-2 was maximum at Attock (F). Genotype 9 performed well in almost all the tested environments due to its highest grain yield and the lowest PCA1 score.

Fig. 4
figure 4

The biplot depicted second standardized principal component axis against first standardized principal component axis of six varietal traits tested across different environments. FDF, FDM, FPH, FNPP, FHSW and FGY: days to flowering, days to maturity, plant height, number of pods per plant, hundred seed weight, and grain yield at environment 1 (Attock), BDF, BDM, BPH, BNPP, BHSW and BGY: days to flowering, days to maturity, plant height, number of pods per plant, hundred seed weight, and grain yield at environment 2 (Bhakkar), KDF, KDM, KPH, KNPP, KHSW and KGY:: days to flowering, days to maturity, plant height, number of pods per plant, hundred seed weight, and grain yield at environment 3 (Karak), LDF, LDM, LPH, LNPP, LHSW and LGY:: days to flowering, days to maturity, plant height, number of pods per plant, hundred seed weight, and grain yield at environment 4 (Larkana)

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Figure 1S shows a straightforward explanation of the pattern of genotypes. In our case, genotype 3 remained stable in performance across all of the selected environments overall. A line with an equation represents this genotype y = 1231 + (−6.1x), where x is the score of environmental PCA1. The most leftward score of -22.6 indicates a yield of 1369 kgha−1, whereas the most right of score 4.5 implies 1259 kgha−1. These estimated values denote two points to draw the line of genotype 3. By considering PCA1, genotype three performance was stable in all environments because the highest and lowest value of PCA1 defines the slope of the line among studied genotypes.

The four quadrants in Fig. 5 showed four classes of genotypes and their interactions with the environment for a combined interpretation of performance and stability. The first quadrant included the most unstable chickpea genotypes, 10, 4, and 1 in environments 1 and 2, in which the response of the grain yield variable was below the grand mean. Genotypes specifically adaptable to these two environments are found in this quadrant. In the second quadrant, the most productive but unstable genotypes were located, showing the high magnitude of responsiveness with a high discriminative genotype value. The genotypes 14 and 9 and environment 4 were located in this quadrant. Similarly, genotypes 11 and 13 with environment 3 were included in the third quadrant, which represents low productive and widely adapted genotypes. The lower the value of WAAS, the more stable the genotype's performance across the different environments. The environment found in this region is considered poorly dynamic with low discriminative ability.

Fig. 5
figure 5

The biplot of chickpea grain yield by a weighted average of absolute score for the best linear unbiased prediction of genotypes vs environment interaction (WAASB) of 14 chickpea genotypes cultivated in four different environments. It represents the four modules of genotypes or environments for a joint interpretation of performance and stability

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The genotype within the fourth quadrant showed high productivity with broad adaptability. The environment included in this area should be considered more productive with low discriminative ability. The genotypes included in this quadrant were 1, 3, and 6. The specific and more comprehensive adaptability of genotype is also crucial. Therefore, it showed that the genotype at the top was long duration, while those in the middle represent medium duration varieties. Similarly, genotypes near the bottom have a short duration, so this interaction appears to be caused by different maturity requirements of the genotypes. Moreover, the environmental index showed that environment 4 was favourable for the genotypes to perform with their capacity, while the remaining environments, including Attock, Bhakkar, and Karak, were unfavourable. However, among the unfavourable, Bhakkar was the worse for all genotypes.

3.3 Genotype ranking and stability

The genotype ranking and stability depend on the number of PCAs included in the WAASB computations. The genotype with identical stability performance may easily be differentiated by the genotype code color on the left side of Fig. 6. For example, genotypes 11, 2, 1, and 6 indicated the lowest WAASB score considering PCA1, PCA2, and PCA3 with first, second, third, and fourth the most consistent performing genotypes, respectively. The most apparent change was genotype 9; which showed the 14 most stable genotypes (Fig. 7).

Fig. 6
figure 6

Heat map for ranking of 14 chickpea genotypes on the basis of WAASBy and mean performance. The horizontal ranking from left to right shows yield performance and right to left indicating stability. The different colours of the genotype (verticle-left) show four different classes of genotype on the basis of the calculated score. Between the utmost, orders obtained different weighs for productivity and stability. The genotypes in green colour are very productive and widely adapted. While in black, the colour shows productive but unstable. The genotypes in red colour are stable and low productive. While genotypes in blue are unstable and low productive

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Fig. 7
figure 7

The heat map elaborating ranking of 14 chickpea genotype in association with principal component axis (PCAs) used in weighted average absolute score for the best linear unbiased prediction for genotype by environment estimation. The genotype ranking altered by the extent to which PCAs are included in the WAASB estimation

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The chickpea genotypes 1, 3, and 2 showed a maximum WAASBY score of 83.4, 77.6, and 69.1, respectively. Therefore, the WAASBY value for WAASB and grain yield was 35 and 65, respectively. As discussed earlier (Fig. 5), these genotypes are distinct and located in quadrant IV. The similar colour on the left side of Fig. 8 showed different groups of the genotypes, indicating similar performance concerning genotype productivity and stability. The genotypes in green colour (genotypes 1, 2, and 3) are very productive and broadly adopted. Genotypes 9 and 14 in black colour were very effective but unstable genotypes because these genotypes indicated a low WAASBY index but maximum value for productivity. The genotypes 4, 8, 10, and 12 in red are stable performances but low productive genotypes as these showed greater weight for stability (high WAASBY index). Similarly, the blue-coloured genotypes 5, 6, 7, 11, and 13 were unstable and had low productivity.

Fig. 8
figure 8

Climatic conditions (temperature, humidity, and rainfall) across four different environments (E1; environemnt 1, E2; environment 2, E3; environment 3, E4; environment 4)

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3.4 Association between stability and simultaneous index

The categorisation of genotypes done against each index data is shown in Supplemental Table S6. Figure 9 explains the correlation matrix of the stability index analyzed from the data. The explained variance of PCA1 and PCA2 was 83%. Our WAAS and WAASB index was highly correlated with EV and ZA, and less correlation was observed with ASV, SIPC, and PCA1. Thus, the lack of a perfect relationship between WAAS and WAASB indicates relative differences and the varied categorization of genotypes based on stability while using fixed and mixed effect models (Table S7). The WAASY and WAASBY represented highly similar categorisation with GY and simultaneous selection indexes. Therefore, this choice of categorization based on the stability and mean performance of the genotype may enable genotypic selection in cases when the study objective needs to prioritise any of the characteristics.

Fig. 9
figure 9

Correlation between stability indexes, ASV; absolute value of first principal component axis, SIPC sum of absolute value of PCAs score, EV average value of squared eignvetcor value, ZA absolute value of the relative contribution of PCAs, WAAS weighted average of absolute score, Y grain yield

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3.5 The multi-trait stability index (MTSI)

The MTSI is used to evaluate the performance and stability of genotypes based on multiple traits. The principal factors were retained with proper varimax rotation, achieving a high commonality mean of 0.83. This high commonality mean indicates that these factors explain a significant portion of trait variance. The six selected traits were grouped into three factors (Table S5), including FA1 (PH, NPP, and GY), FA2 (DM and HSW), FA3 (DF). Figure 10 explains two genotypes, including genotype 3 (Bittal-2016) and genotype 2 (Thal-2006), which were selected with MTSI 3.199 and 3.513, respectively and ranked superior genotypes as shown in Table 5.

Fig. 10
figure 10

Estimated value of WAASBY and mean perfromance of 14 chickpea genotype

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Table 5 Genotype ranking and multi-trait stability index (MTSI) for genotype
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The MTSI 3.513 showed the breaking point (highlighted in red circle) considering the selection intensity. Genotype 1 (Bhakkar-2011) was near the break-even point, which showed that exploring genotype performance near the break-even point would be an interesting study for future prospects. The selection differential for the weighted average absolute of stability and yield index was positive for all characters (Table S7), suggesting the most appropriate way to select stable perfroming and high-yielding genotypes. The MTSI proposed a certain selection differential (SD) for the WAASBY index that was positive for all traits, signifying that the method was effective for categorising the genotypes based on their performance and stability. The average selection differential for WAASBY was highest for the GY (42.87%) and lowest (13.41%) for the PH (Table S7).

The contribution of individual factors to the MTSI is used to categorise genotypes based on their genotypic value. For example, factor FA1 (PH, NPP, and GY) contributed significantly less to the MTSI of genotype 1. Hence, the positive gain was anticipated for GY, demonstrating that genotype 1 was the high yielding out of best selected genotypes (Table 6). The selection intensity of ~ 15% categorizes the top two genotypes used to estimate selection differential. The association of each factor in the MTSI explained that ~ 38% of the distance of genotype 2 to ideotype was correlated with FA1 (Table S8). Conversely, genotype 2 had a higher WAASBY value for PH, NPP, and GY. Regarding genotype 3, most of the contribution to MTSI was due to FA3. This illustrates that the objective of the breeding program is to enhance productivity related traits of PH, NPP, GY (FA1) DM and HSW (FA2) (Table S8). The WAASBY index quantifies the genotypic stability by considering all principal component axes (PCAs).

Table 6 Selection gain for the mean of six selected traits of chickpea
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The GY of the selected genotype was 1150 kgha−1, which is ~ 8 higher than the mean value. Moreover, the selection differential of GY, HSW, and DF was observed at 87.49%, 0.82, and 0.17, respectively. The MTSI also explained the selection gain that most of the selected traits, including GY, HSW and DF, contributed to selecting the chickpea genotype. The percentage selection differential was estimated to be higher for GY and lower for NPP. Conversely, the heritability percentage was higher for HSW (48%), followed by DF (39%) and GY (31%).

Overall, Table 6 shows high selection differential, selection gain for grain yield which is justifed by its higher heritability. High heritability indicates that the trait is largely influenced by genetic factors and is more likely to respond to selection. The positive selection differential means that the selected genotypes showed superior performance than average population. Therefore, the high value of selection differential and heritaility for grain yield result in high selection gain.

4 Discussion

Several methods are used in this study; each has its merits and demerits. For instance, MTSI is complex and challenging to calculate and interpret large datasets that can obscure important trait performance by balancing multiple traits. Careful weighting is necessary to prevent bias in WAASB, which may over-emphasise stability at the expense of absolute performance. The BLUP assume a normal distribution of random effects, which may not always hold true and can be computationally intensive. Despite this limitation, the AMMI model, which effectively analyses genotype by environment interaction and visualises genotypic performance across varying environments, GGE biplot analyses grain yield and stability performance, identify environments and highlights the best genotype for each environment. Furthermore, linear mixed models offer flexibility in modelling genotypes by environment interactions, though they are computationally intensive and require expertise in model specification and interpretation.

The primary challenge causing reduced crop yields in chickpea cultivation is the lack of access to high-yielding varieties that are adaptable to varying environments. This issue has led the farmers in Pakistan to use decades-old chickpea grain as a seed during the crop season. Moreover, diverse climatic conditions across different regions of the country necessitate the breeding of chickpea varieties that are adaptable to specific environmental conditions. To address these challenges, fourteen popular chickpea varieties were tested at the farmer fields across four distinct environments.

The varieties, namely, Fakhr-e-Thal, Bittal-2016, and Bhakkar-2011 emerged as the high-yielding across all the trial locations (Table 4S). It is important to note that the location of the trials and the environmental conditions varied significantly, impacting the grain yield and other agronomic traits. Grain yield is being a multifaceted trait influenced by environmental factors [26]. As a result, the mean performance for yield across locations varied due to diverse climatic conditions (Fig. 8), soil characteristics (Table 1), and inherent differences in the yield of the chickpea varieties. Finding exhibited the presence of mega environments including environment 2 and environment 4 for grain yield, highlighting the importance of identifying climatic conditions conducive to optimal yield. This kind of observation has important implications for choosing a trial location, assessing genotype, and determining soil moisture. Farmers and chickpea breeders can improve crop yield and resilience in a variety of agroecological contexts by taking these aspects into consideration and making well informed decisions.

The categorization of genotypes and their mega-environments based on similarities and differences [27] sheds light on the complex dynamics of genotype by environment interactions. This study indicated three mega environments for yield based on tested genotypes, evaluation, and selection for breeding [28]. The genotype selection was based on the tested genotypes signifies a crucial step toward effective genotype evaluation and selection for breeding purpose.

In this study, the selection of genotypes was guided by the MTSI, which aims to capture wider adaptability across diverse environments. To further refine genotype selection criteria, a weighted average of the absolute score (WAASB) was developed [15]. This method calculates the MTSI, using best linear unbiased predictions (BLUPs) obtained through single value decomposition for genotype x environmental interactions assessed with linear mixed models. WAASBY categorise chickpea genotypes according to grain yield and stability performance. The chickpea genotypes 1 (Bhakkar-2011), 3 (Bittal- 2016), and 2 (Thal-2006) showed high productivity and broad adaptability. MTSI finds genotypes with balanced performance and stability across multiple traits, with Bittal-2016 and Thal-2006 stands out as the best genotypes. BLUP enhances the precision of these predictions by accounting for both genetic and environmental variability. Genotype 9 (Fakhr-e-thal) was highlighted for its consistent high performance across diverse environments.

However, it was observed that certain genotypes showed high grain yield performance, but they lacked stability across the four diverse environments tested. This discrepancy highlights the significant impact of genotype by environment interactions on agronomic traits, highlighting the need for a robust strategy to account for such interactions in a breeding program. The genotype with a lower MTSI value showed maximum stability across all evaluated traits and environments. Based on MTSI, genotypes 3 (Bittal 2016) and 2 (Thal-2006) emerged as the most stable performance among the tested 14 genotypes. Figure 10 shows the selection intensity of genotypic ranking for multi-trait stability analysis for each trait analysed in a multi-environment. It is noteworthy that the estimated values of all the traits in the selected genotypes (Xs) exceeded those of originals average (Xo), across all 14 genotypes. Additionally, traits are classified into four different factors (Table S5) with the percent selection difference varied from 5.51 (NPP) to GY (42.87) in FA1 across four tested environments. This variability suggests the potential for obtaining gain through selection across all traits [29].

The MTSI analysis conducted in this study provided valuable insights into the performance and stability of the 14 tested genotypes across diverse environments (Fig. 10). By allocating ranks to each genotype based on the calculated value of each trait, the MTSI analysis facilitated the identification of top performing genotypes across different environments. This approach enables the effective selection of highly productive and stable performance genotypes, as evidenced by the positive selection differential observed for all traits. The top two genotypes across different environments showed anticipated value for all the traits in the Weighted Average of the Absolute Score by Years (WAASBY) index. The mean per cent selection differential for the WAASBY was 22.98, the minimum for NPP (5.511), and the maximum for HSW (37.53). These findings emphasise the effectiveness of the methodology in selecting genotypes with desirable traits across a range of environmental conditions. However, it's essential to acknowledge the inherent challenges associated with testing and selecting genotypes based on multi-environment performance [30].

In the context of creating variety and trait optimisation in breeding programs, correlation studies are essential for determining the relationship between different traits and uncovering viable parental combinations for improved variety development. The correlation analysis revealed a negative correlation between grain yield and other key characteristics, such as days to maturity, and plant height. Notably, positive correlations were found between grain yield and these traits, indicating that genotypes with larger seed size, earlier maturity, and taller plant height tended to exhibit higher grain yields. Similarly, a positive correlations were observed between grain yield and the number of pods per plant (NPP). This implies that variations in NPP significantly impact grain yield. These findings have important implications for breeding strategies, as they highlight the need for a comprehensive approach that considers both mean genotypic performance and stability across diverse environments. Breeders typically focus on choosing genotypes based on mean performance or unbiased predictor models like Best Linear Unbiased Predictions (BLUP), stability factors are often overlooked in breeding decisions. However, this study emphasizes the importance of comprehensive genotype testing across a wide range of environments to identify superior genotypes with both high mean performance and stability. By incorporating stability considerations into breeding programs, breeders can develop more robust and adaptable crop varieties capable of consistently delivering high yields across diverse environmental conditions.

The stability analysis highlighted that WAASB is an essential statistical tool for the identification of productive and widely adapted genotypes. The analysis demonstrated that genotype 9 emerged as the most stable performing when WAASB was calculated with two PCAs (Fig. 6). The low score of this genotype 9 in both PCA1 and PCA2 further reinforce its stability across environments (Table S6). By calculating the explained variance for genotype 9 using WAASBG6, we can ascertain its stability index, which is calculated as 2.79. Additionally, genotype 9 also indicated the highest stability index when assessed through the ASV. Moreover, consistency between ranking obtained from WAASB and ASV showed in Table S7, demonstrated the robustness of stability assessment approach. The outcome of two PCA’s accurately matched WAASB and ASV ranks, explaining the PCA1 and PCA2 collective account for 82.97% variance of genotype by environment interactions.

The current study has shown the synergistic effect of the BLUP and AMMI which collectively increased the reliability of genotype × environmental interactions analysis. By leveraging BLUP, which provide unbiased estimates of genotypic performance across environments, and the AMMI model which effectively captures genotype by environment interactions, enable chickpea breeder to gain deeper insight into the performance and stability of chickpea genotypes across diverse environmental conditions. Moreover, the biplot analysis assisted in this study played an important role in categorising selected varieties into different environment based on their performance and corelated response to environment. This facilitated the exploitation of genotypes with narrow adaptation or breeding for specialised environmental conditions. Nevertheless, Fig. 5 depicts the WAASB × GY biplot, which is a useful tool for understanding the productivity and stability of the genotype. Through the WAASB × GY biplot, breeders can visually evaluate the stability and performance of various genotypes across several environments. This visualization makes it possible to identify genotypes that are stable and productive under varying environments, as well as those that may have unique environmental adaptations.

In earlier studies, the incorporation of stability analysis was limited due to the inherent challenges associated with weighing mean performance against the stability index [31]. Nonetheless, improvements in breeding techniques have made it possible to create solutions to this problem. One such method is the simultaneous selection index, which finds genotypes with high performance and stability by combining the ranking of ASV with mean performance [32]. The reliability of genotype selection is ensured by the robust framework this simultaneous selection index offers for classifying genotypic stability. When AV computation is possible, the classification of genotypic stability using the simulation selection index (ssiASV) is shown to be reliable. Thus, in simultaneous selection index in future projects utilising a fixed effect framework would consider several stability metrics, such as ssiASV derived from PCAs, ssiZA, ssiEV, ssiSPIC and WAASY. These metrics collectively provide a comprehensive assessment of genotypic stability, enabling breeders to make informed decisions regarding genotypic selection. Moreover, WAASBY is a valuable tool in the simulation selection index for research employing a mixed effect model. By giving varying weights to stability and performance, WAASBY makes it easier to analyse the genotype through environmental interactions.

The MTSI is a very useful approach for plant breeders in selecting genotypes based on their high yield and stable performance. By utilising MTSI, breeders can effectively identify genotypes with the best combination of high performance and adaptability, which is crucial for success across varying climatic conditions. The traits selected through MTSI analysis should be prioritised for hybridization in the chickpea breeding program [33] across severe climatic conditions. In this regard, the WAASB index emerged as a promising decision making tool for the selection of high-yielding and wider adaptable genotypes. WAASB integrates singular value decomposition (SVD) for the BLUP matrix of genotype x environmental interactions, providing a robust assessment of genotypic stability and performance. The genotype with lower WAASB values showed broad adaptability across environments [15]. Figure 10 shows the categorization of genotypes for MTSI, aiding breeders in selecting genotypes with ~ 15% selection intensity. Notably, genotypes 3 (Bittal 2016) and 2 (Thal 2006) were chosen as the most stable performing among the 14 tested genotypes. Additionally, genotype 1, positioned close to the cut point (red circle), exhibits promising traits that warrant further investigation and evaluation. Thus, Fig. 9 and 10 should assist researchers in the selection and recommendation of cultivars in addition to the identification of genotypes with similar genotypic performance and stability. The fluctuation in climatic abnormalities inspires plant breeders to select superior genotypes compatible with the diverse climatic conditions. A genotype affected by significant genotype x environmental interactions could perform better [34]. The genotype chosen from the current study is optimum to be used in the chickpea breeding program to improve their yield and wider adaptable genotypes in diverse conditions.

5 Conclusions

This study analyzed the impact of genotype, environment, and their interaction on grain yield and its contributing traits, and revealed their complex genetic associations with each other. Only one genotype, i.e., “Fakhr-e-Thal” showed the highest overall yield, with varied performance in different environments. Two genotypes, i.e., “Bittal 2016” and “Thal-2006” exhibited more stability across environments. However, one genotype, i.e., “Noor-2013” exhibited more adaptability for environment 4. The location of Larkana emerged as the optimal environment for higher yield, whereas Bhakkar was identified as a challenging environment for testing genotypes due to its discriminating power. These findings highlight the importance of breeding for high-yielding and stable genotypes by taking into account the present study. Furthermore, cross-validation utilising a dataset of the performance of 14 chickpea genotypes across four different environments indicated that the predictive accuracy was higher using BLUP. In addition, utilising stability indices like WAASBY and MTSI was essential for distinguishing genotypes based on their high yield and stability performance. This approach facilitates optimising chickpea productivity by taking genotype-by-environment interactions into account.