BLUP Estimation and Genotype Stability in Arachis hypogaea L. Variety Testing using Mixed Model Equations

Domesticated groundnut (Arachis hypogaea L.) is an important self-pollinating, tropical legume mainly grown for oil production in more than 100 countries. Asia is the major groundnut producing region with China being the major contributor (17.39 million tons) followed by India (6.6 million tons) (FAOSTAT, 2018). However, there is a fluctuation in the annual production due to the sensitive behaviour of the genotypes to different environmental conditions (Mekontchou et al., 2006), referred as Genotype by Environment Interaction (GEI). Since, in plant breeding, high yield is a major goal, it is important to select superior cultivars having wide or specific adaptation, which can be tested by its degree of interaction with different environments (Hardwick et al., 1972; Finlay and Wilkinson, 1963). For this, Multi-Environment Trials (METs) can be used, which provide an estimate of the overall stability and adaptability of the genotype(s), along with GEI. The statistical models developed earlier, for studying GEI were based on the two-way fixed-effects or random-effects models (Cornelius et al., 1996; Cornelius and Crossa, 1999) assuming sites to be independent considering the pairwise covariances between sites be zero and variances within sites, be equal (Crossa et al., 2001; Cornelius et al., 2001). These models further assume the spatial independence of individual field plot errors in each site and the genotypes to be unrelated. However, these assumptions are not realistic as related genotypes i.e., full-sibs, half-sibs, sister lines tend to be more alike than unrelated genotypes. As a result, more complex and informative mixed linear models have been proposed for efficient data analysis. Linear model underlying Best Linear Unbiased Predictors (BLUP) and best linear unbiased estimates (BLUE) is called mixed model because it includes both fixed and random effects. The various advantages associated with these models involve efficient handling of unbalanced or incomplete data, i.e., not all lines or genotypes are tested in all environments, ability to assume some effects for example, variety and/or environment to be random than as fixed effect (Smith et al., 2005).

The general linear mixed model can easily accommodate covariances among observations. The mixed model handles correlated data by incorporating random effects and estimating their associated variance components to model variability over and above the residual error (Wolfinger and Tobias, 1998). Mixed models assume some effects to have arisen from the distribution of random-effects, implying the presence of a broad population of genetic effects and the samples being the realized values from that population, which can be predicted by BLUPs (Henderson, 1975). The analysis of metric data based on mixed linear model can be of the form.
 

y = Xβ + Zµ + e

Where,
y = Vector of observations.
β and µ = Vectors of fixed and random effects, respectively.
X and Z = Associated design matrices.
e = Residual vector.

The random effects are assumed to have a distribution as u ~ MNV (0, G) and e ~ MNV (0, R) with MNV as multivariate normal distribution with mean vector µ and variance co-variance matrix V (Piepho et al., 2008). For variety testing and development of new varieties genotype effects are often considered as fixed effects thus becoming a part of â in the mixed model. But, when genotypes are considered to be random effects, the genotypic effects become a part of u and thus, estimated by BLUP. Smith et al., (2005) argued that genotype effects should be specified as random in a statistical mixed model because this: (1) minimizes selection errors when identifying the best genotypes, (2) provides more realistic estimates of genotype performance (predictions of genetic gain) and (3) allows a valid analysis of data combined across stages/generations of selection. The choice to classify variety effects as fixed or random depends upon the aim and the properties of the two estimation procedures i.e., empirical best linear unbiased prediction (E-BLUP) for random effects and best linear unbiased estimates (E-BLUE) for fixed effects considered for the analysis (Smith et al., 2005). If the analysis aims to identify the best variety out of those under consideration, then, the variety effect should be considered random, implying the use of BLUPs during the early stages of the selection program. However, the same can be considered as a fixed effect at later stages of selection or, if the aim is to determine the difference between specific pair of varieties, as BLUP of a specific difference is biased and hence will be inappropriate to use (Federer 1997; Smith et al., 2005). When, genotypic main effects are taken as random the mixed model can be defined as:
 

µ_ij = µ + G_i + Ej + e_ij

The model has two variance components, one corresponding to the random genotypic main effects  and the other i.e., corresponding to the residual, that involves true GEI and error (Malosetti et al., 2013).

In plant breeding, a breeder as to make selection among a large set of candidate genotypes and thus, it is important to make phenotypic selection based on the estimated genotypic values for varietal testing and commercialization (Piepho et al., 2008). BLUPs can serve as a great tool to select the best individuals as it maximizes the correlation of true genotypic values and the predicted genotypic values (Searle et al., 1992). Hence, in the present investigation, the phenotypic values are partitioned into genetic value (Gg) and their interaction with environments (Gge) using mixed model equations (MME) in BLUPs as suggested by Crossa et al. (2006) including co-ancestry of parents (COP) to elucidate precise estimates of genetic values vis-à-vis their environmental interactions.

 

  

Variance-covariance matrices R and N are assumed to have a simple variance component structure, as defined for MME.

 

 

Analysis of variance
 
Analysis of variance (ANOVA) (Table 3) was performed to determine the significance of genotypes, environments and their interaction effect on the performance of the given groundnut genotypes for the test traits: pod yield (kg/ha), pods per plant, shelling percentage, seeds per pod, sound mature kernels, 100 seed weight (g) and oil % under different crop durations i.e., spring and kharif. The combined analysis of variance showed the significant GEI, depicting the influence of environment on the test genotypes in terms of their response to agronomically important traits.


 
Mean yield performance of genotypes
 
The mean yield of the genotypes is presented in Table 4. The mean yield of genotypes ranged from 4509 kg/ha (CGL-23) to 1784 kg/ha-(CGL-63) and 3474 kg/ha (CGL-22) to 1255 kg/ha (CGL-63) during kharif season. The five top ranked lines for pod yield wereCGL-23 (4509 kg/ha) CGL-11 (4491 kg/ha), J-87 (4423 kg/ha), CGL-22 (4291 kg/ha) and CGL-50 (4193 kg/ha) during spring season. CGL-22 (3474 kg/ha) followed by CGL-23 (3336 kg/ha), J-87 (3199 kg/ha), Mallika (3141 kg/ha) and CGL-11 (3138 kg/ha), was highest yielding during kharif season. Genotypes M-13, Gangapuri, CGL-46 and CGL-63 had consistently low yield performance during both the seasons. All the genotypes had overall 36.87% higher productivity in the spring sown crop than, kharif. This variability in the yield reflects the overall influence of environmental conditions during growing seasons such as temperature, relative humidity and disease pressure. Thus, selection of genotypes based on their phenotypic performance alone may hinder varietal selection and recommendation, as it is not known whether the genotype or the environment is responsible for the interaction causing a change in the genotypic ranking.


 
Stability analysis
 
For estimating the adaptability of genotypes, the pooled data was partitioned into fixed effects of sites across seasons and BLUP genotypic values (Ggge). The BLUP genotypic values are further partitioned into genetic value (Gg) and their interaction with the environment (Gge) to assess the adaptability of genotypes across seasons (Table 5). The ranking of top ten genotypes based on their pooled Gg values is CGL-22 followed by CGL-04, CGL-36, CGL-23, J-87, TG-37A, CGL-53, M-548, CGL-14 and Mallika, but this ranking differs from the ranking with respect to Ggge values (Table 5). Genotype CGL-23 has the highest Ggge value followed by CGL-22 and CGL-11. Although CGL-22 ranks 2 with respect to Ggge but ranks 1 with respect to Gg value with low Gge value, thus performance of the line is not much affected by the environment, implying the genotype is the main contributing factor for the yield performance. Further, CGL-23 having the highest Ggge value (rank 1) but has low Gg value (rank 4) with quite high Gge, implying environment has a significant contribution for the yield performance of the genotype. Similarly, genotype CGL-11 has high Gge value with low Gg value but overall, third highest Ggge value. Thus, these genotypes are adapted to particular season or environmental conditions. Certain genotypes such as CGL-01, CGL-02, CGL-03, CGL-08, CGL-20, CGL-27, CGL-35, CGL-37, CGL-46 CGL-48, CGL-50, CGL-58, CGL-61, CGL-62 had negative Gg values, hence, these genotypes will contribute poorly for their overall yield even if environmental conditions contribute positively for the yield. J-87 (Gg=524 kg/ha, Gge=1064 and Ggge=1588) which was used as a check had overall rank 4 for Ggge value and rank 5 for Gg value. The line had quite high Gge value indicating the significant contribution of the environmental effects for the yield, thus is adapted to particular season.



Table 6 represents the genetic values (Gg), genotype-environment interaction (Gge) values and BLUP (Ggge) genotypic values of lines across the seasons. During spring, genotype CGL-11, followed by CGL-23, CGL-04, CGL-22 and CGL-50 had the highest Ggge value. During kharif, CGL-04, followed by CGL-23, CGL-11, CGL-22 and TG-37A had the highest Ggge. On partitioning of Ggge value, CGL-04 had the highest Gg value (rank 1) during both season but, low and positive Gge during spring and negative Gge during kharif. This positive Gge is responsible for the high yield of CGL-04 during the spring season than kharif. Similarly, although genotype CGL-23 has rank 2 during both the seasons, but there is a significant difference on the Ggge values:  1862 kg/ha and 1220 kg/ha during spring and kharif, respectively. The genotype has high Gg and Gge value during the spring than kharif, thus, environment is a major contributing factor for the high yield of the genotype during spring. Similarly, other top-ranking genotypes with respect to their yield performance CGL-22, CGL-50, SG-99, CGL-49 and CGL-14 were found to be more adapted to spring season. Thus, spring is more favourable growing season as depicted from overall higher fixed effects (2626 kg/ha) than kharif (2333 kg/ha). These, results are in agreement with the released check variety J-87 which has been released for the spring season by Punjab Agricultural University, Ludhiana, Punjab in 2020 for commercial cultivation. J-87 had similar rank during both seasons, but with large difference in the Ggge value 1792 kg/ha and 852 kg/ha during spring and kharif, respectively. This variety had high Gg=778 kg/ha and Gge=1014 kg/ha value during spring season, but low Gg=409 kg/ha and Gge=443 kg/ha during kharif. Similarly, another variety TG-37A having higher yield performance with higher Gge coupled with high Gg values during spring has been released for commercial cultivation in 2019.



In plant breeding, Multi-Environment Trials (MET) are important as it allows the evaluation of genotype(s) under different environmental condition, which enables to assess and compare their response, overall stability and adaptation. Thus, best genotype(s) can be selected for a specific environment and across environments for further testing, but it is not easy because of the presence of Genotype by Environment Interaction (GEI). For sustainable agricultural system the adaptability of genotype(s) is of paramount importance for marginal farmers, as low GEI gives assurance for more guaranteed yield in the targeted environment. In the absence of GEI, means across environments can be used as indicator, however, in the presence of GEI, the use of means across environments ignores the fact that genotypes differ in their relative performance over environments (Voltas et al., 2002). In such situation, if genotype and environment means are used to predict the yield potential of the recommended cultivar(s), it will cause a failure of formal breeding to serve small resource-poor farmers in marginal fragile environments (Ceccarelli et al., 2006).

In Punjab, groundnut is mainly grown during the kharif season in an area of 1.3 thousand hectares (2018-19) but the prevailing cropping pattern of paddy-wheat is diverting some acreage to potato, green pea and other vegetable crops in spring season as these climatic conditions are favourable for high groundnut productivity, therefore characterization of germplasm for spring and kharif season is crucial to get maximum pod yield potential of groundnut as a third crop in paddy-green pea/another vegetable-spring groundnut pattern. The significant differential response of genotypes across the seasons, as implied by crossover interaction, recommended the evaluation of advance breeding lines in the target environment for variety testing for release of stable and adapted varieties to particular ecologies. The selection of candidature genotype(s) solely on the basis of phenotypic value will be misleading. Hence, the selection should be emphasised on genotypic values and its interaction with the environment. The conventional phenotypic values in the present study are sum of the fixed effects and BLUP genotypic values. BLUP serve as a great tool to select best individuals as it maximizes the correlation of true genotypic values and the predicted genotypic values (Searle et al., 1992). The partitioning of BLUP genotypic values specifies the contribution of genotypic value (Gg) and environmental effects (Gge) to the yield potential of the genotype. The change in the ranking of genotypes with respect to Gg and Ggge values indicates the differential response of genotype(s) across the seasons. These observations based on the ranking of genetic values are in agreement with the findings of Smith and Cullis (2018) and Crossa et al., (2006) as they have suggested that the random modelling gives more precise estimate of the genetic values. All the genotypes were found to have high BLUP genotypic values, which on partitioning showed the significant contribution of environment to the overall performance of the genotype, coupled with high genetic values. All the genotypes were found to have high genetic values along with moderate to high Gge value during the spring season, than during the kharif season in which they had low Gge value. Thus, the genotypes were found to be specifically adapted to spring season. Hu (2015) compared two statistical methods for analysing rape cultivar multilocation trials: separate ANOVA and BLUP. He found that BLUP provided more accurate and efficient predictions of location-specific genotype effects compared to separate ANOVA. The Pearson correlation of genotype prediction between locations was higher for BLUP and the average variance of differences between genotype estimates was lower for BLUP. These results suggest that BLUP is a more effective method for analyzing rape cultivar in multilocation trials which corresponds to the result of current study.

The results of the study indicated that the high Gg values of genotypes is alone not a capable factor for the commercialization as, Gge is the deciding factor for the adaptability to the targeted region. Hence, the selection should be emphasized on the high Gg value coupled with low Gge value for wide adaptability or high Gg with high Gge for specific season to harvest maximum yield potential of the genotype. This will ensure the optimum productivity for small scale farmers.

All authors declare that they have no conflicts of interest.