Introgression of Maize Diversity for Drought Tolerance: Subtropical Maize Landraces as Source of New Positive Variants.

ABSTRACTThe maize (Zea mays L.) growing area in India is divided into five zones for cultivar testing. During triannual testing of genotypes in official trials within the All‐India Coordinated Maize Improvement Program (AICMIP), a large number of entries is rejected each year. Therefore, only a low number of entries is carried forward to the advanced stage of testing. The subdivision of the breeding sites into zones results in limited data per zone. Hence, the question arises how to select the best genotypes per zone and how information can be borrowed across zones to improve the accuracy of selection within zones. We compared the performance of best linear unbiased prediction (BLUP) using the correlation of genetic effects between zones with best linear unbiased estimation (BLUE) based on data per zone. In both cases, data were analyzed using a mixed model. We used simulations to calculate correlations between the true simulated values and the predicted genotype values obtained by BLUE and BLUP using the same models. The data structure and the variance components used in simulations were based on the analysis of 40 triannual series of four different maize maturity groups. Best linear unbiased prediction outperformed BLUE in 38 out of 40 series and on average across all series. An advantage of BLUP was observed for varying genetic correlations between zones. We conclude that the use of BLUP enhanced the estimation accuracy in zoned AICMIP maize testing trials and can be recommended for future use in these trials.

Introduction Drought stress is one of the most important abiotic stresses all around the world. The aim of breeding studies and breeding for resistance to drought is that breeders seek to identify varieties and genetic resources to drought resistant and comparison of drought resistance among the varieties and the introduction of superior varieties to farmers. Drought or imbalance between supply and demand for water is one of the most important limiting factors affecting crop production which is very important in this context, effective and economic use of water resources especially for areas with arid and semi-arid climatic conditions which covers about two-thirds of the total area of Iran (Shahram & Daneshi, 2005). Breeders have been trying that by testing different varieties under normal and stress conditions to identify varieties and use them to plant breeding programs. Cowpea (Vigna unguiculata L. Walp), a member of the family leguminous (Fabaceae) is a crop grown under the tropical and sub-tropical areas covering Africa, Asia, South America, and parts of Southern Europe and United States (Singh et al., 1997). Dry seeds of cowpea contain 20-25% protein, 1.8% fat, and 60.3% carbohydrate and are rich sources of iron and calcium (Majnoon Hoseini, 2008). In this study, various drought tolerance indices were used to identify drought resistant in varieties. Indices included drought tolerance, Tolerance Index (TOL), Mean Productivity (MP), Geometric Mean Productivity (GMP), Stress Susceptibility Index (SSI), Yield Stability Index (YSI), Yield Index (YI), Stress Tolerance Index(STI), and Harmonic Mean (HM) (Ahmadi et al., 2000; Fernandez, 1992; Safari et al., 2007; Bouslama & Schapaugh,1984; Gavuzzi et al.,1997). Materials and Methods In order to study and determine the most effective traits, drought tolerance indices and identify tolerant genotypes in vegetative drought stress on the cowpea genotypes, All 32 cowpea genotypes were cultivated in a randomized complete block design with three replications which each replication consisted of 32 experimental units, each unit or plot, three lines with a length of two meters with line spacing of 70 cm were planted. The distance between rows of plants, 10 cm and 50 cm was considered the distance between each plot, in two separate experiments including normal irrigation and water stress conditions. The study was conducted at Experimental Research Farm, University of Tehran, Karaj Agricultural Research Institute at College of Agriculture and Natural Resources in Karaj, Tehran, Iran during 2014. Drought stress was imposed by doubling the irrigation time about 50 days after planting against normal irrigation on thirty-two cowpea genotypes. Evaluation of drought resistant in different genotypes was conducted using eight indices including Tolerance Index (TOL), Mean Productivity (MP), Geometric Mean Productivity (GMP), Stress Susceptibility Index (SSI), Yield Stability Index (YSI), Yield Index (YI), Stress Tolerance Index (STI), and Harmonic Mean (HM). Results and Discussion Analysis of variance showed that there is a significant difference between genotypes for all the indices of drought tolerance and grain yield in both normal and stress conditions (P0.01). This result suggested that the genetic variation among genotypes is capable of selection for drought tolerance. A simple calculation of statistical parameters (mean and standard deviation) for drought tolerance indices indicated that there is a great diversity among the study genotypes which it can be used as rich genetic resources to help breeders to improve and identify resistant varieties. The average yield of all genotypes under drought stress and normal irrigation condition was Ys = 83.57, and Yp =101.82, respectively. Significant differences between two different conditions indicated that cowpea plant has a high potential for tolerance under drought stress condition. TOL index revealed the lowest average value among various indices (TOL =18.24). The low level of stress tolerance index shows a high relative tolerance genotype. In fact, stress tolerance index showed the changes of stress condition in genotypes. It means that genotypes with low TOL index indicate less changes and genotypes with high TOL index show more changes. Correlation coefficient was calculated to determine the relationship between grain yield and drought tolerance indices. The STI, MP, HM and GMP indices which have the most positive and significant correlation with grain yield under stress and non-stress conditions were introduced as the best indices for screening tolerant genotypes to drought and high-yielding in both environmental conditions. Using Biplot scatter graph in 32 cowpea genotypes and according to genotypes situation in Biplot display, genotypes 998, 313, 291 and 7 were identified as tolerant genotypes with high-yield. Cluster analysis based on investigated indices and yield under drought stress and non-stress conditions showed that genotypes were grouped in four clusters and most of the drought tolerant genotypes with high yield were grouped in the second cluster، while most of drought sensitive genotypes were grouped in the fourth cluster. Conclusions In this study, genotypes showed high genetic diversity in terms of drought tolerance using drought tolerance indices. Based on the results obtained in this study genotypes 291, 7, 313, and the Mashhad cultivar (998) can be proposed as drought tolerant genotypes.

Ordinary least squares estimator (OLSE), best linear unbiased estimator (BLUE), and best linear unbiased predictor (BLUP) in the general linear model with new observations are generalized to the general multivariate linear model. The fundamental equations of BLUE and BLUP in the multivariate linear model are derived by two methods, including the vectorization method and projection method. By using the matrix rank method, some new results of linear BLUE-sufficiency, linear BLUP-sufficiency, and the equality of OLSE, BLUE, and BLUP are given in the multivariate linear model.

Assessing genetic diversity and aggregate genotype selection in a collection of cumin (Cuminum cyminum L.) accessions under drought stress: Application of BLUP and BLUE

Measures of biologic and behavioural variables on a patient often estimate longer term latent values, with the two connected by a simple response error model. For example, a subject's measured total cholesterol is an estimate (equal to the best linear unbiased estimate (BLUE)) of a subject's latent total cholesterol. With known (or estimated) variances, an alternative estimate is the best linear unbiased predictor (BLUP). We illustrate and discuss when the BLUE or BLUP will be a better estimate of a subject's latent value given a single measure on a subject, concluding that the BLUP estimator should be routinely used for total cholesterol and per cent kcal from fat, with a modified BLUP estimator used for large observed values of leisure time activity. Data from a large longitudinal study of seasonal variation in serum cholesterol forms the backdrop for the illustrations. Simulations which mimic the empirical and response error distributions are used to guide choice of an estimator. We use the simulations to describe criteria for estimator choice, to identify parameter ranges where BLUE or BLUP estimates are superior, and discuss key ideas that underlie the results.

On equality of ordinary least squares estimator, best linear unbiased estimator and best linear unbiased predictor in the general linear model

SUMMARYThe objective of the present study was to present the theory and application of best linear unbiased prediction (BLUP) in reciprocal recurrent selection (RRS). Seven progeny tests from two RRS programmes with popcorn (Zea mays L. ssp. mays [syn. Zea mays L. ssp. everta (Sturtev.) Zhuk.]) populations were conducted and analysed for expansion volume and grain yield. The interpopulation half- and full-sib family models were fitted using ASReml software. Half-sib selection is equivalent to selection for the general combining ability (GCA) of the common parents. With inbred full-sib progeny and BLUP analysis, it is possible to predict the general and specific combining ability effects. The standard error of prediction of the progeny effect was lower than the standard deviation of the best linear unbiased estimation (BLUE) estimate. For half- and full-sib RRS, the BLUE and BLUP provided highly correlated estimates of progeny genotypic values. The coincidence between selected parents ranged from 64 to 95%. With inbred full-sib progeny, the correlations between the BLUE of progeny genotypic values and the BLUP of GCA effects were lower. Consequently, the coincidence between selected parents was lower, ranging from 0 to 57%. The percentage of common selected inbred progeny based on the BLUE and BLUP of the progeny genotypic value ranged from 57 to 100%.

In this paper, we consider mixed linear models, possibly with singular covariance matrices, by supplementing a particular fixed effects model with appropriate stochastic restrictions. We show that all representations of the best linear unbiased estimator (BLUE) and best linear unbiased predictor (BLUP) can be obtained through the augmented model including stochastic restrictions. Using this approach, we consider two mixed linear models, \({\fancyscript {M}_1}\) and \({\fancyscript {M}_2}\) , say, which have different covariance matrices. We give necessary and sufficient conditions that the BLUP and/or BLUE under the the model \({\fancyscript {M}_{1}}\) continue to be BLUP and/or BLUE also under the model \({\fancyscript {M}_{2}}\) .

Economic constraints on many plant breeding programs have forced breeders to limit the number of environments for performance testing of new genetic material. The use of best linear unbiased predictions (BLUP), which augments predictions of individuals by using observations on their close relatives, should provide improved predictions of performance under such conditions. The objectives of this study were to determine (i) whether BLUP values were more precise predictors than least squares means [i.e, best linear unbiased estimates (BLUE)] from soybean [Glycine max (L.) Merr.] yield trials conducted in one or two environments, and (ii) how much improvement in the precision of BLUP could be gained by inclusion of historical parental data. Bulks and lines of 24 soybean crosses and four check cultivars were evaluated at 11 different environments in Tennessee to estimate the mean seed yield of each cross and cultivar. Historical yield records on parents of each cross were compiled from trials conducted in Tennessee from 1982 through 1990. Using subsets of the 11 environments, we predicted yield using three methods: (i) BLUE, (ii) BLUP(NP), without parental data, and (iii) BLUP(P), with parental data. Standard errors of differences (S‐d) and rank correlations (rs) between the actual and predicted mean yields showed that either method of BLUP was superior to BLUE for providing precise yield estimates. Because of the high genetic relationships among the crosses used in this study, including historical parental information did little to increase the precision of BLUP(P) over BLUP(NP).

Abtsrcat The linear mixed model, with its combination of fixed and random parameters, plays a central role in many statistical applications. Here we review results on conditions for best linear unbiased estimates (BLUEs) of estimable functions of fixed parameters under one linear mixed model to remain BLUEs under a second model, which difiers from the first in covariance structure. Without making full rank assumptions for design matrices or covariance matrices, we also review results for the conditions under which best linear unbiased predictors (BLUPs) of random parameters under the first model remain BLUPs under the second model, and for the conditions under which both BLUEs and BLUPs under the first model remain the BLUEs and BLUPs under the second. We also provide a rather generous list of related references.

Equality of the BLUPs under the mixed linear model when random components and errors are correlated

SUMMARYThe model for analysis of randomized complete block (RCB) experiments usually includes two factors: block and treatment. If treatment is modelled as fixed, best linear unbiased estimation (BLUE) is used, and treatment means estimate expected means. If treatment is modelled as random, best linear unbiased prediction (BLUP) shrinks the treatment means towards the overall mean, which results in smaller root-mean-square error (RMSE) in prediction of means. This theoretical result holds provided the variance components are known, but in practice the variance components are estimated. BLUP using estimated variance components is called empirical best linear unbiased prediction (EBLUP). In small experiments, estimates can be unreliable and the usefulness of EBLUP is uncertain. The present paper investigates, through simulation, the performance of EBLUP in small RCB experiments with normally as well as non-normally distributed random effects. The methods of Satterthwaite (1946) and of Kenward & Roger (1997, 2009), as implemented in the SAS System, were studied. Performance was measured by RMSE, in prediction of means, and coverage of prediction intervals. In addition, a Bayesian approach was used for prediction of treatment differences and computation of credible intervals. EBLUP performed better than BLUE with regard to RMSE, also when the number of treatments was small and when the treatment effects were non-normally distributed. The methods of Satterthwaite and of Kenward & Roger usually produced approximately correct coverage of prediction intervals. The Bayesian method gave the smallest RMSE and usually more accurate coverage of intervals than the other methods.

The missing heritability has been a major problem in the analysis of best linear unbiased prediction (BLUP). We introduced the traditional genome-wide association study (GWAS) into the BLUP to improve the heritability estimation. We analyzed eight pork quality traits of the Berkshire breeds using GWAS and BLUP. GWAS detects the putative quantitative trait loci regions given traits. The single nucleotide polymorphisms (SNPs) were obtained using GWAS results with p value <0.01. BLUP analyzed with significant SNPs was much more accurate than that with total genotyped SNPs in terms of narrow-sense heritability. It implies that genomic estimated breeding values (GEBVs) of pork quality traits can be calculated by BLUP via GWAS. The GWAS model was the linear regression using PLINK and BLUP model was the G-BLUP and SNP-GBLUP. The SNP-GBLUP uses SNP-SNP relationship matrix. The BLUP analysis using preprocessing of GWAS can be one of the possible alternatives of solving the missing heritability problem and it can provide alternative BLUP method which can find more accurate GEBVs.

Drought stress as a trait with increasing importance in the background of climate change is an important factor limiting barley yield. Induced by drought, leaf senescence may occur prematurely, leading to a stop of photosynthesis and to an early translocation of stored assimilates into grains. For barley breeding, the identification of quantitative trait loci (QTL) involved in drought stress and leaf senescence may be an advantage as reliable phenotyping for drought stress is difficult to achieve. Therefore, the aim of the present thesis was to identify markers associated to drought stress response and drought stress induced leaf senescence in juvenile barley through genome wide association studies (GWAS), which will facilitate efficient marker based selection procedures. In a first step, a screening method was developed for analysing drought stress response and early leaf senescence in juvenile barley. Next, in semi controlled greenhouse pot experiments 156 winter barley genotypes were analysed in early developmental stages under control and drought stress treatment. Drought application started at the primary leaf stage and continued for a four weeks stress period. These experiments were used for phenotyping six physiological parameters (biomass yield, leaf colour, electron transport rate at photosystem II, osmolality, content of free proline and total content of soluble sugars), as well as for gene expression analysis of genes involved in drought stress and leaf senescence. Significant genotypic and treatment effects were detected for all phenotypic traits and gene expression data. Based on these data and on 3,212 SNP markers of the Illumina 9k iSelect Chip, GWAS were conducted to detect QTL and expression QTL (eQTL). In total, 47 significant QTL were identified for the traits analysed under drought stress conditions and 15 significant eQTL were found for the relative expression of the 14 genes involved in these traits. Under drought stress conditions, two major QTL regions overlapping for different traits such as biomass yield and leaf colour were detected on chromosome 2H at 50 cM and on chromosome 5H at 45 cM. In these QTL, genes coding for proteins involved in drought stress or leaf senescence were identified. Four of these genes showed a differential expression and thus, eQTL were detected. One eQTL for TRIUR3 coincides with the phenotypic QTL on chromosome 5H. After validation respective markers BOPA1_9766-787 and SCRI_RS_102075 may be used in future barley breeding programmes for improving tolerance to drought stress and leaf senescence.

BackgroundWheat is a major global crop, and increasing its productivity is essential to meet the growing population demand. However limited water resources is the primary constraint. This study aimed to identify genetic factors associated with drought tolerance using a diverse panel of 287 wheat genotypes evaluated under well-watered and drought-stressed conditions. Water Use Efficiency (WUE) and Grain Yield (GY), along with drought tolerance indices, were assessed. A genome-wide association study (GWAS) using 26,814 high-density SNP markers identified loci linked to these traits, with 768 SNPs showing significant associations. Additionally, genomic selection (GS) was performed using the rrBLUP model to predict trait performance across environments.ResultsAmong the 768 significant SNPs associated with the measured traits at -log10 (P) ≥ 3, 81 SNPs were mapped with a higher threshold -log10 (P) ≥ 4, indicating pleiotropic and QTL-by-environment interaction effects. Several novel and known genes, previously reported to have functions related to biotic and abiotic stresses response were linked to significant SNPs. Among the drought indices evaluated, stress tolerance index (STI), geometric mean productivity (GMP), and tolerance index (TOL) were the most reliable indicators for selecting stable, high-yielding genotypes under drought and control conditions. The same three indices exhibited high prediction values under the severe drought stress (SS) condition. Five genotypes were identified as promising candidates for breeding programs based on their superior drought tolerance, high grain yield, and nutritional value.ConclusionThis study provides valuable insights into the genetic basis of drought tolerance in wheat, highlighting key SNPs and genomic regions associated with improved water use efficiency and yield stability. The findings contribute to the development of drought-tolerant wheat varieties with optimized water utilization to achieve increased yield per unit of water at diverse water levels, ultimately contributing to sustainable agriculture and food security.