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Best Linear Unbiased Estimation and Prediction under a Selection Model
Abstract
Mixed linear models are assumed in most animal breeding applications. Convenient methods for computing BLUE of the estimable linear functions of the fixed elements of the model and for computing best linear unbiased predictions of the random elements of the model have been available. Most data available to animal breeders, however, do not meet the usual requirements of random sampling, the problem being that the data arise either from selection experiments or from breeders' herds which are undergoing selection. Consequently, the usual methods are likely to yield biased estimates and predictions. Methods for dealing with such data are presented in this paper.
... Let u denote the random variable of true breeding values (TBVs) and û their BLUPs, obtained by the use of pedigree or "omics" data. As shown by Henderson (1975), the standard deviation u of TGVs and the standard deviation of their BLUPs are related by = u , where is the prediction accuracy, reflecting the shrinkage of BLUPs compared to the TBVs. Hence, we have 1 = 1 u 1 and 2 = 2 u 2 . ...
... Building upon the pioneering research of Henderson (1975) and inspired by the tremendous progress in animal breeding subsequent to the adoption of BLUPs, Bernardo (1994) spearheaded the implementation of BLUPs into plant breeding. With balanced data and when candidates are unrelated or possess identical co-ancestries so that their TGVs are predicted with equal accuracy, the ranking of candidates based on BLUEs and BLUPs is identical (Kennedy and Sorenson 1988). ...
... Consequently, applying identical thresholds ( t * 1 = t * 2 = 0.96 ) to both sets for achieving T = 0.10 leads to a smaller proportion of candidates ( 1 = 0.06 vs. 2 = 0.14 ) and a higher selection intensity (i 1 = 2.02 vs. i 2 = 1.57 ) for Π 1 compared to Π 2 . Given that the regression for TGVs on BLUPs is equal to 1.0 (Henderson 1975), we obtain ΔG 1 = 1.21 and ΔG 2 = 1.42 . Referring to Eqs. 2 and 13, we get * 1 = 0.28 and ΔG Tot (0.96, 0.96, , 1, 1) = 1.36 . ...
Key message
Selection response in truncation selection across multiple sets of candidates hinges on their post-selection proportions, which can deviate grossly from their initial proportions. For BLUPs, using a uniform threshold for all candidates maximizes the selection response, irrespective of differences in population parameters.
Abstract
Plant breeding programs typically involve multiple families from either the same or different populations, varying in means, genetic variances and prediction accuracy of BLUPs or BLUEs for true genetic values (TGVs) of candidates. We extend the classical breeder's equation for truncation selection from single to multiple sets of genotypes, indicating that the expected overall selection response (ΔGTot)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$({\Delta G}_{{\text{Tot}}})$$\end{document} for TGVs depends on the selection response within individual sets and their post-selection proportions. For BLUEs, we show that maximizing ΔGTot\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta G}_{{\text{Tot}}}$$\end{document} requires thresholds optimally tailored for each set, contingent on their population parameters. For BLUPs, we prove that ΔGTot\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta G}_{{\text{Tot}}}$$\end{document} is maximized by applying a uniform threshold across all candidates from all sets. We provide explicit formulas for the origin of the selected candidates from different sets and show that their proportions before and after selection can differ substantially, especially for sets with inferior properties and low proportion. We discuss implications of these results for (a) optimum allocation of resources to training and prediction sets and (b) the need to counteract narrowing the genetic variation under genomic selection. For genomic selection of hybrids based on BLUPs of GCA of their parent lines, selecting distinct proportions in the two parent populations can be advantageous, if these differ substantially in the variance and/or prediction accuracy of GCA. Our study sheds light on the complex interplay of selection thresholds and population parameters for the selection response in plant breeding programs, offering insights into the effective resource management and prudent application of genomic selection for improved crop development.
... Simulation studies reported that the LR method worked well when the model used to estimate breeding values matches the true data-generating process [14,29]. According to these results, one could infer that the LR method would estimate the bias, dispersion, and accuracy properly in the presence of selection if it is correctly taken into account in the model with, for instance, the method of Henderson [53,54]. However, this is rarely used in genetic evaluations, and selection is often ignored in the estimation of breeding values. ...
... The first way affects the location of the confidence interval, and given a biased estimator, it is not possible to correct. The second way affects the confidence interval length because the additive relationships in the validation group change due to selection [53,54]. Specifically, the affected term is G − C 22 p , which is the variance of u p . ...
... Specifically, the affected term is G − C 22 p , which is the variance of u p . According to Henderson [53,54], the variance of u p is reduced under selection. However, the effect on the standard error of the estimators of the dispersion and reliability is hard to assess because the variance of u p is involved in convoluted algebraic operations. ...
Background
Validation by data truncation is a common practice in genetic evaluations because of the interest in predicting the genetic merit of a set of young selection candidates. Two of the most used validation methods in genetic evaluations use a single data partition: predictivity or predictive ability (correlation between pre-adjusted phenotypes and estimated breeding values (EBV) divided by the square root of the heritability) and the linear regression (LR) method (comparison of “early” and “late” EBV). Both methods compare predictions with the whole dataset and a partial dataset that is obtained by removing the information related to a set of validation individuals. EBV obtained with the partial dataset are compared against adjusted phenotypes for the predictivity or EBV obtained with the whole dataset in the LR method. Confidence intervals for predictivity and the LR method can be obtained by replicating the validation for different samples (or folds), or bootstrapping. Analytical confidence intervals would be beneficial to avoid running several validations and to test the quality of the bootstrap intervals. However, analytical confidence intervals are unavailable for predictivity and the LR method.
Results
We derived standard errors and Wald confidence intervals for the predictivity and statistics included in the LR method (bias, dispersion, ratio of accuracies, and reliability). The confidence intervals for the bias, dispersion, and reliability depend on the relationships and prediction error variances and covariances across the individuals in the validation set. We developed approximations for large datasets that only need the reliabilities of the individuals in the validation set. The confidence intervals for the ratio of accuracies and predictivity were obtained through the Fisher transformation. We show the adequacy of both the analytical and approximated analytical confidence intervals and compare them versus bootstrap confidence intervals using two simulated examples. The analytical confidence intervals were closer to the simulated ones for both examples. Bootstrap confidence intervals tend to be narrower than the simulated ones. The approximated analytical confidence intervals were similar to those obtained by bootstrapping.
Conclusions
Estimating the sampling variation of predictivity and the statistics in the LR method without replication or bootstrap is possible for any dataset with the formulas presented in this study.
... Estimation of BV relies on the relationships between individuals, and while such an estimation depends on having recorded phenotypes for the traits of interest, it is possible to predict BV for individuals without phenotypic records through their relationships with phenotyped individuals. Henderson's mixed model equations (MME) [2][3][4] provided a method that yields the so-called best linear unbiased predictors (BLUP) of the individuals' BV, a method which in its original conception used pedigree-based relationships. Combined with the rapid computational advancements during the second half of the twentieth century, Henderson's MME (HMME) revolutionized livestock production systems, enabling largescale genetic evaluations (i.e. the estimation of BV). ...
... such that sub-index 1 indicates the reference population of phenotyped individuals, and sub-index 2 indicates the target population without phenotypes (young candidates). From Henderson's MME [2][3][4], the analytical solutions for the breeding values g 1 for the n 1 animals in the reference population, and the PBV g 2 for the n 2 animals in the target population are: ...
... Finally, since E(Z) = log 1+ρ 1−ρ , as per the distribution in Eq. (3), the inequalities in Eqs. (4) and (5) can be re-written as: ...
Background
Genetic merit, or breeding values as referred to in livestock and crop breeding programs, is one of the keys to the successful selection of animals in commercial farming systems. The developments in statistical methods during the twentieth century and single nucleotide polymorphism (SNP) chip technologies in the twenty-first century have revolutionized agricultural production, by allowing highly accurate predictions of breeding values for selection candidates at a very early age. Nonetheless, for many breeding populations, realized accuracies of predicted breeding values (PBV) remain below the theoretical maximum, even when the reference population is sufficiently large, and SNPs included in the model are in sufficient linkage disequilibrium (LD) with the quantitative trait locus (QTL). This is particularly noticeable over generations, as we observe the so-called erosion of the effects of SNPs due to recombinations, accompanied by the erosion of the accuracy of prediction. While accurately quantifying the erosion at the individual SNP level is a difficult and unresolved task, quantifying the erosion of the accuracy of prediction is a more tractable problem. In this paper, we describe a method that uses the relationship between reference and target populations to calculate expected values for the accuracies of predicted breeding values for non-phenotyped individuals accounting for erosion. The accuracy of the expected values was evaluated through simulations, and a further evaluation was performed on real data.
Results
Using simulations, we empirically confirmed that our expected values for the accuracy of PBV accounting for erosion were able to correctly determine the prediction accuracy of breeding values for non-phenotyped individuals. When comparing the expected to the realized accuracies of PBV with real data, only one out of the four traits evaluated presented accuracies that were significantly higher than the expected, approaching $$\sqrt{{{\text{h}}}^{2}}$$ h 2 .
Conclusions
We defined an index of genetic correlation between reference and target populations, which summarizes the expected overall erosion due to differences in allele frequencies and LD patterns between populations. We used this correlation along with a trait’s heritability to derive expected values for the accuracy ( $${\text{R}}$$ R ) of PBV accounting for the erosion, and demonstrated that our derived $${\text{E}}\left[{\text{R}}|{\text{erosion}}\right]$$ E R | erosion is a reliable metric.
... For the estimation of risk, the BLUP was calculated using the equations of the Henderson mixed model [31] and the Fisher infinitesimal model [32]. Generalized Linear Mixed Models (glmm) are an extension of the generalized linear models that allow the inclusion of response variables of different distributions, such as binary [27]. ...
... Furthermore, to identify individuals at high risk for cancer based solely on family pedigree information, the individual risk was calculated as the mean of the values of their parents. This is because each individual inherits half of his additive genetic component from the father and half from the mother [31]. Pearson´s correlation coefficient was used Fig. 1 (a). ...
Pancreatic ductal adenocarcinoma (PDAC) is the fourth leading cause of cancer-related death in the Western world. The number of diagnosed cases and the mortality rate are almost equal as the majority of patients present with advanced disease at diagnosis. Between 4 and 10% of pancreatic cancer cases have an apparent hereditary background, known as hereditary pancreatic cancer (HPC) and familial pancreatic cancer (FPC), when the genetic basis is unknown. Surveillance of high-risk individuals (HRI) from these families by imaging aims to detect PDAC at an early stage to improve prognosis. However, the genetic basis is unknown in the majority of HRIs, with only around 10–13% of families carrying known pathogenic germline mutations. The aim of this study was to assess an individual’s genetic cancer risk based on sex and personal and family history of cancer. The Best Linear Unbiased Prediction (BLUP) methodology was used to estimate an individual’s predicted risk of developing cancer during their lifetime. The model uses different demographic factors in order to estimate heritability. A reliable estimation of heritability for pancreatic cancer of 0.27 on the liability scale, and 0.07 at the observed data scale as obtained, which is different from zero, indicating a polygenic inheritance pattern of PDAC. BLUP was able to correctly discriminate PDAC cases from healthy individuals and those with other cancer types. Thus, providing an additional tool to assess PDAC risk HRI with an assumed genetic predisposition in the absence of known pathogenic germline mutations.
... EBV values for growth was estimated with best linear unbiased prediction (BLUP) in the mixed model equation (Henderson, 1975) following; ...
... Although mass selection has been practiced in breeding programs for growth improvement in L. calcarifer (Ye et al., 2017), the accuracy of selection is limited. Accuracy of selection can further increase by estimating breeding values using mixed model equation (Henderson, 1975) where information from all relatives is used optimally in the best linear unbiased prediction (BLUP). Selection on BLUP-EBVs can speed up genetic progress through an increase in selection accuracy. ...
... Nowadays genetic association studies are rarely aware of the origin of the samples listed. Z becomes the confounding factor between X and Y [11]- [14]. One challenge of the heterogeneous data variable selection problem is to mitigate the confounding effects brought by Z . ...
... Principal components analysis (PCA) [27], [28] and linear mixed model [29], [30] are two popular and efficient approaches to alleviate the confounding effect. The latter provides a more fine-grained way to model the population structure and won its prominence in the animal breeding literature, where it was used to reveal the underlying kinship and family structure [11], [31]. Many extensions have been developed, however, these measures such as LMM-Select [32] LMM-BOLT [33] and Liability-threshold mixed linear model (LTMLM) [33] along with other algorithms [34]- [36] only rely on univariate testing to select the variable once uncovering the confounding factor. ...
We consider the problem of sparse variable selection on high dimension heterogeneous data sets, which has been taking on renewed interest recently due to the growth of biological and medical data sets with complex, non-i.i.d. structures and huge quantities of response variables. The heterogeneity is likely to confound the association between explanatory variables and responses, resulting in enormous false discoveries when Lasso or its variants are naïvely applied. Therefore, developing effective confounder correction methods is a growing heat point among researchers. However, ordinarily employing recent confounder correction methods will result in undesirable performance due to the ignorance of the convoluted interdependency among response variables. To fully improve current variable selection methods, we introduce a model, the tree-guided sparse linear mixed model, that can utilize the dependency information from multiple responses to explore how specifically clusters are and select the active variables from heterogeneous data. Through extensive experiments on synthetic and real data sets, we show that our proposed model outperforms the existing methods and achieves the highest ROC area.
... From the proposal of the concept of genomic prediction to the present, a multitude of models have emerged. Early models primarily focused on improving best linear unbiased prediction (BLUP), such as ridge regression-based best linear unbiased prediction (rrBLUP) (Henderson, 1975) and genomic best linear unbiased prediction (GBLUP) (VanRaden, 2008), etc. In addition, researchers have proposed various Bayesian methods, including BayesA and BayesB (Meuwissen et al., 2001), BayesC (Habier et al., 2011) and BayesLasso (Park and Casella, 2008), Bayesian ridge regression (BayesRR) (da Silva et al., 2021), BSLMM (Zhou et al., 2013). ...
In modern breeding practices, genomic prediction (GP) uses high-density single nucleotide polymorphisms (SNPs) markers to predict genomic estimated breeding values (GEBVs) for crucial phenotypes, thereby speeding up selection breeding process and shortening generation intervals. However, due to the characteristic of genotype data typically having far fewer sample numbers than SNPs markers, overfitting commonly arise during model training. To address this, the present study builds upon the Least Squares Twin Support Vector Regression (LSTSVR) model by incorporating a Lasso regularization term named ILSTSVR. Because of the complexity of parameter tuning for different datasets, subtraction average based optimizer (SABO) is further introduced to optimize ILSTSVR, and then obtain the GP model named SABO-ILSTSVR. Experiments conducted on four different crop datasets demonstrate that SABO-ILSTSVR outperforms or is equivalent in efficiency to widely-used genomic prediction methods. Source codes and data are available at: https://github.com/MLBreeding/SABO-ILSTSVR.
... It also allows modelling both genetic and nongenetic influences on the traits of interest, thereby revealing environmental factors that may impact breeding and management decisions. Variance components are typically estimated using restricted maximum likelihood, and prediction of EBVs is based on best linear unbiased prediction (Henderson 1950(Henderson , 1975. While the estimation of EBVs in farmed insects is not common outside of honeybee breeding, examples can be found in silkworm (Shabdini et al. 2011) and in evolutionary genetics (Roff & Fairbarn 2011). ...
Insect production for food and feed presents a promising supplement to ensure food safety and address the adverse impacts of agriculture on climate and environment in the future. However, optimisation is required for insect production to realise its full potential. This can be by targeted improvement of traits of interest through selective breeding, an approach which has so far been underexplored and underutilised in insect farming. Here we present a comprehensive review of the selective breeding framework in the context of insect production. We systematically evaluate adjustments of selective breeding techniques to the realm of insects and highlight the essential components integral to the breeding process. The discussion covers every step of a conventional breeding scheme, such as formulation of breeding objectives, phenotyping, estimation of genetic parameters and breeding values, selection of appropriate breeding strategies, and mitigation of issues associated with genetic diversity depletion and inbreeding. This review combines knowledge from diverse disciplines, bridging the gap between animal breeding, quantitative genetics, evolutionary biology, and entomology, offering an integrated view of the insect breeding research area and uniting knowledge which has previously remained scattered across diverse fields of expertise.
... Today, few studies are being conducted in this aspect perhaps because of lack of potential mating stations in some regions of the world. For instance, controlled mating could be an inhibitory factor in successful animal breeding in developing countries [27,37]. To our knowledge, many challenges of controlled breeding in honey bees at natural mating stations remain undefined. ...
Honey bee reproductive behavior involves a complicated mating system that embodies a number of factors, including environmental and human-induced factors. Controlled breeding in isolated mating stations is a prerequisite to maintain the genetic resources of honey bees through natural mating. The concept of controlled mating is a challenge in most beekeeping operations due to its low mating success rate. Therefore, a detailed investigation into the suitability of isolated mating stations is of interest. Thus, we bred two subspecies of honey bees (Apis cerana koreana and Apis mellifera L.) in isolated mating stations (island) from 2021 to 2023 and in an open breeding station in 2023. Our results demonstrate that the highest percentage of the mating success rate in isolated mating stations was recorded in the Wido Island, which had the highest percentage of bare land, coniferous forests, deciduous forests, fields, and mixed forests. The mating success rate was higher in the summer and spring for A. cerana and A. mellifera, respectively. The mating success rate was higher in open mating compared to controlled mating (Island) and did not vary between pure-breeding and cross-breeding lines. Our findings suggested that mating stations with mixed forest and fields are potential sites for the successful breeding of honey bees.
... FastBiCmrMLM involves three steps: estimation of parameters in the null model (3), selection of potentially associated variants, and identification of significant or suggested variants. Following Henderson [29] and Chen et al. [13], the solution of the mixed model (3) for β and U (a d) T is given by ...
Large sample datasets have been regarded as the primary basis for innovative discoveries and the solution to missing heritability in genome-wide association studies. However, their computational complexity cannot consider all comprehensive effects and all polygenic backgrounds, which reduces the effectiveness of large datasets. To address these challenges, we included all effects and polygenic backgrounds in a mixed logistic model for binary traits and compressed four variance components into two. The compressed model combined three computational algorithms to develop an innovative method, called FastBiCmrMLM, for large data analysis. These algorithms were tailored to sample size, computational speed, and reduced memory requirements. To mine additional genes, linkage disequilibrium markers were replaced by bin-based haplotypes, which are analyzed by FastBiCmrMLM, named FastBiCmrMLM-Hap. Simulation studies highlighted the superiority of FastBiCmrMLM over GMMAT, SAIGE and fastGWA-GLMM in identifying dominant, small α (allele substitution effect), and rare variants. In the UK Biobank-scale dataset, we demonstrated that FastBiCmrMLM could detect variants as small as 0.03% and with α ≈ 0. In re-analyses of seven diseases in the WTCCC datasets, 29 candidate genes, with both functional and TWAS evidence, around 36 variants identified only by the new methods, strongly validated the new methods. These methods offer a new way to decipher the genetic architecture of binary traits and address the challenges outlined above.
... Therefore, the lower the BIC value, the better the model balances the goodness of fit with parsimony (i.e., simplicity) [104][105][106]. With the selected model, the best linear unbiased predictors (BLUP) for the genotypes were obtained for further analysis [108]. Broad-sense heritability was calculated following Cullis heritability for unbalanced data, which takes into account the mean variance of the difference between two BLUPs and the genotypic variance [109]. ...
Background
Sucrose accumulation in sugarcane is affected by several environmental and genetic factors, with plant moisture being of critical importance for its role in the synthesis and transport of sugars within the cane stalks, affecting the sucrose concentration. In general, rainfall and high soil humidity during the ripening stage promote plant growth, increasing the fresh weight and decreasing the sucrose yield in the humid region of Colombia. Therefore, this study aimed to identify markers associated with sucrose accumulation or production in the humid environment of Colombia through a genome-wide association study (GWAS).
Results
Sucrose concentration measurements were taken in 220 genotypes from the Cenicaña’s diverse panel at 10 (early maturity) and 13 (normal maturity) months after planting. For early maturity data was collected during plant cane and first ratoon, while at normal maturity it was during plant cane, first, and second ratoon. A total of 137,890 SNPs were selected after sequencing the 220 genotypes through GBS, RADSeq, and whole-genome sequencing. After GWAS analysis, a total of 77 markers were significantly associated with sucrose concentration at both ages, but only 39 were close to candidate genes previously reported for sucrose accumulation and/or production. Among the candidate genes, 18 were highlighted because they were involved in sucrose hydrolysis (SUS6, CIN3, CINV1, CINV2), sugar transport (i.e., MST1, MST2, PLT5, SUT4, ERD6 like), phosphorylation processes (TPS genes), glycolysis (PFP-ALPHA, HXK3, PHI1), and transcription factors (ERF12, ERF112). Similarly, 64 genes were associated with glycosyltransferases, glycosidases, and hormones.
Conclusions
These results provide new insights into the molecular mechanisms involved in sucrose accumulation in sugarcane and contribute with important genomic resources for future research in the humid environments of Colombia. Similarly, the markers identified will be validated for their potential application within Cenicaña’s breeding program to assist the development of breeding populations.
... For statistical analysis, data were collected from three plants per plot per method. Methods for kino evaluation and... Damacena et al, 2024 The restricted maximum likelihood method (REML) (Patterson and Thompson, 1971) was used to estimate genetic parameters, and the best linear unbiased prediction method (BLUP) (Henderson, 1975) was used to predict genotypic values. The following statistical model was applied to assess the significance of the Method × Genotype interaction (Eq. ...
Species within the genus Corymbia are regarded as potential alternatives to Eucalyptus. In addition to having superior wood quality, Corymbia spp. are tolerant to most pests, diseases, and abiotic stresses that affecting Eucalyptus plantations, including physiological disorders, water deficit, and wind damage. However, environmental stresses stimulate kino production, which decreases the quality of pulp and sawn wood. This study aimed to develop a method for evaluating kinoand estimate genetic parameters in Corymbia. For this, 16 Corymbia (C. citriodora × C. torelliana) hybrid clones and 5 clones of Eucalyptus were used. Two evaluation methods (M1 and M2) were tested for kino evaluation; M1 consisted of drilling the bark with Pilodyn and M2 consisted of drilling the heartwood with Pilodyn. The following kino parameters were evaluated: exudation incidence, exudate length which flowed over the stem, and exudate weight. Genetic parameters were estimated by a mixed model method (REML/BLUP). The significance of random effects of the statistical model was tested by the likelihood ratio test. Significant clone effects were obtained for all kino parameters, except for exudate length as assessed by M2. Kino parameters determined by M1 exhibited higher heritability and accuracy. Therefore, M1 should be preferred for kino evaluation in Corymbia.
Keywords:
Forest improvement; wood quality; genotypic correlation; gummosis
... The transmitting ability of sire is half of additive genetic value and therefore genetic trends were obtained as 2 times regression of weighted average of sire's transmitting abilities (WAETA) for each year on year as: (Hintz et al., 1978) WAETA = ∑ nik si/n. k Where, n ik = Number of daughter of sire i ( i= 1, 2, … ..,m ) in k th year S i = Estimated Transmitting ability (ETA) of sire ith n.k = Number of daughters of m sires in the kth year Transmitting ability is half of the additive genetic value and additive genetic value calculated by BLUP (best linear unbiased prediction) method (Henderson, 1975). ...
A total of 284 performance records belonging to 63 Tharparkar cows in at least three lactations or more lactation spread over a period of fifteen years (2002 to 2016) were utilized to estimate the trends in lactation milk yield. Phenotypic trend was observed positive and significant (P0·05) for lactation milk yield and estimated as 19.42±7.21 kg/year (0.96% of HA). The estimates of Genetic trend for this trait by using SM1, SM2, LSMBL and BLUP were 2.301±24.84 (0.114% of HA), 8.62±29.6 (4.30% of HA), 11.97±19.63 (0.59% of HA) and 3.90±1.99 (0.194% of HA), respectively. Comparison of methods of estimation of genetic trend showed that the BLUP method should be used for estimation of genetic trends of economic traits because this method has lower magnitude of standard error in comparison to other methods. For overall improvement in production, emphasis should be given to some reproductive traits like Age at first calving and Service period along with lactation milk yield while planning selection strategies of sire and dam.
... Generally, data from multi-environment trials (MET) are unbalanced and have heterogeneous variances due to differences in environmental conditions, factors that hamper ordinary least square-based inferences. These difficulties are easily overcome using linear mixed models (Henderson 1975). This method deals with statistical and genotypic imbalance, and allows the modeling of covariance structures. ...
In many cases, traditional analysis of breeding trials based on analysis of variance (ANOVA) do not allow a suitable genetic evaluation. Alternatively, mixed model-based approaches create the possibility of dealing with unbalanced data and modeling spatial trends. The aims of this study were to compare the goodness-of-fit of the model and the genotype ranking through different residual modeling approaches and to select the best performing tropical wheat genotypes based on the best-fitting model. A panel of tropical wheat genotypes was evaluated in three field trials conducted between 2020 and 2021 for grain yield. Linear mixed model analyses were used on the data to estimate the genetic parameters and to predict the genotypic values in analyses of single- and multi-environment trials. Accounting for spatial trends in the analyses of single- and multi-environment trials provides better outcomes than the compound symmetry model does.
... However, during the last century, the importance of pedigree-based selection increased. Breeders started selecting animals based on their breeding values and pedigree information by using statistical prediction models, like Best Linear Unbiased Prediction (BLUP) (Henderson, 1975). The field of animal breeding has witnessed a steep increase in the rate of genetic improvements ever since the implementation of genomic selection and modern technologies. ...
BayesRC is an extension of BayesR, in which prior biological information can be used to divide SNPs into different annotation categories. Within each category, SNPs are further categorised into four effect classes (null, low, medium, and high) just like BayesR. In this study, we aim to evaluate the ability of BayesRC in predicting five milk production traits (milk yield, fat content, fat yield, protein content, and protein yield) in a real population of 7483 Holstein bulls. We used three different sources of biological information, namely the Cattle Quantitative Trait Loci database (Cattle QTLdb), the Cattle Genotype-Tissue Expression atlas (cGTEx), and known causal and associated SNPs from INRAE’s updates to EuroG10K SNP chip. We divided this study into two phases, phase 1 comprising Bovine SNP50BeadChip® medium density SNP panel (50K), and phase 2 involving the inclusion of selected sequences from the whole genome sequencing data. We used BayesR as a standard against which to compare the genomic prediction ability of BayesRC. In terms of results, BayesRC did not exhibit higher prediction accuracy than BayesR with both 50K and the imputed sequence data. However, BayesRC tended to give more weightage to SNPs in enriched SNP lists based on prior biological information, which is certainly the most important feature of this prediction model. BayesRC also highlighted some key QTL regions involving genes like DGAT1, HSF1, MGST1, and GHR. Even though BayesRC did not show significant improvement over BayesR in our study, it still has a potential if used in breeds where marker panels are not well calibrated, and also for traits with very low heritabilities.
... The mean components and genotypic effects were predicted using the Best Linear Unbiased Prediction (BLUP) method (Henderson 1975). The predicted genetic values (BLUPs) for the evaluated traits were obtained using the 'randef' function in the sommer package. ...
Eucalyptus pilularis Smith is renowned for its high-quality wood, rapid growth, and adaptability to diverse soil conditions. This study aimed to evaluate the use of the molecular kinship matrix to estimate genetic parameters for E. pilularis selection and the potential establishment of a base population. The experiment involved 13 provenances and 115 progenies, using a randomized complete block design with five replicates and linear plots consisting of five plants each. Genetic parameters for the traits diameter at breast height (DBH), total height, and volume were evaluated at five years of age using the linear mixed model. Results indicated a survival rate for the population of 73.11%, an average total height of 18.65 m, DBH of 14.28 cm, and volume of 14.57 cm³. By adjusting the kinship matrix, the estimated values of heritability and genetic coefficients of variation decreased, indicating that there would be errors in these estimates and in the genetic gains if the progenies were assumed to be half-siblings. The discrepancy in rankings derived from the conventional half-sibling matrix versus molecular kinship matrix poses a significant challenge for experts in forest species genetic improvement. Our findings indicate not only inflated estimations of genetic parameters and gains, but also disparities in rankings when accounting for true levels of relatedness among individuals based on the molecular matrix.
... For BW, high temperatures (30°C-35°C) are known to increase susceptibility in tomato (Lee et al., 2011;Singh et al., 2014;Yeon et al., 2022). Therefore, the phenotypic data of each collection were adjusted using BLUP, which accounts for random effects (Henderson, 1975;Robinson, 1991). Furthermore, the TGC1 and TGC2 data were integrated based on BLUP to produce a large training population. ...
Bacterial wilt (BW) is a soil-borne disease that leads to severe damage in tomato. Host resistance against BW is considered polygenic and effective in controlling this destructive disease. In this study, genomic selection (GS), which is a promising breeding strategy to improve quantitative traits, was investigated for BW resistance. Two tomato collections, TGC1 (n = 162) and TGC2 (n = 191), were used as training populations. Disease severity was assessed using three seedling assays in each population, and the best linear unbiased prediction (BLUP) values were obtained. The 31,142 SNP data were generated using the 51K Axiom array™ in the training populations. With these data, six GS models were trained to predict genomic estimated breeding values (GEBVs) in three populations (TGC1, TGC2, and combined). The parametric models Bayesian LASSO and RR-BLUP resulted in higher levels of prediction accuracy compared with all the non-parametric models (RKHS, SVM, and random forest) in two training populations. To identify low-density markers, two subsets of 1,557 SNPs were filtered based on marker effects (Bayesian LASSO) and variable importance values (random forest) in the combined population. An additional subset was generated using 1,357 SNPs from a genome-wide association study. These subsets showed prediction accuracies of 0.699 to 0.756 in Bayesian LASSO and 0.670 to 0.682 in random forest, which were higher relative to the 31,142 SNPs (0.625 and 0.614). Moreover, high prediction accuracies (0.743 and 0.702) were found with a common set of 135 SNPs derived from the three subsets. The resulting low-density SNPs will be useful to develop a cost-effective GS strategy for BW resistance in tomato breeding programs.
... Fruit quality data were analyzed via the mixed model methodology REML/BLUP (restricted residual maximum likelihood / best linear unbiased prediction) (Patterson & Thompson, 1971;Henderson, 1975), using the R software package lme4. ...
In recent years, several efforts have been made to develop tomato cultivars displaying both late blight resistance and good organoleptic fruit quality. Selection indexes are considered the best option to perform genotype selection when many different traits are being considered to select genotypes as close to the desired ideotype as possible. Therefore, this study aimed at selecting late blight-resistant tomato families based on their fruit quality attributes using factor analysis and ideotype-design / best linear unbiased predictor (FAI-BLUP) index. For this purpose, we assessed the fruit quality parameters of 81 F3:5 tomato families previously selected as late blight resistant. The tomato cultivars Thaise, Argos, and Liberty were included in the trial as checks. The experimental arrangement consisted of complete randomized blocks with three replicates. Each plot was formed by five plants, three of which were used in the fruit quality assessment. The quality parameters assessed were fruit diameter, fruit length, fruit color (L, a*, C, and H), fruit firmness, titratable acidity, soluble solids content, hydrogen potential, and SS:TA ratio. Fruit quality data were analyzed using the mixed model methodology via REML/BLUP (restricted residual maximum likelihood / best linear unbiased prediction) to obtain BLUPs that were further subjected to the FAI-BLUP selection index. The FAI-BLUP was efficient in selecting late blight-resistant tomato genotypes based on their fruit quality attributes. Fourteen tomato families were classified as closest to the desirable ideotype for fruit quality. These genotypes should move on to the following stages of the tomato breeding program.
... Step 2 in the RRN analysis described above), and the correlation between them was estimated. Though it is possible to directly compute these slopes by fitting linear regressions for the data from each participant, using predicted values from mixed models produces more reliable values with a bigger signal-to-noise ratio (Henderson, 1975). ...
Individuals’ reaction time (RT) slopes in tasks of mental rotation have been found to be related to other measures of visual-spatial abilities, and thus are often viewed as a psychometric measure of visual-spatial abilities. The common interpretation of individual RT slopes is as a measure of the speed at which the rotation is carried out. However, electroencephalography studies have found that the process of mental rotation continues after response selection has been carried out, casting doubt on the interpretation of RT slopes as measures of the speed of mental rotation. This study made use of electroencephalography techniques to directly capture individual differences in the speed of mental rotation and assess their association with visual-spatial abilities. We found that individual differences in mental rotation speed are not related to individual differences in RT slopes. Moreover, a computation model supports an alternative explanation by which RT slopes reflect individual differences in differential tolerances for stimulus identification within mental rotation tasks.
... The copyright holder for this preprint (which this version posted May 3, 2024. ; https://doi.org/10.1101/2024.04.30.590804 doi: bioRxiv preprint G, E and G × E) and Best Linear Unbiased Predictors (BLUPs, (Henderson, 1975)), which are 362 also subsequently used in the calculation of heritability. Using function H2cal() in R package inti 363 v0.6.2 we calculated the broad-sense heritability (H 2 ) in three ways: 1) standard heritability, Consequences of G: selection on r-TPC shape parameters and evolutionary potential 372 To understand how TPCs might evolve in different temperatures, we assessed: 1) 373 selection direction/form and magnitude on TPC shape parameters, 2) the impact of temperature 374 on such selection, and, 3) potential evolution of shape parameters under these selection regimes. ...
Microbial respiration alone releases massive amounts of Carbon (C) into the atmosphere per year, greatly impacting the global C cycle that fuels climate change. Larger microbial population growth often leads to larger standing biomass, which in turns leads to higher respiration. How rising temperatures might influence microbial population growth, however, depends on how microbial thermal performance curves (TPCs) governing this growth may adapt in novel environments. This thermal adaptation will in turn depend on there being heritable genetic variation in TPCs for selection to act upon. While intraspecific variation in TPCs is traditionally viewed as being mostly environmental (E, or plastic) as a single individual can have an entire TPC, our study uncovers substantial heritable genetic variation (G) and Gene-by-Environment interactions (GxE) in the TPC of a widely distributed ciliate microbe. G results in predictable evolutionary responses to temperature-dependent selection that ultimately shape TPC adaptation in a warming world. Through mathematical modeling and experimental evolution assays we also show that TPC GxE leads to predictable temperature-dependent shifts in population genetic makeup that constrains the potential for future adaptation to warming. That is, adaptive evolution can select for decreased genetic variation which subsequently lowers the evolutionary potential of microbial TPCs. Our study reveals how temperature-dependent adaptive evolution shapes microbial population growth, a linchpin of global ecosystem function, amidst accelerating climate warming.
... For MLM, a kinship (K) was calculated using PAV matrix and used jointly with population structure (Q). The Q + K approach helps to increase the power of genome-wide association analysis [51]. A Bonferroni threshold was calculated at P-value 0.05, Bonferroni threshold = 0.05/17,855 (Orthogroups in AflaPan) = 2.8 × 10 − 6 . ...
Background
Aspergillus flavus is an important agricultural and food safety threat due to its production of carcinogenic aflatoxins. It has high level of genetic diversity that is adapted to various environments. Recently, we reported two reference genomes of A. flavus isolates, AF13 (MAT1-2 and highly aflatoxigenic isolate) and NRRL3357 (MAT1-1 and moderate aflatoxin producer). Where, an insertion of 310 kb in AF13 included an aflatoxin producing gene bZIP transcription factor, named atfC. Observations of significant genomic variants between these isolates of contrasting phenotypes prompted an investigation into variation among other agricultural isolates of A. flavus with the goal of discovering novel genes potentially associated with aflatoxin production regulation. Present study was designed with three main objectives: (1) collection of large number of A. flavus isolates from diverse sources including maize plants and field soils; (2) whole genome sequencing of collected isolates and development of a pangenome; and (3) pangenome-wide association study (Pan-GWAS) to identify novel secondary metabolite cluster genes.
Results
Pangenome analysis of 346 A. flavus isolates identified a total of 17,855 unique orthologous gene clusters, with mere 41% (7,315) core genes and 59% (10,540) accessory genes indicating accumulation of high genomic diversity during domestication. 5,994 orthologous gene clusters in accessory genome not annotated in either the A. flavus AF13 or NRRL3357 reference genomes. Pan-genome wide association analysis of the genomic variations identified 391 significant associated pan-genes associated with aflatoxin production. Interestingly, most of the significantly associated pan-genes (94%; 369 associations) belonged to accessory genome indicating that genome expansion has resulted in the incorporation of new genes associated with aflatoxin and other secondary metabolites.
Conclusion
In summary, this study provides complete pangenome framework for the species of Aspergillus flavus along with associated genes for pathogen survival and aflatoxin production. The large accessory genome indicated large genome diversity in the species A. flavus, however AflaPan is a closed pangenome represents optimum diversity of species A. flavus. Most importantly, the newly identified aflatoxin producing gene clusters will be a new source for seeking aflatoxin mitigation strategies and needs new attention in research.
... Best linear unbiased prediction (BLUP) or sometimes referred also the best linear unbiased predictor is a well-known technique in earth and environmental sciences [1,2]. It was originally developed by Henderson [3,4] in the context of biosciences and biostatistics. It is also popular in longitudinal analysis. ...
With the advent of massive data sets, much of the computational science and engineering community has moved toward data-intensive approaches in regression and classification. However, these present significant challenges due to increasing size, complexity, and dimensionality of the problems. In particular, covariance matrices in many cases are numerically unstable, and linear algebra shows that often such matrices cannot be inverted accurately on a finite precision computer. A common ad hoc approach to stabilizing a matrix is application of a so-called nugget. However, this can change the model and introduce error to the original solution. It is well known from numerical analysis that ill-conditioned matrices cannot be accurately inverted. In this paper, we develop a multilevel computational method that scales well with the number of observations and dimensions. A multilevel basis is constructed adapted to a kd-tree partitioning of the observations. Numerically unstable covariance matrices with large condition numbers can be transformed into well-conditioned multilevel ones without compromising accuracy. Moreover, it is shown that the multilevel prediction exactly solves the best linear unbiased predictor (BLUP) and generalized least squares (GLS) model, but is numerically stable. The multilevel method is tested on numerically unstable problems of up to 25 dimensions. Numerical results show speedups of up to 42,050 times for solving the BLUP problem, but with the same accuracy as the traditional iterative approach. For very ill-conditioned cases, the speedup is infinite. In addition, decay estimates of the multilevel covariance matrices are derived based on high dimensional interpolation techniques from the field of numerical analysis. This work lies at the intersection of statistics, uncertainty quantification, high performance computing, and computational applied mathematics.
... org.au), where estimated breeding values (EBVs) for DS and FWEC were estimated using best linear unbiased prediction (BLUP) mixed-model methodology (Henderson 1975). Because FWEC and DS are both heritable traits, their EBVs give the best indication of the experimental sheep's genetic resistance to gastrointestinal worms and propensity to develop diarrhoea. ...
Diarrhoea linked to helminth resistance is a major problem in sheep health. Cell-mediated immune mechanisms in the gastrointestinal mucosa enhance resistance to internal parasites but also increase susceptibility to the diarrhoea in sheep. Eosinophil and mast cell responses to helminth infection help explain ‘hypersensitivity diarrhoea’.
... For statistical analysis, data were collected from three plants per plot per method. Methods for kino evaluation and... Damacena et al, 2024 The restricted maximum likelihood method (REML) (Patterson and Thompson, 1971) was used to estimate genetic parameters, and the best linear unbiased prediction method (BLUP) (Henderson, 1975) was used to predict genotypic values. The following statistical model was applied to assess the significance of the Method × Genotype interaction (Eq. ...
Species within the genus Corymbia are regarded as potential alternatives to Eucalyptus. In addition to having superior wood quality, Corymbia spp. are tolerant to most pests, diseases, and abiotic stresses that affecting Eucalyptus plantations, including physiological disorders, water deficit, and wind damage. However, environmental stresses stimulate kino production, which decreases the quality of pulp and sawn wood. This study aimed to develop a method for evaluating kinoand estimate genetic parameters in Corymbia. For this, 16 Corymbia (C. citriodora × C. torelliana) hybrid clones and 5 clones of Eucalyptus were used. Two evaluation methods (M1 and M2) were tested for kino evaluation; M1 consisted of drilling the bark with Pilodyn and M2 consisted of drilling the heartwood with Pilodyn. The following kino parameters were evaluated: exudation incidence, exudate length which flowed over the stem, and exudate weight. Genetic parameters were estimated by a mixed model method (REML/BLUP). The significance of random effects of the statistical model was tested by the likelihood ratio test. Significant clone effects were obtained for all kino parameters, except for exudate length as assessed by M2. Kino parameters determined by M1 exhibited higher heritability and accuracy. Therefore, M1 should be preferred for kino evaluation in Corymbia.
... With the development of quantitative genetics and molecular biology, the selection methods of livestock have been improved gradually [1]. A central methodology is the BLUP method proposed by Henderson in 1975 [2]. Here, genetics parameters can be estimated based on the so-called mixed model equations in which covariance matrices need to be defined. ...
The fleece traits are important economic traits of goats. With the reduction of sequencing and genotyping cost and the improvement of related technologies, genomic selection for goats has become possible. The research collect pedigree, phenotype and genotype information of 2299 Inner Mongolia Cashmere goats (IMCGs) individuals. We estimate fixed effects, and compare the estimates of variance components, heritability and genomic predictive ability of fleece traits in IMCGs when using the pedigree based Best Linear Unbiased Prediction (ABLUP), Genomic BLUP (GBLUP) or single-step GBLUP (ssGBLUP). The fleece traits considered are cashmere production (CP), cashmere diameter (CD), cashmere length (CL) and fiber length (FL). It was found that year of production, sex, herd and individual ages had highly significant effects on the four fleece traits (P < 0.01). All of these factors should be considered when the genetic parameters of fleece traits in IMCGs are evaluated. The heritabilities of FL, CL, CP and CD with ABLUP, GBLUP and ssGBLUP methods were 0.26 ~ 0.31, 0.05 ~ 0.08, 0.15 ~ 0.20 and 0.22 ~ 0.28, respectively. Therefore, it can be inferred that the genetic progress of CL is relatively slow. The predictive ability of fleece traits in IMCGs with GBLUP (56.18% to 69.06%) and ssGBLUP methods (66.82% to 73.70%) was significantly higher than that of ABLUP (36.73% to 41.25%). For the ssGBLUP method is significantly (29% ~ 33%) higher than that with ABLUP, and which is slightly (4% ~ 14%) higher than that of GBLUP. The ssGBLUP will be as an superiors method for using genomic selection of fleece traits in Inner Mongolia Cashmere goats.
... 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 (Henderson, 1975). ...
The study of genotype × environment interaction is crucial for plant breeding to introduce new cultivars with im-proved yield and stable performance. The productivity of chickpea crops is very low in Pakistan, requiring the se-lection of genotypes with optimal productivity for diverse environmental conditions. Fourteen different chickpea genotypes were assessed using the linear mixed model to evaluate genotypes across four diverse chickpea growing regions, including Attock (Punjab), Bhakkar (Punjab), Karak (Khyber Pakhtunkhwa), and Larkana during 2017-19. The environmental effect was very pronounced, contributing significantly to variation (25.8%) in grain yield. Analysing genotype × environmental interaction at multiple locations facilitates ranking superior genotypes that excel in specific or diverse environments. Notably, the genotypes viz. Fakhr-e-Thal and Bhak-kar-2011 demonstrated superior performance in terms of overall grain yield. Utilising a multi-trait stability index, Bittal-2016 and Thal-2006 emerged as the most stable genotypes across various environments, suggesting their suitability for diverse growing regions. On the other hand, for specific environmental conditions, genotypes KK-1, Noor-2013 and Fakhr e thal exhibited high yields but low stability, showcasing their adaptability to a particular environment. The The analysis revealed that Larkana is a mega environment conducive to higher yield, while At-tock, Bhakkar, and Karak were identified as less favorable for KK-3, DG-89, and Dasht. The findings hold signif-icant implications for expediting chickpea breeding efforts to improve the genotypic plasticity and understanding correlation patterns among traits to confer climatic resilience. Finding high-yielding, stable genotypes and their representative environment offers new breeding opportunities and boosts production for chickpea cultivars.
... 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 randomeffects, 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. ...
Background: One of the major goals of plant breeding is the selection of high yielding superior cultivars having wide or specific adaptation. However, there is a fluctuation in the annual production due to the sensitive behaviour of the genotypes under different environmental conditions referred to as Genotype by Environment Interaction (GEI). The current study aimed to study the contribution of GEI for the adaptation of groundnut lines for spring and/or kharif season. Methods: To assess the contribution of GEI, Multi-Environment Trials (METs) were conducted for 40 confectionery purpose groundnut genotypes at F9 generation along with checks, across three locations for two seasons (spring and kharif). The contribution of environmental effects, genotypic values and genotype × environment interaction values were obtained from genotypic variance-covariance matrix Gi = Σg⨂A using mixed models (MM) in Best linear unbiased predictions (BLUPs).The pooled data was first partitioned into fixed effects of sites across the seasons and BLUP genotypic values (Ggge). The BLUP genotypic values are further partitioned into genetic value (Gg) and their interaction with the environment (Gge) for the adaptability of genotypes across seasons. Result: The results of MET revealed the presence of significant crossover interaction. The demarcation of advance breeding lines for adaptability across the environment as well as for season specific adaptation was done for variety testing. Genotypes having moderate to high Gge values along with high Gg values in spring than kharif, owing to their better performance during the spring season. CGL-11, CGL-23 and CGL-04 were the highest yielding genotypes, with quite high Gge values. This is due to the more favourable environmental conditions interacting positively with genotypes during the spring. Thus, the high Gg value(s) of genotype(s) alone is not a capable factor for commercialization as Gge value is the deciding factor for the adaptability for the targeted season.
... To calculate genetic parameters (correlations and heritabilities), variance components were estimated using bivariate animal model analyses (Henderson, 1975). Commonly in bivariate analyses, both traits have the same two variance strata, genetic and residual, or three strata, genetic, animal, and sampling. ...
... For the combined analyses, the broad sense heritability is calculated as (Henderson 1975) where nreps is the number of repetitions, and σ 2 g and σ 2 e are the genotype and error variance components, respectively. Where nEnvs is the number of environments included in the analysis, and the novel term ' σ 2 ge ' refers to the GEI variance component. ...
Common bean ( Phaseolus vulgaris L.) is a grain legume rich in proteins and micronutrients, particularly iron and zinc. In this study, 30 small‐seeded genotypes were planted in five locations in Ethiopia, following an alpha lattice design with three replications, to determine environmental and genotypic influence on the Fe and Zn concentration. Based on their Fe and Zn contents, bean cultivars were evaluated for adaptability and stability using AMMI analysis. The Fe concentrations of raw bean seed varied from 44.4 to 84.4 μg/g within the panel of small‐seeded genotypes, with an average range of variance of 18 μg/g across environments, and its seed Zn concentrations varied from 19.7 to 32.3 μg/g, with an average range of variance of 12.6 μg/g across environments. The averages bean Fe concentration among the small‐seeded genotypes across sites in Ethiopia was 62.2 and 26.1 μg/g for Zn concentrations. Results from the analysis of variance using the AMMI model indicated that genotypes accounted for 20.53% and 9.49% of the total variance in seed Fe and Zn concentrations, respectively. The environment had a greater impact, affecting 60.92% and 81.52% of total sum of squares for Fe and Zn concentrations, respectively. According to the broad‐sense heritability, there appears to be some genetic control over Fe and Zn concentrations. However, the substantial effects of the environment and genotype‐by‐environment interaction on Fe and Zn concentrations in small‐seeded genotypes indicates breeding for higher amounts of trace minerals in new bean varieties could be a challenging task. This means the notion that beans can be biofortified to have higher concentrations of Fe and Zn might not be achievable in Ethiopia. A shift in breeding strategies that focuses on traits to enhance the bioavailability of Fe and Zn from bean is warranted and could be a solution to enhance the delivery of iron from small‐seeded beans produced in Ethiopia.
... The risk of confounded interviewer intercept estimates caused by small samples is mitigated by using the best linear unbiased predictor (BLUP) for random effects (41,42). This estimator is a weighted average of the pooled sample and the sample from the level-specific subgroup, i.e. all measurements taken by one specific interviewer. ...
Health agencies rely upon survey-based physical measures to estimate the prevalence of key global health indicators such as hypertension. Such measures are usually collected by non-healthcare worker personnel and are potentially subject to measurement error due to variations in interviewer technique and setting, termed “interviewer effects”. In the context of physical measurements, particularly in low- and middle-income countries, interviewer-induced biases have not yet been examined. Using blood pressure as a case study, we aimed to determine the relative contribution of interviewer effects on the total variance of blood pressure measurements in three large nationally-representative health surveys from the Global South. We utilized 169,681 observations between 2008 and 2019 from three health surveys (Indonesia Family Life Survey, National Income Dynamics Study of South Africa, and Longitudinal Aging Study in India). In a linear mixed model, we modeled systolic blood pressure as a continuous dependent variable and interviewer effects as random effects alongside individual factors as covariates. To quantify the interviewer effect-induced uncertainty in hypertension prevalence, we utilized a bootstrap approach comparing sub-samples of observed blood pressure measurements to their adjusted counterparts. Our analysis revealed that the proportion of variation contributed by interviewers to blood pressure measurements was statistically significant but small: approximately 0.24-2.2% depending on the cohort. Thus, hypertension prevalence estimates were not substantially impacted at national scales. However, individual extreme interviewers could account for measurement divergences as high as 12%. Thus, highly biased interviewers could have important impacts on hypertension estimates at the sub-district level.
... McGilchrist (1994) developed a class of approximate linearization methods based on the method of best linear unbiased predictions (BLUPs) used to fit general mixed-effects models, and exploited the connection between BLUPs and REML for LMMs, as developed by Henderson (1963Henderson ( , 1975. Consider the model g(µ) = Xβ + K k=1 Z k u k and Cov(u) = D(θ) = diag(σ 2 1 A 1 , . . . ...
Restricted maximum likelihood (REML) estimation is a widely accepted and frequently used method for fitting linear mixed models, with its principal advantage being that it produces less biased estimates of the variance components. However, the concept of REML does not immediately generalize to the setting of non-normally distributed responses, and it is not always clear the extent to which, either asymptotically or in finite samples, such generalizations reduce the bias of variance component estimates compared to standard unrestricted maximum likelihood estimation. In this article, we review various attempts that have been made over the past four decades to extend REML estimation in generalized linear mixed models. We establish four major classes of approaches, namely approximate linearization, integrated likelihood, modified profile likelihoods, and direct bias correction of the score function, and show that while these four classes may have differing motivations and derivations, they often arrive at a similar if not the same REML estimate. We compare the finite sample performance of these four classes through a numerical study involving binary and count data, with results demonstrating that they perform similarly well in reducing the finite sample bias of variance components.
... The solution of both the parametric BLUEs of fixed effects, as well as the prediction of the BLUPs of random effects was performed by solving the Henderson (1975) equations. The variance components were estimated using the REML method (Patterson and Thompson, 1971). ...
A total of 16 gilts (158,158±3.5 kg) were assigned to one of two treatments to determine the effect of a Saccharomyces cerevisiae fermentation product (SCFP) supplementation during lactation on performance of sows and litters. The treatments were: CT) formulated to meet the nutritional requirements according to the National Research Council, NRC (2012); SCFP) similar to CT, plus 0.88% SCFP. Feed intake (FI) was recorded daily from farrowing until day 21 of lactation. At birth and on days 7, 14, and 21 of lactation, the weight of the litters was recorded to determine body weight gain (BWG), and milk samples were taken to determine the nutritional composition of the milk. The FI of the sows and the BWG of the litters were stratified into three phases with 7 days per phase [phase 1 (P1: d1-7); phase 2 (P2: d8-14); phase 3 (P3: d15-21)]. Blood samples were collected from the sows on days 7, 14, and 21 of lactation to determine the hematological profile. A treatment per day interaction was obtained in the FI, with a higher FI in sows fed SCFP during P1 and P2, with no differences in P3 (p<0.05). No differences were found in the BWG of the litters during lactation (p<0.05). Furthermore, there were significant differences in the treatment per day interaction for leukocyte concentration (p<0.05). Sows supplemented with SCFP had a higher percentage of milk fat compared to CT sows (p<0.05). In conclusion, SCFP supplementation stimulated sow feed intake, milk fat content and leukocyte profile of primiparous sows during lactation, without exerting productive improvements in litter performance.
... The package ggplot2 was used for visualization (Wickham, 2016). Best linear unbiased predictions (BLUPs) were calculated from single and multi-environments (years + location), and the values for each RIL were obtained with the following statistical model (Henderson, 1975): ...
Soybean meal is the main protein source for animal feed, but it has low content of the essential amino acids cysteine (Cys) and methionine (Met). In this research, an exotic germplasm (PI 399000) was crossed with ‘Woodruff’ to develop an F 5 ‐derived recombinant inbred line (RIL) population for mapping quantitative trait loci for seed composition. The population was grown in six environments, and protein, oil, Cys, and Met were determined with near‐infrared spectroscopy. RILs were genotyped with the SoySNP6K BeadChip, and 1865 SNPs were used for analysis. QTL analysis identified three loci on chromosomes (Chrs) 6, 15 and 17 in at least five environments for protein; two QTLs on Chrs 14 and 17 in all environments for oil; three QTLs on Chrs 3, 6 and 10 for Cys and Met in at least three environments; and two QTLs for seed size on Chrs 17 and 20 in all environments. Stacking of protein and Cys + Met QTLs can increase both traits simultaneously, and 13 breeding lines were identified with improved seed composition. The markers linked to the QTLs can be used to assist the development of cultivars with improved meal quality.
... The capital letters X 1 and X 2 refer to the incidence matrix for the fixed effects, and Z 1 ,Z 2 and Z 3 are the incidence matrix for the random effects of the respective effects. We estimated the variance components and predicted the genetic values using the residual maximum likelihood-REML [20], and the best linear unbiased predictor-BLUP [21], respectively. The significance tests of the random effects were verified via likelihood ratio test (LRT) [22]. ...
Probabilistic models enhance breeding, especially for the Tahiti acid lime, a fruit essential to fresh markets and industry. These models identify superior and persistent individuals using probability theory, providing a measure of uncertainty that can aid the recommendation. The objective of our study was to evaluate the use of a Bayesian probabilistic model for the recommendation of superior and persistent genotypes of Tahiti acid lime evaluated in 12 harvests. Leveraging the Monte Carlo Hamiltonian sampling algorithm, we calculated the probability of superior performance (superior genotypic value), and the probability of superior stability (reduced variance of the genotype-by-harvests interaction) of each genotype. The probability of superior stability was compared to a measure of persistence estimated from genotypic values predicted using a frequentist model. Our results demonstrated the applicability and advantages of the Bayesian probabilistic model, yielding similar parameters to those of the frequentist model, while providing further information about the probabilities associated with genotype performance and stability. Genotypes G15, G4, G18, and G11 emerged as the most superior in performance, whereas G24, G7, G13, and G3 were identified as the most stable. This study highlights the usefulness of Bayesian probabilistic models in the fruit trees cultivars recommendation.
... In animal breeding, the estimated breeding values (EBVs) are pivotal for predicting genetic potential. Traditionally, the best linear unbiased prediction (BLUP) model has been employed, which utilizes pedigree information (Henderson, 1963(Henderson, , 1975. Genetic parameters, genetic diversity, and precise evaluation of economic traits, such as growth and egg production, are essential in poultry breeding programs to enhance selection efficiency (Gjerde and Schaeffer, 1989). ...
... To better observe the wax compound changes over time, we also performed a similar procedure at each individual time point, respectively. Best linear unbiased estimators (BLUEs) considering each fixed effect with respect to individual sampling time points for each liner was computed by the LSMEANS procedure in SAS [75]. In addition, BLUEs for each fixed effect for each liner across all time points were also calculated. ...
Cuticular waxes of plants impart tolerance to many forms of environmental stress and help shed dangerous human pathogens on edible plant parts. Although the chemical composition of waxes on a wide variety of important crops has been described, a detailed wax compositional analysis has yet to be reported for lettuce (Lactuca sativa L.), one of the most widely consumed vegetables. We present herein the leaf wax content and composition of 12 genetically diverse lettuce cultivars sampled across five time points during their vegetative growth phase in the field. Mean total leaf wax amounts across all cultivars varied little over 28 days of vegetative growth, except for a notable decrease in total waxes following a major precipitation event, presumably due to wax degradation from wind and rain. All lettuce cultivars were found to contain a unique wax composition highly enriched in 22- and 24-carbon length 1-alcohols (docosanol and tetracosanol, respectively). In our report, the dominance of these shorter chain length 1-alcohols as wax constituents represents a relatively rare phenotype in plants. The ecological significance of these dominant and relatively short 1-alcohols is still unknown. Although waxes have been a target for improvement of various crops, no such work has been reported for lettuce. This study lays the groundwork for future research that aims to integrate cuticular wax characteristics of field grown plants into the larger context of lettuce breeding and cultivar development.
... Among these methodologies, the Restricted Maximum Likelihood/Best Linear Unbiased Prediction (REML/BLUP) approach has emerged as a fundamental tool in genetic evaluations and selection processes. The REML/BLUP presents the ability to effectively handle vast and complex datasets, while simultaneously accounting for genetic relationships among individuals (Henderson 1975;Resende 2002;Pereira et al. 2013). By employing the REML/BLUP methodology, challenges posed by incomplete or unbalanced data can be overcome and accurate estimates of breeding values and heritability can be obtained. ...
Cassava, an important subsistence crop in tropical countries, represents the third most important source of starch worldwide. Espírito Santo (Brazil) presents predominance of family farming, where table cassava is cultivated as a food crop. The objective of the study was to evaluate the genetic diversity, estimate the genetic parameters and quantify gains with the selection of traditional cassava genotypes collected in different regions of the state of Espírito Santo, using the methodology of the mixed models (REML/BLUP). A total of 106 genotypes were evaluated in three locations. Each planting date was considered an environment, totaling six environments. The evaluated traits were: shoot height (APH), total number of tuberous roots (NR); weight of commercial roots (WCR); total root weight (TWR), marketable root weight/total root ratio (MRTR); root cortex color (RCC), root pulp color (PC) and cooking time (CT). The studied cassava genotypes presented genetic diversity and selection potential. The highest heritabilities (h² = 0.90; 0.75 and 0.75) were recorded for the traits NRT, WCR and TWR, respectively. Gains from selection were positive for all of the traits evaluated. Higher selection gains (GS = 21.77% and 20.15%) were observed for the WCR and TWR traits, considering animal and human consumption and (GS = 10.89% and 17.45%) for NRT and WCR, when intended for human consumption only. Genotypes 82, 76, 46, T3 and 2 stood out for selection purposes for animal and human consumption. Genotypes 2, 81, 69, 12 and 49 stood out for selection purposes for human food. The assessment of the diverse genotypes has uncovered a selection of superior candidates with tremendous potential for commercial crops, catering to both human and animal consumption markets.
Background
Genetic and genomic selection programs require large numbers of phenotypes observed for animals in shared environments. Direct measurements of phenotypes like meat quality, methane emission, and disease susceptibility are difficult and expensive to measure at scale but are critically important to livestock production. Our work leans on our understanding of the “Central Dogma” of molecular genetics to leverage molecular intermediates as cheaply-measured proxies of organism-level phenotypes. The rapidly declining cost of next-generation sequencing presents opportunities for population-level molecular phenotyping. While the cost of whole transcriptome sequencing has declined recently, its required sequencing depth still makes it an expensive choice for wide-scale molecular phenotyping. We aim to optimize 3′ mRNA sequencing (3′ mRNA-Seq) approaches for collecting cost-effective proxy molecular phenotypes for cattle from easy-to-collect tissue samples ( i.e. , whole blood). We used matched 3′ mRNA-Seq samples for 15 Holstein male calves in a heat stress trail to identify the 1) best library preparation kit (Takara SMART-Seq v4 3′ DE and Lexogen QuantSeq) and 2) optimal sequencing depth (0.5 to 20 million reads/sample) to capture gene expression phenotypes most cost-effectively.
Results
Takara SMART-Seq v4 3′ DE outperformed Lexogen QuantSeq libraries across all metrics: number of quality reads, expressed genes, informative genes, differentially expressed genes, and 3′ biased intragenic variants. Serial downsampling analyses identified that as few as 8.0 million reads per sample could effectively capture most of the between-sample variation in gene expression. However, progressively more reads did provide marginal increases in recall across metrics. These 3′ mRNA-Seq reads can also capture animal genotypes that could be used as the basis for downstream imputation. The 10 million read downsampled groups called an average of 104,386 SNPs and 20,131 INDELs, many of which segregate at moderate minor allele frequencies in the population.
Conclusion
This work demonstrates that 3′ mRNA-Seq with Takara SMART-Seq v4 3′ DE can provide an incredibly cost-effective (<$25/sample) approach to quantifying molecular phenotypes (gene expression) while discovering sufficient variation for use in genotype imputation. Ongoing work is evaluating the accuracy of imputation and the ability of much larger datasets to predict individual animal phenotypes.
Meiotic crossovers are essential for proper chromosome segregation, and provide an important mechanism for adaptation through linking beneficial alleles and purging deleterious mutations. However, crossovers can also break apart beneficial alleles and are themselves a source of new mutations within the genome. The rate and distribution of crossovers shows huge variation both within and between chromosomes, individuals and species, yet the molecular and evolutionary causes and consequences of this variation remain poorly understood. A key step in understanding this variation is to understand the genetic architecture of how many crossovers occur, where they occur, and how they interfere, as this allows us to identify the degree to which these factors are governed by common or distinct genetic processes. Here, we investigate individual variation in crossover count, crossover interference (ν), and crossover positioning measured as both intra-chromosomal allelic shuffling and distance to telomere (Mb), in a large genotyped breeding population of domestic pigs. Using measures from 82,474 gametes from 4,704 mothers and 271 fathers, we show that crossover traits are heritable within each sex (h2 = 0.03 - 0.11), with the exception of male crossover interference. Crossover count and interference have a strongly shared genetic architecture in females, mostly driven by variants at RNF212. Female crossover positioning is mediated by variants at MEI4, PRDM9, and SYCP2. We also identify tentative associations at genomic regions corresponding to CTCF and REC114/REC8/CCNB1IP1 (crossover count), and ZCWPW1 and ZCWPW2 (crossover positioning). Our results show that crossover count and crossover positioning in female pigs have the capacity to evolve somewhat independently in our dataset.
Due to their low frequency, estimating the effect of rare variants is challenging. Here, we propose RareEffect, a method that first estimates gene or region-based heritability and then each variant effect size using an empirical Bayesian approach. Our method uses a variance component model, popular in rare variant tests, and is designed to provide two levels of effect sizes, gene/region-level and variant-level, which can provide better interpretation. To adjust for the case-control imbalance in phenotypes, our approach uses a fast implementation of the Firth bias correction. We demonstrate the accuracy and computational efficiency of our method through extensive simulations and the analysis of UK Biobank whole exome sequencing data for five continuous traits and five binary disease phenotypes. Additionally, we show that the effect sizes obtained from our model can be leveraged to improve the performance of polygenic scores.
This study aimed to evaluate the stability of cacao clone production by analyzing the dynamics of pod production over time. It investigates correlations in multi-year production levels and explores how genetics influence both intra-annual and inter-annual temporal production dynamics of total and healthy pods. To address these questions, data were analysed from a clonal cacao trial conducted over a period of 18 years in Costa Rica. Longitudinal data analysis provided a clearer understanding of the link between yields over successive years. The best-fit model proved to be the ante-dependence model. This model indicated that the correlation between two successive years was relatively stable, and the correlation between years decreased as the interval between years increased. These correlations are also higher as the age of the trees increases. The clones differ more in terms of their production of healthy pods than total pod production. Four dynamic patterns, considering both intra- and inter-annual production, were identified, revealing differences in production timing and distinct peaks for each class. Inter-annual variability analysis revealed differences in healthy pod production among classes, with some displaying more sustainable production dynamics over 18 years. Intra-annual variability analysis showed significant variation in production periods among clones, with different production distributions throughout the year allowing selection of escape and or resistant clones. The study emphasized the importance of genetics in sustainable cacao production, with potential implications for clonal selection. It was suggested to combine clones of different classes to mitigate risks and spread harvests, emphasizing that resilience is a crucial criterion in cacao breeding programs to effectively meet new challenges. Further research is recommended to explore the influence of various environmental factors and facilitate more efficient selection in perennial crops, with the aim of selecting more resilient clones, a particularly important objective in the context of climate change.
Genetic improvement of complex traits in animal and plant breeding depends on the efficient and accurate estimation of breeding values. Deep learning methods have been shown to be not superior over traditional genomic selection (GS) methods, partially due to the degradation problem (i.e. with the increase of the model depth, the performance of the deeper model deteriorates). Since the deep learning method residual network (ResNet) is designed to solve gradient degradation, we examined its performance and factors related to its prediction accuracy in GS. Here we compared the prediction accuracy of conventional genomic best linear unbiased prediction, Bayesian methods (BayesA, BayesB, BayesC, and Bayesian Lasso), and two deep learning methods, convolutional neural network and ResNet, on three datasets (wheat, simulated and real pig data). ResNet outperformed other methods in both Pearson's correlation coefficient (PCC) and mean squared error (MSE) on the wheat and simulated data. For the pig backfat depth trait, ResNet still had the lowest MSE, whereas Bayesian Lasso had the highest PCC. We further clustered the pig data into four groups and, on one separated group, ResNet had the highest prediction accuracy (both PCC and MSE). Transfer learning was adopted and capable of enhancing the performance of both convolutional neural network and ResNet. Taken together, our findings indicate that ResNet could improve GS prediction accuracy, affected potentially by factors such as the genetic architecture of complex traits, data volume, and heterogeneity.
Advances in sequencing technology allow whole plant genomes to be sequenced with high quality. Combining genotypic and phenotypic data in genomic prediction helps breeders to select crossing partners in partially phenotyped populations. In plant breeding programs, the cost of sequencing entire breeding populations still exceeds available genotyping budgets. Hence, the method for genotyping is still mainly single nucleotide polymorphism (SNP) arrays; however, arrays are unable to assess the entire genome- and population-wide diversity. A compromise involves genotyping the entire population using an SNP array and a subset of the population with whole-genome sequencing. Both datasets can then be used to impute markers from whole-genome sequencing onto the entire population. Here, we evaluate whether imputation of whole-genome sequencing data enhances genomic predictions, using data from a nested association mapping population of rapeseed ( Brassica napus). Employing two cross-validation schemes that mimic scenarios for the prediction of close and distant relatives, we show that imputed marker data do not significantly improve prediction accuracy, likely due to redundancy in relationship estimates and imputation errors. In simulation studies, only small improvements were observed, further corroborating the findings. We conclude that SNP arrays are already equipped with the information that is added by imputation through relationship and linkage disequilibrium.
Multilocus genome-wide association study has become the state-of-the-art tool for dissecting the genetic architecture of complex and multiomic traits. However, most existing multilocus methods require relatively long computational time when analyzing large datasets. To address this issue, in this study, we propose a fast mrMLM method, namely, best linear unbiased prediction multilocus random-SNP-effect mixed linear model (BLUPmrMLM). First, genome-wide single-marker scanning in mrMLM is replaced by vectorized Wald tests based on the best linear unbiased prediction (BLUP) values of marker effects and their variances in BLUPmrMLM. Then, adaptive best subset selection is used to identify potentially associated markers on each chromosome to reduce computational time when estimating marker effects via empirical bayes. Finally, shared memory and parallel computing schemes were used to reduce the computation time. In simulation studies, BLUPmrMLM outperformed GEMMA, EMMAX, mrMLM, FarmCPU, and the control method of BLUPmrMLM in terms of computational time, power, accuracy for estimating quantitative trait nucleotide positions and effects, false positive rate, false discovery rate, false negative rate, and F1 score. According to the reanalysis of two large rice datasets, compared with the above methods, BLUPmrMLM significantly reduced the computation time and identified more previously reported genes. This study provides an excellent multilocus model method for the analysis of large-scale and multiomic datasets. The software mrMLM v5.1 is available at BioCode (https://ngdc.cncb.ac.cn/biocode/tools/BT007388) or GitHub (https://github.com/YuanmingZhang65/mrMLM).
Reproductive technologies have led to a wide and global distribution of genetic material from animals with high productivity. However, the distribution of semen from the same bulls to different regions (countries) may not always meet the expectations of livestock breeders. This aspect may be due to the fact that the genetic structure of the breeding stock, breeding goals and environmental conditions vary from region to region. The article presents the results of evaluating the breeding value of 286 sires used on the breeding stock of the pale-motley dairy cattle population in five regions of the Russian Federation (Belgorod, Voronezh, Kursk, Oryol regions and Altai Territory). The evaluation was carried out according to individual traits of daughters' milk productivity, and on multiple traits (selection index). Based on the results of the study, differences were identified in estimates of the breeding value of the same sires at the level of total information (population level) and in the herds of single regions (regional level). The accuracy of evaluating genotypes at the population management level was significantly higher (by 7–15 percent) than it was at regional levels. The correlations between the breeding value of the same sires at different levels of management (population-region) for single traits of daughter’s milk productivity were 0.522–0.960, for the complex of traits (selection index) – from 0.157 to 0.937. This indicates that when selecting the best sires at the level of an individual region, mistakes can reach 4–48 % for single milk productivity traits and from 6.3 to 84 % for their complex.
Three methods of predicting the response to truncated selection based on BLUP of breeding values (BVs) were compared under conditions in which the phenotypic values for the progenies of selected animals were not available. The following methods were used to predict the response to selection: (1) based on the mean of estimated breeding values (EBV) in the candidate population for selection (), (2) based on the variance of EBV in the candidate population for selection (), and (3) based on diagonal elements of the inverse matrix on the left‐hand side of the mixed model equation (). The deviation of the average BV of the selected animals from the average BV of the candidate population for selection was taken as the true response to selection. The pedigree information and phenotypic values used for comparison were generated by Monte Carlo computer simulation. The results showed that had the smallest absolute mean error and had the smallest root‐mean‐square error. We concluded that it is desirable to use or to predict the response to truncated selection based on BLUP of BVs. However, in the population where selection is ongoing, the prediction accuracy of selection response is likely to be affected by the distortion of the distribution and the Bulmer effect for .
Substituting this in (24), we obtain b'y = k'0 + (m'Bu + f'H)t + (m'GZ'V-')(y -X-Bt). (26) Noow from the matrix identities in (6) and (7), b'y = k
- bi0metrics Jutne
1BI0METRICS. JUTNE. 1975 Fromii the second equation of (25), B'V-'(y -X -Bt) O0. Substituting this in (24), we obtain b'y = k'0 + (m'Bu + f'H)t + (m'GZ'V-')(y -X-Bt). (26) Noow from the matrix identities in (6) and (7), b'y = k'" + (m'Bu + f'H)t + mr'v (27) where 0, t, and v are any solution to (28),
Selection index and expected genetic advance. In: Statistical Genetics and Plant Breeding
- C R Henderson
Henderson, C. R. [19631. Selection index and expected genetic advance. In: Statistical Genetics and Plant Breeding. Hanson, W. D. and Robinson, H. F. (Eds.), pp. 141-63. National Academy of Sciences-National Research Council, Washington. Publication 982.
The estimation of en-vironmental and genetic trends from records subject to culling Changes in milk production with age and milking frequerncy This content downloaded from 152.3.102.242 on Fri
- C R Henderson
- O Kempthorne
- S R Searle
- C M Krosigk
- J L Lush
- R R Shrode
- H-1h Hobu
Henderson, C. R., Kempthorne, O., Searle, S. R., and von Krosigk, C. M. [1959]. The estimation of en-vironmental and genetic trends from records subject to culling. Biometrics 15, 192. Lush, J. L. and Shrode, R. R. [19501. Changes in milk production with age and milking frequerncy. J. Dairy Sci. 33, 338. This content downloaded from 152.3.102.242 on Fri, 16 Aug 2013 10:28:48 AM All use subject to JSTOR Terms and Conditions BUC33 -BuHo G -C22 + C23B -BUHoBu' BuH-'HS C33 -Ho -C23' + C33Bu' -HoBU H-1H.