A comparison of identity-by-descent and identity-by-state matrices that are used for genetic evaluation and estimation of variance components

Investigating genotype by environment interaction for beef cattle fertility traits in commercial herds in northern Australia with multi-trait analysis

BACKGROUND

Genotype by environment interactions (GxE) affect a range of production traits in beef cattle. Quantifying the effect of GxE in commercial and multi-breed herds is challenging due to unknown genetic linkage between animals across environment levels. The primary aim of this study was to use multi-trait models to investigate GxE for three heifer fertility traits, corpus luteum (CL) presence, first pregnancy and second pregnancy, in a large tropical beef multibreed dataset (n = 21,037). Environmental levels were defined by two different descriptors, burden of heat load (temperature humidity index, THI) and nutritional availability (based on mean average daily gain for the herd, ADWG). To separate the effects of genetic linkage and real GxE across the environments, 1000 replicates of a simulated phenotype were generated by simulating QTL effects with no GxE onto real marker genotypes from the population, to determine the genetic correlations that could be expected across environments due to the existing genetic linkage only. Correlations from the real phenotypes were then compared to the empirical distribution under the null hypothesis from the simulated data. By adopting this approach, this study attempted to establish if low genetic correlations between environmental levels were due to GxE or insufficient genetic linkage between animals in each environmental level.

RESULTS

The correlations (being less than <0.8) for the real phenotypes were indicative of GxE for CL presence between ADWG environmental levels and in pregnancy traits. However, none of the correlations for CL presence or first pregnancy between ADWG levels were below the 5th percentile value for the empirical distribution under the null hypothesis from the simulated data. Only one statistically significant (P < 0.05) indication of GxE for first pregnancy was found between THI environmental levels, where rg = 0.28 and 5th percentile value = 0.29, and this result was marginal.

CONCLUSIONS

Only one case of statistically significant GxE for fertility traits was detected for first pregnancy between THI environmental levels 2 and 3. Other initial indications of GxE that were observed from the real phenotypes did not prove significant when compared to an empirical null distribution from simulated phenotypes. The lack of compelling evidence of GxE indicates that direct selection for fertility traits can be made accurately, using a single evaluation, regardless of environment.

Use of the linear regression method to evaluate population accuracy of predictions from non-linear models

Background

To address the limitations of commonly used cross-validation methods, the linear regression method (LR) was proposed to estimate population accuracy of predictions based on the implicit assumption that the fitted model is correct. This method also provides two statistics to determine the adequacy of the fitted model. The validity and behavior of the LR method have been provided and studied for linear predictions but not for nonlinear predictions. The objectives of this study were to 1) provide a mathematical proof for the validity of the LR method when predictions are based on conditional means, regardless of whether the predictions are linear or non-linear 2) investigate the ability of the LR method to detect whether the fitted model is adequate or inadequate, and 3) provide guidelines on how to appropriately partition the data into training and validation such that the LR method can identify an inadequate model.

Results

We present a mathematical proof for the validity of the LR method to estimate population accuracy and to determine whether the fitted model is adequate or inadequate when the predictor is the conditional mean, which may be a non-linear function of the phenotype. Using three partitioning scenarios of simulated data, we show that the one of the LR statistics can detect an inadequate model only when the data are partitioned such that the values of relevant predictor variables differ between the training and validation sets. In contrast, we observed that the other LR statistic was able to detect an inadequate model for all three scenarios.

Conclusion

The LR method has been proposed to address some limitations of the traditional approach of cross-validation in genetic evaluation. In this paper, we showed that the LR method is valid when the model is adequate and the conditional mean is the predictor, even when it is a non-linear function of the phenotype. We found one of the two LR statistics is superior because it was able to detect an inadequate model for all three partitioning scenarios (i.e., between animals, by age within animals, and between animals and by age) that were studied.

Single-Step Genomic Prediction of Superovulatory Response Traits in Japanese Black Donor Cows

We assessed the performance of single-step genomic prediction of breeding values for superovulatory response traits in Japanese Black donor cows. A total of 25,332 records of the total number of embryos and oocytes (TNE) and the number of good embryos (NGE) per flush for 1874 Japanese Black donor cows were collected during 2008 and 2022. Genotype information on 36,426 autosomal single-nucleotide polymorphisms (SNPs) for 575 out of the 1,874 cows was used. Breeding values were predicted exploiting a two-trait repeatability animal model. Two genetic relationship matrices were used, one based on pedigree information (A matrix) and the other considering both pedigree and SNP marker genotype information (H matrix). Estimated heritabilities of TNE and NGE were 0.18 and 0.11, respectively, when using the H matrix, which were both slightly lower than when using the A matrix (0.26 for TNE and 0.16 for NGE). Estimated genetic correlations between the traits were 0.61 and 0.66 when using H and A matrices, respectively. When the variance components were the same in breeding value prediction, the mean reliability was greater when using the H matrix than when using the A matrix. This advantage seems more prominent for cows with low reliability when using the A matrix. The results imply that introducing single-step genomic prediction could boost the rate of genetic improvement of superovulatory response traits, but efforts should be made to maintain genetic diversity when performing selection.

Comparing Methods to Select Candidates for Re-Genotyping to Impute Higher-Density Genotype Data in a Japanese Black Cattle Population: A Case Study

As optimization methods to identify the best animals for dense genotyping to construct a reference population for genotype imputation, the MCA and MCG methods, which use the pedigree-based additive genetic relationship matrix (A matrix) and the genomic relationship matrix (G matrix), respectively, have been proposed. We assessed the performance of MCA and MCG methods using 575 Japanese Black cows. Pedigree data were provided to trace back up to five generations to construct the A matrix with changing the pedigree depth from 1 to 5 (five MCA methods). Genotype information on 36,426 single-nucleotide polymorphisms was used to calculate the G matrix based on VanRaden's methods 1 and 2 (two MCG methods). The MCG always selected one cow per iteration, while MCA sometimes selected multiple cows. The number of commonly selected cows between the MCA and MCG methods was generally lower than that between different MCA methods or between different MCG methods. For the studied population, MCG appeared to be more reasonable than MCA in selecting cows as a reference population for higher-density genotype imputation to perform genomic prediction and a genome-wide association study.

Genomic prediction through machine learning and neural networks for traits with epistasis

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Performance of machine learning and neural netowrks in Genomic analysis.

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Heritability and QTL number impacts on performance machine learning methods.

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Machine learning models in genomic analyses.

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Neural networks can present better performance for complex quantitative traits.

Genomic wide selection (GWS) is one contributions of molecular genetics to breeding. Machine learning (ML) and artificial neural networks (ANN) methods are non-parameterized and can develop more accurate and parsimonious models for GWS analysis. Multivariate Adaptive Regression Splines (MARS) is considered one of the most flexible ML methods, automatically modeling nonlinearities and interactions of the predictor variables. This study aimed to evaluate and compare methods based on ANN, ML, including MARS, and G-BLUP through GWS. An F2 population formed by 1000 individuals and genotyped for 4010 SNP markers and twelve traits from a model considering epistatic effect, with QTL numbers ranging from eight to 480 and heritability (h2) of 0.3, 0.5 or 0.8 were simulated. Variation in heritability and number of QTL impacts the performance of methods. About quantitative traits (40, 80, 120, 240, and 480 QTLs) was observed highest R2 to Radial Base Network (RBF) and G-BLUP, followed by Random Forest (RF), Bagging (BA), and Boosting (BO). RF and BA also showed better results for traits to h2 of 0.3 with R2 values 16.51% and 16.30%, respectively, while MARS methods showed better results for oligogenic traits with R2 values ranging from 39,12 % to 43,20 % in h2 of 0.5 and from 59.92% to 78,56% in h2 of 0.8. Non-additive MARS methods also showed high R2 for traits with high heritability and 240 QTLs or more. ANN and ML methods are powerful tools to predict genetic values in traits with epistatic effect, for different degrees of heritability and QTL numbers.

QTLs Associated with Resistance to Cardiomyopathy Syndrome in Atlantic Salmon

Cardiomyopathy syndrome (CMS) caused by piscine myocarditis virus is a major disease affecting the Norwegian Atlantic salmon industry. Three different populations of Atlantic salmon from the Mowi breeding program were used in this study. The first 2 populations (population 1 and 2) were naturally infected in a field outbreak, while the third population (population 3) went through a controlled challenged test. The aim of the study was to estimate the heritability, the genetic correlation between populations and perform genome-wide association analysis for resistance to this disease. Survival data from population 1 and 2 and heart atrium histology score data from population 3 was analyzed. A total of 571, 4312, and 901 fish from population 1, 2, and 3, respectively were genotyped with a noncommercial 55,735 Affymetrix marker panel. Genomic heritability ranged from 0.12 to 0.46 and the highest estimate was obtained from the challenge test dataset. The genetic correlation between populations was moderate (0.51–0.61). Two chromosomal regions (SSA27 and SSA12) contained single nucleotide polymorphisms associated with resistance to CMS. The highest association signal (P = 6.9751 × 10⁻²⁷) was found on chromosome 27. Four genes with functional roles affecting viral resistance (magi1, pi4kb, bnip2, and ha1f) were found to map closely to the identified quantitative trait loci (QTLs). In conclusion, genetic variation for resistance to CMS was observed in all 3 populations. Two important quantitative trait loci were detected which together explain half of the total genetic variance, suggesting strong potential application for marker-assisted selection and genomic predictions to improve CMS resistance.

Effect of genomic selection and genotyping strategy on estimation of variance components in animal models using different relationship matrices

Background

The traditional way to estimate variance components (VC) is based on the animal model using a pedigree-based relationship matrix (A) (A-AM). After genomic selection was introduced into breeding programs, it was anticipated that VC estimates from A-AM would be biased because the effect of selection based on genomic information is not captured. The single-step method (H-AM), which uses an H matrix as (co)variance matrix, can be used as an alternative to estimate VC. Here, we compared VC estimates from A-AM and H-AM and investigated the effect of genomic selection, genotyping strategy and genotyping proportion on the estimation of VC from the two methods, by analyzing a dataset from a commercial broiler line and a simulated dataset that mimicked the broiler population.

Results

VC estimates from H-AM were severely overestimated with a high proportion of selective genotyping, and overestimation increased as proportion of genotyping increased in the analysis of both commercial and simulated data. This bias in H-AM estimates arises when selective genotyping is used to construct the H-matrix, regardless of whether selective genotyping is applied or not in the selection process. For simulated populations under genomic selection, estimates of genetic variance from A-AM were also significantly overestimated when the effect of genomic selection was strong. Our results suggest that VC estimates from H-AM under random genotyping have the expected values. Predicted breeding values from H-AM were inflated when VC estimates were biased, and inflation differed between genotyped and ungenotyped animals, which can lead to suboptimal selection decisions.

Conclusions

We conclude that VC estimates from H-AM are biased with selective genotyping, but are close to expected values with random genotyping.VC estimates from A-AM in populations under genomic selection are also biased but to a much lesser degree. Therefore, we recommend the use of H-AM with random genotyping to estimate VC for populations under genomic selection. Our results indicate that it is still possible to use selective genotyping in selection, but then VC estimation should avoid the use of genotypes from one side only of the distribution of phenotypes. Hence, a dual genotyping strategy may be needed to address both selection and VC estimation.

Potential of genomic selection for improvement of resistance to ostreid herpesvirus in Pacific oyster (Crassostrea gigas)

In genomic selection (GS), genome-wide SNP markers are used to generate genomic estimated breeding values for selection candidates. The application of GS in shellfish looks promising and has the potential to help in dealing with one of the main issues currently affecting Pacific oyster production worldwide, which is the 'summer mortality syndrome'. This causes periodic mass mortality in farms worldwide and has mainly been attributed to a specific variant of the ostreid herpesvirus (OsHV-1). In the current study, we evaluated the potential of genomic selection for host resistance to OsHV-1 in Pacific oysters, and compared it with pedigree-based approaches. An OsHV-1 disease challenge was performed using an immersion-based virus exposure treatment for oysters for 7 days. A total of 768 samples were genotyped using the medium-density SNP array for oysters. A GWAS was performed for the survival trait using a GBLUP approach in blupf90 software. Heritability ranged from 0.25 ± 0.05 to 0.37 ± 0.05 (mean ± SE) based on pedigree and genomic information respectively. Genomic prediction was more accurate than pedigree prediction, and SNP density reduction had little impact on prediction accuracy until marker densities dropped below approximately 500 SNPs. This demonstrates the potential for GS in Pacific oyster breeding programmes, and importantly, demonstrates that a low number of SNPs might suffice to obtain accurate genomic estimated breeding values, thus potentially making the implementation of GS more cost effective.

Inferring trait-specific similarity among individuals from molecular markers and phenotypes with Bayesian regression

Modeling covariance structure based on genetic similarity between pairs of relatives plays an important role in evolutionary, quantitative and statistical genetics. Historically, genetic similarity between individuals has been quantified from pedigrees via the probability that randomly chosen homologous alleles between individuals are identical by descent (IBD). At present, however, many genetic analyses rely on molecular markers, with realized measures of genomic similarity replacing IBD-based expected similarities. Animal and plant breeders, for example, now employ marker-based genomic relationship matrices between individuals in prediction models and in estimation of genome-based heritability coefficients. Phenotypes convey information about genetic similarity as well. For instance, if phenotypic values are at least partially the result of the action of quantitative trait loci, one would expect the former to inform about the latter, as in genome-wide association studies. Statistically, a non-trivial conditional distribution of unknown genetic similarities, given phenotypes, is to be expected. A Bayesian formalism is presented here that applies to whole-genome regression methods where some genetic similarity matrix, e.g., a genomic relationship matrix, can be defined. Our Bayesian approach, based on phenotypes and markers, converts prior (markers only) expected similarity into trait-specific posterior similarity. A simulation illustrates situations under which effective Bayesian learning from phenotypes occurs. Pinus and wheat data sets were used to demonstrate applicability of the concept in practice. The methodology applies to a wide class of Bayesian linear regression models, it extends to the multiple-trait domain, and can also be used to develop phenotype-guided similarity kernels in prediction problems.

Investigating the relationship between vaginal microbiota and host genetics and their impact on immune response and farrowing traits in commercial gilts

Our objectives were to evaluate the interaction between host genetics and vaginal microbiota and their relationships with antibody (Ab) response to porcine reproductive and respiratory syndrome virus (PRRSV) vaccination and farrowing performance in commercial gilts. The farrowing performance traits were number born alive, number weaning (NW), total number born, number born dead, stillborn, mummies and preweaning mortality (PWM). The vaginal microbiota was collected on days 4 (D4) and 52 (D52) after vaccination for PRRSV. Blood samples were collected on D52 for Ab measurement. Actinobacteria, Bacterioidetes, Firmicutes, Proteobacteria and Tenericutes were the most abundant Phyla identified in the vaginal microbiota. Heritability ranged from ~0 to 0.60 (Fusobacterium) on D4 and from ~0 to 0.63 (Terrisporobacter) on D52, with 43 operational taxonomic units (OTUs) presenting moderate to high heritability. One major QTL on chromosome 12 was identified for 5 OTUs (Clostridiales, Acinetobacter, Ruminococcaceae, Campylobacter and Anaerococcus), among other 19 QTL. The microbiability for Ab response to PRRSV vaccination was low for both days (<0.07). For farrowing performance, microbiability varied from <0.001 to 0.15 (NW on D4). For NW and PWM, the microbiability was greater than the heritability estimates. Actinobacillus, Streptococcus, Campylobacter, Anaerococcus, Mollicutes, Peptostreptococcus, Treponema and Fusobacterium showed different abundance between low and high Ab responders. Finally, canonical discriminant analyses revealed that vaginal microbiota was able to classify gilts in high and low Ab responders to PRRSV vaccination with a misclassification rate of <0.02. Although the microbiota explained limited variation in Ab response and farrowing performance traits, there is still potential to explore the use of vaginal microbiota to explain variation in traits such as NW and PWM. In addition, these results revealed that there is a partial control of host genetic over vaginal microbiota, suggesting a possibility for genetic selection on the vaginal microbiota.

Best Prediction of the Additive Genomic Variance in Random-Effects Models

The additive genomic variance in linear models with random marker effects can be defined as a random variable that is in accordance with classical quantitative genetics theory. Common approaches to estimate the genomic variance in random-effects linear models based on genomic marker data can be regarded as estimating the unconditional (or prior) expectation of this random additive genomic variance, and result in a negligence of the contribution of linkage disequilibrium (LD). We introduce a novel best prediction (BP) approach for the additive genomic variance in both the current and the base population in the framework of genomic prediction using the genomic best linear unbiased prediction (gBLUP) method. The resulting best predictor is the conditional (or posterior) expectation of the additive genomic variance when using the additional information given by the phenotypic data, and is structurally in accordance with the genomic equivalent of the classical additive genetic variance in random-effects models. In particular, the best predictor includes the contribution of (marker) LD to the additive genomic variance and possibly fully eliminates the missing contribution of LD that is caused by the assumptions of statistical frameworks such as the random-effects model. We derive an empirical best predictor (eBP) and compare its performance with common approaches to estimate the additive genomic variance in random-effects models on commonly used genomic datasets.

Genome-wide association and genomic prediction of resistance to viral nervous necrosis in European sea bass (Dicentrarchus labrax) using RAD sequencing

BACKGROUND

European sea bass (Dicentrarchus labrax) is one of the most important species for European aquaculture. Viral nervous necrosis (VNN), commonly caused by the redspotted grouper nervous necrosis virus (RGNNV), can result in high levels of morbidity and mortality, mainly during the larval and juvenile stages of cultured sea bass. In the absence of efficient therapeutic treatments, selective breeding for host resistance offers a promising strategy to control this disease. Our study aimed at investigating genetic resistance to VNN and genomic-based approaches to improve disease resistance by selective breeding. A population of 1538 sea bass juveniles from a factorial cross between 48 sires and 17 dams was challenged with RGNNV with mortalities and survivors being recorded and sampled for genotyping by the RAD sequencing approach.

RESULTS

We used genome-wide genotype data from 9195 single nucleotide polymorphisms (SNPs) for downstream analysis. Estimates of heritability of survival on the underlying scale for the pedigree and genomic relationship matrices were 0.27 (HPD interval 95%: 0.14-0.40) and 0.43 (0.29-0.57), respectively. Classical genome-wide association analysis detected genome-wide significant quantitative trait loci (QTL) for resistance to VNN on chromosomes (unassigned scaffolds in the case of 'chromosome' 25) 3, 20 and 25 (P < 1e06). Weighted genomic best linear unbiased predictor provided additional support for the QTL on chromosome 3 and suggested that it explained 4% of the additive genetic variation. Genomic prediction approaches were tested to investigate the potential of using genome-wide SNP data to estimate breeding values for resistance to VNN and showed that genomic prediction resulted in a 13% increase in successful classification of resistant and susceptible animals compared to pedigree-based methods, with Bayes A and Bayes B giving the highest predictive ability.

CONCLUSIONS

Genome-wide significant QTL were identified but each with relatively small effects on the trait. Tests of genomic prediction suggested that incorporating genome-wide SNP data is likely to result in higher accuracy of estimated breeding values for resistance to VNN. RAD sequencing is an effective method for generating such genome-wide SNPs, and our findings highlight the potential of genomic selection to breed farmed European sea bass with improved resistance to VNN.

A novel linkage-disequilibrium corrected genomic relationship matrix for SNP-heritability estimation and genomic prediction

Single nucleotide polymorphism (SNP)-heritability estimation is an important topic in several research fields, including animal, plant and human genetics, as well as in ecology. Linear mixed model estimation of SNP-heritability uses the structures of genomic relationships between individuals, which is constructed from genome-wide sets of SNP-markers that are generally weighted equally in their contributions. Proposed methods to handle dependence between SNPs include, “thinning” the marker set by linkage disequilibrium (LD)-pruning, the use of haplotype-tagging of SNPs, and LD-weighting of the SNP-contributions. For improved estimation, we propose a new conceptual framework for genomic relationship matrix, in which Mahalanobis distance-based LD-correction is used in a linear mixed model estimation of SNP-heritability. The superiority of the presented method is illustrated and compared to mixed-model analyses using a VanRaden genomic relationship matrix, a matrix used by GCTA and a matrix employing LD-weighting (as implemented in the LDAK software) in simulated (using real human, rice and cattle genotypes) and real (maize, rice and mice) datasets. Despite of the computational difficulties, our results suggest that by using the proposed method one can improve the accuracy of SNP-heritability estimates in datasets with high LD.