Modelling QTL effect on BTA06 using random regression test day models

Genetic parameters and genome-wide association studies for mozzarella and milk production traits, lactation length, and lactation persistency in Murrah buffaloes

Genetic and genomic analyses of longitudinal traits related to milk production efficiency are paramount for optimizing water buffaloes breeding schemes. Therefore, this study aimed to (1) compare single-trait random regression models under a single-step genomic BLUP setting based on alternative covariance functions (i.e., Wood, Wilmink, and Ali and Schaeffer) to describe milk (MY), fat (FY), protein (PY), and mozzarella (MZY) yields, fat-to-protein ratio (FPR), somatic cell score (SCS), lactation length (LL), and lactation persistency (LP) in Murrah dairy buffaloes (Bubalus bubalis); (2) combine the best functions for each trait under a multiple-trait framework; (3) estimate time-dependent SNP effects for all the studied longitudinal traits; and (4) identify the most likely candidate genes associated with the traits. A total of 323,140 test-day records from the first lactation of 4,588 Murrah buffaloes were made available for the study. The model included the average curve of the population nested within herd-year-season of calving, systematic effects of number of milkings per day, and age at first calving as linear and quadratic covariates, and additive genetic, permanent environment, and residual as random effects. The Wood model had the best goodness of fit based on the deviance information criterion and posterior model probabilities for all traits. Moderate heritabilities were estimated over time for most traits (0.30 ± 0.02 for MY; 0.26 ± 0.03 for FY; 0.45 ± 0.04 for PY; 0.28 ± 0.05 for MZY; 0.13 ± 0.02 for FPR; and 0.15 ± 0.03 for SCS). The heritability estimates for LP ranged from 0.38 ± 0.02 to 0.65 ± 0.03 depending on the trait definition used. Similarly, heritabilities estimated for LL ranged from 0.10 ± 0.01 to 0.14 ± 0.03. The genetic correlation estimates across days in milk (DIM) for all traits ranged from -0.06 (186-215 DIM for MY-SCS) to 0.78 (66-95 DIM for PY-MZY). The SNP effects calculated for the random regression model coefficients were used to estimate the SNP effects throughout the lactation curve (from 5 to 305 d). Numerous relevant genomic regions and candidate genes were identified for all traits, confirming their polygenic nature. The candidate genes identified contribute to a better understanding of the genetic background of milk-related traits in Murrah buffaloes and reinforce the value of incorporating genomic information in their breeding programs.

Hierarchical mixed-model expedites genome-wide longitudinal association analysis

A hierarchical random regression model (Hi-RRM) was extended into a genome-wide association analysis for longitudinal data, which significantly reduced the dimensionality of repeated measurements. The Hi-RRM first modeled the phenotypic trajectory of each individual using a RRM and then associated phenotypic regressions with genetic markers using a multivariate mixed model (mvLMM). By spectral decomposition of genomic relationship and regression covariance matrices, the mvLMM was transformed into a multiple linear regression, which improved computing efficiency while implementing mvLMM associations in efficient mixed-model association expedited (EMMAX). Compared with the existing RRM-based association analyses, the statistical utility of Hi-RRM was demonstrated by simulation experiments. The method proposed here was also applied to find the quantitative trait nucleotides controlling the growth pattern of egg weights in poultry data.

Invited review: Advances and applications of random regression models: From quantitative genetics to genomics

An important goal in animal breeding is to improve longitudinal traits; that is, traits recorded multiple times during an individual's lifetime or physiological cycle. Longitudinal traits were first genetically evaluated based on accumulated phenotypic expression, phenotypic expression at specific time points, or repeatability models. Until now, the genetic evaluation of longitudinal traits has mainly focused on using random regression models (RRM). Random regression models enable fitting random genetic and environmental effects over time, which results in higher accuracy of estimated breeding values compared with other statistical approaches. In addition, RRM provide insights about temporal variation of biological processes and the physiological implications underlying the studied traits. Despite the fact that genomic information has substantially contributed to increase the rates of genetic progress for a variety of economically important traits in several livestock species, less attention has been given to longitudinal traits in recent years. However, including genomic information to evaluate longitudinal traits using RRM is a feasible alternative to yield more accurate selection and culling decisions, because selection of young animals may be based on the complete pattern of the production curve with higher accuracy compared with the use of traditional parent average (i.e., without genomic information). Moreover, RRM can be used to estimate SNP effects over time in genome-wide association studies. Thus, by analyzing marker associations over time, regions with higher effects at specific points in time are more likely to be identified. Despite the advances in applications of RRM in genetic evaluations, more research is needed to successfully combine RRM and genomic information. Future research should provide a better understanding of the temporal variation of biological processes and their physiological implications underlying the longitudinal traits.

Eigen decomposition expedites longitudinal genome-wide association studies for milk production traits in Chinese Holstein

Background

Pseudo-phenotypes, such as 305-day yields, estimated breeding values or deregressed proofs, are usually used as response variables for genome-wide association studies (GWAS) of milk production traits in dairy cattle. Computational inefficiency challenges the direct use of test-day records for longitudinal GWAS with large datasets.

Results

We propose a rapid longitudinal GWAS method that is based on a random regression model. Our method uses Eigen decomposition of the phenotypic covariance matrix to rotate the data, thereby transforming the complex mixed linear model into weighted least squares analysis. We performed a simulation study that showed that our method can control type I errors well and has higher power than a longitudinal GWAS method that does not include time-varied additive genetic effects. We also applied our method to the analysis of milk production traits in the first three parities of 6711 Chinese Holstein cows. The analysis for each trait was completed within 1 day with known variances. In total, we located 84 significant single nucleotide polymorphisms (SNPs) of which 65 were within previously reported quantitative trait loci (QTL) regions.

Conclusions

Our rapid method can control type I errors in the analysis of longitudinal data and can be applied to other longitudinal traits. We detected QTL that were for the most part similar to those reported in a previous study in Chinese Holstein. Moreover, six additional SNPs for fat percentage and 13 SNPs for protein percentage were identified by our method. These additional 19 SNPs could be new candidate quantitative trait nucleotides for milk production traits in Chinese Holstein.

Electronic supplementary material

The online version of this article (10.1186/s12711-018-0383-0) contains supplementary material, which is available to authorized users.

Assessing the degree of stratification between closely related Holstein-Friesian populations

Genomic information is an important part of the routine evaluation of dairy cattle and provides the wide availability of animals genotyped using single nucleotide polymorphism (SNP) microarrays. We analyzed 2243 Polish and 2294 German Holstein-Friesian bulls genotyped using the Illumina BovineSNP50 BeadChip. For each bull, estimated breeding values (EBVs) calculated from national routine genetic evaluation were available for production traits and for somatic cell score (SCS). Separately for each population, we estimated SNP haplotypes, pairwise linkage disequilibrium (LD), and SNP effects. The SNP genetic covariance between both populations was estimated using a bivariate mixed model. The average LD was lower in the Polish than in the German population and, with increasing genomic distance, LD decays 1.7 times more rapidly in German than in Polish cattle. The comparison of SNP allele frequencies for base populations estimated separately using Polish and German data revealed a very good agreement. The comparison of genetic effects corresponding to various window lengths defined in bp emerged a systematic pattern: regardless of the length of the compared region, few significant differences were found for production traits, while many were observed for SCS. For each trait, the German population had much higher SNP variances than the Polish population and the genetic covariance estimates were all positive. Depending on traits’ inheritance mode, the additive genetic variation can be stored in many genes following the infinitesimal model (like for SCS) or distributed between genes with high effects and the polygenic “background” (like for production traits). Accounting for those differences has implications on the prospective international genomic evaluation.

Performance Gains in Genome-Wide Association Studies for Longitudinal Traits via Modeling Time-varied effects

Complex traits with multiple phenotypic values changing over time are called longitudinal traits. In traditional genome-wide association studies (GWAS) for longitudinal traits, a combined/averaged estimated breeding value (EBV) or deregressed proof (DRP) instead of multiple phenotypic measurements per se for each individual was frequently treated as response variable in statistical model. This can result in power losses or even inflate false positive rates (FPRs) in the detection due to failure of exploring time-dependent relationship among measurements. Aiming at overcoming such limitation, we developed two random regression-based models for functional GWAS on longitudinal traits, which could directly use original time-dependent records as response variable and fit the time-varied Quantitative Trait Nucleotide (QTN) effect. Simulation studies showed that our methods could control the FPRs and increase statistical powers in detecting QTN in comparison with traditional methods where EBVs, DRPs or estimated residuals were considered as response variables. Besides, our proposed models also achieved reliable powers in gene detection when implementing into two real datasets, a Chinese Holstein Cattle data and the Genetic Analysis Workshop 18 data. Our study herein offers an optimal way to enhance the power of gene detection and further understand genetic control of developmental processes for complex longitudinal traits.