scholarly journals Properties of genomic relationships for estimating current genetic variances within and genetic correlations between populations

2017 ◽  
Author(s):  
Yvonne C.J. Wientjes ◽  
Piter Bijma ◽  
Jérémie Vandenplas ◽  
Mario P.L. Calus
Keyword(s):  
Genetic Correlation ◽  
Variance Components ◽  
Genetic Correlations ◽  
Genomic Relationship Matrix ◽  
Relationship Matrix ◽  
Base Population ◽  
Genomic Relationship ◽  
Genetic Variances ◽  
Population Genomic ◽  
Current Population

ABSTRACTDifferent methods are available to calculate multi-population genomic relationship matrices. Since those matrices differ in base population, it is anticipated that the method used to calculate the genomic relationship matrix affect the estimate of genetic variances, covariances and correlations. The aim of this paper is to define a multi-population genomic relationship matrix to estimate current genetic variances within and genetic correlations between populations. The genomic relationship matrix containing two populations consists of four blocks, one block for population 1, one block for population 2, and two blocks for relationships between the populations. It is known, based on literature, that current genetic variances are estimated when the current population is used as base population of the relationship matrix. In this paper, we theoretically derived the properties of the genomic relationship matrix to estimate genetic correlations and validated it using simulations. When the scaling factors of the genomic relationship matrix fulfill the property , the genetic correlation is estimated even though estimated variance components are not necessarily related to the current population. When this property is not met, the correlation based on estimated variance components should be multiplied by to rescale the genetic correlation. In this study we present a genomic relationship matrix which directly results in current genetic variances as well as genetic correlations between populations.

Genetic correlations among female fertility traits and milk production in different parities in Swedish dairy cattle

1999 ◽  
Vol 24 ◽  
pp. 177-181
Author(s):  
A. Roth ◽  
E. Strandberg ◽  
B. Berglund ◽  
U. Emanuelson ◽  
J. Philipsson
Keyword(s):  
Genetic Correlation ◽  
Variance Components ◽  
Genetic Correlations ◽  
Relationship Matrix ◽  
Phenotypic Variance ◽  
Bivariate Model ◽  
Service Period ◽  
Swedish Dairy ◽  
Fertility Traits ◽  
Maternal Grandsire

AbstractThe main objective of this study was to estimate genetic correlations between fertility and production in first and second lactations as well as between fertility traits measured in the same way at different ages. The analyses were carried out for Swedish Red and White cows born from 1986 to 1996, in total about 578 000, 430 000, and 221 000 records in the heifer period, first lactation and second lactation, respectively. The fertility traits studied were: interval between calving and first insemination (CFI), interval between calving and last insemination (CLI), number of inseminations per service period (NINS) and number of treatments for reproductive disturbances (NREPT). Production was measured as the average of the energy-corrected milk yield from the second and third test-days in a lactation (ECM23). A linear, bivariate model that included effects of herd-year, month, age, and sire of the cow was applied. A relationship matrix containing sire and maternal grandsire of the sire was included. The (co)variance components for the random effects were estimated by use of a restricted maximum likelihood algorithm. The genetic correlations between fertility traits and production within first and second lactation were in the range of 0.1 to 0.3, all of them unfavourable. However, the genetic correlation between NREPT and ECM23 was close to zero within both lactations. The heritabilities, calculated without the herd-year variance included in the phenotypic variance, varied between 0.02 and 0.06 for the fertility traits with only minor differences between first and second lactation. The heritability of ECM23 was 0.35 in the first lactation and 0.28 in the second lactation. The genetic correlation between NINS during the heifer period and in first lactation was high, 0.7. The heritabilities for NINS and NREPT during the heifer period were very low, <0.01. In conclusion, there were only minor differences in inter-relationships between fertility and production in first and second lactation and the traits were negatively associated with each other. Based on the genetic correlation between NINS in the heifer period and NINS in first lactation, this study indicated that the traits at least partly are regulated by different sets of genes.

scholarly journals Genetic and genomic relationship between methane production measured in breath and fatty acid content in milk samples from Danish Holsteins

2016 ◽  
Vol 56 (3) ◽  
pp. 298 ◽  
Author(s):  
J. Lassen ◽  
N. A. Poulsen ◽  
M. K. Larsen ◽  
A. J. Buitenhuis
Keyword(s):  
Fatty Acid ◽  
Fatty Acid Content ◽  
Genetic Correlations ◽  
High Standard ◽  
Standard Errors ◽  
Genomic Relationship Matrix ◽  
Relationship Matrix ◽  
Genomic Relationship ◽  
Milk Fatty Acids ◽  
Heritability Estimates

In this study the objective was to estimate the genetic and genomic relationship between methane-related traits and milk fatty acid profiles. This was done using two different estimation procedures: a single nucleotide polymorphism-based genomic relationship matrix and a classical pedigree-based relationship matrix. Data was generated on three Danish Holstein herds and a total of 339 cows were available for the study. Methane phenotypes were generated in milking robots during milking over a weekly period and the milk phenotypes were quantified from milk from one milking. Genetic and genomic parameters were estimated using a mixed linear model. Results showed that heritability estimates were comparable between models, but the standard error was lower for genomic heritabilities compared with genetic heritabilities. Genetic as well as genomic correlations were highly variable and had high standard errors, reflecting a similar pattern as for the heritability estimates with lower standard errors for the genomic correlations compared with the pedigree-based genetic correlations. Many of the correlations though had a magnitude that makes further studies on larger datasets worthwhile. The results indicate that genotypes are highly valuable in studies where limited number of phenotypes can be recorded. Also it shows that there is some significant genetic association between methane in the breath of the cow and milk fatty acids profiles.

scholarly journals Changes in Allele Frequencies When Different Genomic Coancestry Matrices Are Used for Maintaining Genetic Diversity

Genes ◽  
2021 ◽  
Vol 12 (5) ◽  
pp. 673
Author(s):  
Elisabeth Morales-González ◽  
Jesús Fernández ◽  
Ricardo Pong-Wong ◽  
Miguel Ángel Toro ◽  
Beatriz Villanueva
Keyword(s):  
Genetic Variability ◽  
Allele Frequencies ◽  
Stochastic Simulations ◽  
Genomic Relationship Matrix ◽  
Relationship Matrix ◽  
Base Population ◽  
Genomic Relationship ◽  
The Matrix ◽  
Hardy Weinberg Equilibrium ◽  
Loss Of Diversity

A main objective in conservation programs is to maintain genetic variability. This can be achieved using the Optimal Contributions (OC) method that optimizes the contributions of candidates to the next generation by minimizing the global coancestry. However, it has been argued that maintaining allele frequencies is also important. Different genomic coancestry matrices can be used on OC and the choice of the matrix will have an impact not only on the genetic variability maintained, but also on the change in allele frequencies. The objective of this study was to evaluate, through stochastic simulations, the genetic variability maintained and the trajectory of allele frequencies when using two different genomic coancestry matrices in OC to minimize the loss of diversity: (i) the matrix based on deviations of the observed number of alleles shared between two individuals from the expected numbers under Hardy–Weinberg equilibrium (θLH); and (ii) the matrix based on VanRaden’s genomic relationship matrix (θVR). The results indicate that the use of θLH resulted in a higher genetic variability than the use of θVR. However, the use of θVR maintained allele frequencies closer to those in the base population than the use of θLH.

scholarly journals Correction to: Validation of genomic predictions for body weight in broilers using crossbred information and considering breed-of-origin of alleles

2019 ◽  
Vol 51 (1) ◽  
Author(s):  
Pascal Duenk ◽  
Mario P. L. Calus ◽  
Yvonne C. J. Wientjes ◽  
Vivian P. Breen ◽  
John M. Henshall ◽  
...  
Keyword(s):  
Body Weight ◽  
Genomic Relationship Matrix ◽  
Relationship Matrix ◽  
Genomic Relationship ◽  
Genomic Predictions

Following publication of original article [1], we noticed that there was an error: Eq. (3) on page 5 is the genomic relationship matrix that

scholarly journals Accuracy of genomic selection predictions for hip height in Brahman cattle using different relationship matrices

2018 ◽  
Vol 53 (6) ◽  
pp. 717-726 ◽  
Author(s):  
Michel Marques Farah ◽  
Marina Rufino Salinas Fortes ◽  
Matthew Kelly ◽  
Laercio Ribeiro Porto-Neto ◽  
Camila Tangari Meira ◽  
...  
Keyword(s):  
Allele Frequency ◽  
High Density ◽  
Genomic Relationship Matrix ◽  
Relationship Matrix ◽  
Genomic Relationship ◽  
Genomic Information ◽  
Pedigree Data ◽  
Snp Chip ◽  
Numerator Relationship Matrix ◽  
Brahman Cattle

Abstract: The objective of this work was to evaluate the effects of genomic information on the genetic evaluation of hip height in Brahman cattle using different matrices built from genomic and pedigree data. Hip height measurements from 1,695 animals, genotyped with high-density SNP chip or imputed from 50 K high-density SNP chip, were used. The numerator relationship matrix (NRM) was compared with the H matrix, which incorporated the NRM and genomic relationship (G) matrix simultaneously. The genotypes were used to estimate three versions of G: observed allele frequency (HGOF), average minor allele frequency (HGMF), and frequency of 0.5 for all markers (HG50). For matrix comparisons, animal data were either used in full or divided into calibration (80% older animals) and validation (20% younger animals) datasets. The accuracy values for the NRM, HGOF, and HG50 were 0.776, 0.813, and 0.594, respectively. The NRM and HGOF showed similar minor variances for diagonal and off-diagonal elements, as well as for estimated breeding values. The use of genomic information resulted in relationship estimates similar to those obtained based on pedigree; however, HGOF is the best option for estimating the genomic relationship matrix and results in a higher prediction accuracy. The ranking of the top 20% animals was very similar for all matrices, but the ranking within them varies depending on the method used.

scholarly journals Application of Low Coverage Genotyping by Sequencing in Selectively Bred Arctic Charr (Salvelinus alpinus)

2020 ◽  
Vol 10 (6) ◽  
pp. 2069-2078 ◽  
Author(s):  
Christos Palaiokostas ◽  
Shannon M. Clarke ◽  
Henrik Jeuthe ◽  
Rudiger Brauning ◽  
Timothy P. Bilton ◽  
...  
Keyword(s):  
Principal Components ◽  
Salvelinus Alpinus ◽  
Arctic Charr ◽  
Genotyping By Sequencing ◽  
Breeding Value ◽  
Genomic Relationship Matrix ◽  
Relationship Matrix ◽  
Genomic Relationship ◽  
Value Estimation ◽  
Low Coverage

Arctic charr (Salvelinus alpinus) is a species of high economic value for the aquaculture industry, and of high ecological value due to its Holarctic distribution in both marine and freshwater environments. Novel genome sequencing approaches enable the study of population and quantitative genetic parameters even on species with limited or no prior genomic resources. Low coverage genotyping by sequencing (GBS) was applied in a selected strain of Arctic charr in Sweden originating from a landlocked freshwater population. For the needs of the current study, animals from year classes 2013 (171 animals, parental population) and 2017 (759 animals; 13 full sib families) were used as a template for identifying genome wide single nucleotide polymorphisms (SNPs). GBS libraries were constructed using the PstI and MspI restriction enzymes. Approximately 14.5K SNPs passed quality control and were used for estimating a genomic relationship matrix. Thereafter a wide range of analyses were conducted in order to gain insights regarding genetic diversity and investigate the efficiency of the genomic information for parentage assignment and breeding value estimation. Heterozygosity estimates for both year classes suggested a slight excess of heterozygotes. Furthermore, FST estimates among the families of year class 2017 ranged between 0.009 – 0.066. Principal components analysis (PCA) and discriminant analysis of principal components (DAPC) were applied aiming to identify the existence of genetic clusters among the studied population. Results obtained were in accordance with pedigree records allowing the identification of individual families. Additionally, DNA parentage verification was performed, with results in accordance with the pedigree records with the exception of a putative dam where full sib genotypes suggested a potential recording error. Breeding value estimation for juvenile growth through the usage of the estimated genomic relationship matrix clearly outperformed the pedigree equivalent in terms of prediction accuracy (0.51 opposed to 0.31). Overall, low coverage GBS has proven to be a cost-effective genotyping platform that is expected to boost the selection efficiency of the Arctic charr breeding program.

scholarly journals Efficient Algorithms for Calculating Epistatic Genomic Relationship Matrices

Genetics ◽  
2020 ◽  
Vol 216 (3) ◽  
pp. 651-669
Author(s):  
Yong Jiang ◽  
Jochen C. Reif
Keyword(s):  
Hadamard Product ◽  
Association Studies ◽  
Complete Solution ◽  
Natural Generalization ◽  
Genomic Relationship Matrix ◽  
Relationship Matrix ◽  
Genome Wide Association Studies ◽  
Genomic Relationship ◽  
Genome Wide ◽  
High Degree

The genomic relationship matrix plays a key role in the analysis of genetic diversity, genomic prediction, and genome-wide association studies. The epistatic genomic relationship matrix is a natural generalization of the classic genomic relationship matrix in the sense that it implicitly models the epistatic effects among all markers. Calculating the exact form of the epistatic relationship matrix requires high computational load, and is hence not feasible when the number of markers is large, or when high-degree of epistasis is in consideration. Currently, many studies use the Hadamard product of the classic genomic relationship matrix as an approximation. However, the quality of the approximation is difficult to investigate in the strict mathematical sense. In this study, we derived iterative formulas for the precise form of the epistatic genomic relationship matrix for arbitrary degree of epistasis including both additive and dominance interactions. The key to our theoretical results is the observation of an interesting link between the elements in the genomic relationship matrix and symmetric polynomials, which motivated the application of the corresponding mathematical theory. Based on the iterative formulas, efficient recursive algorithms were implemented. Compared with the approximation by the Hadamard product, our algorithms provided a complete solution to the problem of calculating the exact epistatic genomic relationship matrix. As an application, we showed that our new algorithms easily relieved the computational burden in a previous study on the approximation behavior of two limit models.

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