Computing inbreeding coefficients and the inverse numerator relationship matrix in large populations of honey bees

2018 ◽  
Vol 135 (4) ◽  
pp. 323-332 ◽  
Author(s):  
Richard Bernstein ◽  
Manuel Plate ◽  
Andreas Hoppe ◽  
Kaspar Bienefeld
Keyword(s):  
Honey Bees ◽  
Relationship Matrix ◽  
Inbreeding Coefficients ◽  
Numerator Relationship Matrix ◽  
Large Populations

scholarly journals Alternative Ways of Computing the Numerator Relationship Matrix

2021 ◽  
Vol 12 ◽  
Author(s):  
Mohammad Ali Nilforooshan ◽  
Dorian Garrick ◽  
Bevin Harris
Keyword(s):  
Litter Size ◽  
Computation Time ◽  
Computational Time ◽  
Pedigree Information ◽  
Relationship Matrix ◽  
Memory Usage ◽  
Inbreeding Coefficients ◽  
Evaluation Procedures ◽  
Numerator Relationship Matrix ◽  
R Programming

Pedigree relationships between every pair of individuals forms the elements of the additive genetic relationship matrix (A). Calculation of A−1 does not require forming and inverting A, and it is faster and easier than the calculation of A. Although A−1 is used in best linear unbiased prediction of genetic merit, A is used in population studies and post-evaluation procedures, such as breeding programs and controlling the rate of inbreeding. Three pedigrees with 20,000 animals (20K) and different (1, 2, 4) litter sizes, and a pedigree with 180,000 animals (180K) and litter size 2 were simulated. Aiming to reduce the computation time for calculating A, new methods [Array-Tabular method, (T−1)−1 instead of T in Thompson's method, iterative updating of D in Thompson's method, and iteration by generation] were developed and compared with some existing methods. The methods were coded in the R programming language to demonstrate the algorithms, aiming for minimizing the computational time. Among 20K, computational time decreased with increasing litter size for most of the methods. Methods deriving A from A−1 were relatively slow. The other methods were either using only pedigree information or both the pedigree and inbreeding coefficients. Calculating inbreeding coefficients was extremely fast (<0.2 s for 180K). Parallel computing (15 cores) was adopted for methods that were based on solving A−1 for columns of A, as those methods allowed implicit parallelism. Optimizing the code for one of the earliest methods enabled A to be built in 13 s (faster than the 31 s for calculating A−1) for 20K and 17 min 3 s for 180K. Memory is a bottleneck for large pedigrees but attempts to reduce the memory usage increased the computational time. To reduce disk space usage, memory usage, and computational time, relationship coefficients of old animals in the pedigree can be archived and relationship coefficients for parents of the next generation can be saved in an external file for successive updates to the pedigree and the A matrix.

scholarly journals 37 Sibs: an R toolkit for computation of relatedness measures using large pedigrees

2020 ◽  
Vol 98 (Supplement_3) ◽  
pp. 41-42
Author(s):  
B Victor Oribamise ◽  
Lauren L Hulsman Hanna
Keyword(s):  
Family Structure ◽  
Genetic Relatedness ◽  
Current User ◽  
Memory Allocation ◽  
Relationship Matrix ◽  
Additive Effects ◽  
Numerator Relationship Matrix ◽  
Significant Difference ◽  
R Packages ◽  
User Friendly

Abstract Without appropriate relationships present in a given population, identifying dominance effects in the expression of desirable traits is challenging. Including non-additive effects is desirable to increase accuracy of breeding values. There is no current user-friendly tool package to investigate genetic relatedness in large pedigrees. The objective was to develop and implement efficient algorithms in R to calculate and visualize measures of relatedness (e.g., sibling and family structure, numerator relationship matrices) for large pedigrees. Comparisons to current R packages (Table 1) are also made. Functions to assign animals to families, summary of sibling counts, calculation of numerator relationship matrix (NRM), and NRM summary by groups were created, providing a comprehensive toolkit (Sibs package) not found in other packages. Pedigrees of various sizes (n = 20, 4,035, 120,000 and 132,833) were used to test functionality and compare to current packages. All runs were conducted on a Windows-based computer with an 8 GB RAM, 2.5 GHz Intel Core i7 processor. Other packages had no significant difference in runtime when constructing the NRM for small pedigrees (n = 20) compared to Sibs (0 to 0.05 s difference). However, packages such as ggroups, AGHmatrix, and pedigree were 10 to 15 min slower than Sibs for a 4,035-individual pedigree. Packages nadiv and pedigreemm competed with Sibs (0.30 to 60 s slower than Sibs), but no package besides Sibs was able to complete the 132,833-individual pedigree due to memory allocation issues in R. The nadiv package was closest with a pedigree of 120,000 individuals, but took 37 min to complete (13 min slower than Sibs). This package also provides easier input of pedigrees and is more encompassing of such relatedness measures than other packages (Table 1). Furthermore, it can provide an option to utilize other packages such as GCA for connectedness calculations when using large pedigrees.

scholarly journals Reduced Animal Models Fitting Only Equations for Phenotyped Animals

2021 ◽  
Vol 12 ◽  
Author(s):  
Mohammad Ali Nilforooshan ◽  
Dorian Garrick
Keyword(s):  
Animal Model ◽  
Animal Models ◽  
Mixed Model ◽  
Reduced Model ◽  
Relationship Matrix ◽  
Full Model ◽  
Breeding Values ◽  
Reduced Animal Model ◽  
Numerator Relationship Matrix ◽  
Model Equations

Reduced models are equivalent models to the full model that enable reduction in the computational demand for solving the problem, here, mixed model equations for estimating breeding values of selection candidates. Since phenotyped animals provide data to the model, the aim of this study was to reduce animal models to those equations corresponding to phenotyped animals. Non-phenotyped ancestral animals have normally been included in analyses as they facilitate formation of the inverse numerator relationship matrix. However, a reduced model can exclude those animals and obtain identical solutions for the breeding values of the animals of interest. Solutions corresponding to non-phenotyped animals can be back-solved from the solutions of phenotyped animals and specific blocks of the inverted relationship matrix. This idea was extended to other forms of animal model and the results from each reduced model (and back-solving) were identical to the results from the corresponding full model. Previous studies have been mainly focused on reduced animal models that absorb equations corresponding to non-parents and solve equations only for parents of phenotyped animals. These two types of reduced animal model can be combined to formulate only equations corresponding to phenotyped parents of phenotyped progeny.

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.

Use of the numerator relationship matrix in genetic analysis of autopolyploid species

2012 ◽  
Vol 124 (7) ◽  
pp. 1271-1282 ◽  
Author(s):  
Richard J. Kerr ◽  
Li Li ◽  
Bruce Tier ◽  
Gregory W. Dutkowski ◽  
Thomas A. McRae
Keyword(s):  
Genetic Analysis ◽  
Relationship Matrix ◽  
Numerator Relationship Matrix

scholarly journals Restricting coancestry and inbreeding at a specific position on the genome by using optimized selection

2008 ◽  
Vol 90 (2) ◽  
pp. 199-208 ◽  
Author(s):  
T. ROUGHSEDGE ◽  
R. PONG-WONG ◽  
J.A. WOOLLIAMS ◽  
B. VILLANUEVA
Keyword(s):  
Genetic Markers ◽  
Genetic Gain ◽  
Allele Frequencies ◽  
Random Selection ◽  
Relationship Matrix ◽  
Numerator Relationship Matrix ◽  
Specific Position ◽  
The Relationship ◽  
Selection Of

SummaryOver recent years, selection methodologies have been developed to allow the maximization of genetic gain whilst constraining the rate of inbreeding. The desired rate of inbreeding is achieved by constraining the group coancestry using the numerator relationship matrix computed from pedigree. It is shown that when the method is applied to mixed inheritance models, where a QTL is segregating together with polygenes, the rate of inbreeding achieved in the region around a QTL is greater than the desired level. The constraint on group coancestry at specific positions around the QTL is achieved by using a relationship matrix computed from pedigree and genetic markers. However, the rate of inbreeding realized at the position of constraint is lower than that expected given the assumed relationship between group coancestry and the subsequent rate of inbreeding. The use of markers in the calculation of the relationship matrix allows the selection of candidates with very low or zero relationships because they are homozygous for alternative alleles, which results in a heterozygosity amongst their offspring higher than would be expected given their allele frequencies. A generation of random selection restored the expected relationship between group coancestry and inbreeding.

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