Bpop: an efficient program for estimating base population allele frequencies in single and multiple group structured populations

Base population allele frequencies (AF) should be used in genomic evaluations. A program named Bpop was implemented to estimate base population AF using a generalized least squares (GLS) method when the base population individuals can be assigned to groups. The required dense matrix products involving (A22 )-1v were implemented efficiently using sparse submatrices of A-1, where A and A22 are pedigree relationship matrices for all and genotyped animals, respectively. Three approaches were implemented: iteration on pedigree (IOP), iteration in memory (IM), and direct inversion by sparsity preserving Cholesky decomposition (CHM). The test data had 1.5 million animals genotyped using 50240 markers. Total computing time (the product (A22)-11) was 53 min (1.2 min) by IOP, 51 min (0.3 min) by IM, and 56 min (4.6 min) by CHM. Peak computer core memory use was 0.67 GB by IOP, 0.80 GB by IM, and 7.53 GB by CHM. Thus, the IOP and IM approaches can be recommended for large data sets because of their low memory use and computing time

Snp_blup_rel: software for calculating individual animal SNP-BLUP model reliabilities

The snp_blup_rel program computes model reliabilities for genomic breeding values. The program assumes a single trait SNP-BLUP model where the breeding value can include a residual polygenic (RPG) effect. The reliability calculation requires elements of the inverse of the mixed model equations (MME). The calculation has three steps: 1) MME calculation, 2) MME coefficient matrix inversion, and 3) reliability computation. When needed, the inverted matrix can be saved after step 2. Step 3 can be used separately to new genotypes which do not contribute information to Step 2. When an RPG effect is included, an approximate method based on Monte Carlo sampling is applied. This reduces the MME matrix size and allows including many genotyped individuals. The program is written in Fortran 90/95, and uses LAPACK subroutines which enable multi-threaded parallel computing. The program is efficient in terms of computing time and memory requirements, and can be used to analyze even large genomic data. Thus, the program can be used in calculating model reliabilities for large national genomic evaluations

Estimation of genetic parameters for test-day milk production at different stages of lactation of Finnish Ayrshire heifers

Genetic parameters for test-day milk production at different stages of lactation of Finnish Ayrshire heifers were estimated with the REML method using the AI algorithm and animal model. The data consisted of 38 679 first lactation test-day milk yields of 4205 cows from 231 herds in three geographical regions (North Savo, Central Ostrobothnia and Lapland). To identify different test days, records were numbered according to the days in milk after calving, and were further categorized into three part-lactations according to the test-day classification. Expressions in the three part-lactations were considered as separate traits, and tests were treated as repeated observations within the trait. Heritability estimates for test-day milk yield varied between 0.11 and 0.17, being lowest at the beginning of lactation. Genetic correlations between test-day milk yields at different trimesters ranged from 0.64 to 0.91, being highest between consecutive trimesters. Standard errors of the estimates of genetic parameters varied between 0.02 and 0.08. Genetic interrelationships differed from 1.0, supporting the assumption that genetic variation exists in the shape of the lactation curve. The necessity of considering deviations from the general lactation curve in the test-day model, e.g. fitting random regression coefficients, is discussed

Relationship between bull dam herd characteristics and bias in estimated breeding value of bull

The objective of the study was to relate estimated breeding values (EBVs) of the parents’ 305-days protein production and the bull dam herd-year characteristics to the empirical bias in pedigree indices (difference between the pedigree index and the final proof) of young bulls. Two animal model evaluations were carried out; one included records up to 1990 and the other up to spring 1992. The final data set included 242 bulls with pedigree indices, final proofs, parents’ EBVs, production and herd information (the size, the average production and the intraherd standard deviation) of the dams. The average empirical bias in pedigree indices was 13.6 kg. The correlation between the final proof of the bull and the EBVs of the bull sire or dam were 0.45 and 0.17, respectively. The low correlation with bull dam EBV indicates the unreliability of the bull dam EBVs. Size of the herd and the standard deviation of production in the herd when bull dam produced its third lactation were correlated with the empirical bias in pedigree index. Pedigree indices of the bulls coming from small herds with high intraherd standard deviation were more biased than those from the big herds with low intraherd standard deviation. The best bulls, when grouped according to their final proofs, were sons of the highest EBV sires. EBVs of bull dams did not differ in the highest and the lowest final proof groups, but the dams of the best bull group had a higher first lactation record than the dams of the other bull groups

Genomic prediction in a Finnish breeding programme of six-row barley

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Estimation of non-linear growth models by linearization: a simulation study using a Gompertz function

A method based on Taylor series expansion for estimation of location parameters and variance components of non-linear mixed effects models was considered. An attractive property of the method is the opportunity for an easily implemented algorithm. Estimation of non-linear mixed effects models can be done by common methods for linear mixed effects models, and thus existing programs can be used after small modifications. The applicability of this algorithm in animal breeding was studied with simulation using a Gompertz function growth model in pigs. Two growth data sets were analyzed: a full set containing observations from the entire growing period, and a truncated time trajectory set containing animals slaughtered prematurely, which is common in pig breeding. The results from the 50 simulation replicates with full data set indicate that the linearization approach was capable of estimating the original parameters satisfactorily. However, estimation of the parameters related to adult weight becomes unstable in the case of a truncated data set

Employing a Monte Carlo algorithm in Newton-type methods for restricted maximum likelihood estimation of genetic parameters

201

Molecular genetic polymorphism at the κ-casein and β-lactoglobulin loci in Finnish dairy hulls

Dairy bulls have been genotyped for K-casein and P-lactoglobulin from semen samples by methodology based on a polymerase chain reaction (PCR), In this study, a previously described method for κ-casein A and B variants was extended to cover also the detection of the E variant. For β-lactoglobulin the variants A and B were genotyped by another PCR-based method. The frequencies of the κ-casein and β-lactoglobulin alleles were determined from 308 and 291 Finnish Ayrshire and 42 and 44 Finnish Friesian bulls, respectively. The bulls had been born between 1973 and 1988. There was no noticeable trend in the differences between allele frequencies over the years, the overall frequencies of κ-casein A, B and E being 0.62, 0.09 and 0.29 in the Finnish Ayrshires and 0.85, 0.14 and 0.01 in Finnish Friesians. The overall frequencies of β-lactoglobulin A and B alleles were 0.25 and 0.75 in Ayrshires and 0.56 and 0.44 in Friesian