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Estimating heritabilities with large genomic models by established methods such as restricted maximum likelihood (REML) or Bayesian via Gibbs sampling is computationally expensive. Alternatively, heritability can be estimated indirectly by method R and by maximum predictivity, referred to as MaxPred here, at a much lower computing cost. By method R, the heritability used for predictions with whole and partial data is considered the best estimate when the predictions based on partial data are unbiased relative to those with the complete data. By MaxPred, the heritability estimate is the one that maximizes predictivity. This study compared heritability estimation with genomic information using average information REML (AI–REML), method R and MaxPred. A simulated population was generated with ten generations of 5000 animals each and an effective population size of 80. Each animal had one record for a trait with a heritability of 0.3, a phenotypic variance of 10.0 and was genotyped at 50 k SNP. In method R, the heritability estimate is found when the expectation of a regression coefficient is equal to one. The regression is the EBV of selection candidates calculated with the whole dataset regressed on the EBV of candidates calculated from a partial dataset. In this study, we used the GBLUP framework and therefore, GEBV was calculated. The partial dataset was created by removing the last generation of phenotypes. Predictivity was defined as the correlation between the adjusted phenotypes of the selection candidates and their GEBV calculated from the partial data. We estimated the heritability for populations that included between three and 10 generations. In every scenario, predictivity increased as more data was used and was the highest at the simulated heritability. However, the predictivity for all data subsets and all heritabilities compared did not differ more than 0.01, suggesting MaxPred is not the best indication for heritability estimation. For the whole dataset, the heritability was estimated as 0.30 ± 0.01, 0.26 ± 0.01 and 0.30 ± 0.04 for AI–REML without genomics, AI–REML with genomics and method R with genomics, respectively. Heritability estimation with genomics by method R reduced timing by 83%, implying a reduction in computing time from 9.5 to 1.6 h, on average, compared to AI–REML with genomics. Method R has the potential to estimate heritabilities with large genomic information at a low cost when many generations of animals are present; however, the standard error can be high when only a few iterations are used. [ABSTRACT FROM AUTHOR]

The objective of this study was to determine whether the linear regression (LR) method could be used to validate genomic threshold models. Statistics for the LR method were computed from estimated breeding values (EBVs) using the whole and truncated data sets with variances from the reference and validation populations. The method was tested using simulated and real chicken data sets. The simulated data set included 10 generations of 4,500 birds each; genotypes were available for the last three generations. Each animal was assigned a continuous trait, which was converted to a binary score assuming an incidence of failure of 7%. The real data set included the survival status of 186,596 broilers (mortality rate equal to 7.2%) and genotypes of 18,047 birds. Both data sets were analysed using best linear unbiased predictor (BLUP) or single‐step GBLUP (ssGBLUP). The whole data set included all phenotypes available, whereas in the partial data set, phenotypes of the most recent generation were removed. In the simulated data set, the accuracies based on the LR formulas were 0.45 for BLUP and 0.76 for ssGBLUP, whereas the correlations between true breeding values and EBVs (i.e. true accuracies) were 0.37 and 0.65, respectively. The gain in accuracy by adding genomic information was overestimated by 0.09 when using the LR method compared to the true increase in accuracy. However, when the estimated ratio between the additive variance computed based on pedigree only and on pedigree and genomic information was considered, the difference between true and estimated gain was <0.02. Accuracies of BLUP and ssGBLUP with the real data set were 0.41 and 0.47, respectively. This small improvement in accuracy when using ssGBLUP with the real data set was due to population structure and lower heritability. The LR method is a useful tool for estimating improvements in accuracy of EBVs due to the inclusion of genomic information when traditional validation methods as k‐fold validation and predictive ability are not applicable. [ABSTRACT FROM AUTHOR]

Independent chromosome segments for a population with Ne effective population size and L genome length can be approximately defined as 4NeL non-overlapping haplotypes of L/2 length derived from any Ne animals. The number of independent chromosome segments (Me) can be approximated as 4NeL. The genetic selection with a genomic relationship matrix (GRM) using such haplotypes approaches that with a GRM using the SNP markers. The objective of this study was to investigate the statistical nature of independent chromosome segments. Data were simulated using QMSim and contained a population of ten nonoverlapping generations, each including 2,000 animals with Ne equal to 20, and a polygenic trait with a heritability of 0.6. The last three generations were genotyped, and each genome contained ten 1 M long chromosomes, for a total genome length of 10 M and 50,000 SNP. Chromosome segments of each animal were organized in non-overlapping haplotypes by the SNP code using in-house software written in Fortran. The effects of the hypothetical independent chromosome segments were estimated using a model that included an overall mean plus the segment effects. To analyze the behavior around Me, the number of segments chosen to estimate segment effects varied around 4NeL. Accuracies were calculated for animals in the last generation by cor (TBV, Zsŝ), where Zs ŝ is a vector of breeding values based on segments and TBV is a vector of the true breeding values outputted by QMSim. Accuracies of segment effects were compared with the true accuracy, i.e., cor (TBV,GEBV). The maximum accuracy of segment effects was 0.84, and the true accuracy was 0.96. The results suggest that 4NeL segments contain most of the additive information in the population. However, the accuracy of GBLUP is greater than that of the chromosome segment effects, suggesting that arranging chromosome segments based solely on the statistical nature is not enough to account for all the genetic variation. [ABSTRACT FROM AUTHOR]