Comparing Genomic Prediction Models by Means of Cross Validation

In the two decades of continuous development of genomic selection, a great variety of models have been proposed to make predictions from the information available in dense marker panels. Besides deciding which particular model to use, practitioners also need to make many minor choices for those parameters in the model which are not typically estimated by the data (so called “hyper-parameters”). When the focus is placed on predictions, most of these decisions are made in a direction sought to optimize predictive accuracy. Here we discuss and illustrate using publicly available crop datasets the use of cross validation to make many such decisions. In particular, we emphasize the importance of paired comparisons to achieve high power in the comparison between candidate models, as well as the need to define notions of relevance in the difference between their performances. Regarding the latter, we borrow the idea of equivalence margins from clinical research and introduce new statistical tests. We conclude that most hyper-parameters can be learnt from the data by either minimizing REML or by using weakly-informative priors, with good predictive results. In particular, the default options in a popular software are generally competitive with the optimal values. With regard to the performance assessments themselves, we conclude that the paired k-fold cross validation is a generally applicable and statistically powerful methodology to assess differences in model accuracies. Coupled with the definition of equivalence margins based on expected genetic gain, it becomes a useful tool for breeders.

A generic hidden Markov model for multi-parent populations

A common step in the analysis of multi-parent populations is genotype reconstruction: identifying the founder origin of haplotypes from dense marker data. This process often makes use of a probability model for the pattern of founder alleles along chromosomes, including the relative frequency of founder alleles and the probability of exchanges among them, which depend on a model for meiotic recombination and on the mating design for the population. While the precise experimental design used to generate the population may be used to derive a precise characterization of the model for exchanges among founder alleles, this can be tedious, particularly given the great variety of experimental designs that have been proposed. We describe an approximate model that can be applied for a variety of multi-parent populations. We have implemented the approach in the R/qtl2 software, and we illustrate its use in applications to publicly-available data on Diversity Outbred and Collaborative Cross mice.

A general hidden Markov model for multi-parent populations

A common step in the analysis of multi-parent populations is genotype reconstruction: identifying the founder origin of haplotypes from dense marker data. This process often makes use of a model for the exchange process along chromosomes, including the relative frequency of founder alleles and of the probability of exchanges among them. While the precise experimental design used to generate the population may be used to derive a precise characterization of the exchange process, this can be tedious, particularly given the great variety of experimental designs that have been proposed. We describe an approximate model that can be applied for a variety of multi-parent populations. We have implemented the approach in the R/qtl2 software, and we illustrate its use in applications to publicly available data on Diversity Outbred and Collaborative Cross mice.

A study of Genomic Prediction across Generations of Two Korean Pig Populations

Genomic models that incorporate dense marker information have been widely used for predicting genomic breeding values since they were first introduced, and it is known that the relationship between individuals in the reference population and selection candidates affects the prediction accuracy. When genomic evaluation is performed over generations of the same population, prediction accuracy is expected to decay if the reference population is not updated. Therefore, the reference population must be updated in each generation, but little is known about the optimal way to do it. This study presents an empirical assessment of the prediction accuracy of genomic breeding values of production traits, across five generations in two Korean pig breeds. We verified the decay in prediction accuracy over time when the reference population was not updated. Additionally we compared the prediction accuracy using only the previous generation as the reference population, as opposed to using all previous generations as the reference population. Overall, the results suggested that, although there is a clear need to continuously update the reference population, it may not be necessary to keep all ancestral genotypes. Finally, comprehending how the accuracy of genomic prediction evolves over generations within a population adds relevant information to improve the performance of genomic selection.

FarmCPUpp: Efficient Large-Scale GWAS

Genome-wide association studies (GWAS) are computationally demanding analyses that use large sample sizes and dense marker sets to discover associations between quantitative trait variation and genetic variants. FarmCPU is a powerful new method for performing GWAS. However, its performance is hampered by details of its implementation and its reliance on the R programming language. In this paper we present an efficient implementation of FarmCPU, called FarmCPUpp, that retains the R user interface but improves memory management and speed through the use of C++ code and parallel computing.

Estimating inbreeding using dense marker panels and pedigree information

The aim of this simulation study was to compare the accuracy and bias of different inbreeding (F) estimators exploiting dense panels of diallelic markers and pedigree information. All genotype simulations were started by generating an ancestral population at mutation-drift equilibrium considering an effective size of 1000 and a mutation rate (µ) of 5.10-4. Two types of subpopulation were derived from the ancestral population for 10 discrete generations. They differed by the level of selection applied both on males and females: no selection or a structure close to a breeding program with selection of the best 40 males and 500 females on EBV with accuracy of 0.85 and 0.71, respectively, on a trait with heritability of 0.3. Marker panels were made up of 36 000 biallelic markers (18 per cM) and were available for animals in the last 4 generations. Pedigrees were recorded on the last 8 generations. For each scenario, 30 replicates were carried out. Analysed estimators were the correlation (VR1) and regression (VR3) estimators described to build the genomic relationship matrix by VanRaden in 2008. Other estimators included the weighted corrected similarity (WCS) estimator published by Ritland in 1996 and a modified WCS estimator accounting for pedigree information (WPCS). Pedigree-based inbreeding (PED) was also estimated using exhaustive pedigree information. Inbreeding estimates were correlated and regressed to the true simulated genomic F values to assess the precision and bias of estimators, respectively. Main results show that use of dense marker information improves the estimation of F, whatever the scenario. The accuracy of F estimates and the bias were increased in presence of selection, except for PED. Across scenarios, VR3, WCS and WPCS were the most correlated with true F values. In the situation where pedigree was exhaustive, VR3 performed as well as WCS and WPCS but had a larger variability over replicates. Although less biased on average, VR1 was less accurate than other estimators especially when allele frequencies were not properly defined. Accounting for pedigree information into WCS did not increase its estimation accuracy and did not reduce bias in the tested scenarios. Finally, error in estimating inbreeding trends over time in selected populations was greater for some marker-based estimators (VR3, VR1) than PED estimator. WCS and WPCS rendered the most accurate estimations of inbreeding trends. Thus, results indicate that WCS, which can be also used with multiallelic markers, is a promising estimator both to build the genomic relationship matrix for genomic evaluations and to better assess genetic diversity in selected populations.