DOI: 10.5061/dryad.nm290/4
title: Simulated Data - Part 3

description: Ten replicates of a livestock data structure were simulated. The structure was designed to cover a spectrum of QTL distributions, relationship structures, and SNP densities and to mimic some of the scenarios where genomic selection is applied. In each replicate sequence data for 4000 base haplotypes for each of thirty chromosomes was simulated using the Markovian Coalescence Simulator (MaCS) (Chen et al., 2009). The thirty chromosomes were each 100 cM in length comprising approximately 108 base pairs and were simulated using a per site mutation rate of 2.5*10-8 and an effective population size (Ne) of 100 in the final generation of the sequence simulation. The reduction of Ne in the preceding generations was modeled with a Ne 1,000 years ago of 1,256, a Ne 10,000 years ago of 4,350, and a Ne 100,000 years ago of 43,500 with linear changes in between. This reflects estimates by Villa-Angulo et al. (2009) for the Holstein population. A pedigree was simulated comprising 10 generations of individuals, with 50 sires per generation, 10 dams per sire, and 2 offspring per dam. Base individuals in the pedigree had their gametes randomly sampled from the 4000 haplotypes of the sequence simulation allowing for recombination according to the genetic distance using 1% probability of a recombination event per cM. Subsequent generations in the pedigree had their gametes generated through Mendelian inheritance with recombination. The total number of segregating sites across the resulting genome was approximately 1,670,000. A random sample of 60,000 segregating sites was selected from the sequence to be used as SNP on a 60,000 SNP array. In addition a set of 9,000 segregating sites were randomly selected from the sequence to be used as candidate QTL loci in two different ways, one a randomly sampled set and the other being a randomly sampled set with the restriction that their minor allele frequency could not exceed 0.30. Four different traits were simulated assuming an additive genetic model. The first pair of traits was generated using the 9,000 unrestricted candidate QTL loci. For the first trait (PolyUnres) the allele substitution effect at each QTL locus was sampled from a normal distribution with a mean of zero and standard deviation of one unit. For the second trait (GammaUnres) a random subset of 900 of the candidate QTL loci were selected and their allele substitution effects at each QTL locus were sampled from a gamma distribution with a shape of 0.4 and scale of 1.66 (Meuwissen et al., 2001) and a 50% chance of being positive or negative. The second pair of traits (PolyRes and GammaRes) was generated in the same way as the first pair except that the candidate QTL loci comprised the 9,000 with the restriction that their minor allele frequency could not exceed 0.30. Phenotypes with a heritability of 0.25 were generated for each trait. To ensure that the heritability of the four traits remained constant the residual variance was scaled relative to the variance of the breeding values of individuals in the base generation, which was given by a'a/(n-1), where a is a vector of breeding value of individuals in the base generation and n is the number of individuals in that generation. Ten replicates of each scenario were simulated.

Training and validation data sets Subsets of the data were extracted for training and validation. The training set comprised the 2000 individuals in generations 4 and 5. Three validation sets were extracted. The first (Gen6) comprised 500 individuals sampled at random from generation 6. The second (Gen8) comprised 500 individuals sampled at random from generation 8. The third (Gen10) comprised 500 individuals sampled at random from generation 10.