Understanding the genetic architecture underpinning quantitative traits in wild populations is pivotal to understanding the processes behind trait evolution. The ‘animal model’ is a popular method for estimating quantitative genetic parameters such as heritability and genetic correlation and involves fitting an estimate of relatedness between individuals in the study population. Genotypes at genome‐wide markers can be used to estimate relatedness; however, relatedness estimates vary with marker density, potentially affecting results. Increasing density of markers is also expected to increase the power to detect quantitative trait loci (QTL). In order to understand how the density of genetic markers affects the results of quantitative genetic analyses, we estimated heritability and performed genome‐wide association studies (GWAS) on five body size traits in an unmanaged population of Soay sheep using two different SNP densities: a dataset of 37,037 genotyped SNPs and an imputed dataset of 417,373 SNPs. Heritability estimates did not differ between the two SNP densities, but the high‐density imputed SNP dataset revealed four new SNP‐trait associations that were not found with the lower density dataset, as well as confirming all previously‐found QTL. We also demonstrated that fitting fixed and random effects in the same step as performing GWAS is a more powerful approach than pre‐correcting for covariates in a separate model.

Estimates of narrow sense heritability derived from genomic data that contain related individuals may be biased due to the within-family effects such as dominance, epistasis and common environmental factors. However, for many wild populations, removal of related individuals from the data would result in small sample sizes. In 2013, Zaitlen et al. proposed a method to estimate heritability in populations that include close relatives by simultaneously fitting an identity-by-state genomic relatedness matrix (GRM) and an identity-by-descent GRM. The IBD GRM is identical to the IBS GRM, except relatedness estimates below a specified threshold are set to 0. We applied this method to a sample of 8557 wild Soay sheep from St. Kilda, with genotypic information for 419,281 single nucleotide polymorphisms to investigate polygenic and monogenic traits. We also implemented a variant of the model in which the IBD GRM was replaced by a GRM constructed from SNPs with low minor allele frequency to examine whether any additive genetic variance is captured by rare alleles. Each model was compared to an animal model with a single GRM based on all genotyped markers (the IBS GRM) using a log likelihood ratio test. Whilst the inclusion of the IBD GRM did not significantly improve the fit of the model for the monogenic traits, it improved the fit for some of the polygenic traits, suggesting that dominance, epistasis and/or common environment not already captured by the non-genetic random effects fitted in our models may influence these traits.

Understanding the genetic architecture underpinning quantitative traits in wild populations is pivotal to understanding the processes behind trait evolution. The ‘animal model’ is a popular method for estimating quantitative genetic parameters such as heritability and genetic correlation and involves fitting an estimate of relatedness between individuals in the study population. Genotypes at genome-wide markers can be used to estimate relatedness; however, relatedness estimates vary with marker density, potentially affecting results. Increasing density of markers is also expected to increase the power to detect quantitative trait loci (QTL). We estimated heritability and performed genome-wide association studies (GWAS) on five body size traits in an unmanaged population of Soay sheep using two different SNP densities: a dataset of 37,037 genotyped SNPs, and an imputed dataset of 417,373 SNPs. Heritability estimates did not differ between the two SNP densities, but the high-density imputed SNP dataset revealed five new SNP-trait associations that were not found with the lower density dataset. Conditional GWAS analyses after fitting the most significant SNPs revealed two more novel SNP-trait associations.