Conservation & local programs

Rapid approximation of principal components from hybrid pedigree and genomic relatedness for population structure analysis

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Abstract

Visualising the patterns of relatedness is important for understanding population structure, managing genetic diversity, and the definition of sup-populations for estimation of breeding values. Current tools for visualising patterns of genetic relatedness among individuals, such as principal component analysis (PCA), use either pedigree or genotype data, but not both. They work with the pedigree or genotype relatedness matrices A and G, but not with the hybrid (pedigree-genotype) relatedness matrix H. The use of the H matrix is increasingly popular in breeding programmes, because it combines all the available data and hence provides a more accurate picture of relatedness between individuals. This is because information from genotyped animals is propagated through the pedigree, updating the pedigree relatedness between non-genotyped individuals. However, a naïve construction and PCA of the H matrix require combining a dense G with a large A. As the size of these matrices grows, direct computation becomes infeasible. Here, we implement an efficient PCA of the hybrid relatedness matrix H, by using randomised singular value decomposition and indirect matrix-vector product algorithms. We use Colleau's algorithms for indirect matrix-vector products Ax and Hx, which exploit the sparsity of the pedigree data and associated precision matrices A-1 and H-1. The implemented PCA method thence does not need to form A, G, nor H. The method is available in the function rhpca, in the RandPedPCA R package. To test the method, we used a synthetic pedigree and genotype data for a simulated population with strong structure generated with the forward-in-time simulator AlphaSimR. We evaluated the performance of hybrid-PCA on whole population and compare it with pedigree-PCA on whole population and genotype-PCA on the genotyped individuals and whole population (for comparison). Consistent with previous work, the resulting principal components of genetic relatedness matrices can be computed efficiently using randomised singular value decomposition and provide an intuitive way to visualise genetic relatedness and population structure.

Keywords: 2026

How to Cite:

Ortiz-Cuadros, J., Becher, H., Tsairidou, S. & Gorjanc, G., (2026) “Rapid approximation of principal components from hybrid pedigree and genomic relatedness for population structure analysis”, World Congress on Genetics Applied to Livestock Production Digital Archive 2026(1): 2283847. doi: https://doi.org/10.31274/wcgalp.23525

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