ArticleGenetics2020
Efficient Algorithms for Calculating Epistatic Genomic Relationship Matrices.
Article in Genetics, 2020. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 17 papers.
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17 citing papers in PubMed, 28 citations in OpenAlex.
- Haplotype applications in genomic selection.Genome biology · 2026Review
- The effect of haplotype size on genomic selection accuracy and epistasis: An empirical study in rice.The plant genome · 2025Article
- Powerful one-dimensional scan to detect heterotic quantitative trait loci.Nature communications · 2025Article
- Genomic Prediction and Heritability Estimation for Daughter Pregnancy Rate in U.S. Holstein Cows Using SNP, Epistasis and Haplotype Effects.International journal of molecular sciences · 2025Article
- ACOCMPMI: An Ant Colony Optimization Algorithm Based on Composite Multiscale Part Mutual Information for Detecting Epistatic Interactions.Human mutation · 2025Article
- GA-GBLUP: leveraging the genetic algorithm to improve the predictability of genomic selection.Briefings in bioinformatics · 2024Article
- Article
- Genomic prediction for sugarcane diseases including hybrid Bayesian-machine learning approaches.Frontiers in plant science · 2024Article
- Genomic prediction with machine learning in sugarcane, a complex highly polyploid clonally propagated crop with substantial non-additive variation for key traits.The plant genome · 2023Article
- Comparison of the Accuracy of Epistasis and Haplotype Models for Genomic Prediction of Seven Human Phenotypes.Biomolecules · 2023Article
- Genomic predictions to leverage phenotypic data across genebanks.Frontiers in plant science · 2023Article
- Impact of epistasis effects on the accuracy of predicting phenotypic values of residual feed intake in U. S Holstein cows.Frontiers in genetics · 2022Article
- Incorporating Omics Data in Genomic Prediction.Methods in molecular biology (Clifton, N.J.) · 2022Article
- Genomic Prediction Methods Accounting for Nonadditive Genetic Effects.Methods in molecular biology (Clifton, N.J.) · 2022Article
- Multifactorial methods integrating haplotype and epistasis effects for genomic estimation and prediction of quantitative traits.Frontiers in genetics · 2022Article
- Accounting for epistasis improves genomic prediction of phenotypes with univariate and bivariate models across environments.TAG. Theoretical and applied genetics. Theoretische und angewandte Genetik · 2021Article
- Genomic prediction with non-additive effects in beef cattle: stability of variance component and genetic effect estimates against population size.BMC genomics · 2021Article
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Authors and funding
2 authors at 1 institution in 1 country.
Funding
No grant is acknowledged in the PubMed record.
Abstract
The genomic relationship matrix plays a key role in the analysis of genetic diversity, genomic prediction, and genome-wide association studies. The epistatic genomic relationship matrix is a natural generalization of the classic genomic relationship matrix in the sense that it implicitly models the epistatic effects among all markers. Calculating the exact form of the epistatic relationship matrix requires high computational load, and is hence not feasible when the number of markers is large, or when high-degree of epistasis is in consideration. Currently, many studies use the Hadamard product of the classic genomic relationship matrix as an approximation. However, the quality of the approximation is difficult to investigate in the strict mathematical sense. In this study, we derived iterative formulas for the precise form of the epistatic genomic relationship matrix for arbitrary degree of epistasis including both additive and dominance interactions. The key to our theoretical results is the observation of an interesting link between the elements in the genomic relationship matrix and symmetric polynomials, which motivated the application of the corresponding mathematical theory. Based on the iterative formulas, efficient recursive algorithms were implemented. Compared with the approximation by the Hadamard product, our algorithms provided a complete solution to the problem of calculating the exact epistatic genomic relationship matrix. As an application, we showed that our new algorithms easily relieved the computational burden in a previous study on the approximation behavior of two limit models.
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