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On the approximation of interaction effect models by Hadamard powers of the additive genomic relationship

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  • Martini, Johannes W.R.
  • Toledo, Fernando H.
  • Crossa, José

Abstract

Whole genome epistasis models with interactions between different loci can be approximated by genomic relationship models based on Hadamard powers of the additive genomic relationship. We illustrate that the quality of this approximation reduces when the degree of interaction d increases. Moreover, considering relationship models defined as weighted sum of interactions of different degree, we investigate the impact of this decreasing quality of approximation of the summands on the approximation of the weighted sum. Our results indicate that these approximations remain on a reliable level, but their quality reduces when the weights of interactions of higher degrees do not decrease quickly.

Suggested Citation

  • Martini, Johannes W.R. & Toledo, Fernando H. & Crossa, José, 2020. "On the approximation of interaction effect models by Hadamard powers of the additive genomic relationship," Theoretical Population Biology, Elsevier, vol. 132(C), pages 16-23.
    • Handle: RePEc:eee:thpobi:v:132:y:2020:i:c:p:16-23
    DOI: 10.1016/j.tpb.2020.01.004
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    References listed on IDEAS

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    1. Ulrike Ober & Wen Huang & Michael Magwire & Martin Schlather & Henner Simianer & Trudy F C Mackay, 2015. "Accounting for Genetic Architecture Improves Sequence Based Genomic Prediction for a Drosophila Fitness Trait," PLOS ONE, Public Library of Science, vol. 10(5), pages 1-17, May.
    2. Guosheng Su & Ole F Christensen & Tage Ostersen & Mark Henryon & Mogens S Lund, 2012. "Estimating Additive and Non-Additive Genetic Variances and Predicting Genetic Merits Using Genome-Wide Dense Single Nucleotide Polymorphism Markers," PLOS ONE, Public Library of Science, vol. 7(9), pages 1-7, September.
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