Background: Genetic interactions involving more than two loci have been thought to affect quantitatively inherited traits and diseases more pervasively than previously appreciated. However, the detection of such high-order interactions to chart a complete portrait of genetic architecture has not been well explored. Methods: We present an ultrahigh-dimensional model to systematically characterize genetic main effects and interaction effects of various orders among all possible markers in a genetic mapping or association study. The model was built on the extension of a variable selection procedure, called iFORM, derived from forward selection. The model shows its unique power to estimate the magnitudes and signs of high-order epistatic effects, in addition to those of main effects and pairwise epistatic effects. Results: The statistical properties of the model were tested and validated through simulation studies. By analyzing a real data for shoot growth in a mapping population of woody plant, mei (Prunus mume), we demonstrated the usefulness and utility of the model in practical genetic studies. The model has identified important high-order interactions that contribute to shoot growth for mei. Conclusion: The model provides a tool to precisely construct genotype-phenotype maps for quantitative traits by identifying any possible high-order epistasis which is often ignored in the current genetic literature.
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