Estimation and Interpretation of Genetic Effects with Epistasis Using the NOIA Model

  • José M. Álvarez-CastroEmail author
  • Örjan Carlborg
  • Lars Rönnegård
Part of the Methods in Molecular Biology book series (MIMB, volume 871)


We introduce this communication with a brief outline of the historical landmarks in genetic modeling, especially concerning epistasis. Then, we present methods for the use of genetic modeling in QTL analyses. In particular, we summarize the essential expressions of the natural and orthogonal interactions (NOIA) model of genetic effects. Our motivation for reviewing that theory here is twofold. First, this review presents a digest of the expressions for the application of the NOIA model, which are often mixed with intermediate and additional formulae in the original articles. Second, we make the required theory handy for the reader to relate the genetic concepts to the particular mathematical expressions underlying them. We illustrate those relations by providing graphical interpretations and a diagram summarizing the key features for applying genetic modeling with epistasis in comprehensive QTL analyses. Finally, we briefly review some examples of the application of NOIA to real data and the way it improves the interpretability of the results.

Key words

Change of reference Epistasis Genetic effects Hardy–Weinberg disequilibrium Multiple alleles NOIA QTL 



Rong-Cai Yang has contributed to the development of the models of genetic effects that we have reviewed within this book chapter. Carl Nettelblad has extensively worked on the IMI, on which we have also commented. JÁC acknowledges funding by an “Isidro Parga Pondal” contract from the autonomous administration Xunta de Galicia and from project BFU2009-11988 from the Spanish Ministry of Science. ÖC is funded by a EURYI Award from ESF and a Future Research Leader Grant from the Swedish Foundation for Strategic Research. LR recognizes financial support by the Swedish Research Council FORMAS.


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Copyright information

© Springer Science+Business Media 2012

Authors and Affiliations

  • José M. Álvarez-Castro
    • 1
    Email author
  • Örjan Carlborg
    • 2
    • 3
  • Lars Rönnegård
    • 4
  1. 1.Department of GeneticsUniversity of Santiago de CompostelaLugoSpain
  2. 2.Department of Animal Breeding and GeneticsSwedish University of Agricultural SciencesUppsalaSweden
  3. 3.Department of Cell and Molecular BiologyUppsala UniversityUppsalaSweden
  4. 4.Statistics UnitDalarna UniversityBorlängeSweden

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