Skip to main content
SpringerLink
Log in
Book cover

Quantitative Trait Loci (QTL) pp 191–204Cite as

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

  • Protocol
  • First Online:

Part of the book series: Methods in Molecular Biology ((MIMB,volume 871))

Abstract

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.

This is a preview of subscription content, log in via an institution.

Protocol
USD   49.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   89.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Springer Nature is developing a new tool to find and evaluate Protocols. Learn more

References

  1. Fisher RA (1918) The correlation between relatives on the supposition of Mendelian inheritance. Trans Roy Soc Edinburgh 52:339–433

    Google Scholar 

  2. Edwards AW (2000) The genetical theory of natural selection. Genetics 154:1419–1426

    PubMed  CAS  Google Scholar 

  3. Kempthorne O (1997) Heritability: uses and abuses. Genetica 99:109–112

    PubMed  CAS  Google Scholar 

  4. Fisher RA (1930) The genetical theory of natural selection. Clarendon, Oxford

    Google Scholar 

  5. Wright S (1931) Evolution in Mendelian populations. Genetics 16:93–159

    Google Scholar 

  6. Dobzhansky T (1936) Studies on hybrid sterility. II. Location of sterility factors in Drosophila pseudoobscura hybrids. Genetics 21:113–135

    PubMed  CAS  Google Scholar 

  7. Muller HJ (1942) Isolating mechanisms, evolution, and temperature. Biol Symp 6:71–125

    Google Scholar 

  8. Waddington CH (1953) Genetic assimilation of an acquired character. Evolution 7:118–126

    Article  Google Scholar 

  9. Kempthorne O (1954) The correlation between relatives in a random mating population. Proc R Soc Lond B Biol Sci 143:102–113

    Article  PubMed  CAS  Google Scholar 

  10. Kempthorne O (1957) An introduction to genetic statistics. Wiley, New York

    Google Scholar 

  11. Cockerham CC (1954) An extension of the concept of partitioning hereditary variance for analysis of covariances among relatives when epistasis is present. Genetics 39:859–882

    PubMed  CAS  Google Scholar 

  12. Cheverud JM, Routman EJ (1995) Epistasis and its contribution to genetic variance components. Genetics 139:1455–1461

    PubMed  CAS  Google Scholar 

  13. Cheverud JM (2000) Detecting epistasis among quantitative trait loci. In: Wolf JB, Brodie ED, Wade MJ (eds) Epistasis and the evolutionary process. Oxford University Press, Oxford

    Google Scholar 

  14. Mather K, Jinks JL (1982) Introduction to biometrical genetics. Chapman and Hall, London

    Google Scholar 

  15. Hansen TF, Wagner GP (2001) Modeling genetic architecture: a multilinear theory of gene interaction. Theor Popul Biol 59:61–86

    Article  PubMed  CAS  Google Scholar 

  16. Phillips PC (2008) Epistasis—the essential role of gene interactions in the structure and evolution of genetic systems. Nat Rev Genet 9:855–867

    Article  PubMed  CAS  Google Scholar 

  17. Álvarez-Castro JM, Carlborg Ö (2007) A unified model for functional and statistical epistasis and its application in quantitative trait loci analysis. Genetics 176:1151–1167

    Article  PubMed  Google Scholar 

  18. Yang R-C, Álvarez-Castro JM (2008) Functional and statistical genetic effects with multiple alleles. Curr Topics Genet 3:49–62

    Google Scholar 

  19. Tiwari HK, Elston RC (1997) Deriving components of genetic variance for multilocus models. Genet Epidemiol 14:1131–1136

    Article  PubMed  CAS  Google Scholar 

  20. Yang R-C (2004) Epistasis of quantitative trait loci under different gene action models. Genetics 167:1493–1505

    Article  PubMed  CAS  Google Scholar 

  21. Noguera JL, Rodriguez C, Varona L et al (2009) A bi-dimensional genome scan for prolificacy traits in pigs shows the existence of multiple epistatic QTL. BMC Genomics 10:636–648

    Article  PubMed  Google Scholar 

  22. Rönnegård L, Besnier F, Carlborg Ö (2008) An improved method for quantitative trait loci detection of within-line segregation in F2 intercross designs. Genetics 178:2315–2326

    Article  PubMed  Google Scholar 

  23. Wei W-H, Knott SA, Haley CS, de Koning D-J (2010) Controlling false positives in the mapping of epistatic QTL. Heredity 104(4):401–409

    Article  PubMed  Google Scholar 

  24. Carlborg Ö, Haley CS (2004) Epistasis: too often neglected in complex trait studies? Nat Rev Genet 5:618–625

    Article  PubMed  CAS  Google Scholar 

  25. Malmberg RL, Mauricio R (2005) QTL-based evidence for the role of epistasis in evolution. Genet Res 86:89–95

    Article  PubMed  CAS  Google Scholar 

  26. Álvarez-Castro JM, Yang RC (2011) Multiallelic models of genetic effects and variance decomposition in non-equilibrium populations. Genetica 139:1119–1134

    Article  PubMed  Google Scholar 

  27. Van der Ween JH (1959) Tests of non-allelic interaction and linkage for quantitative characters in generations derived from two diploid pure lines. Genetica 30:201–232

    Article  Google Scholar 

  28. Kao CH, Zeng ZB (2002) Modeling epistasis of quantitative trait loci using Cockerham’s model. Genetics 160:1243–1261

    PubMed  Google Scholar 

  29. Nettelblad C, Carlborg Ö, Álvarez-Castro JM (2010) On orthogonal QTL parameter estimates with incomplete genotype information. In: Science GSfA (ed) 10th WCGALP, Leipzig, Germany

    Google Scholar 

  30. Fisher RA (1941) Average excess and average effect of a gene substitution. Ann Eugen 11:53–63

    Article  Google Scholar 

  31. Bürger R (2000) The mathematical theory of selection, recombination and mutation. Wiley, Chichester

    Google Scholar 

  32. Haley CS, Knott SA (1992) A simple regression method for mapping quantitative trait loci in line crosses using flanking markers. Heredity 69:315–324

    Article  PubMed  CAS  Google Scholar 

  33. Martínez O, Curnow RN (1992) Estimating the locations and the sizes of the effects of quantitative trait loci using flanking markers. Theor Appl Genet 85:480–488

    Article  Google Scholar 

  34. Álvarez-Castro JM, Le Rouzic A, Carlborg Ö (2008) How to perform meaningful estimates of genetic effects. PLoS Genet 4:e1000062

    Article  PubMed  Google Scholar 

  35. Le Rouzic A, Álvarez-Castro JM, Carlborg Ö (2008) Dissection of the genetic architecture of body weight in chicken reveals the impact of epistasis on domestication traits. Genetics 179:1591–1599

    Article  PubMed  Google Scholar 

  36. Besnier F, Le Rouzic A, Álvarez-Castro JM (2010) Applying QTL analysis to conservation genetics. Conserv Genet 11:399–408

    Article  Google Scholar 

Download references

Acknowledgments

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.

Author information

Authors and Affiliations

  1. Department of Genetics, University of Santiago de Compostela, Lugo, Galiza, Spain

    José M. Álvarez-Castro

  2. Department of Animal Breeding and Genetics, Swedish University of Agricultural Sciences, Uppsala, Sweden

    Örjan Carlborg

  3. Department of Cell and Molecular Biology, Uppsala University, Uppsala, Sweden

    Örjan Carlborg

  4. Statistics Unit, Dalarna University, Borlänge, Sweden

    Lars Rönnegård

Authors
  1. José M. Álvarez-Castro
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Örjan Carlborg
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lars Rönnegård
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to José M. Álvarez-Castro .

Editor information

Editors and Affiliations

  1. University of California, San Diego, Gilman Drive 9500, La Jolla, 92093, California, USA

    Scott A. Rifkin

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer Science+Business Media

About this protocol

Cite this protocol

Álvarez-Castro, J.M., Carlborg, Ö., Rönnegård, L. (2012). Estimation and Interpretation of Genetic Effects with Epistasis Using the NOIA Model. In: Rifkin, S. (eds) Quantitative Trait Loci (QTL). Methods in Molecular Biology, vol 871. Humana Press. https://doi.org/10.1007/978-1-61779-785-9_10

Download citation

  • DOI: https://doi.org/10.1007/978-1-61779-785-9_10

  • Published:

  • Publisher Name: Humana Press

  • Print ISBN: 978-1-61779-784-2

  • Online ISBN: 978-1-61779-785-9

  • eBook Packages: Springer Protocols

Publish with us

Policies and ethics

Search

Navigation