Theoretical and Applied Genetics

, Volume 86, Issue 8, pp 1014–1022 | Cite as

Power of tests for QTL detection using replicated progenies derived from a diallel cross

  • A. Rebai
  • B. Goffinet


In crop species, most QTL (quantitative trait loci) mapping strategies use segregating populations derived from an initial cross between two lines. However, schemes including more than two parents could also be used. We propose an approach using a high-density restriction fragment length polymorphism (RFLP) map established on six F2 populations derived from diallel crosses among four inbred lines and the phenotypic performances of two types of replicated progenies (F3 and topcross). The QTL is supposed to be on the marker locus considered. Three linear model tests for the detection of QTL effects (T1, T2 and T3) are described and their power studied for the two types of progeny. T1 tests the global genetic effects of the QTL (additivity and dominance) and T2 tests only additive effects assuming dominance is absent when it could exist. The models of these two tests assume that the main effects of QTL alleles are constant in different genetic backgrounds. The additive model of test T3 considers the six F2 populations independently, and T3 is the equivalent of the classical mean comparison test if we neglect dominance; it uses only contrasts between the homozygote marker classes. The results show that T2 is much more powerful than T3. The power of T1 and T2 depends on the relative sizes of the additive and dominance effects, and their comparison is not easy to establish. Nevertheless, T2 seems to be the more powerful in most situations, indicating that it is often more interesting to ignore dominance when testing for a QTL effect. For a given size of genetic effects, the power is affected by the total number of individuals genotyped in F2 and the recombination rate between the marker locus and the putative QTL. The approach presented in this paper has some drawbacks but could be easily generalized to other sizes of diallels and different progeny types.

Key words

Diallel Restriction fragment length polymorphism markers Replicated progenies Linear models Power of test 


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  1. Beckmann JS, Soller M (1986) Restriction fragment length polymorphism in plant genetic improvement. In: Miflin BJ (ed) Oxford surveys of plant molecular and cell biology vol 3. Oxford Press, Oxford, pp 197–250Google Scholar
  2. Beckmann JS, Soller M (1988) Detection of linkage between marker loci and loci affecting quantitative traits in crosses between segregating populations. Theor Appl Genet 76:228–236Google Scholar
  3. Carbonell EA, Gerig TM, Balansard E, Asins MJ (1992). Interval mapping in the analysis of nonadditive quantitative trait loci. Biometrics 48:305–315Google Scholar
  4. Cowen NM (1988) The use of replicated progenies in marker-based mapping of QTLs. Theor Appl Genet 75:857–862Google Scholar
  5. Edwards MD, Stuber CW, Wendel JF (1987) Molecular-marker-facilitated investigation of quantitative-trait loci in maize. I. Numbers, genomic distribution and types of gene action. Genetics 116:113–125PubMedGoogle Scholar
  6. Edwards MD, Helentjaris T, Wright S, Stuber CW (1992) Molecular-markar-facilitated investigations of quantiative trait loci in maize. 4. Analysis based on genome saturation with isozyme and restriction fragment length polymorphism markers. Theor Appl Genet 83:765–774Google Scholar
  7. Ellis THN (1986) Restriction fragment length polymorphism markers in relation to quantitative characters. Theor Appl Genet 72:1–2Google Scholar
  8. Graybill FA (1976) Theory and application of the linear model. Wadsworth, Belmont, Calif.Google Scholar
  9. Jayakar SD (1970) On the detection and estimation of linkage between a locus influencing a quantitative character and a marker locus. Biometrics 26:466–479Google Scholar
  10. Knapp SJ, Bridges WC (1990) Using molecular markers to estimate quantitative trait locus parameters: power and genetic variances for unreplicated and replicated progeny. Genetics 126:769–777PubMedGoogle Scholar
  11. Knapp SJ, Bridges WC, Brikes D (1990) Mapping quantitative trait loci using molecular marker linkage maps. Theor Appl Genet 79:583–592Google Scholar
  12. Lander ES, Botstein D (1989) Mapping Mendelian factors underlying quantitative traits using RFLP linkage maps. Genetics 121:185–199PubMedGoogle Scholar
  13. Luo ZW, Kearsey MJ (1989) Maxiumum likelihood estimation of linkage between a marker gene and a quantitative trait locus. Heredity 63:401–408Google Scholar
  14. Luo ZW, Kearsey MJ (1991) Maximum likelihood estimation of linkage between a marker gene and a quantitative trait locus. II. Application to backcross and doubled haploid populations. Heredity 66:117–124Google Scholar
  15. Ooijen JW van (1992) Accuracy of mapping quantitative trait loci in autogamous species. Theor Appl Genet 84:803–811Google Scholar
  16. Sax K (1923) The association of size differences with seed coat pattern and pigmentation in Phaseolus vulgarus. Genetics 8:552–560Google Scholar
  17. Simpson SP (1989) Detection of linkage between quantitative trait loci and restriction fragment length polymorphisms using inbred line. Theor Appl Genet 77:815–819Google Scholar
  18. Smith OS, Smith JSC, Bowen SL, Tenborg RA, Wall SJ (1990) Similarities among a group of elite maize imbreds as measured by pedigree, F1 grain yield, grain yield, heterosis and RFLPs. Theor Appl Genet 80:833–840Google Scholar
  19. Soller M, Beckmann JS (1990) marker-based mapping of quantitative trait loci using replicated progenies. Theor Appl Genet 80:205–208Google Scholar
  20. Soller M, Genizi A (1978) The efficiency of experimental designs for the detection of linkage between a marker locus and a locus affecting a quantitative trait in segregating populations. Biometrics 34:47–55Google Scholar
  21. Soller M, Genizi A, Brody T (1976) On the power of experimental designs for the detection of linkage between marker loci and quantiative loci in crosses between inbred lines. Theor Appl Genet 47:35–39Google Scholar
  22. Stuber CW, Edwards MD, Wendel JF (1987) Molecular-marker-facilitated investigations of quantitative-trait loci in maize. II. Factors influencing yield and its component traits. Crop Sci 27:629–648Google Scholar
  23. Tanksley SD, Medina-Filho H, Rick CM (1982) Use of naturally-occurring enzyme variation to detect and map genes controlling quantitative traits in an interspecific backcross of tomato. Heredity 49:11–25Google Scholar
  24. Thompson JN, Thoday JM (1979) Quantitative genetic variation. Academic Press, LondonGoogle Scholar
  25. Weller JI (1986) Maximum likelihood techniques for the mapping and analysis of quantitative trait loci with the aid of genetic markers. Biometrics 42:627–640Google Scholar
  26. Weller JI, Soller M, Brody T (1988) Linkage analysis of quantitative traits in an interspecific cross of tomato (Lycopersicon esculentum x Lycopersicon pimpinellifolium) by means of genetic markers. Genetics 118:3229–339Google Scholar

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • A. Rebai
    • 1
  • B. Goffinet
    • 1
  1. 1.National Institute of Agronomy Research, Centre de Toulouse, Chemin Borde RougeLaboratory of BiometryCastanet-TolosanFrance

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