Abstract
Deterministic sampling was used to numerically evaluate the expected log-likelihood surfaces of QTL-marker linkage models in large pedigrees with simple structures. By calculating the expected values of likelihoods, questions of power of experimental designs, bias in parameter estimates, approximate lower-bound standard errors of estimates and correlations among estimates, and suitability of statistical models were addressed. Examples illustrated that bracket markers around the QTL approximately halved the standard error of the recombination fraction between the QTL and the marker, although they did not affect the standard error of the QTL's effect, that overestimation of the distance between the markers caused overestimation of the distance between the QTL and marker, that more parameters in the model did not affect the accuracy of parameter estimates, that there was a moderate positive correlation between the estimates of the QTL effect and its recombination distance from the marker, and that selective genotyping did not introduce bias into the estimates of the parameters. The method is suggested as a useful tool for exploring the power and accuracy of QTL linkage experiments, and the value of alternative statistical models, whenever the likelihood of the model can be written explictly.
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References
Bovenhuis H, Weller JI (1994) Mapping and analysis of dairy cattle quantitative trait loci by maximum-likelihood methodology using milking protein genes as genetic markers. Genetics 137:267–280
Darvasi A, Soller M (1992) Selective genotyping for determination of linkage between a marker locus and a quantitative trait locus. Theor Appl Genet 85:353–359
Darvasi A, Weinreb A, Minke V, Weller JI, Soller M (1993) Detecting marker-QTL linkage and estimating QTL gene effect and map location using a saturated genetic map. Genetics 134:943–951
Edwards, AFW (1984) Likelihood Chapters 5 and 7. Cambridge University Press, Cambridge
Edwards MD, Stuber CW, Wendel JF (1987) Molecular-marker-facilitated investigations of quantitative trait loci in maize. 1. Numbers, genomic distribution, and types of gene action. Genetics 116:113–125
Georges M, Nielsen D, Mackinnon MJ, Mishra A, Okimoto R, Pasquino AT, Sargeant LS, Sorensen A, Steele MR, Zhao X, Womack JE, Hoeschele I (1995) Mapping genes controlling milk production: towards marker-assisted selection in livestock. Genetics 139:907–920
Guo SW, Thompson EA (1992) A Monte Carlo method for combined segregation and linkage analysis. Am J Hum Genet 51:1111–1126
Haley CS, Archibald A, Andersson L, Bosnia AA, Davies W, Fredholm M, Geldermann H, Groenen M, Gustavsson I, Ollivier L, Tucker EM, Van de Weghe A (1990) The pig gene mapping project — PiGMaP. 4th World Congr Genet Appl Livest Prod, Edinburgh 13:67–70
Hoeschele I (1994) Bayesian QTL mapping via the Gibbs sampler. 5th World Congr Genet Appl Livest Prod, Guelph, Canada 21:241–244
Jensen J (1989) Estimation of recombination fraction between a quantitative trait locus (QTL) and two marker gene loci. Theor Appl Genet 78:613–618
Keim P, Diers BW, Olson TC, Shoemaker RC (1990) RFLP mapping in soybean: association between marker loci and variation in quantitative traits. Genetics 126:735–742
Kendall MG and Stuart A (1979) The advanced theory of statistics, vol 2, Griffin, London
Kinghorn BP, Kennedy BW, Smith C (1993) A method of screening for genes of major effect. Genetics 134:351–360
Knott SA, Haley CS (1992) Maximum-likelihood mapping of quantitative trait loci using full-sib families. Genetics 132:1211–11222
Lander ES, Botstein D (1989) Mapping Mendelian factors underlying quantitative traits using RFLP linkage maps. Genetics 121:185–199
Luo, ZW and Kearsey, MJ (1989) Maximum-likelihood estimation of linkage between a marker gene and a quantitative trait locus. Heredity 63:401–408
Mackinnon MJ, Weller JI (1995) Methodology and accuracy of estimation of quantitative trait loci parameters in a half-sib design using maximum likelihood. Genetics (in press)
Ott J (1991) Analysis of human genetic linkage, chapter 5. John Hopkins University Press
Paterson AH, Lander ES, Hewitt JD, Peterson S, Lincoln SE, Tanksley SD (1988) Resolution of quantitative traits into Mendelian factors by using a complete linkage map of restriction fragment length polymorphisms. Nature 335:721–726
Soller M, Brody T, Genizi A (1976) On the power of experimental designs for the detection of linkage between marker loci and quantitative loci in crosses between inbred lines. Theor Appl Genet 77:35–39
Van Ooijen, JW (1992) Accuracy of mapping quantitative trait loci in autogamous species. Theor Appl Genet 84:803–811
Weller JI (1986) Maximum-likelihood techniques for the mapping and analysis of quantitative trait loci with the aid of genetic markers. Biometrics 42:627–640
Weller JI (1987) Mapping and analysis of quantitative trait loci in Lycopersicon. Heredity 59:413–421
Weller JI, Kashi Y, Soller M (1990) Power of daughter and granddaughter designs for determining linkage between marker loci and quantitative trait loci in dairy cattle. J Dairy Sci 73:2525–2537
Wilks SS (1938) The large sample distribution of the likelihood ratio for testing composite hypotheses. Ann Math Statist 9:60–62
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Mackinnon, M.J., van der Beek, S. & Kinghorn, B.P. Use of deterministic sampling for exploring likelihoods in linkage analysis for quantitative traits. Theoret. Appl. Genetics 92, 130–139 (1996). https://doi.org/10.1007/BF00222963
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DOI: https://doi.org/10.1007/BF00222963