Summary
High-density restriction fragment length polymorphism (RFLP) and allozyme linkage maps have been developed in several plant species. These maps make it technically feasible to map quantitative trait loci (QTL) using methods based on flanking marker genetic models. In this paper, we describe flanking marker models for doubled haploid (DH), recombinant inbred (RI), backcross (BC), F1 testcross (F1TC), DH testcross (DHTC), recombinant inbred testcross (RITC), F2, and F3 progeny. These models are functions of the means of quantitative trait locus genotypes and recombination frequencies between marker and quantitative trait loci. In addition to the genetic models, we describe maximum likelihood methods for estimating these parameters using linear, nonlinear, and univariate or multivariate normal distribution mixture models. We defined recombination frequency estimators for backcross and F2 progeny group genetic models using the parameters of linear models. In addition, we found a genetically unbiased estimator of the QTL heterozygote mean using a linear function of marker means. In nonlinear models, recombination frequencies are estimated less efficiently than the means of quantitative trait locus genotypes. Recombination frequency estimation efficiency decreases as the distance between markers decreases, because the number of progeny in recombinant marker classes decreases. Mean estimation efficiency is nearly equal for these methods.
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References
Allard RW (1956) Formulas and tables to facilitate the calculation of recombination values in heredity. Hilgardia 24:235–278
Cowen NM (1988) The use of replicated progenies in markerbased mapping of QTLs. Theor Appl Genet 75:857–862
Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood from incomplete data via the EM algorithm (with discussion). JR Stat Soc Ser B 39:1–38
Edwards MD, Stuber CW, Wendel JF (1987) Molecular markerfacilitated investigations of quantitative trait loci in maize. I. Numbers, distribution, and types of gene action. Genetics 116:113–125
Gallant RA (1987) Nonlinear statistical models. Wiley, New York
Haldane JBS, Waddington CH (1931) Inbreeding and linkage. Genetics 16:357–374
Jennrich RI, Ralston ML (1978) Fitting nonlinear models to data. Tech Rept 46. BMDP, Los Angeles
Knapp SJ (1989) Quasi-Mendelian analysis of quantitative trait loci using molecular marker linkage maps: an overview of parameter estimation methods. In: Roebellen G (ed) Proc 12th Eucarpia Congr, Goettingen, FRG, pp 51–67
Knapp SJ, Bridges WC (1990) Programs for mapping quantitative trait loci using flanking markers and nonlinear models. J Hered (in press)
Lander ES, Botstein D (1989) Mapping Mendelian factors underlying quantitative traits using RFLP linkage maps. Genetics 121:185–199
Little RJA, Rubin DB (1987) Stastical analysis with missing data. Wiley, New York
McLachlan GJ, Basford KE (1988) Mixture models: inference and applications to clustering. Marcel Dekker, New York
Osborne TC, Alexander DC, Fobes JF (1987) Identification of restriction fragment length polymorphisms linked to genes controlling soluble solids content in tomato fruit. Theor Appl Genet 73:350–356
Soller M, Brody T (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 47:35–59
Soller M, Brody T, Genizi A (1979) The expected distribution of marker-linked quantitative effects in crosses between inbred lines. Heredity 43:179–190
Stuber CW, Edwards MD, Wendel JF (1987) Molecular markerfacilitated investigations of quantitative trait loci. II. Factors influencing yield and its component traits. Crop Sci 27:639–648
Tanksley SD, Hewitt J (1988) Use of molecular markers in breeding for soluble solids content in tomato — a reexamination. Theor Appl Genet 75:811–823
Titterington DM, Smith AFM, Markow UE (1985) Statistical analysis of finite mixture distributions. Wiley, New York
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 (tomato) with the aid of genetic markers using approximate maximum likelihood methods. Heredity 59:413–421
Young ND, Zamir D, Ganal MW, Tanksley SD (1988) Use of isogenic lines and simultaneous probing to identify DNA markers tightly linked to the Tm-2a gene in tomato. Genetics 120:579–585
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Communicated by A. R. Hallauer
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Knapp, S.J., Bridges, W.C. & Birkes, D. Mapping quantitative trait loci using molecular marker linkage maps. Theoret. Appl. Genetics 79, 583–592 (1990). https://doi.org/10.1007/BF00226869
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DOI: https://doi.org/10.1007/BF00226869