Date of Submission


Date of Award


Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name



Human Genetics Unit (HGU-Kolkata)


Majumder, Partha Pratim (HGU-Kolkata; ISI)

Abstract (Summary of the Work)

Maty qualitative tralts - such an, milk yield la cows, blood pressure in lumans --are known to be determined primarly, though zot exclusively, by inherited genetic luctora. It ls the of coasklerable impartance to identify chromosontal locations of tho genes that control a quantitative character. Linkage analysis (Ou 1990), which deals with the deduction of linkagn and estimation of recombination fractions among the loci controlling a qualitative/quantitative character and major loci wkoo poertions are knows aprfori, is widely used for localisation of gens. Although statistical methodologies for magplag gemen determining dichotomos qualitative charactes in humans aro well-developed, the demicrant of such methodologien - especially those that are statistically and computationally efficient - for human quantitative tralts is an active arne of curent reserch in human genotion. It has been amphalad that many traits that have traditionally baen treaied na qualitative are Inherently quantitative in nature.Although the idea of mapping quantitative tealt loci (QTL mapping) can be traced beck to Sax (1923), whio studied the nature of sociaties of sod slue with seed-cont pattern and pignastation In bears, the recent development of dense mape of highly polymorphie DNA markorn in plarta ond animals has vesulted in a remurgencn of starst in QTL. napping, Statistical linkago analysis ralas on the nature cantent of heritancs of alleles st the trait and marker loei. Por many plants and animals experimental crosses can be set up such that the trait locus genotype of an offspring can be unambiguously inferred. This simplifies the statistical investigation of co- inheritance of alleles at the trait and marker loci. However, it is not possible to set up experimental crosses for humans. Hence, QTL mapping in humans is statistically more difficult than in experimental plants and animals.In this Chapter, we provide an overview, albeit non-exhaustive, of the different statistical procedures that have been developed for QTL mapping. A quantitative trait (Y) can be modelled in a general way as Y = G +E, where G and E are the genetic and environmental contributions to the phe- notype, respectively. While this general form of the model can be used in an exploratory way to provide some broad statistical inferences about the quantitative trait, such as heretability of the trait, for making specific inferences or for QTL mapping, it is necessary to formulate a more detailed model. Olten models are formulated on the basis of exploratory data analyses.A quantitative trait may be determined, in addition to an environmental component whose axpectation is usually assumed to be zero, by one or more loci, each biallelic or multiallelic, linked or unlinked. There may be dominance effects at various loci, and unlinked loci may also interact epistatically in the determination of the tralt values.For a quantitative trait that is determined by a single biallelic locus, a general model is: M,A,~ Sil,01), 1A1,A2 ja, - fa(2, o) and Yajas Ja(43, os?), whore A, and a, are the two alleles at the locus, and f1. Ja and fs are goneral probability distribution functions with meana 4a and variances a,?a. If allele effects are assumed to be additive, and there is no dominance, then = 2a, pa 8 are the allelic effects of Aj and an, respectively. In the presence of a dominance effect, 6, 1 = 2a, pg = a +8+ 6 and pa = three-parameter model can sometlmes, but not always, be reduced to a two- parameter model by appropriate scaling (Mather and Jinks 1982, chapter 4), thereby greatly simplifying statistical treatment. Therefore, the popular two-parameter statistical model is (Haseman and Elston 1972, eqn. 2; Hill 1975, p. 439; Amos and Eiston 1989, p. 351; Amos et al.


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