Genetic restoration on complex pedigrees
Sheehan, Nuala A. (Nuala Ann), 1959-
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Analyses of genetic data observed on groups of related individuals frequently require the computation of probabilities on pedigrees. Existing methods are computationally intensive and can be infeasible on large and complex pedigrees. The estimation of genotypic configurations on pedigrees from phenotypic data, whether for prior studies of the likely power of potential data to decide between alternative genetic hypotheses, as an implicit stage in fitting a genetic model, or as an end result in a genetic counselling context, is one component of such analyses. An alternative approach to this reconstruction problem can be based on procedures used in Imaging Analysis, all closely related to the method of Metropolis. These procedures exploit the local nature of the information in a pedigree thus permitting the definition of a neighbourhood system whereby, conditional on the neighbours, the genotypes of individuals are independent.The ICM procedure iteratively updates the genotype estimate of each individual in turn, replacing the current estimate by the mode of the local conditional posterior distribution. Increase and convergence of the overall posterior probability of genotypes given phenotypes is assured, but the restoration does not necessarily converge to a global maximum of the posterior distribution. Alternatively, one can update a vector of single-individual genotype probabilities rather than the discrete genotype, again conditionally on current neighbouring values. Another possibility is to update each individual's genotype estimate by sampling from the local conditional posterior distribution. This method is known as the Gibbs sampler. Multiple realisations of the Gibbs sampler can provide estimates of the true posterior distribution of genotypes given phenotypes on the pedigree, and, when used in conjunction with simulated annealing can find the global maximum of this distribution.These approaches to genotypic restoration are modified and tested by application to a very complicated pedigree of Greenland Eskimos. The areas of Pedigree Analysis to which such approaches are most directly relevant include genetic counselling and selective animal breeding together with questions about ancestral genotypes and the ancestral paths of rare alleles.
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