Mathematical Biology Program

University of Utah
Department of Mathematics

Mathematical Biology Program


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Mathematical Biology seminar

Alun Thomas
Genetic Epidemiology, University of Utah
"Graphical modelling of the joint distribution of alleles at associated loci. HapGraphs not HapMaps"
September 10, 2003
3:05pm in LCB 225

Pairwise linkage disequilibrium, haplotype blocks and recombination hot spots provide only a partial description of the patterns of dependences and independences between the allelic states at proximal loci. On the gross scale, where recombination and spatial relationships dominate, the associations can be reasonably described in these terms. However, on the fine scale of current high density maps the mutation process is also important and creates associations between loci which are independent of the physical ordering and which can not be summarized with pairwise measures of association. Graphical modeling provides a standard statistical framework for characterizing precisely this sort of complex stochastic data. While graphical models are often used in situations where assumptions lead naturally to specific models, it is less well known that estimation of graphical models is also a developed field. We show how decomposable graphical models can be fitted to dense genetic data. The objective function is the maximized log likelihood for the model penalized by a multiple of the model's degrees of freedom. Simulated annealing is used to find good solutions. The great potential of this approach is that categorical phenotypes can be included in the same analysis and association with polymorphisms assessed jointly with the inter locus associations. We illustrate our method and its potential with phenotypic data on sex, prostate cancer and genotypic data from 25 SNPs in the ELAC2 gene. The results show clear non spatial and non pairwise dependences.

For more information contact J. Keener, 1-6089