The coalescent process in genetics : mapping complex diseases and other applications

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The coalescent process, a stochastic process used to simulate population genealogies, has attracted much attention during then past fifteen years, mostly due to the numerous applications in human genetics research. We have introduced a method that uses the coalescent process with recombination (Larribe et al., 2002, Larribe, 2004), in order to estimate the location of a genetic mutation influencing a disease, i.e. in order to do genetic fine mapping. Using a composite-conditional-likelihood strategy (Larribe and Lessard, 2008) on "windows" of genetic markers, we have improved the stability of the estimates and greatly increased the number of genetic markers usable by the method. Then, we have further developed the approach in the context of complex genetic diseases, by devising methods for estimating haplotypes and causal alleles from phenotypes and genotypes (Larribe et al., 2015); moreover, the method is now able to take into account genetic models allowing incomplete penetrance and phenocopy. It is still common practice in the genetics world to base the analysis on thousands of association statistics, each for a pair of genetic markers, and thus to ignore the dependence between individuals and the spatial genetic dependency between markers. Therefore, in our proposal we continue the difficult task of offering a refined solution to this problem by addressing both dependency issues mentioned above. In contrast with many other approaches, our method is not based on testing association, but is a genetic mapping methodology based on the likelihood; as such, it incorporates rich genetic models.