Graph theory algorithm for solution of computational problems of gene mapping

Motivation: Pedigrees coming from isolated populations are very informative for gene mapping of complex traits due to their low genetic heterogeneity. Usually these pedigrees contain a lot of loops, which make impossible an application of likelihood-based methods of linkage analysis. The loops have to be broken to calculate likelihood using approximate methods. Optimal selection of breakers allows us to reduce the loss of genetic informativity. Existent algorithms of breakers selection are not effective for pedigrees from isolated populations where many individuals are unobserved and large number of loci are analysed. Results: We used classical graph-theory Kruskal approach for selection of optimal loop breakers. This algorithm needs to define weights of edges for pedigree-graph. We propose to estimate edge weight by relative loss of mean relationship after the elimination of this edge from the graph. We estimated the loss of pedigree informativity in a series of inbred families with hundreds of loops under different algorithms of loop breaking and demonstrated that our algorithm provides minimal loss of information. In addition we compared power of linkage analysis of a pedigree with multiple loops using our and alternative methods for simplification of pedigree structure and demonstrated that our method is characterised by higher power.