Uncovering multiloci-ordering by algebraic property of Laplacian matrix and its Fiedler vector.

Abstract

The loci-ordering, based on two-point recombination fractions for a pair of loci, is the most important step in constructing a reliable and fine genetic map. Using the concept from complex graph theory, here we propose a Laplacian ordering approach which uncovers the loci-ordering of multiloci simultaneously. The algebraic property for a Fiedler vector of a Laplacian matrix, constructed from the recombination fraction of the loci-ordering for 26 loci of barley chromosome IV, 846 loci of Arabidopsis thaliana and 1903 loci of Malus domestica, together with the variable threshold uncovers their loci-orders. It offers an alternative yet robust approach for ordering multiloci. Source code program with data set is available as supplementary data and also in a software category of the website (http://biophysics.dgist.ac.kr) crkim@pusan.ac.kr or iksoochang@dgist.ac.kr Supplementary data are available at Bioinformatics online.