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

Abstract

Motivation: 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. Results: 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. Availability and implementation: 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) Contact: or iksoochang@dgist.ac.kr. Supplementary information: Supplementary data are available at Bioinformatics online. © 2015 The Author 2015. Published by Oxford University Press. All rights reserved.