Synchronized-TSP as a model for multilocus genetic consensus mapping

Abstract

Numerous mapping projects conducted on different organisms have generated an abundance of mapping data. Consequently, many multilocus maps were constructed using diverse mapping populations and marker sets for the same species. The quality of maps varied broadly between populations, marker sets, and applied software. There might be some inconsistencies between different versions of the maps for the same organism, calling for the integration of mapping information and building of consensus maps. The problem of multilocus consensus genetic mapping (MCGM) is even more challenging, compared to multilocus mapping based on one data set, due to several complications: differences in recombination rate and distribution along chromosomes, and different subsets of markers used by different labs. We developed an approach to solve MCGM problems, by searching multilocus orders with the maximum number of shared markers yielding maps with minimum total length. The approach is based on re-analysis of raw data and is implemented in a two-phase algorithm. In Phase 1, for each data set, multilocus ordering is performed combined with iterative re-sampling to evaluate the stability of marker orders. In this phase, the ordering problem is reduced to the well known Traveling Salesperson Problem (TSP). In Phase 2, consensus mapping is conducted by reducing the problem to a specific version of TSP that can be referred to as synchronized TSP. The optimal consensus order of shared markers is defined by the minimal total length of non-conflicting maps of the chromosome. This criterion includes various modifications that take into account the variation in the quality of the original data (e.g., population size, marker quality, etc.). We use our powerful Guided Evolution Strategy algorithm for discrete optimization of constrained problems that was adapted to solve MCGM problems. The developed approach was tested on a wide range of simulated data.