Efficient and Accurate Construction of Genetic Linkage Maps from the Minimum Spanning Tree of a Graph

Genetic linkage maps are cornerstones of a wide spectrum of biotechnology applications, including map-assisted breeding, association genetics, and map-assisted gene cloning. During the past several years, the adoption of high-throughput genotyping technologies has been paralleled by a substantial increase in the density and diversity of genetic markers. New genetic mapping algorithms are needed in order to efficiently process these large datasets and accurately construct high-density genetic maps. In this paper, we introduce a novel algorithm to order markers on a genetic linkage map. Our method is based on a simple yet fundamental mathematical property that we prove under rather general assumptions. The validity of this property allows one to determine efficiently the correct order of markers by computing the minimum spanning tree of an associated graph. Our empirical studies obtained on genotyping data for three mapping populations of barley (Hordeum vulgare), as well as extensive simulations on synthetic data, show that our algorithm consistently outperforms the best available methods in the literature, particularly when the input data are noisy or incomplete. The software implementing our algorithm is available in the public domain as a web tool under the name MSTmap

Genetic Algorithms for Genetic Mapping

. Constructing genetic maps is a prerequisite for most in-depth genetic studies of an organism. The problem of constructing reliable genetic maps for any organism can be considered as a complex optimization problem with both discrete and continuous parameters. This paper shows how genetic algorithms can been used to tackle this problem on simple pedigree. The approach is embodied in an hybrid algorithm that relies on the statistical optimization algorithm EM to handle the continuous variables while genetic algorithms handle the discrete side. The efficiency of the approach lies critically in the introduction of greedy local search in the fitness evaluation of the genetic algorithm, using a neighborhood structure which has been inspired by an analogy between the marker ordering problem and a variant of the famous traveling salesman problem. This shows how genetic algorithms can easily benefit from existing efficient neighborhood structures developed for local search algorithms. The resu..