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

Abstract

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.

High-density sex-specific linkage maps of a European tree frog (Hyla arborea) identify the sex chromosome without information on offspring sex

“…We constructed sex-specific genetic maps using MSTmap (Wu et al, 2008), using cross type 'DH. ' Following Gadau et al (2001), to account for the unknown phase of markers in each parent we added each marker to the data set twice, once with each possible phase.…”

R Package ASMap: Efficient Genetic Linkage Map Construction and Diagnosis

“…Again, the linkage map reconstruction only requires optimal ordering of the markers within linkage groups. Wu et al (2008) contains extensive information on the comparative performance of the MSTmap algorithm for constructing linkage maps. However, it was not outlined in Wu et al (2008) how well the algorithm scaled for complete linkage map construction of large genetic marker sets.…”

“…Computational methods that exploited this knowledge were quickly adopted in construction algorithms including the evolution-strategy algorithm (Mester, Ronin, Hu, Peng, Nevo, and Korol 2003a;Mester, Ronin, Minkov, Nevo, and Korol 2003b) implemented in Multipoint and the RECORD algorithm (Van Os, Stam, Visser, and Van Eck 2005) available as command line software and later implemented in software packages IciMapping (Meng, Li, Zhang, and Wang 2015) and onemap (Margarido and Mollinari 2015). Other construction algorithm variants involving efficient solutions of the traveling salesman problem included the unidirectional growth (UG) algorithm (Tan and Fu 2006), the AntMap algorithm (Iwata and Ninomiya 2006), the MSTmap algorithm (Wu et al 2008) and Lep-MAP (Rastas, Paulin, Hanski, Lehtonen, and Auvinen 2013). Unfortunately these more recent algorithms have only been available as downloadable low-level source codes that require compilation before use.…”

Characterizing Uncertainty in High-Density Maps from Multiparental Populations

“…Perhaps the most challenging step in map construction is ordering markers within a linkage group. Methods for ordering markers in biparental populations have been well studied and include techniques such as seriation (Buetow and Chakravarti 1987), ant colony optimization (Iwata and Ninomiya 2006), minimum spanning trees (Wu et al 2008), rapid chain delineation (Nascimento et al 2010), and simulated annealing (Van Ooijen 2011). These in turn form the basis of numerous map-construction software packages.…”

“…These in turn form the basis of numerous map-construction software packages. These can be roughly divided up into those relying on multipoint approaches, which incorporate information across the genome to maximize the likelihood of the map (MAPMAKER, Lander et al 1987; CRI-MAP, Green et al 1990;JoinMap, Stam 1993;R/qtl, Broman et al 2003;CARTHAGENE, deGivry et al 2005), and those relying on two-point approaches, which achieve much greater speed by using only pairwise recombination estimates (RECORD, van Os et al 2005;OneMap, Margarido et al 2007; MSTmap, Wu et al 2008;Lep-MAP, Rastas et al 2013;HighMap, Liu et al 2014). The gain in accuracy from multipoint approaches must therefore be balanced against the accompanying computational burden.…”