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R Package ASMap: Efficient Genetic Linkage Map Construction and Diagnosis

Julian Taylor, David Butler

arXiv:1705.06916v1stat.CO

TL;DR

ASMap addresses the limited availability of efficient linkage-map construction tools in R. It integrates MSTmap for clustering and ordering with tools for diagnosing and repairing constructed maps. The package is presented as efficient for large marker datasets and demonstrated on a high-density barley Backcross dataset.

  • Problem

    R had limited linkage-map construction options, including qtl’s computationally cumbersome ordering and onemap’s restricted population support.

  • Method

    ASMap integrates MSTmap-based construction with marker diagnosis, repair, and post-construction manipulation tools.

  • Results

    ASMap provides efficient linkage-map construction and diagnosis, with negligible computational-efficiency loss relative to the equivalent MSTmap source code.

  • Takeaways & Limitations

    The package supports construction and manipulation of large genetic marker maps, including flexible diagnosis and repair workflows.

  • Takeaways & Limitations

    MSTmap performance can be constrained by the potentially enormous number of pairwise comparisons for large marker sets and small populations.

Abstract

from arXiv · show

Although various forms of linkage map construction software are widely available, there is a distinct lack of packages for use in the R statistical computing environment. This article introduces the ASMap linkage map construction R package which contains functions that use the efficient MSTmap algorithm for clustering and optimally ordering large sets of markers. Additional to the construction functions, the package also contains a suite of tools to assist in the rapid diagnosis and repair of a constructed linkage map. The package functions can also be used for post linkage map construction techniques such as fine mapping or combining maps of the same population. To showcase the efficiency and functionality of ASMap, the complete linkage map construction process is demonstrated with a high density barley backcross marker data set.

1. Introduction

ASMap addresses the limited availability of efficient linkage-map construction tools in R by integrating MSTmap with diagnostic, repair, and post-construction functions.

  • 1. Introduction: R previously offered few linkage-map construction packages, while qtl relied on computationally cumbersome combinatoric ordering and onemap targeted restricted population types.These limitations motivated a more efficient and flexible R-based package.
  • 1. Introduction: ASMap uses MSTmap to cluster markers into linkage groups and find optimal marker orders efficiently without multiple ordering stages.The algorithm supports Backcross, Doubled Haploid, and Recombinant Inbred populations, including selfed F populations.
  • 1. Introduction: The package provides construction functions alongside tools for pulling and restoring marker types and diagnosing linkage-map statistics graphically.These functions support map construction and reconstruction workflows.
  • 1. Introduction: ASMap uses the qtl cross-object format where possible, allowing its functions and qtl functions to be used together for constructing, exploring, and manipulating genetic objects.The package is demonstrated through complete linkage-map construction for a barley Backcross population.

2. MSTmap algorithm

MSTmap clusters markers using distance-based graph pruning and orders them through minimum-spanning-tree optimization, with integrated imputation and error detection. Its extensions support RIL populations but impose population-specific estimation and feature constraints.

  • 2.1. Clustering: MSTmap estimates recombination probabilities from marker Hamming distances and uses Hoeffding’s inequality to determine whether markers belong to the same linkage group.For a DH population, the estimate is d_jk/n, where d_jk is the number of nonmatching alleles.
  • 2.1. Clustering: Markers are vertices in an edge-weighted complete graph, and removing edges above the estimated threshold partitions the markers into linkage groups.The remaining connected components define the groups.
  • 2.2. Marker ordering: Co-locating markers with zero pairwise distance are binned, and one representative marker per bin forms a reduced marker set before ordering.This reduces the marker set while preserving the genomic location represented by each bin.
  • 2.2. Marker ordering: MSTmap obtains a minimum-weight travelling-salesman path using a minimum spanning tree, then applies local optimization when errors or small populations prevent a complete path.The integrated K-opt, node-relocation, and block-optimization procedures produce a true one-stage ordering algorithm.
  • 2.2. Marker ordering: Missing allele scores are imputed probabilistically with an EM-type procedure integrated into iterative marker ordering and weight-matrix recalculation.For missing entries, the imputation uses posterior probability based on estimated recombination fractions with neighboring markers.
  • 2.2. Marker ordering: MSTmap detects suspicious allele observations using weighted nearby-marker expectations, treats them as missing, and imputes them through the EM procedure.An observation is suspicious when the absolute difference between expected and observed allele values exceeds 0.75.
  • 2.3. Extension to RIL populations: The algorithm supports selfed F2 through Fr and advanced RIL populations, using population-specific recombination estimates for clustering and ordering.For non-advanced RIL populations, recombination probabilities are approximated by recurrence relations and stepwise optimization.
  • 2.3. Extension to RIL populations: For non-advanced RIL populations, a 10 cM+ reduction in genetic distance between markers requires squaring the p-value threshold, and missing-allele imputation and error detection are unavailable.These additional MSTmap features are not implemented for non-advanced RIL populations.

3. ASMap package

ASMap provides flexible linkage-map construction and diagnostic tools built around MSTmap, while supporting marker management, visual quality assessment, and compatibility with qtl objects. Its functions also address reconstruction choices and known handling limitations for auxiliary marker data.

  • Map construction functions: ASMap provides two linkage-map construction functions that expose MSTmap parameters and accept either data frames or qtl-compatible cross objects.The data-frame interface requires markers in rows and genotypes in columns, while the cross-object interface supports unconstructed or constructed objects.
  • Map construction functions: The bychr setting determines whether selected linkage groups are reconstructed separately or bulked together before reconstruction.With bychr = TRUE, reconstruction is confined within each selected linkage group; with bychr = FALSE, the groups are bulked.
  • Map construction functions: Users may need trial and error when selecting p.value because marker clustering depends strongly on population size.The package documentation highlights p.value as a crucial determinant of marker separation into linkage groups.
  • Marker management: Markers that are co-located, segregation-distorted, or missing above defined thresholds can be pulled from maps and later pushed back with retained information.This supports temporary pruning during construction or reconstruction rather than permanent removal of potentially important markers.
  • Visual diagnostics: ASMap supplies graphical diagnostics for genotype and marker or interval statistics, including missingness, allele proportions, crossovers, recombination fractions, LOD scores, and map distances.Its multi-panel displays can annotate significant segregation distortion and weak linkage, while crossover and double-crossover rates help identify problematic lines.
  • Visual diagnostics: The improved heatMap displays LOD scores and estimated recombination fractions on separate triangles, with values beyond 0.5 revealing potential out-of-phase marker regions.The function also supports subsetting by linkage group and marker.
  • Miscellaneous functions: subsetCross() keeps auxiliary marker data and summary tables aligned with a reduced linkage map, unlike subset.cross().This prevents stale components from causing inaccurate marker-pushing decisions after subsetting.

4. Illustrative example

The barley backcross example demonstrates ASMap’s checklist-driven construction, diagnosis, repair, and post-construction marker integration workflow. Successive filtering and reconstruction steps produced a linkage map with clustered groups, controlled recombination profiles, and merged linkage groups.

  • 4.1. Pre-construction: The workflow began with a pre-construction checklist covering missing data, clones, segregation distortion, switched alleles, and co-locating markers.These checks target genotype and marker-quality issues that can compromise linkage-map construction.
  • 4.1. Pre-construction: Genotype diagnostics identified lines with large amounts of missing data, and genotypes exceeding 50% missing alleles were omitted before construction.The missingness plot showed problematic genotypes, while statGen() supported their identification.
  • 4.1. Pre-construction: 847 markers were removed and placed aside, leaving 2173 markers for linkage-map construction; clone screening also formed consensus genotypes for remaining clone groups.The clone table contained 13 groups sharing more than 0.95 of their alleles, while the marker filtering step retained the remaining markers for construction.
  • 4.2. MSTmap construction: The constructed map showed consistent within-group heat and distinct linkage-group clustering, while genotype profiles identified seven lines with recombination rates above 20 and excessive missing values.A conservative expected genome-wide recombination rate of 14 was used for the barley backcross population.
  • 4.2. MSTmap construction: Marker profiles revealed few double crossovers and suggested merging L.3 with L.5 and L.8 with L.9; the resulting genuine linkages supported formation of seven linkage groups.The two pairs were merged using mergeCross(), after which the map was reconstructed.
  • 4.3. Pushing back markers: After additional marker integration, two problematic lines with high genome-wide missingness were removed, and segregation-distortion checks isolated a non-biological spike on L.2 for removal.The final object retained only the pheno and geno list elements after the diagnostic and repair process.

5. Performance of MSTmap and ASMap

ASMap delivers efficient MSTmap-based linkage-map construction across varied marker sets and population sizes, while diagnostics reduce computational burdens from co-locating markers. Initial clustering remains a performance limitation for very large datasets.

  • Table 2 reports efficient complete-map construction across marker sets and population sizes, with timings averaged over five chromosomes.The simulations covered DH and F2 populations with 100–300 individuals and 1K–20K markers.
  • MSTmap incurs a moderate computational increase for marker sets containing error because it identifies and remedies potential genotyping errors during construction.For simulated F2 sets, additional reduction in efficiency reflects iterative optimization of pairwise marker information.
  • Initial marker clustering creates a clear performance disadvantage, especially when pairwise comparisons become enormous for more than 100K markers across small populations.The cited performance issues arise before clustering markers into linkage groups.
  • ASMap mitigates this burden by temporarily removing co-locating markers, retaining their links so they can be restored after construction.The reduced marker set can be processed by mstmap.cross(), and the procedure supports very large linkage maps.

6. Summary

ASMap provides efficient, flexible tools for constructing and diagnosing linkage maps using MSTmap, with negligible computational-efficiency loss relative to the equivalent MSTmap source code. Continued development targets additional workflow diagnostics and linkage-group alignment.

  • ASMap combines efficient linkage-map construction and diagnosis for large genetic marker datasets using MSTmap source code.
  • The package is expected to gain visual and numerical diagnostics that improve linkage-map workflow efficiency and assist linkage-group assignment and alignment.These developments are described as short-term plans, with updates distributed through CRAN.
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