Linkage maps are important for fundamental and applied genetic research. New sequencing techniques have been created opportunities to increase substantially the density of genetic markers. With such revolutionary advances in technology come new challengesin methodologies and informatics. In this article, we introduce a novel linkage map algorithm to construct high-quality and high-density linkage maps for diploid and polyploid species. We propose to construct linkage maps using graphical models either via a sparse Gaussian copula or via a nonparanormal skeptic approach. Linkage groups (LGs), typically chromosomes, and the order of markers in each LG is determined by revealing the conditional independence relationships among a large number of markers in the genome. We illustrate the efficiency of the inference method on a broad range of synthetic data with varying rates of missingness and genotyping errors. We show that our method outperforms other available methods in terms of determining the correct number of linkage groups and ordering markers both when the data are clean and contain no missing observations and when data are noisy and incomplete. In addition, we implement the method on real genotype data of barley and potato from diploid and tetraploid populations, respectively. Given that most tetraploid potato linkage maps have been generated either from diploid populations (Felcher et al., 2012) or from a subset of marker types (e.g. both parents were heterozygous) (Grandke et al., 2017), developing a map construction method based on discrete graphical models opens the opportunities to construct high-quality linkage maps for any biparental diploid and polyploid species containing all different marker types. We have implemented the method in the R package netwgwas (Behrouzi and Wit, 2017b).
Linkage maps are important tools for genetic research. New sequencing techniques have created opportunities to substantially increase the density of genetic markers. Such revolutionary advances in technology have given rise to new challenges, such as creating high-density linkage maps . Current multiple testing approaches based on pairwise recombination fractions are underpowered in the high-dimensional setting and do not extend easily to polyploid species. We propose to construct linkage maps using graphical models either via a sparse Gaussian copula or a nonparanormal skeptic approach. Linkage groups (LGs), typically chromosomes, and the order of markers in each LG are determined by inferring the conditional independence relationships among large numbers of markers in the genome. Through simulations, we illustrate the utility of our map construction method and compare its performance with other available methods , both when the data are clean and contain no missing observations and when data contain genotyping errors and are incomplete. We apply the proposed method to two genotype datasets: barley and potato from diploid and polypoid populations, respectively. Whereas most tetraploid potato linkage maps until now have been created either from diploid populations or from a subset of marker types , our comprehensive map construction method will be able to deal with realistic data settings for any biparental diploid and polyploid species containing arbitrary marker types. We have implemented the method in the R package netgwas which is freely available at URL
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