title: A hybrid method for the imputation of genomic data in livestock populations.
abstract: This paper describes a combined heuristic and hidden Markov model (HMM) method to accurately impute missing genotypes in livestock datasets. Genomic selection in breeding programs requires high-density genotyping of many individuals, making algorithms that economically generate this information crucial. There are two common classes of imputation methods, heuristic methods and probabilistic methods, the latter being largely based on hidden Markov models. Heuristic methods are robust, but fail to impute markers in regions where the thresholds of heuristic rules are not met, or the pedigree is inconsistent. Hidden Markov models are probabilistic methods which typically do not require specific family structures or pedigree information, making them very flexible, but they are computationally expensive and, in some cases, less accurate.
  
  
  
  We implemented a new hybrid imputation method that combined heuristic and HMM methods, AlphaImpute and MaCH, and compared the computation time and imputation accuracy of the three methods. AlphaImpute was the fastest, followed by the hybrid method and then the HMM. The computation time of the hybrid method and the HMM increased linearly with the number of iterations used in the hidden Markov model, however, the computation time of the hybrid method increased almost linearly and that of the HMM quadratically with the number of template haplotypes. The hybrid method was the most accurate imputation method for low-density panels when pedigree information was missing, especially if minor allele frequency was also low. The accuracy of the hybrid method and the HMM increased with the number of template haplotypes. The imputation accuracy of all three methods increased with the marker density of the low-density panels. Excluding the pedigree information reduced imputation accuracy for the hybrid method and AlphaImpute. Finally, the imputation accuracy of the three methods decreased with decreasing minor allele frequency.
  
  
  
  The hybrid heuristic and probabilistic imputation method is able to impute all markers for all individuals in a population, as the HMM. The hybrid method is usually more accurate and never significantly less accurate than a purely heuristic method or a purely probabilistic method and is faster than a standard probabilistic method.
authors.affiliation: The Roslin Institute and Royal (Dick) School of Veterinary Studies, The University of Edinburgh, Easter Bush Research Centre, Midlothian, EH25 9RG, Scotland, UK.
authors.forename: Roberto
authors.initials: R
authors.lastname: Antolín
authors.affiliation: Division of Scientific Computing, Department of Information Technology, Science for Life Laboratory, Uppsala University, Lägerhyddsvägen 2, Box 337, 751 05, Uppsala, Sweden.
authors.forename: Carl
authors.initials: C
authors.lastname: Nettelblad
authors.affiliation: The Roslin Institute and Royal (Dick) School of Veterinary Studies, The University of Edinburgh, Easter Bush Research Centre, Midlothian, EH25 9RG, Scotland, UK.
authors.forename: Gregor
authors.initials: G
authors.lastname: Gorjanc
authors.affiliation: The Roslin Institute and Royal (Dick) School of Veterinary Studies, The University of Edinburgh, Easter Bush Research Centre, Midlothian, EH25 9RG, Scotland, UK.
authors.forename: Daniel
authors.initials: D
authors.lastname: Money
authors.affiliation: The Roslin Institute and Royal (Dick) School of Veterinary Studies, The University of Edinburgh, Easter Bush Research Centre, Midlothian, EH25 9RG, Scotland, UK. john.hickey@roslin.ed.ac.uk.
authors.forename: John M
authors.initials: JM
authors.lastname: Hickey
mesh_terms: D000818:Animals; D001947:Breeding / Q000379:methods* / Q000592:standards; D005787:Gene Frequency; D055106:Genome-Wide Association Study / Q000379:methods* / Q000592:standards; D005838:Genotype; D058751:Livestock / Q000235:genetics*; D012984:Software