Phasing

The human genome is diploid, meaning each individual carries two copies of each chromosome (one inherited from each parent). A haplotype is the combination of alleles on a single chromosome copy that are inherited together. Phasing (also called haplotype phasing) is the process of determining which alleles at different variant sites are located on the same chromosome copy (i.e., on the same haplotype).

Standard genotyping methods typically produce unphased data, where we know an individual's genotypes at each position but not which alleles are physically linked together on the same chromosome. The distribution of variants between the two homologous chromosomes can significantly affect the interpretation of genotype data. For example, phasing is essential for:

• Allele-specific expression: Understanding which parental allele is expressed
• Context-informed annotation: Determining the functional impact of variant combinations
• Loss-of-function compound heterozygous events: Identifying when different mutations on different chromosomes result in gene knockout

Trio data and long read sequencing can directly solve the haplotyping problem, but these approaches are not always available. When direct phasing is not possible, statistical phasing methods are used.

On this page

The Li & Stephens 2003 Model

Statistical phasing is fundamentally based on the Li & Stephens 2003 Markov model, which provides a probabilistic framework for reconstructing haplotypes from unphased genotype data. The model operates under the key assumption that an individual's haplotype can be modeled as a mosaic of haplotypes from a reference panel (or other individuals in the cohort).

Key Concepts

The Li & Stephens model treats haplotype reconstruction as a hidden Markov model (HMM) where:

1. Reference panel: A set of known haplotypes (typically from a reference population) serves as templates
2. Mosaic structure: Each target haplotype is modeled as a series of segments copied from different reference haplotypes
3. Recombination events: Transitions between copied segments represent historical recombination events
4. Mutation/error model: Allows for differences between the target haplotype and the copied reference segments

Mathematical Framework

For a diploid individual, the model treats the two haplotypes (maternal and paternal) as independent. The unphased genotype at each position is constructed by combining alleles from the two haplotypes. The haploid version of this model (used in imputation) is conceptually simpler, as it only needs to reconstruct a single haplotype rather than two.

The model uses:

• Transition probabilities: Govern how often the model switches between copying from different reference haplotypes (related to recombination rates)
• Emission probabilities: Account for differences between the observed genotype and the reference haplotypes (related to mutation and genotyping error rates)

Modern Extensions

Recent methods have incorporated long IBD (Identity by Descent) sharing, local haplotype clustering, and other computational advances to make phasing tractable for large-scale datasets. The following methods are commonly used for statistical phasing:

• PHASE
• MaCH
• EAGLE2
• SHAPEIT5
• BEAGLE3

How to do phasing

In most cases for GWAS, phasing is now a pre-step of imputation (a strategy known as "pre-phasing" Howie et al. 2012). This two-step approach—first statistically estimating haplotypes for each study individual, then imputing missing genotypes into these estimated haplotypes—offers significant computational advantages:

1. Efficiency: GWAS samples need to be phased only once, whereas traditional imputation methods implicitly re-phase with each reference panel update
2. Speed: It is much faster to match a phased GWAS haplotype to one reference haplotype than to match unphased GWAS genotypes to a pair of reference haplotypes
3. Flexibility: The same phased haplotypes can be reused with different or updated reference panels without re-phasing, which is particularly valuable as reference panels evolve and expand

The specific phasing method may not be critical for downstream imputation accuracy, but there are several important considerations when choosing a phasing method, including whether to use reference-based or reference-free phasing, sample size (large vs. small cohorts), and rare variant cutoffs. There is no single method that best fits all cases.

We will show two examples:

• Reference-based phasing using SHAPEIT2
• Cohort-based phasing using Eagle2

Prepare for phasing

Before phasing, alleles should match the reference base on the genome assembly you use for the reference panel (here GRCh37 / b37). With PLINK 2, point --fa at that assembly’s FASTA and use --ref-from-fa so each variant’s reference allele is taken from the sequence at the .bim position (see also Alleles — reference from FASTA).

If you do not already have human_g1k_v37 (1000 Genomes GRCh37 reference), download and decompress it (optional: the .fai index for random access):

mkdir -p "${HOME}/refs"
cd "${HOME}/refs"
wget https://ftp.1000genomes.ebi.ac.uk/vol1/ftp/technical/reference/human_g1k_v37.fasta.gz
wget https://ftp.1000genomes.ebi.ac.uk/vol1/ftp/technical/reference/human_g1k_v37.fasta.fai
gunzip human_g1k_v37.fasta.gz
cd -

before_alignment_bfile="../04_Data_QC/sample_data.clean"
after_alignment_bfile="./sample_data.clean.alignment"
ref_fasta="${HOME}/refs/human_g1k_v37.fasta"   # same build as 1KG tutorial data / SHAPEIT2 refs

plink2 \
    --bfile ${before_alignment_bfile} \
    --fa ${ref_fasta} \
    --ref-from-fa \
    --make-bed \
    --out ${after_alignment_bfile}

Subset PLINK data for phasing (shared input)

The SHAPEIT2 and Eagle2 examples below intentionally use the same PLINK binary prefix (sample_data.chr22.clean) so both tools read identical samples and SNPs (JPT only, chromosome 22, MAF ≥ 0.05). Run this once after Prepare for phasing; do not rebuild a separate extract for each tool.

inputbed=./sample_data.clean.alignment
jptsample=../01_Dataset/JPT.sample
inputbedchr22=./sample_data.chr22.clean

plink2 \
    --bfile ${inputbed} \
    --make-bed \
    --keep ${jptsample} \
    --maf 0.05 \
    --chr 22 \
    --out ${inputbedchr22}

Eagle2 uses this prefix as --bfile=${inputbedchr22} for cohort phasing. SHAPEIT2 needs the further restriction described in Restrict study SNPs to the SHAPEIT2 reference panel: it phases a subset sample_data.chr22.shapeit_ref that matches the Phase I legend (same samples as above, fewer SNPs).

Phasing using SHAPEIT2

Here, we show an example using SHAPEIT2, which is another commonly used tool for haplotype phasing. SHAPEIT2 is usually used for small cohorts.

We will conduct a reference-based phasing using SHAPEIT2 for chromosome 22.

First, download SHAPEIT2 from SHAPEIT2 website. Unzip and add it to your environment. We also need reference files (1000 Genomes Phase I integrated haplotypes (produced using SHAPEIT2) b37 June 2014) and genetic maps, which are also available on SHAPEIT2 website

Use inputbedchr22 from Subset PLINK data for phasing (shared input) (sample_data.chr22.clean).

Restrict study SNPs to the SHAPEIT2 reference panel

The IMPUTE2 / SHAPEIT2 Phase I integrated reference haplotypes only cover a fixed SNP list. The tutorial chr22 extract usually contains extra SNPs (e.g. from a later 1KG release), which makes shapeit -check fail with Reference and Main panels are not well aligned.

To avoid reading the large legend.gz every time, this repository ships chr22_phase1_shapeit_panel_positions.txt: one GRCh37 bp position per line (with # comments), precomputed as the intersection of the Phase I chr22 SNP legend and sample_data.chr22.clean.bim (including allele match). At runtime, only the study .bim is scanned: keep variant IDs whose physical position (column 4) is in that list, then plink2 --extract.

inputbedchr22=./sample_data.chr22.clean
shapeit_positions=./chr22_phase1_shapeit_panel_positions.txt
shapeit_extract=./shapeit_chr22.refpanel_snps.txt
inputbedshapeit=./sample_data.chr22.shapeit_ref

awk -v chr=22 -v posfile=${shapeit_positions} '
BEGIN {
  while ((getline p < posfile) > 0) {
    if (p ~ /^#/ || p == "") continue
    keep[p + 0] = 1
  }
  close(posfile)
}
$1 == chr && keep[$4] {
  print $2
}' ${inputbedchr22}.bim > ${shapeit_extract}

plink2 \
    --bfile ${inputbedchr22} \
    --extract ${shapeit_extract} \
    --make-bed \
    --out ${inputbedshapeit}

Use inputbedshapeit (not inputbedchr22) in all SHAPEIT2 commands below. Eagle2 keeps inputbedchr22 (same samples, full SNP set).

Then check alignment between this reduced study panel and the reference haplotypes:

out=./1KG.JPT.chr22.phased.shapeit2.reference_based
outputhaps=${out}.haps
outputsample=${out}.sample
outputlog=${out}
outputlogcheck=${out}.check

geneticmap=~/tools/shapeit2/shapeit.v2.904.3.10.0-693.11.6.el7.x86_64/reference/ALL.integrated_phase1_SHAPEIT_16-06-14.nomono/genetic_map_chr22_combined_b37.txt
inputrefhap=~/tools/shapeit2/shapeit.v2.904.3.10.0-693.11.6.el7.x86_64/reference/ALL.integrated_phase1_SHAPEIT_16-06-14.nomono/ALL.chr22.integrated_phase1_v3.20101123.snps_indels_svs.genotypes.nomono.haplotypes.gz
inputreflegend=~/tools/shapeit2/shapeit.v2.904.3.10.0-693.11.6.el7.x86_64/reference/ALL.integrated_phase1_SHAPEIT_16-06-14.nomono/ALL.chr22.integrated_phase1_v3.20101123.snps_indels_svs.genotypes.nomono.legend.gz
inputrefsample=~/tools/shapeit2/shapeit.v2.904.3.10.0-693.11.6.el7.x86_64/reference/ALL.integrated_phase1_SHAPEIT_16-06-14.nomono/ALL.integrated_phase1_v3.20101123.snps_indels_svs.genotypes.sample

shapeit -check \
        -B ${inputbedshapeit} \
        -M ${geneticmap} \
        --input-ref ${inputrefhap} ${inputreflegend} ${inputrefsample} \
        --output-log ${outputlogcheck}

Finally, exclude the mismatched variants and run phasing using 1KG PhaseI EAS samples as reference.

excludesnp=${outputlogcheck}.snp.strand.exclude
echo "EAS" > group.list
includegrp=group.list

shapeit --input-bed ${inputbedshapeit} \
        --input-map ${geneticmap} \
        --input-ref ${inputrefhap} ${inputreflegend} ${inputrefsample} \
        --output-max ${outputhaps} ${outputsample} \
        --output-log ${outputlog} \
        --exclude-snp  ${excludesnp} \
        --thread 1 \
        --include-grp ${includegrp} \
        --seed 123 \
        --states 200 \
        --window 2

This command will generate a haplotype file .hap and a sample file .sample. We need to convert the files to VCF, compress and index the VCF for downstream analysis.

outputvcf=${out}.vcf

shapeit \
    -convert \
    --input-haps ${outputhaps} ${outputsample} \
    --output-vcf ${outputvcf}

bgzip ${outputvcf} && \
tabix -p vcf ${outputvcf}.gz

A look at the phased VCF:

| indicates that the genotypes are phased.

After bgzip and tabix, you get a standard VCF whose GT field uses | for phased alleles. A verbatim header and first-variant line from the current tutorial file 1KG.JPT.chr22.phased.eagle2.cohort_based.vcf.gz (cohort-based Eagle2, then the same shapeit -convert step) are shown at the end of the Phasing using Eagle section. Reference-based SHAPEIT2 uses the same VCF layout after conversion; phasing calls need not match Eagle site-for-site.

Phasing using Eagle

Next, we will use Eagle2 as an example for cohort-based phasing.

Download Eagle from Eagle2 website. Unzip and add it to your environment. We also need genetic maps, which are also available on Eagle2 website

Cohort-based phasing (without reference) using Eagle2. Use the same inputbedchr22 prefix as SHAPEIT2 (shared subset); do not run a second plink2 extract with different filters.

inputbedchr22=./sample_data.chr22.clean   # same PLINK prefix as SHAPEIT2 (shared subset step)
geneticmap=~/tools/eagle/genetic_map_hg19_withX.txt.gz
out=./1KG.JPT.chr22.phased.eagle2.cohort_based

eagle \
    --bfile=${inputbedchr22} \
    --geneticMapFile=${geneticmap} \
    --outPrefix=${out} \
    --maxMissingPerSnp=1 \
    --maxMissingPerIndiv=1 \
    --numThreads=4 \
    --chrom=22

Use shapeit2 to convert .hap and .sample to VCF

outputhaps=${out}.haps.gz
outputsample=${out}.sample
outputvcf=${out}.vcf

shapeit \
    -convert \
    --input-haps ${outputhaps} ${outputsample} \
    --output-vcf ${outputvcf}

bgzip ${outputvcf} && \
tabix -p vcf ${outputvcf}.gz

Excerpt from 1KG.JPT.chr22.phased.eagle2.cohort_based.vcf.gz after a tutorial run (##fileDate / ##log_file will change when you rerun):

##fileformat=VCFv4.1
##fileDate=06042026_14h11m12s
##source=SHAPEIT2.v904
##log_file=shapeit_06042026_14h11m12s_d2d9364e-df91-419a-99c5-4fa00c90526e.log
##FORMAT=<ID=GT,Number=1,Type=String,Description="Phased Genotype">
#CHROM  POS ID  REF ALT QUAL    FILTER  INFO    FORMAT  NA18939 NA18940 NA18941 NA18942 NA18943 NA18944 NA18945 NA18946 NA18947 NA18948 NA18949 NA18950 NA18951 NA18952 NA18953 NA18954 NA18956 NA18957 NA18959 NA18960 NA18961 NA18962 NA18964 NA18965 NA18966 NA18967 NA18968 NA18969 NA18970 NA18971 NA18972 NA18973 NA18974 NA18975 NA18976 NA18977 NA18978 NA18979 NA18980 NA18981 NA18982 NA18983 NA18984 NA18985 NA18986 NA18987 NA18988 NA18989 NA18990 NA18991 NA18992 NA18993 NA18994 NA18995 NA18997 NA18998 NA18999 NA19000 NA19001 NA19002 NA19003 NA19004 NA19005 NA19006 NA19007 NA19009 NA19010 NA19011 NA19012 NA19054 NA19055 NA19056 NA19057 NA19058 NA19059 NA19060 NA19062 NA19063 NA19064 NA19065 NA19066 NA19067 NA19068 NA19070 NA19072 NA19074 NA19075 NA19076 NA19077 NA19078 NA19079 NA19080 NA19081 NA19082 NA19083 NA19084 NA19085 NA19086 NA19087 NA19088 NA19089 NA19090 NA19091
22  16051453    22:16051453:A:C C   A   .   PASS    .   GT  1|1 1|1 1|1 1|1 1|1 1|1 0|1 1|1 1|1 1|1 1|1 1|0 1|0 1|1 1|1 1|1 1|1 1|1 1|1 1|1 1|1 1|1 1|1 1|1 1|1 1|1 1|1 1|1 1|1 1|1 1|1 1|1 0|1 1|1 0|1 1|1 1|1 1|1 1|1 1|1 1|1 1|1 0|1 1|1 0|1 1|1 1|1 1|1 1|1 1|1 0|1 1|1 1|0 1|1 1|1 1|1 1|1 1|1 1|1 1|1 1|1 1|1 1|1 1|1 1|1 1|1 1|1 1|1 1|1 1|1 1|1 1|1 1|1 0|1 0|1 1|1 1|1 1|1 0|1 1|1 1|1 1|0 1|1 1|1 1|1 1|1 1|1 1|1 1|0 1|1 1|0 1|1 1|1 1|1 1|1 1|1 1|1 1|1 1|1 1|1 1|1 1|1 1|1

References

• (Li & Stephens model) Li, N., & Stephens, M. (2003). Modeling linkage disequilibrium and identifying recombination hotspots using single-nucleotide polymorphism data. Genetics, 165(4), 2213-2233. https://doi.org/10.1093/genetics/165.4.2213

• (Pre-phasing strategy) Howie, B., Fuchsberger, C., Stephens, M., Marchini, J., & Abecasis, G. R. (2012). Fast and accurate genotype imputation in genome-wide association studies through pre-phasing. Nature Genetics, 44(8), 955-959. https://doi.org/10.1038/ng.2354

• (PHASE) Stephens, M., Smith, N. J., & Donnelly, P. (2001). A new statistical method for haplotype reconstruction from population data. The American Journal of Human Genetics, 68(4), 978-989. https://doi.org/10.1086/319501

• (MaCH) Li, Y., Willer, C. J., Ding, J., Scheet, P., & Abecasis, G. R. (2010). MaCH: using sequence and genotype data to estimate haplotypes and unobserved genotypes. Genetic Epidemiology, 34(8), 816-834. https://doi.org/10.1002/gepi.20533

• (EAGLE2) Loh, P. R., Danecek, P., Palamara, P. F., Fuchsberger, C., A Reshef, Y., K Finucane, H., ... & L Price, A. (2016). Reference-based phasing using the Haplotype Reference Consortium panel. Nature Genetics, 48(11), 1443-1448. https://doi.org/10.1038/ng.3679

• (SHAPEIT2) Delaneau, O., Zagury, J. F., & Marchini, J. (2013). Improved whole-chromosome phasing for disease and population genetic studies. Nature Methods, 10(1), 5-6. https://doi.org/10.1038/nmeth.2307

• (SHAPEIT5) Delaneau, O., Zagury, J. F., Robinson, M. R., Marchini, J. L., & Dermitzakis, E. T. (2019). Accurate, scalable and integrative haplotype estimation. Nature Communications, 10(1), 5436. https://doi.org/10.1038/s41467-019-13225-y

• (BEAGLE) Browning, S. R., & Browning, B. L. (2007). Rapid and accurate haplotype phasing and missing-data inference for whole-genome association studies by use of localized haplotype clustering. The American Journal of Human Genetics, 81(5), 1084-1097. https://doi.org/10.1086/521987