Author: Simon Rio

# AdmixPoly-vignette

#### Simon Rio

Table of Contents

- Simulate admixed population
- Unsupervised global admixture inference
- Semi-supervised global admixture inference
- Local admixture inference
- Import genotyping data

## Simulate admixed population

First, an admixed dataset is simulated using the `SimulatePop` function, considering `N=50` individuals of ploidy `P=8`, `M=200` markers with `L=10` alleles distributed on `C=5` chromosomes, and `K=4` ancestral groups.

    DataSim <- AdmixPoly::SimulatePop(K=3L, N=50L, P=8L, M=200L, C=2L, L=10L, NbThreads = 1)

The resulting `DataSim` object includes:

1. `Geno`: list of genotyping matrices over markers

    head(DataSim$Geno[[1]])
    #>      Allele1 Allele2 Allele3 Allele4 Allele5 Allele6 Allele7 Allele8 Allele9
    #> Ind1       0       1       0       0       1       1       1       0       1
    #> Ind2       0       2       3       0       1       0       1       0       0
    #> Ind3       0       5       2       0       0       0       1       0       0
    #> Ind4       0       1       2       2       0       0       1       2       0
    #> Ind5       0       3       1       1       0       0       2       0       0
    #> Ind6       0       1       1       1       1       2       1       1       0
    #>      Allele10
    #> Ind1        3
    #> Ind2        1
    #> Ind3        0
    #> Ind4        0
    #> Ind5        1
    #> Ind6        0

2. `Prop`: matrix of admixture proportions

    head(DataSim$Prop)
    #>            K1       K2       K3
    #> Ind1 0.120000 0.358125 0.521875
    #> Ind2 0.511250 0.386250 0.102500
    #> Ind3 0.826875 0.000000 0.173125
    #> Ind4 0.532500 0.467500 0.000000
    #> Ind5 0.802500 0.000000 0.197500
    #> Ind6 0.288125 0.242500 0.469375

3. `Freq`: list of matrices of allele frequencies in ancestral groups

    DataSim$Freq[[1]]
    #>       Allele1      Allele2   Allele3    Allele4    Allele5    Allele6   Allele7
    #> K1 0.02999937 0.3216599409 0.2827303 0.06252135 0.04569980 0.01259175 0.1560145
    #> K2 0.06062462 0.0007481235 0.3483231 0.01478613 0.04326888 0.04442491 0.1591765
    #> K3 0.00337067 0.0736675715 0.3034438 0.06786697 0.17255898 0.11904414 0.1678521
    #>       Allele8     Allele9   Allele10
    #> K1 0.01215938 0.019408693 0.05721497
    #> K2 0.19739411 0.001450772 0.12980285
    #> K3 0.03792193 0.036377344 0.01789647

4. `GeneticMap`: genetic map dataframe

    head(DataSim$GeneticMap)
    #>    Marker Chromosome Distance
    #> 1 Marker1       Chr1 0.000000
    #> 2 Marker2       Chr1 1.010101
    #> 3 Marker3       Chr1 2.020202
    #> 4 Marker4       Chr1 3.030303
    #> 5 Marker5       Chr1 4.040404
    #> 6 Marker6       Chr1 5.050505

## Unsupervised global admixture inference

From simulated data, admixture proportions can be estimated using the `AdmixGlobal` function:

    ResGlobalAdmix <- AdmixPoly::AdmixGlobal(Geno=DataSim$Geno, K=3L, MaxIter=100, Verbose=F, NbThreads = 1)

The estimated admixture proportions are available from:

    head(ResGlobalAdmix$Prop)
    #>              K1          K2           K3
    #> Ind1 0.07282037 0.586631814 0.3405478203
    #> Ind2 0.54379083 0.028524007 0.4276851646
    #> Ind3 0.99986987 0.000129129 0.0000010000
    #> Ind4 0.52300965 0.000001000 0.4769893518
    #> Ind5 0.89501427 0.104977331 0.0000084024
    #> Ind6 0.30286023 0.475294026 0.2218457398

They can be represented using the ggplot2-based `GlobalPlot` function:

    AdmixPoly::GlobalPlot(ResGlobalAdmix$Prop)

Estimated proportions are very close to simulated ones (up to an arbitrary labeling of groups), as indicated by the root mean square error (RMSE):

    group_corresp <- apply(cor(DataSim$Prop, ResGlobalAdmix$Prop), 2, which.max)
    sqrt(mean((DataSim$Prop-ResGlobalAdmix$Prop[,group_corresp])^2))
    #> [1] 0.05411083

Estimated allele frequencies are available from:

    ResGlobalAdmix$Freq[[1]]
    #>       Allele1    Allele2   Allele3    Allele4   Allele5   Allele6   Allele7
    #> K1 0.02606307 0.27612436 0.2928982 0.08291088 0.0966980 0.0000010 0.1683648
    #> K2 0.00000100 0.09006483 0.1418759 0.08626547 0.1543653 0.1179365 0.2086484
    #> K3 0.10961349 0.00000100 0.3478162 0.00000100 0.0000010 0.0866857 0.1102827
    #>       Allele8    Allele9   Allele10
    #> K1 0.00000100 0.00000100 0.05693766
    #> K2 0.09163336 0.04238131 0.06682790
    #> K3 0.17349010 0.00000100 0.17210782

The convergence can be checked from the log-likelihood:

    plot(ResGlobalAdmix$LogLik, xlab="Iterations", ylab="LogLik", type="o")

## Semi-supervised global admixture inference

Let us consider a second admixed population from the same ancestral groups with a higher admixture level by specifying a higher ‘AlphaProp’ value.

    DataSim2 <- AdmixPoly::SimulatePop(K=3L, N=50L, P=8L, M=200L, C=2L, L=10L,
                                       AlphaProp=10, Freq=DataSim$Freq, NbThreads = 1)

The higher admixture level can be illustrated using a barplot of simulated amdixture proportions.

    AdmixPoly::GlobalPlot(DataSim2$Prop)

In this case, it can be beneficial to initialize the algorithm with ancestral allele frequencies estimated using the first population ‘FreqInit=ResGlobalAdmix$Freq’ and only update admixture proportions ‘ParamToUpdate=“Prop”’.

    ResGlobalAdmix2 <- AdmixPoly::AdmixGlobal(Geno=DataSim2$Geno, K=3L, MaxIter=100, Verbose=F,
                                              FreqInit=ResGlobalAdmix$Freq, ParamToUpdate="Prop",
                                              NbThreads=1)

Again, estimated proportions are very close to simulated ones, as indicated by the RMSE:

    sqrt(mean((DataSim2$Prop-ResGlobalAdmix2$Prop[,group_corresp])^2))
    #> [1] 0.04976261

## Local admixture inference

Based on global admixture results, local admixture can be estimated for a given individual using the `AdmixLocal` function:

    Ind <- "Ind1"
    ResLocalAdmix <- AdmixPoly::AdmixLocal(Geno=DataSim$Geno, ResAdmixGlobal=ResGlobalAdmix,
                                           GeneticMap=DataSim$GeneticMap, Ind=Ind, P = 8L,
                                           SmoothParam=1, Verbose=F, NbThreads = 1)

Local ancestry dosages based on posterior probabilities are available from:

    head(ResLocalAdmix$Posterior$Chr1)
    #>                 K1       K2       K3
    #> Marker1 0.02703237 5.294020 2.678948
    #> Marker2 0.02187958 5.289784 2.688336
    #> Marker3 0.01811682 5.259741 2.722142
    #> Marker4 0.01743961 5.202371 2.780189
    #> Marker5 0.01576887 5.137736 2.846495
    #> Marker6 0.01484104 5.129085 2.856074

Alternatively, local ancestry dosages based on the Viterbi algorithm are available from:

    head(ResLocalAdmix$Viterbi$Chr1)
    #>         K1 K2 K3
    #> Marker1  0  5  3
    #> Marker2  0  5  3
    #> Marker3  0  5  3
    #> Marker4  0  5  3
    #> Marker5  0  5  3
    #> Marker6  0  5  3

The RMSE of estimated local ancestry proportions (ancestry dosages divided by the ploidy) is:

    sqrt(mean((DataSim$Ancestry[[Ind]]$Chr1/8-ResLocalAdmix$Posterior$Chr1[,group_corresp]/8)^2))
    #> [1] 0.07136965
    sqrt(mean((DataSim$Ancestry[[Ind]]$Chr1/8-ResLocalAdmix$Viterbi$Chr1[,group_corresp]/8)^2))
    #> [1] 0.07971303

Local ancestry dosages can be represented using the ggplot2-based `LocalPlot` function:

    AdmixPoly::LocalPlot(Ancestry = ResLocalAdmix$Posterior, GeneticMap=DataSim$GeneticMap)

Local admixture inference over the five first individuals can be run using:

    ResLocalAdmix_list <- lapply(paste0("Ind",1:5),function(i){
      res_i <- AdmixPoly::AdmixLocal(Geno=DataSim$Geno, ResAdmixGlobal=ResGlobalAdmix,
                                   GeneticMap=DataSim$GeneticMap, Ind=i, P=8L,
                                   SmoothParam=1, Verbose=F, NbThreads=1)
      return(res_i)
    })

When computing time is large, each individual can be run in parallel on a high-performance computing cluster.

## Import genotyping data

Genotyping data formatted as a variant call format (VCF) can be imported as:

    vcf_path <- system.file("extdata", "Test.vcf", package="AdmixPoly")
    DataVCF <- AdmixPoly::ReadVCF(File=vcf_path, NbThreads=1)

The resulting `DataVCF` object includes:

1. `MarkerInfo`: first eight columns of the VCF

    head(DataVCF$MarkerInfo)
    #> # A tibble: 6 × 9
    #>   MARKER        CHROM      POS ID    REF   ALT   QUAL  FILTER INFO
    #>   <chr>         <chr>    <int> <chr> <chr> <chr> <chr> <chr>  <chr>
    #> 1 Chr1_15892318 Chr1  15892318 .     A     T     .     .      .
    #> 2 Chr1_31209423 Chr1  31209423 .     T     C     .     .      .
    #> 3 Chr1_39962954 Chr1  39962954 .     C     G     .     .      .
    #> 4 Chr1_40515463 Chr1  40515463 .     G     A     .     .      .
    #> 5 Chr1_44904209 Chr1  44904209 .     A     T     .     .      .
    #> 6 Chr1_47542399 Chr1  47542399 .     T     C     .     .      .

2. `Geno`: list of genotyping matrices

    head(DataVCF$Geno[[1]])
    #>      A T
    #> IND1 4 4
    #> IND2 5 3
    #> IND3 1 7
    #> IND4 4 4
    #> IND5 0 8
    #> IND6 4 4

3. `GeneticMap`: genetic map dataframe in which physical between first and last marker of each chromosome are scaled to 100 cM

    head(DataVCF$GeneticMap)
    #> # A tibble: 6 × 3
    #>   Chromosome Marker        Distance
    #>   <chr>      <chr>            <dbl>
    #> 1 Chr1       Chr1_15892318      0
    #> 2 Chr1       Chr1_31209423     20.4
    #> 3 Chr1       Chr1_39962954     32.1
    #> 4 Chr1       Chr1_40515463     32.9
    #> 5 Chr1       Chr1_44904209     38.7
    #> 6 Chr1       Chr1_47542399     42.2

Instead of estimated dosages, read depth ratios can be imported by specifying the allele read depths field of the FORMAT column:

    DataVCF2 <- AdmixPoly::ReadVCF(File = vcf_path,AlleleDepthField = "AD",NbThreads = 1)

    head(DataVCF2$Geno[[1]])
    #>               A         T
    #> IND1 0.41935484 0.5806452
    #> IND2 0.50000000 0.5000000
    #> IND3 0.08108108 0.9189189
    #> IND4 0.68181818 0.3181818
    #> IND5 0.03125000 0.9687500
    #> IND6 0.53125000 0.4687500

Please note that read depth ratios are not scaled to the ploidy level, which must then be informed in the inference functions.

Another function can be used to read the haplotype presence-absence (HPA) format obtained from HaploCharmer:

    hpa_path <- system.file("extdata", "Test.hpa", package="AdmixPoly")
    DataHPA <- AdmixPoly::ReadHPA(File=hpa_path, NbThreads=1)

    head(DataHPA$Geno[[1]])
    #>            hap1      hap2      hap3
    #> IND1 0.54545455 0.1818182 0.2727273
    #> IND2 0.48888889 0.2444444 0.2666667
    #> IND3 0.08823529 0.6764706 0.2352941
    #> IND4 0.08108108 0.4054054 0.5135135
    #> IND5 0.00000000 0.3684211 0.6315789
    #> IND6 0.45454545 0.1818182 0.3636364