Population Structure and Relatedness Inference using the GENESIS Package
2022-03-15
Contents
1 Overview
GENESIS provides statistical methodology for analyzing genetic data from samples with population structure and/or familial relatedness. This vignette provides a description of how to use GENESIS for inferring population structure, as well as estimating relatedness measures such as kinship coefficients, identity by descent (IBD) sharing probabilities, and inbreeding coefficients. GENESIS uses PC-AiR for population structure inference that is robust to known or cryptic relatedness, and it uses PC-Relate for accurate relatedness estimation in the presence of population structure, admixutre, and departures from Hardy-Weinberg equilibrium.
2 Data
2.1 Reading in Genotype Data
The functions in the GENESIS package can read genotype data from a GenotypeData class object as created by the GWASTools package. Through the use of GWASTools, a GenotypeData class object can easily be created from:
- an R matrix of SNP genotype data
- a GDS file
- PLINK files
Example R code for creating a GenotypeData object is presented below. Much more detail can be found in the GWASTools package reference manual.
GENESIS can also work with genotype data from sequencing, starting with a VCF file. For examples using this format, see the vignette “Analyzing Sequence Data using the GENESIS Package”.
2.1.1 R Matrix
geno <- MatrixGenotypeReader(genotype = genotype, snpID = snpID,
chromosome = chromosome, position = position,
scanID = scanID)
genoData <- GenotypeData(geno)genotypeis a matrix of genotype values coded as 0 / 1 / 2, where rows index SNPs and columns index samplessnpIDis an integer vector of unique SNP IDschromosomeis an integer vector specifying the chromosome of each SNPpositionis an integer vector specifying the position of each SNPscanIDis a vector of unique individual IDs
2.1.2 GDS files
geno <- GdsGenotypeReader(filename = "genotype.gds")
genoData <- GenotypeData(geno)filenameis the file path to the GDS object
2.1.3 PLINK files
The SNPRelate package provides the snpgdsBED2GDS function to convert binary PLINK files into a GDS file.
snpgdsBED2GDS(bed.fn = "genotype.bed",
bim.fn = "genotype.bim",
fam.fn = "genotype.fam",
out.gdsfn = "genotype.gds")bed.fnis the file path to the PLINK .bed filebim.fnis the file path to the PLINK .bim filefam.fnis the file path to the PLINK .fam fileout.gdsfnis the file path for the output GDS file
Once the PLINK files have been converted to a GDS file, then a GenotypeData object can be created as described above.
2.2 HapMap Data
To demonstrate PC-AiR and PC-Relate analyses with the GENESIS package, we analyze SNP data from the Mexican Americans in Los Angeles, California (MXL) and African American individuals in the southwestern USA (ASW) population samples of HapMap 3. Mexican Americans and African Americans have a diverse ancestral background, and familial relatives are present in these data. Genotype data at a subset of 20K autosomal SNPs for 173 individuals are provided as a GDS file.
gdsfile <- system.file("extdata", "HapMap_ASW_MXL_geno.gds", package="GENESIS")3 Principal Components Analysis in Related Samples (PC-AiR)
3.1 LD pruning
Before running PCA, we use LD pruning to select a set of independent SNPs for analysis. We use the snpgdsLDpruning in the SNPRelate package, which returns a list of snp IDs.
library(SNPRelate)
# read in GDS data
gds <- snpgdsOpen(gdsfile)
snpset <- snpgdsLDpruning(gds, method="corr", slide.max.bp=10e6,
ld.threshold=sqrt(0.1), verbose=FALSE)
pruned <- unlist(snpset, use.names=FALSE)
length(pruned)## [1] 3826head(pruned)## [1] 6 7 15 17 22 31snpgdsClose(gds)3.2 Pairwise Measures of Ancestry Divergence
It is possible to identify a subset of mutually unrelated individuals in a sample based solely on pairwise measures of genetic relatedness (i.e. kinship coefficients). However, in order to obtain accurate population structure inference for the entire sample, it is important that the ancestries of all individuals in the sample are represented by at least one individual in this subset. In order to identify a mutually unrelated and ancestry representative subset of individuals, PC-AiR also utilizes measures of ancestry divergence. These measures are calculated using the KING-robust kinship coefficient estimator (Manichaikul et al., 2010), which provides systematically negative estimates for unrelated pairs of individuals with different ancestry. The number of negative pairwise estimates that an individual has provides information regarding how different that individual’s ancestry is from the rest of the sample, which helps to prioritize individuals that should be kept in the ancestry representative subset.
The relevant output from the KING software is two text files with the file extensions .kin0 and .kin. The kingToMatrix function can be used to extract the kinship coefficients (which we use as divergence measures) from this output and create a matrix usable by the *[GENESIS](https://bioconductor.org/packages/3.15/GENESIS)* functions.
# create matrix of KING estimates
library(GENESIS)
KINGmat <- kingToMatrix(
c(system.file("extdata", "MXL_ASW.kin0", package="GENESIS"),
system.file("extdata", "MXL_ASW.kin", package="GENESIS")),
estimator = "Kinship")
KINGmat[1:5,1:5]## 5 x 5 Matrix of class "dsyMatrix"
## NA19625 NA19649 NA19650 NA19651 NA19652
## NA19625 0.5000 -0.0761 -0.0656 -0.0497 -0.0486
## NA19649 -0.0761 0.5000 0.2513 -0.0187 -0.0141
## NA19650 -0.0656 0.2513 0.5000 -0.0037 -0.0033
## NA19651 -0.0497 -0.0187 -0.0037 0.5000 0.0112
## NA19652 -0.0486 -0.0141 -0.0033 0.0112 0.5000The column and row names of the matrix are the individual IDs, and each off-diagonal entry is the KING-robust estimate for the specified pair of individuals.
Alternative to running the KING software, the snpgdsIBDKING function from the SNPRelate package can be used to calculate the KING-robust estimates directly from a GDS file. The ouput of this function contains a matrix of pairwise estimates, which can be used by the GENESIS functions.
3.3 Running PC-AiR
The PC-AiR algorithm requires pairwise measures of both kinship and ancestry divergence in order to partition the sample into an “unrelated subset” and a “related subset.” The kinship coefficient estimates are used to identify relatives, as only one individual from a set of relatives can be included in the “unrelated subset,” and the rest must be assigned to the “related subset.” The ancestry divergence measures calculated from KING-robust are used to help select which individual from a set of relatives has the most unique ancestry and should be given priority for inclusion in the “unrelated subset.”
The KING-robust estimates read in above are always used as measures of ancestry divergence for unrelated pairs of individuals, but they can also be used as measures of kinship for relatives (NOTE: they may be biased measures of kinship for admixed relatives with different ancestry). The pcair function performs the PC-AiR analysis.
We use the GWASTools package to create the GenotypeData object needed by GENESIS.
library(GWASTools)
HapMap_geno <- GdsGenotypeReader(filename = gdsfile)
# create a GenotypeData class object
HapMap_genoData <- GenotypeData(HapMap_geno)
HapMap_genoData## An object of class GenotypeData
## | data:
## File: /tmp/RtmpoUJbO4/Rinst18496c12e17b9c/GENESIS/extdata/HapMap_ASW_MXL_geno.gds (901.8K)
## + [ ] *
## |--+ sample.id { Int32,factor 173 ZIP(40.9%), 283B } *
## |--+ snp.id { Int32 20000 ZIP(34.6%), 27.1K }
## |--+ snp.position { Int32 20000 ZIP(34.6%), 27.1K }
## |--+ snp.chromosome { Int32 20000 ZIP(0.13%), 103B }
## \--+ genotype { Bit2 20000x173, 844.7K } *
## | SNP Annotation:
## NULL
## | Scan Annotation:
## NULL# run PC-AiR on pruned SNPs
mypcair <- pcair(HapMap_genoData, kinobj = KINGmat, divobj = KINGmat,
snp.include = pruned)## Principal Component Analysis (PCA) on genotypes:
## Excluding 16,174 SNPs (non-autosomes or non-selection)
## Excluding 0 SNP (monomorphic: TRUE, MAF: NaN, missing rate: NaN)
## # of samples: 97
## # of SNPs: 3,826
## using 1 thread
## # of principal components: 32
## PCA: the sum of all selected genotypes (0,1,2) = 185850
## CPU capabilities: Double-Precision SSE2
## Tue Mar 15 16:31:01 2022 (internal increment: 32048)
##
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## Tue Mar 15 16:31:01 2022 Begin (eigenvalues and eigenvectors)
## Tue Mar 15 16:31:01 2022 Done.
## SNP Loading:
## # of samples: 97
## # of SNPs: 3,826
## using 1 thread
## using the top 32 eigenvectors
## SNP Loading: the sum of all selected genotypes (0,1,2) = 185850
## Tue Mar 15 16:31:01 2022 (internal increment: 65536)
##
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## Tue Mar 15 16:31:01 2022 Done.
## Sample Loading:
## # of samples: 76
## # of SNPs: 3,826
## using 1 thread
## using the top 32 eigenvectors
## Sample Loading: the sum of all selected genotypes (0,1,2) = 144468
## Tue Mar 15 16:31:01 2022 (internal increment: 65536)
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## Tue Mar 15 16:31:01 2022 Done.genoDatais aGenotypeDataclass objectkinobjis a matrix of pairwise kinship coefficient estimatesdivobjis a matrix of pairwise measures of ancestry divergence (KING-robust estimates)snp.includeis a vector of snp IDs
If better estimates of kinship coefficients are available, then the kinobj input can be replaced with a similar matrix of these estimates. The divobj input should always remain as the KING-robust estimates.
3.3.1 Reference Population Samples
As PCA is an unsupervised method, it is often difficult to identify what population structure each of the top PCs represents. In order to provide some understanding of the inferred structure, it is sometimes recommended to include reference population samples of known ancestry in the analysis. If the data set contains such reference population samples, we may want to make sure that these reference population samples are included in the “unrelated subset.” This can be accomplished by setting the input unrel.set equal to a vector, IDs, of the individual IDs for the reference population samples.
mypcair <- pcair(HapMap_genoData, kinobj = KINGmat, divobj = KINGmat,
snp.include = pruned, unrel.set = IDs)This will force individuals specified with unrel.set into the “unrelated subset,” move any of their relatives into the “related subset,” and then perform the PC-AiR partitioning algorithm on the remaining samples.
3.3.2 Partition a Sample without Running PCA
It may be of interest to partition a sample into an ancestry representative “unrelated subset” of individuals and a “related subset” of individuals without performing a PCA. The pcairPartition function, which is called within the pcair function, enables the user to do this.
part <- pcairPartition(kinobj = KINGmat, divobj = KINGmat)The output contains two vectors that give the individual IDs for the “unrelated subset” and the “related subset.”
head(part$unrels); head(part$rels)## [1] "NA19708" "NA19711" "NA19712" "NA19737" "NA19740" "NA19741"## [1] "NA19686" "NA20346" "NA20345" "NA20347" "NA19664" "NA19677"As with the pcair function, the input unrel.set can be used to specify certain individuals that must be part of the “unrelated subset.”
3.4 Output from PC-AiR
An object returned from the pcair function has class pcair. A summary method for an object of class pcair is provided to obtain a quick overview of the results.
summary(mypcair)## Call:
## .pcair(gdsobj = gdsobj, kinobj = kinobj, divobj = divobj, kin.thresh = kin.thresh,
## div.thresh = div.thresh, unrel.set = unrel.set, sample.include = sample.include,
## snp.include = snp.include, num.cores = num.cores, verbose = verbose)
##
## PCA Method: PC-AiR
##
## Sample Size: 173
## Unrelated Set: 97 Samples
## Related Set: 76 Samples
##
## Kinship Threshold: 0.02209709
## Divergence Threshold: -0.02209709
##
## Principal Components Returned: 32
## Eigenvalues: 2.946 1.717 1.326 1.292 1.277 1.255 1.242 1.223 1.219 1.201 ...
## SNPs Used: 3826The output provides the total sample size along with the number of individuals assigned to the unrelated and related subsets, as well as the threshold values used for determining which pairs of individuals were related or ancestrally divergent. The eigenvalues for the top PCs are also shown, which can assist in determining the number of PCs that reflect structure. The minor allele frequency (MAF) filter used for excluding SNPs is also specified, along with the total number of SNPs analyzed after this filtering. Details describing how to modify the analysis parameters and the available output of the function can be found with the command help(pcair).
3.4.1 Plotting PC-AiR PCs
The GENESIS package also provides a plot method for an object of class pcair to quickly visualize pairs of PCs. Each point in one of these PC pairs plots represents a sample individual. These plots help to visualize population structure in the sample and identify clusters of individuals with similar ancestry.
# plot top 2 PCs
plot(mypcair)
# plot PCs 3 and 4
plot(mypcair, vx = 3, vy = 4)
The default is to plot PC values as black dots and blue pluses for individuals in the “unrelated subset” and “related subsets” respectively. The plotting colors and characters, as well as other standard plotting parameters, can be changed with the standard input to the plot function.
4 Relatedness Estimation Adjusted for Principal Components (PC-Relate)
4.1 Running PC-Relate
PC-Relate uses the ancestry representative principal components (PCs) calculated from PC-AiR to adjust for the population structure and ancestry of individuals in the sample and provide accurate estimates of recent genetic relatedness due to family structure. The pcrelate function performs the PC-Relate analysis.
The training.set input of the pcrelate function allows for the specification of which samples are used to estimate the ancestry adjustment at each SNP. The adjustment tends to perform best when close relatives are excluded from training.set, so the individuals in the “unrelated subset” from the PC-AiR analysis are typically a good choice. However, when an “unrelated subset” is not available, the adjustment still works well when estimated using all samples (training.set = NULL).
In order to run PC-Relate, we first need to create an iterator object to read SNPs in blocks. We create the iterator such that only pruned SNPs are returned in each block.
# run PC-Relate
HapMap_genoData <- GenotypeBlockIterator(HapMap_genoData, snpInclude=pruned)
mypcrelate <- pcrelate(HapMap_genoData, pcs = mypcair$vectors[,1:2],
training.set = mypcair$unrels,
BPPARAM = BiocParallel::SerialParam())genoDatais aGenotypeIteratorclass objectpcsis a matrix whose columns are the PCs used for the ancestry adjustmenttraining.setis a vector of individual IDs specifying which samples are used to esimate the ancestry adjustment at each SNP
If estimates of IBD sharing probabilities are not desired, then setting the input ibd.probs = FALSE will speed up the computation.
4.2 Output from PC-Relate
The pcrelate function will return an object of class pcrelate, which is a list of two data.frames: kinBtwn with pairwise kinship values, and kinSelf with inbreeding coefficients.
plot(mypcrelate$kinBtwn$k0, mypcrelate$kinBtwn$kin, xlab="k0", ylab="kinship")
A function is provided for making a genetic relationship matrix (GRM). Using a threshold for kinship will create a sparse matrix by setting kinship for pairs less than the threshold to 0. This can be useful to reduce memory usage for very large sample sizes.
iids <- as.character(getScanID(HapMap_genoData))
pcrelateToMatrix(mypcrelate, sample.include = iids[1:5], thresh = 2^(-11/2), scaleKin = 2)## 5 x 5 sparse Matrix of class "dsCMatrix"
## NA19703 NA19919 NA19916 NA19835 NA20282
## NA19703 1.02340583 0.02751476 . . .
## NA19919 0.02751476 0.95198442 . . .
## NA19916 . . 1.013003 . .
## NA19835 . . . 0.9736479 .
## NA20282 . . . . 0.9667705pcrelobjis the output frompcrelate; either a classpcrelateobject or a GDS filesample.includeis a vector of individual IDs specifying which individuals to include in the table or matrixthreshspecifies a minimum kinship coefficient value to include in the GRMscaleKinspecifies a factor to multiply the kinship coefficients by in the GRM
5 References
Conomos M.P., Reiner A.P., Weir B.S., & Thornton T.A. (2016). Model-free Estimation of Recent Genetic Relatedness. American Journal of Human Genetics, 98(1), 127-148.
Conomos M.P., Miller M.B., & Thornton T.A. (2015). Robust Inference of Population Structure for Ancestry Prediction and Correction of Stratification in the Presence of Relatedness. Genetic Epidemiology, 39(4), 276-293.
Gogarten, S.M., Bhangale, T., Conomos, M.P., Laurie, C.A., McHugh, C.P., Painter, I., … & Laurie, C.C. (2012). GWASTools: an R/Bioconductor package for quality control and analysis of Genome-Wide Association Studies. Bioinformatics, 28(24), 3329-3331.
Manichaikul, A., Mychaleckyj, J.C., Rich, S.S., Daly, K., Sale, M., & Chen, W.M. (2010). Robust relationship inference in genome-wide association studies. Bioinformatics, 26(22), 2867-2873.