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.
Principal Components Analysis (PCA) is commonly applied to genome-wide SNP genotype data from samples in genetic studies for population structure (i.e. ancestry) inference. PCA takes genotype values at hundreds of thousands of SNPs as input and performs a dimension reduction to principal components (PCs) that best reflect the variability of the data. Typically the top PCs calculated from the genotype data reflect population structure among the sample individuals. However, when a sample contains familial relatives, either known or unknown (cryptic), the top PCs obtained from a standard PCA are often confounded by this family structure and reflect clusters of close relatives.
The PC-AiR method is used to perform a PCA for the detection of population structure that is robust to possible familial relatives in the sample. Unlike a standard PCA, PC-AiR accounts for relatedness (known or cryptic) in the sample and identifies PCs that accurately capture population structure and not family structure. In order to accomplish this, PC-AiR uses measures of pairwise relatedness (kinship coefficients) and measures of pairwise ancestry divergence to identify an ancestry representative subset of mutually unrelated individuals. A standard PCA is performed on this "unrelated subset" of individuals, and PC values for the excluded "related subset" of indivdiuals are predicted from genetic similarity.
Many estimators exist that use genome-wide SNP genotype data from samples in genetic studies to estimate measures of recent genetic relatedness such as pairwise kinship coefficients, pairwise IBD sharing probabilities, and individual inbreeding coefficients. However, many of these estimators either make simplifying assumptions that do not hold in the presence of population structure and/or ancestry admixture, or they require reference population panels of known ancestry from pre-specified populations. When assumptions are violated, these estimators can provide highly biased estimates.
The PC-Relate method is used to accurately estimate measures of recent genetic relatedness in samples with unknown or unspecified population structure without requiring reference population panels. PC-Relate uses ancestry representative principal components to account for sample ancestry differences and provide estimates that are robust to population structure, ancestry admixture, and departures from Hardy-Weinberg equilibirum.
The functions in the GENESIS
package 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:
Example R code for creating a GenotypeData
object is presented below. Much more detail can be found in the GWASTools
package reference manual.
geno <- MatrixGenotypeReader(genotype = genotype, snpID = snpID, chromosome = chromosome, position = position, scanID = scanID) genoData <- GenotypeData(geno)
genotype
is a matrix of genotype values coded as 0 / 1 / 2, where rows index SNPs and columns index samplessnpID
is an integer vector of unique SNP IDschromosome
is an integer vector specifying the chromosome of each SNPposition
is an integer vector specifying the position of each SNPscanID
is a vector of unique individual IDsgeno <- GdsGenotypeReader(filename = "genotype.gds") genoData <- GenotypeData(geno)
filename
is the file path to the GDS objectThe 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.fn
is the file path to the PLINK .bed filebim.fn
is the file path to the PLINK .bim filefam.fn
is the file path to the PLINK .fam fileout.gdsfn
is the file path for the output GDS fileOnce the PLINK files have been converted to a GDS file, then a GenotypeData
object can be created as described above.
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.
library(GENESIS) library(GWASTools)
# read in GDS data gdsfile <- system.file("extdata", "HapMap_ASW_MXL_geno.gds", package="GENESIS") HapMap_geno <- GdsGenotypeReader(filename = gdsfile) # create a GenotypeData class object HapMap_genoData <- GenotypeData(HapMap_geno) HapMap_genoData
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 king2mat
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
functions. The iids
input of the king2mat
function should be used to ensure that the output matrix orders individuals in the same way as the GenotypeData
object.
# read individual IDs from GenotypeData object iids <- getScanID(HapMap_genoData) head(iids) # create matrix of KING estimates KINGmat <- king2mat(file.kin0 = system.file("extdata", "MXL_ASW.kin0", package="GENESIS"), file.kin = system.file("extdata", "MXL_ASW.kin", package="GENESIS"), iids = iids) KINGmat[1:5,1:5]
The 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.
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.
# run PC-AiR mypcair <- pcair(genoData = HapMap_genoData, kinMat = KINGmat, divMat = KINGmat)
genoData
is a GenotypeData
class objectkinMat
is a matrix of pairwise kinship coefficient estimatesdivMat
is a matrix of pairwise measures of ancestry divergence (KING-robust estimates)If better estimates of kinship coefficients are available, then the kinMat
input can be replaced with a similar matrix of these estimates. The divMat
input should always remain as the KING-robust estimates.
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 use only those individuals as the "unrelated subset" for performing the PCA and predict values for all other sample individuals. 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(genoData = HapMap_genoData, unrel.set = IDs)
If, instead, we want to make sure that these reference population samples are included in the "unrelated subset," but also allow for the PC-AiR algorithm to select additional individuals from the sample to be a part of the "unrelated subset," then this can be accomplished by using the inputs kinMat
, divMat
, and unrel.set
together.
mypcair <- pcair(genoData = HapMap_genoData, kinMat = KINGmat, divMat = KINGmat, 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.
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(kinMat = KINGmat, divMat = 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)
As with the pcair
function, the input unrel.set
can be used to specify certain individuals that must be part of the "unrelated subset."
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)
The 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)
.
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.
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
).
# run PC-Relate mypcrelate <- pcrelate(genoData = HapMap_genoData, pcMat = mypcair$vectors[,1:2], training.set = mypcair$unrels)
genoData
is a GenotypeData
class objectpcMat
is a matrix whose columns are the PCs used for the ancestry adjustmenttraining.set
is a vector of individual IDs specifying which samples are used to esimate the ancestry adjustment at each SNPIf estimates of IBD sharing probabilities are not desired, then setting the input ibd.probs = FALSE
will speed up the computation.
The pcrelate
function will either return an object of class pcrelate
(when the input write.to.gds = FALSE
) or it will save the output to a GDS file (when the input write.to.gds = TRUE
). Saving the output to a GDS file is useful for large samples, as it allows for efficient storage and access to the estimates (see the package gdsfmt
for more details). The following command can be used to read in the results from a previous PC-Relate analysis saved to the GDS file "tmp_pcrelate.gds"
library(gdsfmt) mypcrelate <- openfn.gds("tmp_pcrelate.gds")
Functions are provided for easily reading the output from pcrelate
(either a class pcrelate
object or a GDS file) and making a table of pairwise relatedness estimates, a table of individual inbreeding coeficients, and a genetic relationship matrix (GRM).
pcrelateReadKinship(pcrelObj = mypcrelate, scan.include = iids[1:40], kin.thresh = 2^(-9/2)) pcrelateReadInbreed(pcrelObj = mypcrelate, scan.include = iids[1:40], f.thresh = 2^(-11/2)) pcrelateMakeGRM(pcrelObj = mypcrelate, scan.include = iids[1:5], scaleKin = 2)
close(HapMap_genoData)
pcrelObj
is the output from pcrelate
; either a class pcrelate
object or a GDS filescan.include
is a vector of individual IDs specifying which individuals to include in the table or matrixkin.thresh
specifies a minimum kinship coefficient value to include in the tablef.thresh
specifies a minimum inbreeding coefficient value to include in the tablescaleKin
specifies a factor to multiply the kinship coefficients by in the GRMConomos 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.
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