A log-ratio biplot approach for exploring genetic relatedness based on identity by state

Relatedness:

• UN = unrelated
• 6TH = sixth degree relationships (second cousins once removed)
• 5TH = fifth degree relationships (second cousins)
• 4TH = fourth degree relationships (first cousins once removed)
• 3RD = third degree relationships (first cousins)
• 2ND = second degree relationships (half siblings, avuncular, grandparent-grandchild)
• 3/4S = three quarter siblings
• FS = full siblings
• PO = parent-offspring
• MZ = monozygotic twins

Dependencies

• R (https://www.r-project.org/)
• PLINK 1.9 (https://www.cog-genomics.org/plink2/)

LR_kinbiplot() function

Input parameters:

Parameter	Description
data.in	path of your PLINK files
data.out	name of your dataset (no spaces allowed)
chr	chromosomes used for the analysis (default 1-22)
geno	missing call rate threshold (default 0)
hwe	Hardy Weingberg equilirbium mid p-value threshold (default 0.05)
MAF	minor allele frequency threshold (default 0.40)
LD.window	LD window size in kb (default 50)
LD.step	number of variants to shift the window at each step (default 5)
LD.correlation	pairwise LD correlation (r2) threshold (default 0.2)
rel.cutoff	kinship coefficient threshold to detect potential unrelated individuals (default 0.025)
mz.ibd2	IBD2 threshold to detect potential MZ pairs (default 0.7)
po.ibd1	IBD1 threshold to detect potential PO pairs (default 0.7)
relationships	predicted relationships in the analysis (default UN, 6TH, 5TH, 4TH, 3RD, 2ND, 3/4S and FS)
nsim.rel	number of simulations for each relationship used as training set (default 20). The prediction of relationships is sensitive to this parameter. We recommend using nsim.rel = 100
rel.colors	colors used to represent each predicted relationship in the log-ratio biplot (default forestgreen, darkorange, deeppink2, cyan2, darkgoldenrod2, darkorchid2, black and dodgerblue2)
peel.and.zoom	peel and zoom log-ratio biplot approach (default TRUE)

Example of the CEU population from 1000Genomes project

Log-ratio biplot analysis for 165 individuals and 1,457,897 variants from the CEU population. Computation time: 7 minutes in a single CPU processor (Intel Core i5-4300U, 1.90-2.50 GHz, 64bits) with 4GB RAM.

setwd("github")
source("LR-kinbiplot.R")

# logratio biplot with UN, 6TH, 5TH, 4TH, 3RD, 2ND, 3/4S and FS relationships and peel and zoom approach

logpca = LR_kinbiplot(data.in="data/CEU",
                                data.out = "CEU_population",
                                nsim.rel = 20,
                                peel.and.zoom = T)

table(logpca$pairs.ids$prediction)

  2ND  3.4S   3RD   4TH   5TH   6TH    FS    UN 
    2     0     1     5    22  2884     1 10519

References

• Chang CC, Chow CC, Tellier LCAM, Vattikuti S, Purcell SM, Lee JJ (2015) Second-generation PLINK: rising to the challenge of larger and richer datasets. GigaScience, 4.
• Graffelman J, Moreno V (2013). The mid p-value in exact tests for Hardy-Weinberg equilibrium. Statistical applications in genetics and molecular biology, 12(4), 433-448.
• Graffelman J, Galván Femenía I, de Cid R and Barceló Vidal C (2019) A Log-Ratio Biplot Approach for Exploring Genetic Relatedness Based on Identity by State. Front. Genet. 10:341. doi: 10.3389/fgene.2019.00341