A Log-Ratio Biplot Approach for Exploring Genetic Relatedness Based on Identity by State

Abstract

The detection of cryptic relatedness in large population-based cohorts is of great importance in genome research. The usual approach for detecting closely related individuals is to plot allele sharing statistics, based on identity-by-state or identity-by-descent, in a two-dimensional scatterplot. This approach ignores that allele sharing data across individuals has in reality a higher dimensionality, and neither regards the compositional nature of the underlying counts of shared genotypes. In this paper we develop biplot methodology based on log-ratio principal component analysis that overcomes these restrictions. This leads to entirely new graphics that are essentially useful for exploring relatedness in genetic databases from homogeneous populations. The proposed method can be applied in an iterative manner, acting as a looking glass for more remote relationships that are harder to classify. Datasets from the 1,000 Genomes Project and the Genomes For Life-GCAT Project are used to illustrate the proposed method. The discriminatory power of the log-ratio biplot approach is compared with the classical plots in a simulation study. In a non-inbred homogeneous population the classification rate of the log-ratio principal component approach outperforms the classical graphics across the whole allele frequency spectrum, using only identity by state. In these circumstances, simulations show that with 35,000 independent bi-allelic variants, log-ratio principal component analysis, combined with discriminant analysis, can correctly classify relationships up to and including the fourth degree.

A likelihood ratio approach for identifying three-quarter siblings in genetic databases

“…The LR approach can be of great help to detect such cases. The LR approach developed in this paper confirmed eight 3/4S pairs previously uncovered by a log-ratio biplot (LR-kinbiplot) approach (Graffelman et al, 2019 ) for genome-wide SNP array data from the GCAT cohort. The assessment of the precise relationship of a pair based on the numerical values of the LRs, or on a plot of the LRs, ignores the uncertainty in these statistics.…”

“…In the present work, we consider 5075 GCAT participants of Caucasian ancestry and 756,003 SNPs that passed strict quality control (Galvan-Femenia et al, 2018 ). A previous relatedness research analysis of this dataset reported 63 FS, eight 3/4S, and 12 2nd-degree candidate pairs (Graffelman et al, 2019 ).…”

“… FS~UN, 3/4S~UN and 2nd~UN are the LR values for each pair. LR-kinbiplot is the inferred relationship from Graffelman et al ( 2019 ). : estimated kinship coefficient.…”

“…In this paper, we therefore develop a likelihood ratio (LR) approach that will allow us to identify three-quarter siblings (3/4S), a family relationship whose individuals share fewer alleles than 1st-degree relationships but more alleles than 2nd-degree relatives (Table 1 ). A 3/4S pair has one common parent, whereas their unshared parents have a first-degree relationship (FS or PO; see Graffelman et al 2019 Fig. S 2 ).…”

Immune Cell Landscape Identification Associates Intrarenal Mononuclear Phagocytes With Onset and Remission of Lupus Nephritis in NZB/W Mice

“…Therefore, PCA was utilized in the current study to ascertain primary sources of variance in the fraction of diverse infiltrating immune cell types among different groups, and the prominent sources of variance can likely be the diagnostic clues for LN onset or predictive biomarkers for early LN remission induction. To be specific, log-ratio PCA is proposed as an efficient tool for the exploration of compositional data ( Graffelman et al, 2019 ); thus, we followed that approach by applying the centered log-ratio ( clr ) transformation to the compositional data. In brief, the compositional data of immune cell fractions derived from CIBERSORT was expressed in isometric coordinates.…”