Kinship, inbreeding & relatedness coefficients¶
Terms
Definition
These quantities all involve identity by descent (IBD) but target different random experiments: kinship phi describes two individuals; inbreeding F describes one individual's two homologues; relatedness r (the usual coefficient of relatedness) is the pairwise IBD probability linked to kinship by r = 2phi under standard diploid conventions. Pipeline outputs differ in scaling - check whether a matrix stores phi, 2phi, or something else.
Topics
How they differ¶
| Kinship coefficient (φ) | Inbreeding coefficient (F) | Relatedness coefficient (r) | |
|---|---|---|---|
| Who / what | A pair of individuals | A single individual (two alleles at a locus) | A pair of individuals |
| Core idea | Pick one random allele from A and one from B (same locus); probability they are IBD. | The two alleles within the individual are IBD more (or less) often than under random mating—seen in HWE departures and heterozygosity. | Pick one random allele from A and one from B; probability they are IBD—in standard diploid pedigree usage this is the quantity r, equal to twice kinship: r = 2φ. |
| Typical GWAS use | Genetic relationship matrix (GRM), linear mixed models, KING / PLINK kinship tables. | Sample QC (F-hat, PLINK --het), flags for contamination or structure; ties to diagonal self-relatedness in some matrix conventions. |
Relationship filters (“r above threshold”), pedigree expectations; often reported interchangeably with coefficient of relatedness (r). |
Rule of thumb: Pairwise sharing → φ and/or r (read the docs for scaling); within-person IBD excess → F. If a column is named “kinship” or “relatedness,” confirm whether values are φ, r, or 2φ.
Other meanings (optional)¶
- F vs FST: The symbol F also appears in fixation indices (e.g. FST)—population structure, not individual inbreeding. See F-statistics and fixation index.
- Software rescaling: Some tools report kinship so that duplicates or identical genomes map to 0.5 instead of 0.25; always read the tool’s definition before comparing to textbook φ. See kinship.
- “Relatedness coefficient” naming: Many papers use r for the same concept as coefficient of relatedness (r); the short relatedness coefficient entry points there.
Related terms¶
- Coefficient of relatedness (r)
- Coefficient of relationship
- Genetic relationship matrix (GRM)
- Identity by descent (IBD)
- Relatedness
- Relatedness and sample structure
- Linear mixed model (LMM)
- KING-robust kinship
- PI_HAT
References¶
- Hartl DL, Clark AG. (2007). Principles of Population Genetics. Sinauer Associates.
- Manichaikul A, et al. (2010). Robust relationship inference in genome-wide association studies. Bioinformatics.
- GWASTutorial: Relatedness and sample structure; Genotype Data QC.