GRI (Genetic Relatedness Index) Calculators

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Genetic relatedness quantifies the probability that two individuals share alleles that are identical by descent (IBD) from a common ancestor. The coefficient of relatedness (r) is the standard measure: r = 0.5 for parent-offspring and full siblings, r = 0.25 for half-siblings, and r = 0.125 for first cousins. Relatedness underlies inclusive fitness theory, kin selection, and Hamilton's rule in evolutionary biology. It is estimated from pedigree data or from molecular markers (genomic relatedness). Applications include forensic DNA analysis, wildlife population studies, conservation genetics, and breeding program design.

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Coefficient of Relatedness (r)

The coefficient of relatedness (r) is the probability that a randomly chosen allele in one individual is identical by descent (IBD) to an allele at the same locus in another. Common values:

  • Parent-offspring: r = 0.5
  • Full siblings: r = 0.5
  • Half-siblings: r = 0.25
  • First cousins: r = 0.125
  • Second cousins: r = 0.0313
  • Unrelated individuals: r ≈ 0

Kinship Coefficient (φ)

The kinship coefficient φ is the probability that a randomly drawn allele from one individual and a randomly drawn allele from another are IBD. φ = r/2. For parent-offspring: φ = 0.25. For full siblings: φ = 0.25. Kinship coefficients are used in genomic relationship matrices (GRMs) in animal breeding and GWAS mixed models.

Genomic Relatedness

Genomic relatedness is estimated from SNP data: GRM = ZZ'/m, where Z is the centered genotype matrix and m is the number of SNPs. Genomic estimates are more accurate than pedigree-based estimates for distant relatives because they capture actual allele sharing rather than expected probabilities.

Hamilton's Rule and Kin Selection

rb > c: Altruistic behavior evolves when the cost (c) to the actor is outweighed by the benefit (b) to the recipient weighted by relatedness (r). Higher r makes cooperation more likely — explaining why organisms are more cooperative with close relatives.

Glossary

Coefficient of Relatedness (r)
The probability that a random allele in one individual is identical by descent (IBD) to an allele in another; r = 0.5 for parent-offspring and full siblings; r = 0.125 for first cousins.
Kinship Coefficient (φ)
Probability that randomly drawn alleles from two individuals are IBD; φ = r/2; used in genomic relationship matrices for GWAS and animal breeding programs.
Hamilton's Rule
rb > c; altruistic behavior evolves when the benefit (b) to the recipient weighted by relatedness (r) exceeds the cost (c) to the actor; the foundation of kin selection theory.

Frequently Asked Questions

The coefficient of relatedness (r) is the probability that a randomly chosen allele in one individual is identical by descent (IBD) to an allele in another. Standard pedigree values: parent-offspring r = 0.5; full siblings r = 0.5; half-siblings r = 0.25; grandparent-grandchild r = 0.25; first cousins r = 0.125. Genomic estimates from SNP data can be more precise for distant relatives by measuring actual allele sharing rather than expected pedigree probabilities.

The kinship coefficient (φ) is the probability that a randomly drawn allele from individual A and a randomly drawn allele from individual B are IBD. It relates to the coefficient of relatedness as φ = r/2. For parent-offspring: r = 0.5, φ = 0.25. For full siblings: r = 0.5, φ = 0.25. Kinship coefficients populate genomic relationship matrices (GRMs) used in mixed-model association studies and genomic selection in animal and plant breeding.

In forensic genetics, DNA profiles from evidence are compared to suspects or database profiles using likelihood ratios that account for possible relatedness. Close relatives share more alleles, increasing the chance of a partial or full profile match. Kinship analysis also identifies remains in mass disasters by matching DNA profiles to family members. In immigration cases, DNA testing is used to verify claimed family relationships when documentary evidence is absent.

Hamilton's rule: rb > c. Altruistic behavior evolves when the benefit (b) to the recipient, weighted by relatedness (r), exceeds the cost (c) to the actor. For full siblings (r = 0.5), the benefit to the sibling needs to be just over twice the cost to self. For first cousins (r = 0.125), the benefit must exceed 8× the cost. This explains why social behavior and helping are most common among close relatives, and why cooperative societies (bees, ants) typically consist of highly related individuals.