The math of kinship: How we calculate biological relatedness
In short: How much of your DNA do you actually share with a distant cousin? Genetics uses a specific mathematical framework to quantify these connections. By tracing paths back to common ancestors, scientists can determine the exact degree of consanguinity between any two individuals, from siblings to remote lineages.
The coefficient of relationship (r) is a metric used to measure the degree of biological relatedness between two individuals. Formally defined by Sewall Wright in 1922, the measure is derived from his earlier work on the coefficient of inbreeding. It essentially quantifies the probability that two alleles sampled from different individuals are identical by descent, meaning they were inherited from a common ancestor. For example, first-degree relatives like parents, siblings, or children share approximately 50% of their genes, while second-degree relatives share about 25%, and third-degree relatives share roughly 12.5%.
The calculation relies on summing path coefficients for every line of connection to common ancestors. A path coefficient (p) between an ancestor and an offspring is calculated using a formula that accounts for the number of generations separating them and the inbreeding coefficients of both individuals. In a simplified model—assuming a population of perfectly random-bred stock—the coefficient of relationship is the sum of 2 to the power of negative L, where L is the length of the path connecting the two people via a unique common ancestor. This mathematical approach allows for precise tracking of genetic overlap across complex family trees.
Accuracy depends heavily on the depth of the known pedigree. If a family tree is known for five generations, the coefficient can be determined to within a few percent. If known to ten generations, accuracy improves to a tenth of a percent. Conversely, the genetic contribution from ancestors 20 generations ago (roughly 500 years in human genealogy) falls below one part-per-million. While human genealogy often focuses on three or four generations, these calculations provide a lower bound; the actual value may be a few percent higher due to deeper, unrecorded connections. In clinical settings, a coefficient of r = 3.125% (or 2 to the power of negative 5) is often used as the threshold for defining consanguineous marriage.
Distinguishing these terms is vital for both genealogy and medicine. While the coefficient of relationship measures the degree of consanguinity, the kinship coefficient (Φ) is a related but distinct measure. For a non-inbred individual, the kinship coefficient with themselves is 1/2, reflecting the fact that humans are diploid. The coefficient of relatedness is simply twice the kinship coefficient. These metrics are essential for diagnosing risks for common diseases by analyzing family history and for understanding the genetic composition of populations. , else
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- Summary by Intellect · source: Coefficient of relationship
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