Coefficient of relatedness

The coefficient of relatedness is a measure of the average genetic connection between two individuals: the probability that a particular gene in one is also present in the other. In the book’s account of kin altruism, it makes the consequences of helping relatives comparable across relationships. Its central implication is not that organisms consciously calculate genetic probabilities, but that behavior influenced by genes can, on average, favor the survival of copies shared with relatives. The measure therefore connects patterns of inheritance to the evolution of behavior, while requiring care about uncertainty, development, and the difference between genetic kinship and social kinship.

Definition and Inheritance

The coefficient is introduced as an index of relatedness: it expresses the chance that a gene is shared between two relatives. A parent and child have a relatedness of one half, because half of a parent’s sex cells carry any particular copy of a gene. Two siblings also have an average relatedness of one half: a particular gene in one sibling has a 50 percent chance of being present in the other. The sibling figure is an average, not a guarantee for any particular pair; the genetic contribution inherited by siblings can vary.

The measure can be calculated by tracing shared ancestors. First identify the most recent common ancestor or ancestors, then count the generation steps from one individual up to an ancestor and down to the other. For each common ancestor, the contribution to relatedness is one half multiplied by itself once for each step: if the distance is three generations, that contribution is one eighth. Where there is more than one common ancestor, add the contributions. First cousins, for example, have two shared grandparents, with a generation distance of four through each; each contributes one sixteenth, yielding an overall relatedness of one eighth. The calculation is presented as a practical rule for simple cases, with incestuous mating and certain insects identified as cases where it breaks down.

The comparisons produced by the rule show how relatedness declines across family connections. A great-grandparent and great-grandchild have a relatedness of one eighth, the same as first cousins; an uncle and a nephew have a relatedness of one quarter. Third cousins, at one one-hundred-and-twenty-eighth, approach the baseline probability that a gene in one individual will be found in a randomly chosen member of the population. Identical twins, by contrast, have a relatedness of one. These figures represent expected sharing, not an inventory of precisely matching genes in every particular pair.

From Relatedness to Kin Altruism

The coefficient lets the book compare the genetic effects of an action across its possible beneficiaries. A hypothetical gene for suicidal altruism would not spread by saving five cousins, but could spread by saving more than two siblings, children, or parents; more than four half-siblings, aunts, uncles, nieces, nephews, grandparents, or grandchildren; or more than eight first cousins. The relevant comparison is between the altruist’s loss and the copies of the gene that may persist in those saved. The examples make the arithmetic of kin altruism explicit: more distant relatives can count, but each carries a smaller expected share.

Parental care is treated as one form of kin altruism rather than a genetically unique relationship. An adult is, on this account, equally related to its own child and an orphaned younger sibling: the relatedness in either case is one half. A gene influencing an older sibling to care for a younger one could therefore spread on the same genetic accounting as a gene influencing parental care, though the book notes that sibling care is much less common in nature and that this comparison is an oversimplification. The distinction matters because direct parent-to-child transmission is not the only route by which copies of a gene can persist.

The coefficient also appears in a model of decision-making. For each available behavior, benefits and risks to the actor are counted at full value, while benefits and risks to relatives are weighted by their relatedness to the actor. The resulting net benefit score compares possible actions; the model selects the behavior with the highest score, even if every option has a negative result. Relatedness is thus not a claim that an animal consciously performs arithmetic. It is a way to describe how a behavioral tendency could be favored when its effects, averaged across generations, preserve copies of the genes associated with it.

Uncertainty and Recognition

In practice, the coefficient may itself be uncertain. If two individuals might be either half-siblings or full siblings, their relatedness could be one quarter or one half; the usable estimate is an average weighted by the likelihood of each relationship. The book’s example supposes that they share a mother, while the chance of sharing a father is one in ten. The resulting effective relatedness is 0.275: a 10 percent chance of one half and a 90 percent chance of one quarter. The figure therefore depends not only on a family connection but also on what is known about that connection.

This raises a further question: whether the relevant estimate belongs to a human observer or to the animal whose behavior is under discussion. People may identify relatives through names, marriage, written records, memory, and social instruction. Cultural kinship and genetic kinship are not identical, even when they shape overlapping loyalties. Family obligations, ancestor worship, blood-feuds, and inter-clan warfare are discussed as practices that can be interpreted in relation to genetic kinship, while the incest taboo is distinguished from altruism: the proposed genetic advantage of avoiding close inbreeding concerns the harmful effects of recessive genes, not the benefits of helping relatives.

Wild animals cannot be assumed to identify kin through human systems of names and records. Instead, the book asks what simple behavioral rules might, under ordinary conditions, have the indirect effect of favoring relatives. A tendency to behave altruistically toward individuals who physically resemble oneself could sometimes do so, but it would be statistically imperfect: if a species began living in larger groups, the rule might produce more errors. The argument is about tendencies that work on average, not infallible recognition or conscious knowledge of genetic relationships.

Misfires and the Limits of the Measure

The gap between genetic relationship and practical recognition helps explain cases where care appears to go to unrelated young. Orphan adoption among social animals may result from a general rule that prompts a female to care for a youngster, even when she is not in fact related to it. Such care can divert time and energy from her own kin, including possible future offspring; the book suggests that the error may be too uncommon for selection to have made the maternal response more selective. Sometimes adoption does not occur, and an orphan is left to die.

A more extreme case is that of bereaved monkey mothers observed taking and caring for another female’s baby. The book treats this as a particularly difficult apparent misfire: the adopter’s care may benefit her own genes little, while also relieving the infant’s mother of the burden of child-rearing. It does not settle the explanation. It calls for evidence about how often the behavior occurs, the likely average relatedness between adopter and infant, and the response of the infant’s mother, including whether mothers might deliberately induce adoption. The case exposes a limit of using a coefficient as an explanation by itself: a numerical account of relatedness must be joined to evidence about recognition, behavior, and circumstances.

The concept also depends on keeping two levels of explanation distinct. Genes interact in development: a body is shaped by many genes and environmental influences, and no single gene independently builds a complex trait. A gene associated with a behavior is shorthand for a genetic influence on development that makes the behavior more likely, not a solitary cause or an instruction consciously followed by an organism. Likewise, the coefficient is a population-level accounting device for average sharing, not a promise that a particular relative carries a particular gene.

Significance

By translating family relationships into expected genetic sharing, the coefficient supplies a common measure for comparing kin-directed benefits and costs. It explains why the same act can have different evolutionary consequences depending on whether it aids a sibling, cousin, or unrelated individual, and why care for a child is not the only possible route by which a gene can persist through relatives. Its use shifts attention from an individual’s apparent sacrifice to the distribution of gene copies that may survive as a result.

That analytical role does not turn biological description into moral instruction. The book’s broader argument distinguishes how behavior may have evolved from how people ought to behave. The coefficient helps explain conditions under which limited altruism could be favored by gene-level selection; it does not prescribe indifference to strangers or define human obligations. Its strongest use is explanatory, and its limits are equally instructive: relatedness is probabilistic, kin recognition can be fallible, social kinship is culturally organized, and behavior develops through complex genetic and environmental interactions.