Kin Selection, Relatedness and When Helping Pays
Kin selection concerns reproductive effects on relatives. In a one-recipient additive model, a heritable helping trait is favored when relatedness times the recipient's reproductive benefit exceeds the helper's direct reproductive cost. Pedigree calculations and matching fitness units make the comparison meaningful.
What a learner can do afterwards
- Calculates expected relatedness in stated outbred diploid pedigrees and applies Hamilton's rule.
- Explains why the same costly act can satisfy Hamilton's rule for a full sibling but not for a recipient assigned r = 0.
- Separates kin selection from cooperation between unrelated individuals.
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Kin selection is natural selection through effects on relatives' reproductive success. An allele is a version of a gene. Here r is expected pedigree relatedness: the expected fraction of autosomal allele copies shared by descent from recent common ancestors in an outbred diploid pedigree. It is not overall DNA similarity. Unrelated individuals can share alleles; r = 0 means no extra relatedness relative to the population background used in this model.
For these outbred diploid pedigrees, use 1/2 for each parent-to-child link. Multiply along each path through a shared ancestor, then add the paths. Parent and child: r = 1/2. Half siblings share one parent: r = (1/2)^2 = 1/4. Full siblings share two parents: r = 2 times 1/4 = 1/2. First cousins share two grandparents, with four links per path: r = 2 times (1/2)^4 = 1/8. The ancestors are unrelated and non-inbred.
Hamilton's rule is r times B > C. B is the recipient's gain in expected reproductive success; C is the helper's loss in its own expected reproductive success. Use matching fitness units. For a heritable helping trait in this one-recipient additive model, multiply r by B, then compare with C. If rB > C, helping is favored; if rB = C, this comparison gives no net advantage. Relatedness alone does not settle the result.
For a full sibling, let r = 0.5, B = 10 and C = 3 in matching fitness units. The weighted benefit is 0.5 times 10 = 5. Since 5 > 3, helping is favored in this model. For the same benefit and cost with r = 0, the weighted benefit is 0 times 10 = 0. Hamilton's rule is not met because 0 cannot exceed 3. This does not rule out other explanations of cooperation.
A later return of help is reciprocity. Cooperation between nonrelatives can also bring an immediate shared benefit or benefits through reputation. Kin selection concerns reproductive effects through relatives. Familiarity does not determine r: a stranger may be a relative. Human motives, such as empathy, are separate from reproductive effects. A person may help without expecting repayment. Hamilton's rule does not tell people whom they ought to help.
Direct fitness concerns one's own reproduction. A nonreproducing worker can gain indirect fitness by helping the queen's related offspring survive and reproduce. Such helping can be favored when relatedness-weighted gains exceed direct fitness costs. Workers need not calculate these payoffs. Worker reproduction and relatedness vary among colonies and species. Do not assume the diploid sibling values above apply unchanged to every ant or bee.
Calculate r under stated pedigree assumptions. In the additive model, helping is favored when r times B > C in matching fitness units. This prediction does not establish a person's motive or duty.
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More to read
Reproduction through two routes
A helping act can change reproductive success in more than one individual. Start by separating the helper's own reproduction from the recipient's reproduction. Direct fitness concerns the helper's own offspring. Indirect fitness concerns effects on relatives' reproductive success, weighted by relatedness.
A relative does not pass on the helper's body cells. The relative can pass on allele copies shared with the helper by descent. That distinction explains why raising relatives can matter even when a helper produces no offspring.
In biology, an altruistic act has a direct fitness cost to the actor and a reproductive benefit to another individual. An indirect gain through relatives can help explain how a heritable helping trait is favored. It does not remove the act's direct cost. Nor does this accounting show what an animal consciously intends.
Tracing shared ancestry
The lesson uses expected relatedness for autosomal inheritance in outbred diploid pedigrees. Each parent-to-child link contributes a factor of 1/2. In the simple pedigrees here, trace a path through a shared ancestor and multiply its link factors. Then add the separate path contributions.
Half siblings share one parent. Their two-link path contributes 1/2 times 1/2 = 1/4. Full siblings share two parents, so two contributions of 1/4 give r = 1/2. First cousins share two grandparents. Each grandparent path has four links, giving r = 2 times (1/2)^4 = 1/8. These examples assume unrelated, non-inbred ancestors.
Pedigree values are expectations, not exact measurements of overall DNA similarity. Inbreeding changes the calculation. Different inheritance systems also need different treatment, so these values cannot be assumed for every social-insect colony.
Relatedness is not familiarity
Calling someone a stranger tells us about familiarity, not ancestry. An unfamiliar individual may be a relative, while two familiar individuals may have r = 0 in the pedigree model. We need ancestry information rather than a social label to assign relatedness.
Nonrelatives can cooperate when both gain immediately or when help is returned later. Reputation can affect future interactions too. These routes differ from indirect fitness effects through relatives. Seeing a helpful act does not by itself identify the mechanism that maintains it.
A human motive is another question. Someone may help from empathy without expecting repayment. A reproductive-effect calculation does not establish that person's intention. Psychological altruism concerns motives; biological altruism concerns fitness effects. Hamilton's rule is a model of selection, not advice about whom a person should help.
Checking a proposed payoff
Before using Hamilton's rule, identify what changes because of the helping act. B measures the recipient's increase in expected reproductive success. C measures the helper's loss in its own expected reproductive success. Both need matching fitness units. Spending energy alone does not establish how much reproduction was lost.
In the lesson's one-recipient additive model, calculate r times B and compare it with C. A larger weighted benefit favors the heritable helping trait under the model's assumptions. Equality gives zero net gain in this comparison. A smaller weighted benefit does not favor helping through this route.
Kinship alone is therefore insufficient. A close relative may receive too little reproductive benefit to offset the cost. A worker example needs the colony's relevant relatedness and reproductive effects. Shared ancestry alone also does not justify a general claim that relatives will avoid aggression.
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