Hamilton's Rule Calculator
Calculate kin selection benefit-cost ratio and predict altruistic behavior evolution.
Inclusive Fitness
Hamilton's rule states that an altruistic act spreads when rB > C — when the benefit to the recipient, weighted by relatedness, exceeds the cost to the actor. Genes can propagate by helping copies of themselves in other bodies.
| Relationship | r |
|---|---|
| Identical twin | 1.0 |
| Parent–offspring, full sibling | 0.5 |
| Haplodiploid full sisters | 0.75 |
| Half sibling, grandchild, nephew | 0.25 |
| First cousin | 0.125 |
Haldane's remark captures the arithmetic: he would lay down his life for two brothers or eight cousins. At r = 0.5, two siblings carry one sibling's worth of shared genes; at r = 0.125, eight cousins do.
Haplodiploidy and Eusociality
In Hymenoptera, males are haploid so all their sperm is identical. Full sisters therefore share all paternal genes and half their maternal genes, giving r = 0.75 — higher than to their own offspring at 0.5.
A worker bee propagates her genes more effectively by raising sisters than by reproducing herself, which is the classic explanation for eusociality in bees, wasps and ants.
The hypothesis is now contested. Termites are eusocial but diploid; naked mole rats likewise. And multiple mating by queens lowers average sisterly relatedness below 0.75. Ecological factors — defensible nests, high dispersal cost — are increasingly emphasised alongside relatedness.
Where the Rule Applies and Where It Does Not
| Mechanism | Basis |
|---|---|
| Kin selection | Shared genes — rB > C |
| Reciprocal altruism | Expected return; needs repeated interaction |
| Group selection | Contested; effects usually weaker than individual selection |
| Manipulation | Benefit to the manipulator, not the actor |
Not all cooperation is kin selection. Reciprocal altruism explains help between unrelated individuals when interactions repeat and defectors can be recognised. Distinguishing them requires knowing both relatedness and whether interactions are repeated — observing cooperation alone does not identify its cause.
Note also that r is a measure of relatedness above the population baseline. In a highly inbred population, everyone is related, and it is the excess relatedness that drives the calculation.
Worked Examples
Common Mistakes
It measures relatedness above the population baseline. In inbred populations everyone shares most genes, and only the excess matters.
Reciprocal altruism explains help between unrelated individuals when interactions repeat. Relatedness and repetition must both be assessed.
Termites and naked mole rats are eusocial and diploid, and multiple mating lowers sisterly relatedness. Ecological factors matter alongside.
They are measured in offspring equivalents, not effort or resources. A costly act with little fitness consequence has a low C.