🤝 Hamilton's Rule Calculator
Enter relatedness, benefit, and cost to test the single inequality at the heart of social evolution — rB > C — and see whether kin selection favours an act of altruism, plus its inclusive-fitness effect.
🤝 Hamilton's rule: rB vs C
A gene for this helping behaviour spreads: the relatedness-weighted benefit (2.25) exceeds the cost (2), for a net inclusive-fitness gain of 0.25.
The equation behind cooperation
In 1964 W. D. Hamilton showed that self-sacrifice can be favoured by natural selection whenever it helps enough relatives reproduce. His rule, rB > C, discounts the benefit to a recipient by how related they are to the altruist, then weighs it against the altruist's own loss. It reframes fitness as inclusivefitness — an individual's own offspring plus the extra offspring of kin it helps.
The idea explains why a sterile worker bee that never reproduces can still be a winner in gene's-eye terms, and why cooperation and conflict in animal societies so often track lines of kinship.
❓ Frequently Asked Questions
What is Hamilton's rule?
Hamilton's rule states that a gene for altruistic behaviour is favoured by natural selection when rB > C: the relatedness (r) between actor and recipient, multiplied by the benefit (B) the recipient gains, exceeds the cost (C) the actor pays. All quantities are measured in the same units of reproductive fitness — typically extra offspring.
What is the inclusive-fitness effect?
It is rB − C, the net change in copies of the altruism gene passed on when you count both the actor's own reproduction and the extra reproduction of relatives it helps. A positive value means the behaviour is favoured; a negative value means it is selected against.
How do I choose the relatedness value?
Use Wright's coefficient of relatedness for the pair involved — 0.5 for full siblings or parent and offspring in diploids, 0.75 for haplodiploid full sisters in bees, ants, and wasps, 0.125 for first cousins, and so on. The dropdown fills in common values, or the coefficient of relatedness calculator works them out.
Is real behaviour really this tidy?
The rule captures the core logic of kin selection, but real cases fold in ecology, the reliability of the benefit, diminishing returns, and conflict within colonies. Treat the result as the direction selection pushes, not a precise prediction of what any individual will do.