The Components of Hamilton’s Rule

• C: The cost of the behavioral act to the actor (the individual performing the altruistic act).

• B: The benefit of that act to the beneficiary (the recipient of the altruistic act).

• r: The genetic relatedness between the actor and the beneficiary (the probability that a gene present in one individual is also present in the other due to shared ancestry).

The Correct Expression

Hamilton’s rule states that altruism will evolve when the benefit to the recipient, multiplied by the genetic relatedness, exceeds the cost to the actor. Mathematically, this is expressed as:

$$rB>C$$

Or, rearranged:

$$C<rB$$

This means that an altruistic act is favored by natural selection if the cost to the actor is less than the benefit to the recipient, discounted by how closely related the two individuals are.

Why This Expression Matters

• Predicts Altruism: Hamilton’s rule predicts when genes for altruistic behavior can spread in a population.

• Explains Kin Selection: It underpins the concept of kin selection, showing that helping relatives can increase an individual’s inclusive fitness.

• Broad Application: The rule has been confirmed in a wide range of species and social behaviors.

Conclusion

The correct expression of Hamilton’s rule for the evolution of altruism is:

(1) C < r.B