✦ In fact, this inequality describes the relationship among three factors:

B = Benefit to others

C = Cost to the actor

r = Coefficient of relatedness

This relationship is known as Hamilton’s rule, which can take three forms:

rB > C | rB < C | rB = C

Hamilton’s rule is central to evolutionary biology as it explains the concept of kin selection. This concept refers to a form of natural selection that favors altruistic behavior toward relatives because it increases the reproductive success of individuals who share one’s genes.

In general, natural selection favors altruism when:

rB ≥ C

✦ Example:

Suppose a woman sees her brother drowning and considers helping him. If her brother could potentially father 2 children, then the benefit (B) of saving him is 2 offspring. The coefficient of relatedness between a brother and sister is r = 0.5, so rB = 0.5 × 2 = 1.

Now, let’s consider the cost (C) to the sister: She faces a 0.25 probability (risk) of drowning while trying to save him. If she could also have 2 offspring, then her expected cost is: C = 0.25 × 2 = 0.5.

Thus, rB = 1 > C = 0.5. Since rB > C, Hamilton’s rule is satisfied, indicating that natural selection would favor this altruistic act!

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