The Scenario

• C: Number of offspring sacrificed by the donor (cost)

• B: Number of offspring gained by the recipient (benefit)

• γ: Coefficient of genetic relatedness between donor and recipient

Hamilton’s Rule Explained

Hamilton’s rule states that an altruistic trait will be favored by kin selection if the following condition is met:

$$\gamma B-C>0$$

Or, equivalently,

$$C<\gamma B$$

This means that the cost to the donor must be less than the benefit to the recipient, discounted by how closely related they are. In other words, the donor’s loss is outweighed by the gain to a relative, multiplied by the probability that the relative shares the same gene for altruism.

Why This Condition?

• If the benefit to the recipient (B), weighted by relatedness (γ), exceeds the cost to the donor (C), the gene for altruism can spread in the population.

• This rule explains why animals are more likely to help close relatives: the shared genes make the indirect fitness gains worthwhile.

The Correct Option

Among the options, the correct mathematical condition is:

(4) γB – C > 0

This directly matches Hamilton’s rule and accurately describes when kin selection will favor an altruistic trait.

Conclusion

Kin selection favors the evolution of altruistic traits when the donor’s cost is outweighed by the relatedness-weighted benefit to the recipient. This is captured mathematically by γB – C > 0, the essence of Hamilton’s rule.