Charlesworth's paradox

Hamilton's rule states that altruistic genes or strategies (in a prisoner's dilemma for example) should increase in frequency if

${\displaystyle rb>c}$

Where

• ${\displaystyle r}$ is the genetic relatedness of individuals concerned.
• ${\displaystyle b}$ is the benefit gained by the recipient of altruism.
• ${\displaystyle c}$ is the cost to the individual performing the act.

Charlesworth imagines a species of bird in which young can stay behind to help their parents care for the next season's young, rather than founding their own nests.

A situation arises where an individual can sacrifice its own reproductive success to save the lives of its four younger siblings. This will result in ${\displaystyle b=4}$ and ${\displaystyle c=1}$ (the 4 young survive and the older sibling dies). For siblings ${\displaystyle r=0.5}$. Since ${\displaystyle rb=2>c=1}$ this behaviour should evolve by Hamilton's rule. However it cannot be viable, because any individual exhibiting this behaviour sacrifices itself and does not reproduce.

McElreath and Boyd^[3] suggest that Hamilton's rule only applies in cases of weak selection, which is an underlying assumption in deriving it. Other authors^[5] resolve the paradox for strong selection through a modified version of inclusive fitness.