Charlesworth's paradox

Charlesworth's Paradox is a paradox related to kin selection, Hamilton's Rule and the evolution of altruism. The paradox was proposed by Brian Charlesworth ^[1] and is sometimes used as a teaching example to discuss kin selection. ^{[2] [3] [4]}

The 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.

Resolution

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.

References

1. Charlseworth, Brian (1978). "Some Models of the Evolution of Altruistic Behaviour between Siblings". Journal of Theoretical Biology. 72: 297–319.
2. Dawkins, R. (1979). "Twelve misunderstandings of kin selection". Zeitschrift für Tierpsychologie. 51 (2): 184–200.
3. McElreath, R; Boyd, R (2008). Mathematical models of social evolution: A guide for the perplexed. University of Chicago Press. ISBN   9780226558288.
4. Ehud Lamm (2011). "A Gentle Introduction to The Price Equation" (PDF).
5. Garcia‐Costoya, Guillermo; Fromhage, Lutz (2021). "Realistic genetic architecture enables organismal adaptation as predicted under the folk definition of inclusive fitness". Journal of Evolutionary Biology. 34 (7): 1087–1094. doi:10.1111/jeb.13795.