Determining Relatedness: Half-Siblings

For full siblings, the coefficient of relatedness (r) is 0.5, since they share half their genes. However, half-siblings (brothers with the same father but different mothers) share only one parent, so their relatedness is:

$$r=0.5\times 0.5=0.25$$

This is supported by standard kinship calculations and evolutionary biology resources.

Applying Hamilton’s Rule

Given:

• Cost to A (C): 30 fitness units

• Relatedness (r): 0.25 (for half-siblings)

• Benefit to B (b): unknown; we want to find the threshold

Hamilton’s rule predicts A should help B if:

$$r\times b>C$$$$0.25\times b>30$$b>300.25b>0.2530$$b>120$$

Conclusion

According to Hamilton’s rule, A should help B only if the benefit to B exceeds 120 fitness units. This ensures that the act of altruism is favored by natural selection given their genetic relationship as half-siblings.

Correct answer: (3) only if b > 120.