Step 1: Calculate the Relatedness Threshold

According to Hamilton’s rule, A should help B if:

r×40>12  ⟹  r>1240=0.3r×40>12⟹r>4012=0.3

A should help a relative only if their genetic relatedness is greater than 0.3.

Step 2: Genetic Relatedness of Family Members

Standard coefficients of relatedness:

• Daughter or Son: r = 0.5

• Grandson or Granddaughter: r = 0.25

• Nephew or Niece: r = 0.25

• Full Sibling (Brother or Sister): r = 0.5

These values are widely accepted in genetics and kin selection theory.

Step 3: Apply the Threshold

• Daughter or Son: r = 0.5 (> 0.3) — A should help.

• Grandson or Granddaughter: r = 0.25 (< 0.3) — A should not help.

• Nephew or Niece: r = 0.25 (< 0.3) — A should not help.

Step 4: Match to the Options

• Option 1: Nephew — r = 0.25 (No)

• Option 2: Grandson or Granddaughter — r = 0.25 (No)

• Option 3: Niece — r = 0.25 (No)

• Option 4: Daughter or Son — r = 0.5 (Yes)

Conclusion

According to Hamilton’s rule, A should perform the altruistic act only if B is his daughter or son, because only this relationship meets the relatedness threshold required for the act to be favored by natural selection.

Correct answer: (4) daughter or son