The question asks us which of the following statements about the mechanisms that enable organisms to recognize their close relatives is supported by the passage?
(B) is correct and is supported by lines 4-6 "improvements in the general understanding of mechanisms," i.e. mechanisms became more clearly understood.." have turned some biologists' attention to the question of why kin recognition occurs," i.e. prompted interest in the purpose of kin recognition.
(A) is incorrect because the passage focuses on the theories around the purpose of kin recognition, not the enabling mechanisms.
(C) is incorrect because even though the passage mentions the exclusive fitness theory developed in 1960s, it never says that there were no prior theories.
(D) is incorrect because the passage never says that detailed workings of these mechanisms are insufficiently understood to ascertain their purpose.
(E) is incorrect because the passage never discusses how exactly these mechanisms operate aside from the fact that the general understanding has been improved over time.