I was reading an article about Homo sapiens and I read:
"We believe their ancestors may have reached the island using bamboo rafts."

Is the use of present perfect correct? I'd have used simple past or past perfect?
Can someone explain me?
It can be done with the simple past-- 'We believe their ancestors reached the island using bamboo rafts.'-- but not with the past perfect.

The present perfect was chosen to stress the relevance of the fact to the present speaker (plus, of course, it allows the additional hypotheticality of 'may', which we cannot form in simple past).

California Jim may have more to say on this topic.
This is not a present perfect. It is a modal construction; the modal is "may".

In this context, "may"* means "it is possible that ... [present or future]"; "may have" means "it is possible that ... [past]".

Thus, "We believe they may reach the island on a raft" is "We believe that it is possible that they will reach the island on a raft".
And "We believe they may have reached the island on a raft." is "We believe that it is possible that they reached the island on a raft".

With the modals, the only two possibilities for tense are the modal alone (making the proposition which follows non-past) and the modal followed by "have" (making the proposition which follows past).

*without the "have".

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Ok, I understand, thaks Jim (Y)
Just a matter of terminology, Jim. As you say, in meaning, 'may' is restricted in its reference to time. The modals can however, take the forms of present perfect tense, continuous aspect, passive voice -- 'may have reached', 'may be reaching', 'may be reached [by them]'.

I am not competent to speak on the origins-- did the form come before content? The chicken before the egg?