Good points, Piedmontcat.
If somebody asked why Switzerland had so many good ski jumpers or why California had so many good water polo and beach volleyball players, an intelligent response would probably say something about a combination of environment and culture. I realize that the sprints make a slightly different demand on the body, but still: it's remarkable that whenever the issue is why black people do something well, the first response is "Genes!" or something in that direction.
An intelligent response to this particular question might, for example, look to the fact that the Caribbean nations were, many of them, originally English colonies, with English schools. Soccer and track came with that. Cinder tracks are cheap to build. I know nothing about the particulars of how the island school systems have nurtured track talent over the past half-century, but an intelligent response to the initial question would naturally look at this element. Who are the charismatic coaches, and who taught them? What sort of organizational structure has emerged, and how does it correlate with the superior times that have been referenced? What is the sociology of track culture? Are track stars culture heroes in the Caribbean and, if so, how long has that been true and who were the sporting culture heroes in a previous generation.?
Answers to these questions might help explain why West African ancestored peoples in the Caribbean achieve more success in the sprints than West Africans themeselves.
If it was all about natural selection of strong young bucks during the slavery era, than Brazil would obviously dominate the sprints, since slavery there was just as brutal as slavery in the Caribbean and there is a much larger pool of talent to draw on. Curious: not a whole lot of Brazilian track stars. Slavery in the USA was, by contrast with the Caribbean and Brazil, somewhat more benign--notably less deadly to black men--and yet American sprinters do awfully well. The natural selection argument doesn't work. Culture plays a large role, and so does the price of the requisite equipment and/or playing fields. Sprinting is cheap. So is soccer. So is basketball. So is football, relatively speaking.
Cricket might provide a useful counterpart in this investigation, since it, too, is popular in the former English colonies.