The conventional wisdom seems to be that the Caribbean's tropical climate (and the accompanying disease and hazards) made the islands unsuitable for European settlement but I recently came across a genetic study that I found very interesting. The average Jamaican person is apparently around 90% African whereas the average puerto rican is 65% European. What explains this difference? Puerto Rico and Jamaica are neighbors, are approximately the same size, and have essentially the same climate yet they have completely different genetic structures.
I had always heard that there was so little European settlement in the Caribbean because of disease, yet the (formerly) Spanish islands all have populations that descend in large part from Europeans. Did the Spaniards adapt more readily to the climate, were the British simply uninterested in settling the islands?
One of the reasons was the Cédula de Gracia of 1815. Spain feared losing Cuba and Puerto Rico to independence movements so it tried to send as many Spaniards as possible to the islands to try to make them more loyal to Spain. In the case of Puerto Rico the result was about half a million European immigrants and among them were some members of my family.
Coincidentally today I commented to a colleague of mine after almost passing out from the heat that I questioned the judgement of my ancestors when they chose to move to the tropics.
About the 65% European figure it is important to notice that there is a great deal of racial variety on the island and that the studies that have been published haven't been thorough. It is quite normal to see predominantly Spanish Puerto Ricans and predominantly west African Puerto Ricans. Native American Taíno DNA exists in about 60% of the population in small quantities.
I just wanted to add a bit to /u/adolfojp's comment as everything they said was right but I want to talk about the British and French side of the answer. As for the French, most of their white colonists fled or died during the Haitian revolution and many blacks immigrated to the island to escape discrimination after the revolution so that explains the lack of European DNA in that gene pool.
As for the English colonies, the difference lies in the system of colonization that the British used as opposed to the Spanish. The Spanish originally granted land to individual Spaniards on the condition that they would evangelize their slaves (at first this was Amerindians then Africans). The British on the other hand did not have this obligation and many owners of plantations were not even on the island. They may have started off there but once they made enough money, they would return to England and live off their earnings from their plantation.
Finally, there is the issue of gender ratios in these colonies. British colonies (especially Jamaica) had 4:1 ratio of white males to white females. Many of the men never married and while this did not preclude them from having children, they more than likely did it with a slave. The Spanish colonies on the other hand had an almost equal ratio of white women to white men and this allowed for more marriages and more white exclusively European DNA bearing children.
Sources:
Burnard, Trevor. Mastery, Tyranny, and Desire: Thomas Thistlewood and his Slaves in the Anglo-Jamaican World. Chapel Hill, NC: University of North Carolina Press, 2004.
Davis, David Brion. Inhuman Bondage. The Rise and Fall of Slavery in the New World. Electronic Edition. Oxford and New York: Oxford University Press, 2006.
Actually, even the islands that were not Spanish colonies had a large amount of European settlement. Jamaica and Barbados both have large established white communities, and in fact at one point the latter actually had a majority white population. I can't explain how that proportion came to be reduced though.