Because they did not have a written language, we cannot really know why the indigenous peoples of the Caribbean (like the Taino and the Caribs) migrated from the mainland of South America to the islands where they lived when the Europeans came.
The impact of European settlement is much more clear. It caused the near-extermination of the indigenous population. The native population was decreased by European diseases, by war with the Europeans, by abuse of natives by the Europeans and by psychological trauma caused by the death and by suddenly being dominated by an unfamiliar group of people. Different historians have different attitudes as to which of these caused how much of the damage, but these are the causes of population decline that are most often cited.
the tainos were forced to move higher up the continent of south america due to the kalinagos and their war-like behaviour.they eventually moved to the islands and settled. when columbus RE-DISCOVERED the caribbean, he made false accusations how the kalinagoes were cannibalist so he could get permission from queen isabella to enslave them. this was the introduction of the encomienda system and the first form of slavery in the new worlds. the amerindians, both tainos and kalinagos were both untrained and un accustomed to the labor their encomiendero were putting on them. they hardly had food, sleep and were affected badly. the old world animals eg. horses only damaged the amerindians crops and the europeans raped the indeginous women. also, they had weak immune systems so they could not stand the new diseases like malaria, yellow fever etc. this caused the decline of the amerindians. there are not much full blood or pure amerindians. there are amerindian communities though, found in dominica and in a village called arima, located in trinidad.
There is not a lot of information that actually validates when or how the indigenous people arrived at the Caribbean. However, there have been some carbons dating of artifacts that the first people who migrated to Haiti, Cuba, and he Dominican Republic came from the Yucatan Peninsula. Measures of carbon dating and traits tracing have led scientists and archaeologists to believe that the Taino people had decended from the Casmiroid people making them descendents of the Mayan tribe. The tribes of the indigenous people and their way of life changed with the arrival of the Spaniards. The Spaniards saw profit from the resources held by the tribes as well as land and laborers and fought to control their empires and communities. As a result most of the indigenous tribes have become extinct.
Other groups of the Arawak tribes of South America were able to survive better because they consisted of splintered groups that were less likely to be found or subjugated by the Spaniards. They did not have a complex structure and began to trade with the English. Many of them assimilated with the English, Dutch, and Spanish through the years, but there are still Arawark languages spoken in South America.