The only indigenous mammal in the Virgin Islands [1] is the bat. All others were introduced by people who migrated through and eventually settled in the islands. Amerindians introduced dogs, pigs, guinea pigs, and agoutis (although the latter two have not survived in the wild). European settlers introduced a wide range of domesticated animals, including goats, sheep, and horses.
Europeans are also responsible for two of the islands’ worst pests: the rat, which arrived as a stowaway on ships, and the mongoose, introduced to kill rats that had taken up residence in sugarcane fields. The mongoose was a disappointment to rat control; it was active during the day while rats slept and could not climb trees in pursuit of the more agile rodents. Instead, mongooses fed on lizards, birds, turtle eggs, and chickens. They have been responsible for wiping out whole species of lizards on some islands. Today, mongooses remain a problem for conservationists and farmers.
Links:
[1] http://www.moon.com/destinations/virgin-islands/discover-the-virgin-islands