Can Companys own Uninhabited Islands?

Juric park was fictional story and science has not progressed to the same point as the story. Private individuals and companies can and do own islands, but those are subject to the laws of the country that claims the island. Those laws vary as far as animal testing, genetic engineering, and experimentation. In addition the right money in the right place can get an official or unofficial waiver of those laws in a lot of countries. A small 15 mile by 15 mile island would not be able to support a lot of predators, porobably not enough for a sustainable population.