Peripatric speciation is a special case of allopatric speciation in which a comparatively small group of organisms becomes isolated, usually geographically, from the main population. An example of a condition that encourages peripatric speciation is the colonization of new islands.
Peripatric speciation is likely to occur if a small group of organisms finds itself cut off from gene flow with the parent species. The small size of the population encourages new mutations to become fixed very quickly, which allows a rapid diversification in a new environment. A real-world example of this is the radiation of aquatic iguanas in the Galapagos archipelago.