Peripatric speciation is a version of the allopatric speciation mode and happens when one of the isolated populations has very few individuals. In peripatric speciation, small population size would make full-blown speciation a more likely result of the geographic isolation because genetic drift acts more quickly in small populations. Genetic drift, and perhaps strong selective pressures, would cause rapid genetic change in the small population. This genetic change could lead to speciation.
The relative over-representation of rare alleles in such species is called the Founder Effect. This simply states that any rare alleles possessed by the small number of founding individuals will increase disproportionately in the population, and thus the species.