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 essential characteristic of this mode is that genetic drift plays a role in speciation. There are likely many cases where a population is split into two unequally-sized populations and they become separate species. However, it is very difficult for us to tell after the fact what role genetic drift played in the divergence of the two populations—so gathering evidence to support or refute this mode is challenging.