An isolated population is more likely to undergo allopatric speciation. The isolated group may be under different environmental pressures than its parent population, and over time an isolated group will be subject to random mutations which will create unique attributes.
If the isolated population is small in numbers, then it is subject to additional pressures. The first of these is the founder effect. If the frequency of any allele is different between the isolated group and the parent population at the time the isolation occurs, then the isolated group experiences genetic changes from a different starting point than the parent population, and is likely to follow a different path over time, resulting in different allele frequencies.
Very small populations are also prone to the bottleneck effect, which results in a loss of genetic diversity. Small populations are also prone to inbreeding, which again may reduce the diversity of alleles.