I would predict that is may not be in the Hardy-Weinberg equilibrium because the allele and genotype frequencies might not stay constant from generation to generation since other evolutionary influences (inbreeding) are present. The Hardy-Weinberg principle requires that mates are chosen at random without preference for a particular trait, and in this case, mates were likely chosen based on the limited amount of choices on the island, and inbreeding is a unique form of nonrandom mating.