Insular dwarfism, a form of
One is a selective process where only smaller animals trapped on the island survive, as food periodically declines to a borderline level. The smaller animals need fewer resources and smaller territories, and so are more likely to get past the break-point where population decline allows food sources to replenish enough for the survivors to flourish. Smaller size is also advantageous from a reproductive standpoint, as it entails shorter
Among herbivores, large size confers advantages in coping with both competitors and predators, so a reduction or absence of either would facilitate dwarfing; competition appears to be the more important factor. 
Among carnivores, the main factor is thought to be the size and availability of prey resources, and competition is believed to be less important.