A stabilizing population on an island with limited space seems like a good thing. A little more space opens up for living and real-estate prices might become more favorable. Maybe there's room for more parks and other things that make life good. When conditions become more favorable, people will be able to reproduce more.
We see in the animal kingdom the predator-prey cycle that population takes care of itself. When there's too many rabbits or deer, there's no cause for concern: the plentiful food supply means that wolves and foxes will be able to reproduce more and take care of the situation. When there's too many wolves/foxes and the situation reverses, the scarce food supply means that the predators aren't able to flourish and the rabbits and deer are able to reproduce more.
I'd say that the human desire for reproduction might work in the same way, only instead of prey, maybe real-estate prices and quality of life is the cyclical variable to note.