What do we do about such high birth rates?

The world is seeing a population increase like never before, and it is putting tremendous strains on our environment. I am from Serbia, but I currently live in Canada. I was looking over population growths of Serbia for a project, and looked at Kosovos as well. It is unbeleivabley high, and the population is so small. In other words, they are popping out babies by the dozens. If the birth rate of one country is much, much larger than that of another country, what's to stop that country from taking over? Countries that have a high birth rate can simply move into neighboring countries and make dozens of babies, and in 100 years or so, drastically change the ethnic divisions of that country, like with what happened to Kosovo. This will only continue to spread, so what can a person do to cope with this in todays world?