Reincarnation

I have read about reincarnation and karma. They say that we reincarnate because we are also paying our karma in the process. I really can not put the exact words, but, there were instances researched by Jaime Lijauco on reincarnation like there was this kid who was able to say the exact description of a place and stuff, and when they looked at that stuff, what the kid was the precisely the same as described. And when asked how did he know of this, he just plainly said I have been here before. So basically, for him reincarnation happens. Well, you have a point as to the fact that if indeed we're reincarnating, then there should be no overpopulation at all, because there will only be limited souls thriving on the earth.