This somehow touches one of the reasons why I think reincarnation cannot be more than a nice idea.. population fluctuation doesn't reflect either a constant number of individuals, nor a continual increase due to "new" and "old" individuals.
What if reincarnation covers animals too? What with so many species disappearing, could very well be the souls. Not to mention reincarnation may cover the whole universe.
If reincarnation covers all animals, think of all the myriads of insects. Even when assuming only higher vertebrates, there are still millions of mice and such. Unlikely.
Or think of it this way, for reincarnation to work, the process of reincarnation after death is dependent on the events on earth (or other planets), dependent on "vacant places" created by reproduction. Would that mean that it could theoretically be possible to reach a sort of limit, where no being can enter the world until the next one dies? Or are then new beings created? Then why even have reincarnation?