Population questions are fuzzy. Even an apparently simple term like "overpopulation" is hard to define exactly. Part of the reason is that evaluating the consequences of rapid population growth falls in the odd academic space where ecology, economics, anthropology, and demography overlap. Another part of the reason is that attempts to isolate specific social or environmental consequences of rapid population growth tend to sink into ideological quicksand.
What becomes of the surplus of human life? It is either, 1st. destroyed by infanticide, as among the Chinese and Lacedemonians; or 2nd. it is stifled or starved, as among other nations whose population is commensurate to its food; or 3rd. it is consumed by wars and endemic diseases; or 4th. it overflows, by emigration, to places where a surplus of food is attainable. (James Madison, 1791).