The malthusian limit used to happen to people all the time. You can graph population against various supporting resources and watch it rise and fall in large regions historically. What is confusing the issue is that the industrial age has exploded productivity so much that we have not had a modern malthusian disaster. We came within a few inventions of having one in the 1960s or 1970s but the green revolution inventions aced that one out.

Current trends suggest the mid-term future of earth's population is maxing at about 10 billion and then falling slowly. This will put off any malthusian disasters through the mid-term.

I HIGHLY recommend "The Rational Optimist" by Matt Ridley. Most amazing collection of useful points of view and information I have seen in a long time. Collapse by Jared Diamond is also a fun compendium of local malthusian disasters over the millenia.