There are 8 billion of us. I think it's a little premature to be worrying about the extinction of homo sapiens. Something tells me when we're not all working 40+ hours a week scrabbling for the same 20% of the resources, just maybe our birth rate will sort itself out.
This population shift has a seriously high risk of causing the global failure of egalitarian democracies, and pushing humanity back into a highly repressive and dangerous state.