I don't know if "demise" is the right term to use, but the basic biological principal is that once a creature uses up the resources in its area, it either moves to another area, discovers new ways of using the resources given, or the population declines until the available resources more accurately reflect the number a creatures using it. Demise seems like the whole human race will disappear, but its more likely that we'll suffer a decline in numbers until the resources we use aren't as strained. Alternatively, we could evolve into a species that is able to use available resources more efficiently.