The cycle doesn't always repeat. The cycle only repeats if fertility rates stay where they always have been... the elk continue to attempt procreation at the rates they always have.

Then,once the foraging/pasture regrows, that rate being the same, the elk rebound.

Calhoun proved this. The mice would, despite having everything they needed, despite the population crash giving them the space they apparently required, just not procreate. Lots of bizarre behaviors, but no procreation.

No little girl who has grown up an only child, most of the adults in her life either having just one child or even none at all, will say "I want to have 2.1 children when I grow up!". And it would have to be every little girl that did that for replacement fertility. If only a few do it, then the number has to be higher than 2.1 for it to average out.

The implication is that fertility rates can only ever fall, and never rise. We're more like Calhoun's mice than we are like some cervines that have outgrown their food supply.