I disagree on both points. If you've ever taken a decent biology class, you will have studied predator-prey cycles.
Basically, for those who haven't:
1) The predator population is less than the prey's population.
2) The prey population increases because there aren't many predators.
3) The predator population increases because of the excess of prey.
4) The prey population starts to decline because there are more predators.
5) The predator's population declines because there is less prey.
And back to step 1. Humans disrupt that; that's how it works perfectly naturally and would continue to do so if humans didn't interfere!