So what happens when the rate of resource consumption becomes greater than the rate of resource renewal? i.e., the current situation on Earth?
Whether you realize it or not, trees do not grow as fast as chainsaws cut them down. The petroleum underground was produced by plankton millions of years ago. That's why you find it in places that aren't oceans anymore. Theoretically it's still being produced but not at a rate equal or greater to our rate of consumption. Earth's atmosphere and oceans can remove a lot of pollutants from water, but nature isn't able to remove all the harmful manmade substances from it, especially not stuff like the horrible plastic soup in the ocean. No, water treatment plants really do not sufficiently clean water either. You can't remove radioactive isotopes from the rivers and lakes they're using to cool nuclear power plants. We're running out of rare earth minerals because we're close to having mined them all for use in lasers and LCD televisions. All these parts of the ecosystem will take millions of years to return to their proper balance if we ever manage to stop screwing things up. In short, learn science.