How can this be possible when there is only one Earth? Just as it is possible to withdraw money from a bank account faster than to wait for the interest this money generates, renewable resources can be harvested faster than they can be re-grown. But just like overdrawing from a bank account, eventually the resource will be depleted.
At present, people are often able to shift their sourcing when this happens; however at current consumption rates, these sources will eventually run out of resources too – and some ecosystems will collapse even before the resource is completely gone.
The consequences of excess greenhouse gases in the atmosphere are also already being seen, like climate change and ocean acidification. These place additional stresses on biodiversity and ecosystems.