Yes. Read through https://www.the-scientist.com/universe-25-experiment-69941 to see that, given a good enough environment, mice can wipe themselves out. Here is a particularly telling passage:

Eventually Universe 25 took another disturbing turn. Mice born into the chaos couldn’t form normal social bonds or engage in complex social behaviors such as courtship, mating, and pup-rearing. Instead of interacting with their peers, males compulsively groomed themselves; females stopped getting pregnant. Effectively, says Ramsden, they became “trapped in an infantile state of early development,” even when removed from Universe 25 and introduced to “normal” mice. Ultimately, the colony died out. “There’s no recovery, and that’s what was so shocking to [Calhoun],” says Ramsden.

Like the mice, our population is going into reverse. And that description of behavior, looks awfully prescient when I compare to humans on social media today...

Lack of personal space is certainly not the cause of our declining birth rates. People in wealthy countries with lots of personal space actually tend to have lower birth rates than poorer countries with less. https://data.worldbank.org/indicator/SP.DYN.TFRT.IN?most_rec...