In the Netherlands and Belgium there is an official list of animals people are allowed to keep as pets, the so-called positive list (Dutch: positieflijst). Animal not listed are not allowed as pets and people who still do so, are subject to penalties.
A positive list is the opposite of a negative list, which states which animals are not allowed as pets. The main disadvantage of such negative list is that species unsuitable to be kept should put on the list beforehand and it is too easy to forget to include a species.
We think it would be good idea that space settlements should use a similar system of allowed pets. Both for public security as for reasons of animal welfare. People who want to keep an unapproved pet should apply for a license.