While exploring the island, you may encounter a wild creature (not Rogue Males). These creatures are uncontrollable until you invite them into your pack. Similar to bunnies, they will steal berries off of your bushes. You can also attack them; they won't attack back nor turn aggressive. To invite a creature into your pack, you must have one of your creatures adjacent to the wild creature, and an "invite to pack" option will be on the wild creature's tile. Clicking this will add them to your pack and take away 5 food from your storage. If you do not have enough food, you cannot invite them into the pack.
Rogue Males are uncontrollable creatures with undesirable traits- usually Blind Eye, Spit Snout, and/or No Paw. You can not invite them into your pack- there isn't an option to, even if you wanted to. They follow your pack in search of non-pregnant females, with which they will mate as soon as they're adjacent. You can attack them, however they give no food when killed. Rogue Males will move whenever any one of your creatures makes an action, similar to fish or the Bluebird. To protect your females, either mate them with your own pack-mates immediately, kill off the Rogue Male, or set up a protective blockade around them.
At the end of each day, 1 food will be eaten for each member of the pack. (5 members = 5 food taken.) This does not include pack members dying of old age or babies born that night.
If you don't have enough food to feed all your creatures, or just had a baby born with no good traits, banishing may be your best bet for your pack to function well. To banish a creature, it must be 2 gems or older. The banished creature will behave just as normally wild creatures would act.