When encountering deer a lot of them are froze in place and when you kill them they disappear, so Im assuming they are actually dropping dead somewhere else on the map or just despawning completely. Another Deer issue is they seem super fast like they are running NASCAR / cheetah speed. Cows have a few issues sometimes they will phase in and out of an area and existence. I play all over the map and all I ever see is deer / cow I think the balancing of what / where animals spawn should be tweaked. I have yet to see boar again and or chickens. I never mess with domestic other than cows, so I don't know if those have issues. Just putting this out there because hunting and all of that is fun when it works properly. The amount of wild animals should increase it seems with less hunting of them in this kind of scenario I think.
Additional Note
Hopefully the new improvised fishing net is on the docket for getting fixed or implemented .