Originally posted by umop-apisdn:

Deer, for example, will have zero stars if they spawned less than a kilometer from the stone circle we spawn in. I have no idea whether a similar mechanic exists for necks, but you might try simply ranging farther afield.

Deers can spawn with 2 stars at any distance from the spawn. I know because i shot one literally meters out of the circle (I built my main base directly across the spawn)