Hrm, I never thought of animal traps...
Maybe add a "snare" for each small game type (beavers?) (decays in 1-2 days, guaranteed animal spawn of that type, the spawned animal is tethered shortly when first attacked). Snares have a chance to fail proportional to the number of snares in a 15 tile radius. Animals running over a snare of their type are tethered.
Add in some other traps (Toffee treat, requires sugar to make, prevents bears from roaring when triggered), boozy berries (Prevents deer from charging, requires large amount of berries and a small amount of sugar?), those being on trigger traps and now easy spawns. Same decay rate as snares.
Again, all single use. Can be built anywhere.