It might be interesting to make the spawn rate of certain animals dependent on predator-prey relationships.
I am not entirely sure how animal spawning happens, but the way I would imagine this happening is by counting each species individual as it is de-spawned. These animals could count as the living population, which could be tallied every set period of time. The number of the species, and the number of each species it interacts with would determine the amount of animals that spawn over the next time period.
While this may be frivolous, and could end up with weird patterns, it would make the world more dynamic, and I think it would be cool to see the effects of player-animal / animal-animal interaction.
Scenarios I imagine: rabbit population explosions followed by fox population explosions; rabbit population drops leading to player created hunting moratoriums; rabbit/chicken/rat/frog population recovery by players releasing all the animals they have stored in chests.