Don't animal spawns happen within a certain range of the player, similar to mobs? I have not seen any animals in the hills. I have even been checking tree tops. I'm ready to start burning down the jungle.
Mobs spawn naturally within a square group of chunks centered on the player. In single-player mode, this area will be 15×15 chunks (240×240 blocks), but in multi-player mode the size can vary with the server settings. When there are multiple players, mobs can spawn within the given distance of any of them. However, hostile mobs (and some others) that move farther than 128 blocks from the nearest player will soon despawn (see Despawning), so even with a larger chunk loading radius, the mob spawning area is more-or-less limited to spheres with a radius of 128 blocks, centered at each player.
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There must be no players and no player spawn points within a 24 block distance (spherical) of the spawning block