just let the number of animals be based on the chunk they are in.. like say 5 per chunk (maybe more) if the animals walk off, they more can spawn, and it's all based on the size of the pen.
I think the area limiting natural population growth would need to be larger than a single chunk. The range would probably need to make it 25(radius 2) or 49(radius 3) at least. We need to consider that there will be at least the 4 farm animal types breeding this way over one area, and perhaps future ocean life.
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More Ocean Life: Kelp, Coral, Crabs and Jellyfish; Coconut Palm trees for beaches and islands. Terrain Generation Changes: Which biomes and world-building features are most in need of change?