Thanks all! Not Conway's game in the mechanics - different matrix, but similar concept. The animals are grazing the plants, the amount of sustenance depends on the phase of the plant, the animals are helping to fertilize the soil and also leaving some waste behind. The waste impacts the fertility of the animals. The plants need the fertilized soil and also break down the waste.
If I had more time, I would work out the weight of those interactions -- it's why the carnivores so rarely stick around.