It's quite easy to see how a "real business cycle" could occur in the natural world. Imagine a pond teeming with life. One year a parasite infects the lily pads. Without the lily pads the frogs can't catch flies, the flies swarm, but the frogs go hungry and the pike have less to eat. If we measured the gross pond biota (gpb) we could see natural cycles. Indeed, if we measured different pond sectors (the frog sector, the fly sector etc.) we could trace out a whole sequence of events as each sector of the pond responds to the initial shock and to changes in every other sector (ala a vector auto regression).
Can there be a Keynesian business cycle in the pond? i.e. Could animal spirits drive a natural business cycle? It's harder for me to see exactly how this would work. We would need "money" or something similar to generate a rush to liquidity and a decline in investment. We could perhaps get a coordination type business cycle (ala Roger Farmer) with herd behavior. Interestingly, the trend in biology–as I read it at least–has been to think of herd behavior as optimal for the herd but this is not necessarily the case. We know that slime molds self-organize and aggregate during times of stress could this process be set off with no or little exogenous shock? Could a natural system provide a model for business cycle behavior? It would be odd if only people had animal spirits. Biology and economics have much to offer one another.