All concepts in ecology are simplifications and generalizations. That's pretty much the way our knowledge system works, anyway. Most of reality is too complicated and rich with too much uniqueness to be precisely described or cataloged. Humans are driven to categorize and catalog — we have to if we're going to make sense out of things — so we ignore a lot of the uniqueness for the sake of being able to pay attention to the similarities. Ecological systems demonstrate this better than any other phenomenon we've tried to study.
When I talk about a "stable ecosystem," the first idea that springs to mind is that I'm talking about a system that's the same all the time. Of course, there's no such thing. No ecosystem is the same even two days in a row. But in order to get an idea of how ecosystems work, and how they are structured, we ignore a lot of the flux and movement and pay attention to the broad things that stay constant. For instance, even though population sizes cycle — so the number of bunnies in the meadow may be different year after year — in many cases if we observe bunny populations over a series of years, we can see that the population remains close to a particular average size (the carrying capacity). So we can ignore the year to year ups and downs and say that this population is stable.
We do this on a larger scale for the whole ecosystem. If we can observe the ecosystem for a series of years, and things stay roughly the same (always remembering those ups and downs, and all of the unique things we're ignoring), we can safely say that we are studying a stable ecosystem. This is important, because if the system is stable, it means that we can make predictions based on what has happened in the past, and we have a reasonable chance of being correct. Of course, the more detailed we make our predictions, the more likely it is that they will be wrong, because it's the details — the ups and downs — that we've ignored in describing our ecosystem as stable.
So stable doesn't mean "unchanging" — it means "pretty much the same." Another important thing to remember is that nothing stays stable forever. An ecosystem that is stable and has been stable for many years (or centuries) may lose its stability if, for instance, the climate changes, or if certain kinds of disasters strike which alter so many things that the ecosystem is destabilized. So "stable" doesn't' mean permanent, either.
You can begin to see the difficulties inherent in trying to predict the effects of, say, a reduction in the amount of ozone cover our planet enjoys. Ozone is very important to us, since it protects the surface of our planet from harmful ultraviolet radiation from the sun. (We need some UV, but too much causes sunburn, mutations and/or skin cancer. Those we can do without.) We understand the big picture — the damage excess UV can do, and the role ozone plays in protecting us — but the details escape us. We can't provide the "facts and figures" that so delight politicians, because those are part of the "ups and downs."
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