If you can't usefully connect your abstractions to the historical record, I sure hope you have some data you can connect it to. Otherwise I can't imagine how you could have much confidence in them.

Depends on how much stress I want to put on them, doesn't it? If I want to predict that the next growth curve will be an exponential and put bounds around its doubling time, I need a much finer fit to the data than if I only want to ask obvious questions like "Should I find rabbit fossils in the pre-Cambrian?" or "Do the optimization curves fall into the narrow range that would permit a smooth soft takeoff?"