Wolfram Science Group
Phoenix, AZ USA
Registered: Aug 2003
From the standpoint of every possible bit flip in a DNA sequence, sure. (But life can't be that sensitive, or it wouldn't work - see below). From the standpoint of the basic tendency of life forms to reproduce themselves almost exactly, no. Most imaginable random changes won't have any appreciable effect, or will have an immediately harmful one. If others have the sort of effects traditional mathematical methods are good at modeling - linearly additive continuous behaviors e.g. - then again it is hard to get variety.
In a sense, in the older continuous picture the fitness terrain has to already contain that variety, and natural selection then has to transfer it inward. The usual picture of small adaptive steps toward some local extreme, accumulating to find that extreme, is fundamentally based on this sort of calculus-inspired formal image. As the investigation of systems based on constraints shows, this is not an efficient process unless the fitness terrain is particularly smooth. If it looks like a spikey pegboard, it will quickly get stuck.
But if the dependence on small changes is of the algorithmic, simple programs variety, one can expect much more substantial changes. A large pattern difference between two shells can arise from a small change in the rule that determines pigment placement or not. Is this just a point about sensitive dependence? No, because simply unbounded dependence on small changes, not even keeping the same algorithm, would typically produce something broken, unviable. We wouldn't see the stable types we do see.
This does not mean, incidentally, that such continuous model changes don't happen. Clearly they can, when the right "problem" characteristics are present (a smooth fitness landscape with a clear local maximum, reachable by varying a single parameter e.g.). Such adaptation, of an "engineering efficiency" type, can be explained by that kind of process. But it isn't a process particularly good at producing complexity or variety. Simple programs and discrete changes to them, are good at that. That is my reason for calling them a "variety engine". I hope this clarifies what I meant.
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