> ***What does it mean to have a "numerically consistent model of
> evolution
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> record -- with or without allowing for extinction events to match a
> model of simple exponential growth in number of taxa.
A model of growth in taxon numbers is quite another thing from a "model
of evolution".
> The equation for
> exponential growth is pretty simple N = R ^ T where N is the number of
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> Cambrian -- say 500 taxa (which seems low) and a value for today say
> 5,000,000 taxa.
What exactly do you mean by "taxa"? Do you mean species? Or something else?
> That implies a growth rate of about 1.0000000176.
> Which says that the number of taxa doubles roughly roughly every 5.68
> million years. So when was there only one taxon? I make it somewhere
> before 1000ma.
This is not a good model. You have to consider both origination and
extinction. Your model assumes no extinction. That would be, if
anything, only one "taxon" with living descendants; there would have
been many other taxa at the time. Look up "coaleascence".
> The fossil record OTOH would seem to indicate that metazoans appeared
> later and diversified much more rapidly than that. You can try
> juggling the numbers, allowing for extinction events, etc. My very
> cursory efforts lead me to believe that any model that matches the
> fossil record is way too contrived to be credible.
No? Try Sepkoski's logistic model. It seems to fit fairly well. However,
it fits not a single curve, but three separate ones for three different
fauna. This is not to say that diversification is really random, with
constant parameters. But it can be surprisingly hard to show that it isn't.
> Neither do I think
> (could be wrong) that magic with fractal distributions, etc is going to
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> numbers actually could be made to work plausibly, I think a numerical
> model of evolution would be a standard element of paleontology.
Again, this would be a numerical model of only a small part of
evolution, the growth in number of species over time. But you want to
look up the work of Dave Raup and Jack Sepkoski, among others.
> So, I think that, The problem isn't that evolution isn't constrained.
> It's that we don't understand the constraint.
Growth in diversity is not the sort of evolution we were previously
talking about. "Constraint" is generally used in reference to
morphological change, what's generally called disparity, in contrast to
diversity, which is just numbers of species.
> ===
>
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> our view of the Early Cambrian would be greatly different without the
> Chengjiang fauna.
I think you would find it hard to support this. Are there other
localities with body fossils of armored lobopods, for example?
> Also, I personally think that the rules of fossil
> preservation probably changed significantly around 550 million years
> ago with the advent of active sediment feeders and the destruction of
> widespread microbial mats.
Makes sense. There are other theories too. Are you familiar with
Butterfield, N.J. Secular distribution of Burgess-Shale-type
preservation. Lethaia 28, 1-13 (1995)?
> My guess is that Ediacaran fossils will
> probably prove eventually to be substantially more common than we think
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> altered exposures of my local Ediacaran formation, but I'll be damned
> if I can tell you what kind of plants or animals they might represent.
Quite possible.
> ***This is nonsense. Almost every modern evolutionist believes that the
> mechanism behind adaptive evolution (there are other kinds, but that's
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> he was. I did not say that Evolution en toto had been disproved. Nor
> do I think that.
Nor did I claim you thought that. I just said you were wrong about
Darwin being wrong on this one point. And you are.
> As for mutations being small steps. Not really that clear. Most
> aren't visible at all. (And, for that matter, most surely are lethal).
No. Where do you get this idea? Most are neutral.
> But the mutation mechanism permits much larger changes than gradual
> change. If anything, this supports evolution as it allows for large
> enough changes to matter. Not that big a deal nowdays I think, but
> maybe important in the Ediacaran and Lower Cambrian when there seems to
> have been quite remarkable (by modern standards) diversification in a
> relatively short time span.
I was just pointing out that the objection you had stated was bogus.
That doesn't rule out the possibility of macromutations. But in fact
very few modern biologists credit any such thing. Your statement (which
you snipped) was just wrong on many counts, as I noted.
I note that you have once again confused diversity (number of species)
with disparity (extent of morphological differences). Nor is it clear
that we need any mechanism other than natural selection of small
mutations to account for the Cambrian explosion.
> ***I'm not sure they're at all relevant to the OP's post. ***
>
> Nor, in retrospect, am I.