I was already aware that Bill was largely clueless about maths, but this is very basic maths that I think I would have covered in the junior level of highschool in my early teens.
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The total size of sequences space for functional alpha actins is irrelevant, as alpha actins evolved from other highly similar actins, so the probability of a blind de novo discovery by randomly sampling into sequence space isn’t an indication of how likely they were to evolve when they did. Because that’s not how they evolved.
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Wait, hold on… Does Bill think that all changes to the sequence consist of replacing letters?
Then this would make some sense, actually. That a hundreds of digits long section at one address should match up at all with that at some completely different address if the only way to achieve this is randomly swap out individual base pairs is exceedingly unlikely (though it has a likelihood, and one could actually put a numerator and a denominator to it - unlike magic-man-dun-didit, but that’s neither here nor there).
@colewd do you know what recombination is? Do you know what insertion mutations are?
The space of all conceivable DNA sequences is not a good starting point. Finding a sequence shared between different loci would be an instance of finding the same pattern in vastly different parts of that space, but that’s just neglecting mechanisms that can displace whole gene sections. Noone would assume, that if a page 73 of a book happened to lie torn out between pages 220 and 221, that therefore these are different books from different publishers, occupying vastly different points in the space of all possible arrangements of letters. No, we would conjecture that rather the page broke out and someone just put it back in somewhere without ensuring that it be the original location.
Likewise, DNA is not some data in some random access memory, but very much a physical entity, a chemical substance. “Pages” of DNA can be displaced, or “xeroxed” more than once in reproduction. These aren’t speculative saving devices either, but well-documented events that do happen with some measurable rate. Generally, if you find a great deal of overlap at different loci, chances are that one of the sections was duplicated at some point. If it is in different places between different organisms, again, the much, much likelier explanation than “it just so happened by sheer luck to evolve twice just like it is” is that one of the loci is at least close to the ancestral location of that gene, and there was one or more insertion mutations in the other lineage that displaced their variant to where it is now.
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I can’t even…
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Yes I know what both of these are and they certainly can play a role in the variation inside populations.
No. Because you haven’t provided any actual numbers.
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Fractions have numerators and denominators. Ratios do not.
What level did you achieve, Bill?
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False.
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Ratios and fractions are routinely calculated from tesselations, crystal lattices, orbital resonances and other cases where the ‘denominator’ is unknown and even potentially infinite.
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Ratios and fractions are routinely estimated for large populations by statistical sampling where the total population size is not needed and may not be known.
What level of maths did you achieve, Bill?
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Hi Roy
I have several university courses in both calculus and statistics and my major included applied mathematics. I have also studied tensor calculus.
What type of mathematics have you studied?
Why would you not use a denominator for a calculation if it was readily available? In the case above it is 20^371.
Now you are advocating that an estimate is a good way to get an understanding. I agree with you.
Here I have shown you how to calculate the denominator we then need to estimate the numerator.
It is somewhere between 1 and 10^371 vs a denominator of 10^482. Since the latter simply gets you a successful protein fold (a sequence without a null mutation) and not a complex function that is highly resistant to mutation I would estimate that the real number is much closer to 1 then to 10^371.
… but then you got kicked in the head by a horse?
How is that a response to anything he said? You’re just making your obvious and overwhelming incompetence all the more mysterious.
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You’re empirically wrong about the functional fraction. It is on the order of 10^-9 or so, which is plenty large enough relative to the mutation rate.
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What are you estimating for the mutation rate? How many generations would be required for this type of search?
You need to square this with @rumraket when he gets off his high horse 
What you are going to find with a broader search that Rums estimate of a 50% null rate is close enough for simpler bacterial enzymes.
The number will obviously go up as complexity of the protein family increases such as in the case of the actin family that are performing multiple cellular functions.
I’m not estimating it, we have empirical data for that.
Every possible mutation happens in every generation for all reasonably sized natural populations.
You need to explain why you think it’s incompatible. Because it isn’t.
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This is not the question I asked. Every possible mutation happening is in individual species is different than a search which requires 10^9 trials. How is the search occurring such that a new enzyme appears somewhere in the population.
The calculation comes from 50% of substitutions generating a null enzyme. This becomes a 2^N calculation. The numerator comes from this calculation.
I have never stated anything approaching a “50% null rate” you lunatic.
By enzymes evolving from substrate binding proteins, or by divergence of duplicate genes that are already enzymes. Directly demonstrated to be how novel enzymes evolve in experiments, and by ancestral sequence reconstruction.
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There is literally zero evidence that supports that claim. You are confusing “null enzyme” with “mutations that are deleterious.” Once again you have failed to comprehend some discussion here in which the terms “null” and “deleterious” were used, and you are apparently unaware that they are not the same.
That on average 50% of mutations to protein coding genes are deleterious just means they will diverge at roughly half the rate of mutation. So, on average, still very fast.
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In his next post Bill will either change the topic (move the goalposts), write something outright nonsensical, or toss out the old “could you be wrong?” Red Herring rhetorical question to distract from his millionth failure on this forum. Or whine about tone.
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I agree that a deleterious mutation may or may not be a null mutation. Behe was talking about deleterious mutations that were null mutations. Did you not understand this. Way more the 50% of residue substituting mutations are deleterious.
A major route of evolutionary innovation is thought to pass through gene duplication (Ohno 1970; Lynch and Conery 2000; Wagner 2001; Chothia et al. 2003). Because one copy of the gene can continue to fulfill the original function, in this view a duplicate, redundant copy of a gene is substantially free from purifying selection, allowing it to freely accumulate mutations. Although the great majority of non-neutral mutations to duplicated genes are expected to result in a null allele (Walsh 1995; Lynch and Walsh 1998), that is, a gene that no longer codes for a functional protein, occasionally one might confer a novel function on the incipient paralog. If this occurs, then the duplicated gene can be refined by mutation and positive selection, independent of the parent gene.
You omitted the possibility that he’d emit another garbled word salad that demonstrates that he has no idea what he is talking about:
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That’s the materialistic thinking speaking.
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