Annoying creationists

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Ah, so you took his question to mean "Is there another mechanism we can use to infer common descent?" I'm not sure if that's what he meant or not (figuring out his word salad is almost impossible sometimes,) but you gave a very interesting response.

We found a genome wide duplication event in the poplar genome project, which was probably caused by a paleopolyploid event sometime over the course of its divergence from its common ancestor with A. thaliana. Apparently these events happen very often in plants. There has been some speculation that they are a major cause of speciation in plants.

Well, as Kleinman apparently lack the mental skills to understand anything of what I said in my last two posts (as evidenced by his almost complete lack of response to them), I may as well ignore him, and continue talking to you.

I took his question to mean both any process which would give common descent and any process from which we may infer common descent, as the latter, it seems to me, is a subset of the former. Of course, just sexual reproduction, regardless of if mutations happen or not, will "give" common descent of the progeny of any given stage. Even asexual reproduction will do so, provided each individual gives rise to more than one progeny. That's how I see it, at least. In a sense, at least, common descent does not require evolution. Me and my sister would be of common descent even if our respective genomes were 100% identical, so his question is what we could expect of a man who has no idea what he is talking about.

However, if he means some mechanism or process or evidence we can use in present day organisms to infer common descent of at least some organisms (1), and we cannot use (random point) mutation and selection, then polyploidisation immediately springs to mind. Of course polyploidisation is often coupled to mutation and selection (2) (and to a change to an asexual lifestyle, at least in animals), but even without it, common descent could still be inferred.

I think it is telling that Kleinman choose not to comment on that post at all. My guess is that, again, he has no idea what is being talked about in his presence, and thus he runs below deck and closes the hatches behind him.

As for the last part of your post, I have seen that as well --- 80% of all flowers have polyploid forms or some such number (I think this number was from Otto and Whitton, 2000). The numbers in animals are less, which I have seen explained as a result of animals being less inclined to self-fertilize, but this is doubtlessly only part of the explanation. However, Okano (I think) found evidence that polyploidisation had occurred at least twice basally in the vertebrate phylum, but I don't know the details of it. I've also come to understand that it's more common in colder climates (Little et al., 1997 springs to mind, and also some papers the now infamous Paul Hebert were involved in, but I can't remember who were the first authors of those papers).

In all, I find polyploidisation extremely interesting, and sort of miss working with it. Do you work with it at present?

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(1) Interesting side question: if we could show beyond any doubt that a certain group of organisms had evolved in a way that even someone as dense as Kleinman would accept it, would that be perceived as a localized evolution event or evidence that all organisms have evolved?
(2) Again, Song et al., 1999 is an excellent example of this. However, it is a study of allopolyploidisation, not autopolyploidisation.
 
Kotatsu, once you understand that mutation and selection is simply a sorting/optimization problem, you will understand why this process can not transform large numbers of genes simultaneously. I harbor no ill will toward you or anyone else. I just think your ideas are illogical and irrational. They don’t make mathematical or empirical sense.

Do you have any useful response to my two longer posts? I mean the one about polyploidisation giving rise to common descent in a way we can actually measure and infer more easily than (random point) mutation and selection, and the elaboration of the dinosaur-to-bird evolutionary scenario I provided you with? If at any point in either of those two posts I am unclear or too technical --- I understand, for instance, if the polyploidisation post may be too convoluted for someone who has never specifically studied the area --- I would be happy to provide more details and explain it in simpler terms. Just say the word. Also: if you have problem accessing the papers I cite, I would be glad to send them to you. I wouldn't want to just copy and paste, sinc ethat could lead to allegations of cherry picking; far better for you to read the papers in full and get the whole picture.
 
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Well, as Kleinman apparently lack the mental skills to understand anything of what I said in my last two posts (as evidenced by his almost complete lack of response to them), I may as well ignore him, and continue talking to you.
Well, if he won't provide interesting answers or thoughts, maybe we can!
Of course, just sexual reproduction, regardless of if mutations happen or not, will "give" common descent of the progeny of any given stage. Even asexual reproduction will do so, provided each individual gives rise to more than one progeny. That's how I see it, at least. In a sense, at least, common descent does not require evolution. Me and my sister would be of common descent even if our respective genomes were 100% identical, so his question is what we could expect of a man who has no idea what he is talking about.
This was how I originally interpreted his question. You could imagine a universe where organisms were all related to each other, but didn't evolve. Instead of mutation and natural selection, you could have God the post-hoc Kludge Designer come in and incrementally "fix" his creation once in a while.
However, if he means some mechanism or process or evidence we can use in present day organisms to infer common descent of at least some organisms (1), and we cannot use (random point) mutation and selection, then polyploidisation immediately springs to mind. Of course polyploidisation is often coupled to mutation and selection (2) (and to a change to an asexual lifestyle, at least in animals), but even without it, common descent could still be inferred.
We could also use simple gene homology for this. It might not be a perfect model if we go at it blind to mutation mechanisms, but string similarity would certainly allow us to infer a tree of relationships among species.
I think it is telling that Kleinman choose not to comment on that post at all. My guess is that, again, he has no idea what is being talked about in his presence, and thus he runs below deck and closes the hatches behind him.
What about his inability to answer a direct question with a YES or a NO?
As for the last part of your post, I have seen that as well --- 80% of all flowers have polyploid forms or some such number (I think this number was from Otto and Whitton, 2000). The numbers in animals are less, which I have seen explained as a result of animals being less inclined to self-fertilize, but this is doubtlessly only part of the explanation. However, Okano (I think) found evidence that polyploidisation had occurred at least twice basally in the vertebrate phylum, but I don't know the details of it. I've also come to understand that it's more common in colder climates (Little et al., 1997 springs to mind, and also some papers the now infamous Paul Hebert were involved in, but I can't remember who were the first authors of those papers).
The image that I linked in my previous post includes more than one event in vertebrates! That's definitely something I'll have to read up on over Thanksgiving break!
In all, I find polyploidisation extremely interesting, and sort of miss working with it. Do you work with it at present?
No. I'm working on gene regulation in insects these days. Gene regulation is amazing, but I do miss investigating larger structural and comparative evolutionary questions about genomes. It was great to have such a deep sense of vast amounts of time in my every day work.

Fortunately, I think things will get interesting really fast with this insect stuff. We have a lot of fully sequenced genomes to work with these days, and the model organisms for development (fruit fly) and social behavior (honey bee) are closely related to all them.
 
Perhaps you think because humans and chimpanzees have the same insulin might make evolutionists think we arose from a common ancestor but then you have to show why humans and chimpanzees have different preproinsulin.
I don't know anything about this protein. I went to NCBI. I got the sequence for human preproinsulin. I blasted (searched) it against the NR database (all the non redundant DNA we know of in the whole world.) Here are the first three hits:
Code:
ref|NP_000198.1|  proinsulin precursor [Homo sapiens] >sp|P013...   214    2e-54 
gb|AAP36446.1|  Homo sapiens insulin [synthetic construct] >gb...   213    2e-54
ref|NP_001008996.1|  proinsulin precursor [Pan troglodytes] >s...   212    5e-54

Pan troglodytes is chimp, in case you didn't know.

Here is the human amino acid sequence aligned against the chimp's:
Code:
Query  1    MALWMRLLPLLALLALWGPDPAAAFVNQHLCGSHLVEALYLVCGERGFFYTPKTRREAED  60
            MALWMRLLPLL LLALWGPDPA+AFVNQHLCGSHLVEALYLVCGERGFFYTPKTRREAED
Sbjct  1    MALWMRLLPLLVLLALWGPDPASAFVNQHLCGSHLVEALYLVCGERGFFYTPKTRREAED  60

Query  61   LQVGQVELGGGPGAGSLQPLALEGSLQKRGIVEQCCTSICSLYQLENYCN  110
            LQVGQVELGGGPGAGSLQPLALEGSLQKRGIVEQCCTSICSLYQLENYCN
Sbjct  61   LQVGQVELGGGPGAGSLQPLALEGSLQKRGIVEQCCTSICSLYQLENYCN  110

CURSES!!! OUR THEORY IS RUINED! HOW DID NATURE EVER CREATE SUCH DIVERSITY?!?!?!?!?!

ETA For those who are curious, here is the result of the chimp preproinsulin searched against the NR database:
ref|NP_001008996.1| proinsulin precursor [Pan troglodytes] >s... 215 7e-55
ref|NP_000198.1| proinsulin precursor [Homo sapiens] >sp|P013... 212 5e-54
gb|AAP36446.1| Homo sapiens insulin [synthetic construct] >gb... 212 6e-54
 
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I haven’t made any discovery.
Thank you. At last you admit the truth.

All I am doing is reporting the mathematical and empirical facts of how mutation and selection actually works.
You know, we have read your posts, so we know that that isn't true.

For example, you've also misreported the facts, misinterpreted the facts, lied, talked gibberish, made silly mistakes in basic mathematics, and raved about cheese.

I’m not the only one who understands this.
If you claim that there is one other person in the world who has fallen for your silly gibberish, perhaps you could name him.

What you do claim Adequate is that n+1 selection pressures evolve more rapidly than n selection pressures.
What a silly lie. I claim no such thing.

Adequate said:
Since you ask, I think that combination therapy is better than monotherapy for HIV, just like every other evolutionist does, as you know perfectly well.
I posted a citation from a 50 year old Nobel laureate speech that said the same thing.
Actually, if you ever take the trouble to read the speech you're lying about, you'll find that he said no such thing, principally because HIV was then unknown.

Adequate said:
We even patiently explained to you why it's better, remember? About, I don't know, a hundred pages back?
Why haven’t you evolutionists explained this before?
We did. About, I don't know, a hundred pages back?

Oh, that’s right; you say that n+1 selection pressures evolve more rapidly than n selection pressures.
Reciting the same silly lie twice in the same post won't make it any truer, it just makes you slightly more boring.
 
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This was how I originally interpreted his question. You could imagine a universe where organisms were all related to each other, but didn't evolve. Instead of mutation and natural selection, you could have God the post-hoc Kludge Designer come in and incrementally "fix" his creation once in a while.

Or not even that if we imagine that the environment the creatures live in is completely homogeneous all the time, and there are endless resources. Of course, that kind of universe is even more unlikely, but it could perhaps exist in theory.

We could also use simple gene homology for this. It might not be a perfect model if we go at it blind to mutation mechanisms, but string similarity would certainly allow us to infer a tree of relationships among species.

I haven't read much about this, but you mean the sequence in which the genes on a particular chromosome, say, occurs, no? That's basically just the same as the sequence similarities, but at a higher level --- at least theoretically. As such, it's subject to the same lame objections as Kleinman has towards nucleotide sequence similarities, i.e. that we have no mechanism to get from one state to another (which of course is not true in the real world, but seems to be true in whatever bizarre world Kleinman inhabits).

Thus, while I understand that it's a good example, I think that for the purpose of arguing with Kleinman, polyploidisation is actually a better one, as it is instantaneous, we have known mechanisms from it, it is not dependant on mutations and selection, or sexual selection, and so on. But I do see your point. To a person educated in these matters, your example is as good as mine.

What about his inability to answer a direct question with a YES or a NO?

Well, since he doesn't understand the subject you are asking about, he doesn't know what is the correct answer and what is the incorrect one, and thus he cannot chose the latter just to be contrary. He cannot answer it, because he might by mistake chose the option which is actually correct, and then we'll go on and on about that forever.

The image that I linked in my previous post includes more than one event in vertebrates! That's definitely something I'll have to read up on over Thanksgiving break!

I think the ones Okano (if that's his name, I can't remember really) were postulating were the one just "after" the Amphioxus[/quote] and the one just "after" the lamprey. I seem to recall that his polyploidisation events were basal to all of Vertebrata, but I can't remember where I read about it.

Regardless of that, I have always believed that polyploidisation seems to be one of those things that are underrated unduly, just like sympatric speciation. It's stuff that I feel are probably much more common than most people think, but which are not as common in vertebrates as in invertebrates, and thus it is generally disregarded.

I have no hard data to back this up with, though, just a feeling. However, your tree seems to give some vague support to the feeling, as does several papers I have read over the last few years.

No. I'm working on gene regulation in insects these days. Gene regulation is amazing, but I do miss investigating larger structural and comparative evolutionary questions about genomes. It was great to have such a deep sense of vast amounts of time in my every day work.

Fortunately, I think things will get interesting really fast with this insect stuff. We have a lot of fully sequenced genomes to work with these days, and the model organisms for development (fruit fly) and social behavior (honey bee) are closely related to all them.

I have just recently started my PhD and work with co-evolution of shore birds and their lice, which I think will be extremely interesting. Nothing really revolutionary, I expect, as I approach the matter from a systematic and alpha-taxonomical point of view. However, I already have some great ideas to test, and I am becoming more and more satisfied with having been given this opportunity every day.

I think co-evolution is another thing Kleinman will have a hard time explaining satisfactorily (1). Why would the phylogenetic trees of parasites and those of their hosts ever be similar if the two groups had not evolved in parallel? The theory of evolution explains this elegantly, of course, but if you reject this theory, how do you explain it? My guess is that it will be called yet another example of wishful thinking or so, just like phylogenetic trees in general.

Isn't whole-genome sequencing immensely expensive?

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(1) Meaning something he will dismiss with a platitude, an insult, or a simply misunderstanding of the concept.
 
I don't know anything about this protein. I went to NCBI. I got the sequence for human preproinsulin. I blasted (searched) it against the NR database (all the non redundant DNA we know of in the whole world.) Here are the first three hits:
Code:
ref|NP_000198.1|  proinsulin precursor [Homo sapiens] >sp|P013...   214    2e-54 
gb|AAP36446.1|  Homo sapiens insulin [synthetic construct] >gb...   213    2e-54
ref|NP_001008996.1|  proinsulin precursor [Pan troglodytes] >s...   212    5e-54

Pan troglodytes is chimp, in case you didn't know.

What are the percentage matches? I never learn to find my way around GenBank, as I use it so rarely (there are extremely few sequences there for the Clitellates I work with, and I haven't started looking for lice sequnces yet).

Also, as I have reread the abstract you linked to, could you explain tandem gene duplication for me? I'm not familiar with that term.

EDIT:
Hooray! 300 posts, of which I estimate at least 200 have been in this thread!
 
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Why would you think that Shalamar is mediocre?

Which such a bad grasp of grammar, Klein, it's no wonder you think evolution is mathematically impossible by reading examples that contradict this.

You should know the answer to that one Belz, the fewer the selection conditions, the faster it evolves.

Yeah, but that doesn't answer my question. Do you contend that HIV is naturally under only a very few pressures ?

Belz, how many variants are there, 10?, 100?, 1000?, millions? Consider that for hemoglobin, there are only a few hundred variants of this gene that still give viability. In time, most or all variants of viable resistant HIV genes will be identified.

Answer the question, Klein: is it deterministic or not ?
 
But isn't that still mutation ?

Hmmm. When Kleinman says "mutation", I always think of that as short-hand for "random point mutation" as the dropping of these words are the only thing that differs between his ramblings today and those of a year ago. Maybe he doesn't mean that, though, and I have misinterpreted him. It's similar to how "slow and eventually stop" has gradually changed to "confound" over a similar amount of time.

And yes, they would count as mutations, or not as mutations, depending on what you really call a mutation. I believe it could be argued that mutations actually change something in the genome, which polyploidisation events, strictly speaking, don't. It would depend on context, I believe.

EDIT:
I would call the mutations if asked, but I could also see the need for a subgrouping of mutations that actually by definition alter the exact sequences (random point mutations, gene duplications and so on) and those that don't necessarily do that (polyploidisation, and possibly other processes)
 
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kleinman said:
What you do claim Adequate is that n+1 selection pressures evolve more rapidly than n selection pressures.
What a silly lie. I claim no such thing.

What was claimed is that n+1 selection pressures evolve more rapidly per pressure than do n. So if t(n+1) is the time it takes 90% of the population to evolve in response to n+1 pressures, then t(n+1)/(n+1) < t(n)/n.

I demonstrated that this is the case using kleinman's own model (which he proposed and incorrectly analyzed a few pages back), as did rocketdodger with a somewhat more realistic model.
 
Or not even that if we imagine that the environment the creatures live in is completely homogeneous all the time, and there are endless resources. Of course, that kind of universe is even more unlikely, but it could perhaps exist in theory.
Imagining unreal universes is fun... but mostly useless.
Thus, while I understand that it's a good example, I think that for the purpose of arguing with Kleinman, polyploidisation is actually a better one, as it is instantaneous, we have known mechanisms from it, it is not dependant on mutations and selection, or sexual selection, and so on. But I do see your point. To a person educated in these matters, your example is as good as mine.
I totally agree with you. I was just pointing out that there are more "large" features on the genome that point to common heredity.
He cannot answer it, because he might by mistake chose the option which is actually correct, and then we'll go on and on about that forever.
I'm so glad we're not going on forever and ever now. :D
I think the ones Okano (if that's his name, I can't remember really) were postulating were the one just "after" the Amphioxus and the one just "after" the lamprey. I seem to recall that his polyploidisation events were basal to all of Vertebrata, but I can't remember where I read about it.

If you find out, send me the link!
Regardless of that, I have always believed that polyploidisation seems to be one of those things that are underrated unduly, just like sympatric speciation. It's stuff that I feel are probably much more common than most people think, but which are not as common in vertebrates as in invertebrates, and thus it is generally disregarded.
I think most people's common understanding of evolution is biased toward "human-like" evolution. One example of this that pops to mind of is genetic algorithms. "Crossover" or "mating" was included from the very beginning of the field, but most of evolution's heavy lifting, so to speak, was conducted without any kind of "mating."
I have just recently started my PhD and work with co-evolution of shore birds and their lice, which I think will be extremely interesting. Nothing really revolutionary, I expect, as I approach the matter from a systematic and alpha-taxonomical point of view. However, I already have some great ideas to test, and I am becoming more and more satisfied with having been given this opportunity every day.
Very interesting! What is your field of study? I'm in bioinformatics, so all the research I've done has been from the computational side of things.
My guess is that it will be called yet another example of wishful thinking or so, just like phylogenetic trees in general.
That's the problem. This denialist mentality takes every piece of evidence and tries to pedantically attack every detail of it. They never take a step back and look at the big picture. They never think, "Wow, all this evidence from all these different fields is consistent."
Isn't whole-genome sequencing immensely expensive?
Yes, but it's getting cheaper by the minute! There was a time when I could list all of the genome sequencing projects going on off the top of my head. Now, there are too many to keep track of. Very exciting times!
 
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What are the percentage matches? I never learn to find my way around GenBank, as I use it so rarely (there are extremely few sequences there for the Clitellates I work with, and I haven't started looking for lice sequnces yet).
If you get to a point where you need help using or understanding any of the bioinformatics applications or databases, I'd be glad to assist!
Also, as I have reread the abstract you linked to, could you explain tandem gene duplication for me? I'm not familiar with that term.
As I understand it, it's exactly what it sounds like. Large stretches DNA get copied in 5' -> 3', 5'->3' order. Some of those regions contain genes. When this kind of mutation happens, the organism ends up with two tandem copies of that gene.
 
What was claimed is that n+1 selection pressures evolve more rapidly per pressure than do n. So if t(n+1) is the time it takes 90% of the population to evolve in response to n+1 pressures, then t(n+1)/(n+1) < t(n)/n.
The word "rapidly" is rather ambiguous, since it can refer either to rate or to duration, and you must know by now that if kleinman can misunderstand something, he will.

In my own model, I continued the simulation to fixation of all alleles. Hence, my own statement of my result was that if the selection pressures are simultaneous, then the rate of evolution (fixations/generation) increases with the number of selection pressures.

Mind you, kleinman managed to misunderstand that too, as you can see by his absurd lies about what I "claim".
 
That's the problem. This denialist mentality takes every piece of evidence and tries to pedantically attack every detail of it.
Pedantry implies a certain degree of precision. What denialists do is seize on each point separately and use their powers of incomprehension to rephrase it as a vague gray flabby mush of nonsense. Then they whine about how the mess they've made is nonsense.
 
I totally agree with you. I was just pointing out that there are more "large" features on the genome that point to common heredity.

Indeed. The very existence of discrete chromosomes and not just some sort of gene soup, and the usage of the same bases everywhere and the fact that while the same code is not used to decipher these bases into amino acids in all groups of organisms, the different codes --- as far as I am aware --- are at least consistent within groups and a billion other things could also be used for this purpose.

f you find out, send me the link!

I am not sure if this is the article I was thinking of (as I haven't looked in this folder of articles for a year or so), but the guy's name was Ohno, not Okano (1), and he published a book called "Evolution of Gene Duplication" with which you may be familiar; I have never even seen the book. However, the only article I could find in my Endnote register was Furlong & Holland, 2004. Biological Journal of the Linnean Society 82, 425-430. Mind you, I haven't looked at more than the headline of the article yet, so it could be an entirely different article I was thinking about. I have a few folders filled with the little buggers...

I think most people's common understanding of evolution is biased toward "human-like" evolution. One example of this that pops to mind of is genetic algorithms. "Crossover" or "mating" was included from the very beginning of the field, but most of evolution's heavy lifting, so to speak, was conducted without any kind of "mating."

This miscomprehension is not limited to evolution. I think anyone who's ever worked with invertebrates (apart perhaps from insects and invertebrates we eat, such as clams) will sooner or later find that no one can really understand why they do it, unless they are scientists themselves. It's the "stuffed animal syndrome" --- people care about cute animals which can be made into stuffed toys. If they can't, or the animal is in any way ugly, bothersome, slimy or very small, there seems to be no understanding of why anyone would ever want to do any research on them...

And I made the "mistake" of moving from slimy worms to lice, and no one understand why.

Very interesting! What is your field of study? I'm in bioinformatics, so all the research I've done has been from the computational side of things.

My work is two-fold. First of all an alpha-taxonomic inventory of the feather lice parasitizing birds of Sweden and the other Nordic countries. This is done for the Swedish Taxonomy Initiative, which aims to catalogue all multicellular organisms here. Second, I will do phylogenetic work on some genera of lice infesting shore birds, primarily the subfamily Calidrinae (Charadriiformes: Scolopacidae). In both of these projects, there'll be some description of new species (I've already found 12 presumably undescribed ones!) and some morphological work. In the latter, I will also erect phylogenies over the relevant bird species, something which has not been done before, and then compare the trees (if I can ever get the bloody programs to work). I will work primarily with PAUP* and MrBayes, but also with some strange programs I've never used before, like TreeMap, TreeFit and Parafit, but I haven't got these to work yet.

I collect all my material myself, and am in the process of applying for money to go to Japan next autumn and collect from Siberian shorebirds. As a spin-off project, I'll also collect from species and genera of birds which occur both in Sweden and in Japan (such as Anas, Emberiza, Corvus, Parus and so on) to see if the lice fauna is homogenous on the same species of birds across Eurasia. Further on, I hope I'll be able to collect in Canada and Australia as well, and maybe Israel. It's hard work, but VERY fun. There are some pictures of the practical part of my work in the Forum picture thread (just click on my profile, I don't have that many posts), if you're interested.

That's the problem. This denialist mentality takes every piece of evidence and tries to pedantically attack every detail of it. They never take a step back and look at the big picture. They never think, "Wow, all this evidence from all these different fields is consistent."

It could be worse, though. I was in a debate on the forum of a Swedish TV channel once, arguing against a bunch of creationists. One kept explaining different stuff in nature --- "Spiders use five different kinds of nets for different purposes!" --- and claiming that evolution had no explanation for that ---- I find it quite obvious that spiders would not wrap their eggs in the same sort of net that they use to wrap their prey... --- while another kept repeating that he was "just a simple carpenter and couldn't understand all those difficult words, but he had a gut feeling I might be correct in the details but not in the big picture". In the end, I had to resort to invectives and eventually got myself banned, I believe.

Yes, but it's getting cheaper by the minute! There was a time when I could list all of the genome sequencing projects going on. Now, there are too many to keep track of. Very exciting times!

It would be very interesting to try that some day, if and when I could get the funding. With Clitellates, we usually use six genes --- COI, ITS1+5.8S.ITS2, 18S, 28S, 16S, and 12S --- and with lice five --- EF1a, COI, 16S, 18S, and 12S. To me, it's always seemed so uneconomical, as we get good results from just this data. However, whole genome sequencing would perhaps give much better data.

---
(1) The Okano I was thinking about worked with cement glands in barnacles, by the way.
 
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The word "rapidly" is rather ambiguous, since it can refer either to rate or to duration, and you must know by now that if kleinman can misunderstand something, he will.

In my own model, I continued the simulation to fixation of all alleles. Hence, my own statement of my result was that if the selection pressures are simultaneous, then the rate of evolution (fixations/generation) increases with the number of selection pressures.

Mind you, kleinman managed to misunderstand that too, as you can see by his absurd lies about what I "claim".

Exactly. This is why I have been careful to always say "rate" as well, just like Adequate.

It is a testimony to the stupidity of Alan Kleinman that he can take my statement "for some n != 0, the average rate of fixation under n + 1 pressures is higher than the average rate of fixation under n pressures" and twist it into "n + 1 pressures evolve faster than n pressures." How the f--- does a pressure even "evolve" anyway?
 
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