Since you have zero evidence that any of the putatively novel genes in that diagram had to pass through this made-up hurdle to evolve, I think the waiting time for that is a complete irrelevancy.
And how is that a response to what I wrote? How is anything you write a response? Why do you ignore basically everything and then just throw in this meaningless red herring?
You claimed the duplication rate is a problem (but you found a rate of fixation in a single-celled organism rather than “vertebrates”) using a method you reject to derive rates for anything else. Bill why do you think the species in the Gao and Innan 2004 paper you dug up share common ancestry? What measure did you use to derive their common ancestry? Why do the novel genes in the Howe diagram refute the common ancestry of those four species, but the novel gene in the yeast species don’t?
This is right but it is only the front end of the process of generating a de novo gene by gene duplication. Gene duplication and fixation is a challenge but could be workable if the assumptions you are assigning to it are correct.
The next step maybe more challenging which is the divergence from the original gene. The duplication hypothesis is claiming that you are going to find new function by randomly changing the original gene.
The mathematical model is complex here but it starts with trying to get a new enzyme binding site by randomly changing nucleotides inside a functioning duplicated enzyme. My first shot at it is randomly changing an exons nucleotides that are positioned to be part of the active site of an enzyme fold. I am assuming 500 amino acids and 2% of the enzyme as the active site.
The challenge is getting the right order of nucleotides such that the correct order and type of amino acids are part of the sequence and can bind with an existing ligand. This must be accomplished before random change makes the duplicated enzyme inactive.
@John_Harshman If we observe new functioning enzymes inside the Howe diagram then it is the opposite of the TSS fallacy. It is almost equivalent to observing bullet holes what spell the word Texas.
No. In so far as you pick out some specific outcome of a contingent historical process, whether an entire class of results (such as enzymes), or just a particular sequence, both logically constitute drawing a target around something specific and thus commits the fallacy. So when you specify a 10 amino acid active site (with allowance for 6 alternative residues), you’ve drawn a target. The size of the target is irrelevant, you’ve still drawn a target around something.
Then you have no understanding of the Texas sharpshooter fallacy. And let me, in consciousness of its utter futility, remind you of something else you don’t understand: all this is at most an objection to evolution by known processes, not common descent. Incomprehension of this magnitude must be at least partially intentional.
I am going to quote in full section entitled “An analytical approximation” from the Lynch paper that @colewd keeps citing. The reason I am doing this is to simply to give an idea of the type of mathematics involved in solving the problem Bill has addressed with his “rough calculation.” We obviously have underestimated him if he is able to do this. I can’t make heads or tails of this stuff.
Insight into the mechanisms driving these patterns can be achieved with a population-genetic approximation. Although neofunctionalization can be precipitated by initial duplications of either type-1 or type-2 alleles, type-2 alleles are much more likely to be neofunctionalized because they have acquired one of the two key contributory residues prior to duplication. Thus, as a first approximation, the focus is only on the subset of initial duplications to type-5 alleles, which usually comprise a fraction n /(20+ n ) of initial duplication events, an exception noted below.
The fact that θ can greatly exceed 1 at large population sizes (Fig. 2) is revealing. If a type-5 allele were simply neutral with respect to the pre-existing single-copy alleles, then fixation would occur with probability 1/ N , and θ would have a maximum value of n /(20+ n )<1. Although duplicated genes are, indeed, assumed to be selectively neutral in the preceding simulations, two-copy alleles still have a slight intrinsic advantage over one-copy alleles in that the latter mutate to nulls at rate μ, whereas two-copy alleles must acquire two such mutations (one in each copy) to be inactivated. This weak mutational advantage acts like selection, yielding the probability of fixation of a newly arisen pair of linked duplicates:
(2)
which approaches a maximum of 2μ at large N (Lynch 2002). This expression also applies to founder events involving type-3 alleles.
Should fixation occur, then the ultimate fate of a two-copy allele will be determined by subsequent mutations. The next mutation to arise will be one of three types: (1) a reversion of a type-5 to a type-2 allele arises at rate 2μ, has a mutational disadvantage, and fixes with probability ud , defined by Equation 2 with −μ substituted for μ; (2) a conversion to a type-4 allele arises at rate 2 v 0, and fixes with the neutral probability 1/ N ; and (3) a conversion to a type-7 allele arises at rate 2 v 2, is beneficial, and fixes at rate:
(3)
Thus, assuming no selective interference between competing fixation events, the next mutation to fix results in neofunctionalization with probability:
(4)
Although there are additional paths to neofunctionalization (e.g., having mutated to a type-4 allele, a second mutation can resurrect a type-5 allele, which can then acquire a mutation to a type-7 allele), these indirect paths are of relatively low probability and can be ignored as a first approximation.
The preceding logic suggests that the scaled probability of neofunctionalization (θ) should be approximately equal to Num α n /(20+ n ), but if this were the only factor involved in the establishment of a two-copy allele, then θ would approach a maximum value of ∼2 N μ n /(20+ n ) at large N , as um → 2μ and α → 1. In contrast, θ attains values much greater than this prediction (Fig. 2). For example, with n =50, θ would be expected to approach (1.43 × 10−6) N at large N independent of s , whereas the values observed with s =0.01 are ∼22.4 times higher and those observed with s =0.0001 are ∼1.8 times higher.
The discrepancy is due to the chance occurrence of neofunctionalizing mutations during the initial phase of establishment of the duplicate. Without such mutations, a newly arisen type-5 allele would be destined to be lost by random genetic drift with probability 1− um . However, prior to loss, an approximately neutral allele destined to loss in a haploid population yields a cumulative average number of N descendant copies, each of which is subject to mutation. Should a two-copy allele en route to loss acquire a neofunctionalizing mutation prior to being silenced by a degenerative mutation, it will then have a boost in the probability of fixation defined by Equation 3. A simple expression for this rescue effect is not available, but a recursive approach developed in Lynch et al. (2001) is adapted for the purposes of this paper in the Appendix. Letting r denote the probability that a type-5 allele initially destined to loss is rescued by a neofunctionalizing mutation, then
(5)
The fit of this expression to the simulation data is quite good, except at very low n when selection is weak ( s =0.0001) and the population size is large ( N μ>1) (Fig. 2). At large N and small s , violations of the assumption that no more than two alleles are simultaneously segregating may cause the breakdown in the mathematical approximations, which ignore the reduction in fixation probability resulting from selective interference.
One technical modification needs to be made to the above theory at very large N . Because they are one mutation removed from acquiring a two-residue function that eliminates the essential ancestral function, type- 2 alleles have a very weak mutational disadvantage. When the product of population size and the excess mutation rate to nulls is on the order of 1 or larger, this effect reduces the pre-duplication frequency of type-2 alleles to that expected under selection-mutation balance, . With the parameters used in analyses herein, this condition was only approached in a few extreme situations, and in any event the deviation between these two results is not great unless n is large. For example, with n =2, both the preceding formula and n /(20+ n ) yield an expected frequency of type-2 alleles of 0.091, and with n =10, the respective frequencies are 0.333 and 0.282. Comparison of the simulated results including this modification with the analytical approximation just noted shows that this added complication at large N is of minor effect.
That’s an absurd assumption. We know that for the ID favorite, beta-lactamase, activity is present in the juxtaposition of two 110-residue variable Ig regions. This happens multiple times in 10^8 random trials.
That enzymatic activity is present in the immunoglobulin fold, btw. I don’t think you know what “fold” means.
If the enzyme is not of historical record (older species) and we then observe it (humans) we need to explain its origin. What I am showing is that gene duplication and divergence is not a likely explanation for the observation. As we add to the length of the functional sequence we are observing the problem gets exponentially more difficult.
The Texas sharp shooter argument is a poor analogy and uses a label instead of a proper counter argument. It is similar to the lottery argument that surfaced on Sandwalk 5 or so years ago.
Yes, sure. But picking out that enzyme(assuming some particular de novo gene is an enzyme) after the fact, and then calculating the odds that it would evolve from the ancestral state, out of all the other things that could in principle have evolved instead, is a textbook example of the Texas Sharpshooter fallacy.
I have explained exactly what is wrong with that type of thinking, and why it really does qualify for the Texas sharpshooter fallacy here:
Imagine you have this sequence:
AAAAGCCCCTTTT (the ancestral state)
And it randomly suffers a single substitution once every 100 times it is copied. So you wait 500 copy events and find 5 mutations have occured. Then you say, how long would it take for those 5 particular mutations to occur, on average?
Say these are the mutations(in bold) that changed from the above sequence: TATAGTCCCCTGT (your new enzyme)
How long would you have to wait, on average, before those specific 5 mutations occur? If we started all over again, an exceptionally long time. Because there’s no guarantee that at any point the mutation that happens to occur is the one you’re waiting for. So you could wait for the first 100 copies(lets just call them generations) to see whether a mutation has occurred, and then check if it’s one of the mutations you wanted.
Since there are many more mutations possible than those 5 I have highlighted, chances are much greater that it is not the one you’re waiting for that occurs, so now you have to wait again for another 100 generations. And then the problem repeats, there’s still many more possible than the one you’re waiting for, so it’s likely another one than the one you want. And so on.
This would be very different from asking how long you would have to wait, on average, for just any 5 mutations to occur. We already know that, we waited 500 generations to get 5 mutations. If you just need to wait for any 5 mutations, you just need to wait, on average, for 500 generations to have occurred. Because on average there’s a new mutation every 100 generations.
But since we already know the first 5 mutations evolved in 500 generations, what use is it then to turn around and calculate how long we would have to wait on average for those 5 specific ones to evolve again if we started over? It doesn’t matter which 5 mutations that evolve in those 500 generations, you would always be able to calculate that it should take an extraordinary amount of time for those 5 specific mutations. And yet, we just need to wait 500 generations for some such set of 5 mutations.
When you pick out a particular gene that evolved in some species, and then trying to calculate how long you would have to wait for that gene to evolve from the ancestral state, you are committing the fallacy.
No you aren’t showing that at all. You’re repeatedly asserting that, but you’ve got nothing that shows this. Merely saying, stating, or declaring X, is not to show that X. I can say, state, and declare my ability to fly, but showing that I can fly involves actually flying.
That isn’t showing, that is just talk.
I have just explained above with a hypothetical example that your argument commits this fallacy.
Some times the label is actually correct, and the names for particular fallacies are entirely appropriate. I concede you might have been unable to work out for yourself how and why your statement commits the fallacy, and so needed to have that explained to you. That has now been done. Again.
We are not comparing only sequences we are comparing the waiting time to find a sequence that binds a new ligand.
A long time even in your example because of the overall mutation rate and the small probability of 100 mutations per generation hitting an area composed of 13 nucleotides.
With the caveat that one can never really be sure just what is going on in Bill’s head at any given moment, I am not sure that is the error he is making here. Rather it seems to me his thinking is something like this:
Michael Lynch accepts evolution and he wrote a paper in which he modelled that, under some circumstances, it might take a million generations for a new functional gene to evolve that requires two mutations. So if a gene requires 10 mutations, it will take 5 million generations, since 10 is 5 times as large as 2.
And if a species has evolved 1000 such genes, it would take 5000 million generations, because if one gene takes 5 million generations, then 1000 genes would take 1000 times as long.
What does that mean? What historical record? What do you mean by “older species”? More word salad.
You are showing nothing. You are asserting.
Only because you don’t understand it. You are imagining a particular sequence of 10 bases to perform a particular function. But that’s post hoc specification of both sequence and function. What you need is to consider the probability of some sequence of some number of bases performing some function or other. And you also need to consider the number of duplications that happen, most of which end up deleted. Finally, you need to consider that the initial sequence of the duplicated protein does perform a function, so a modified function may not require many changes. All of these are components of your Texas sharpshooter fallacy.
There are some things in biology that only make sense in the light of evolution, and the gradual and de novo gain of novel protein coding genes is one such thing. I mean just take a look at this section in this paper:
De Novo Genes Have Unique Sequence Characteristics as Compared with Conserved Genes
The de novo candidates share a number of structural properties that differentiate them from the genes conserved outside the two genera. They are significantly shorter, have a lower codon adaptation index and a higher aggregation propensity compared to conserved genes (supplementary fig. S5, Supplementary Material online). Their biosynthetic cost is also lower than those of noncoding sequences, in agreement with an intermediate stage from a noncoding to a coding state (supplementary fig. S5, Supplementary Material online). When recent, de novo genes are not enriched in intrinsically disordered regions compared to conserved genes. The low propensity of recent genes to disorder was previously reported in S. cerevisiae (Carvunis et al. 2012). When ancient, but in Lachancea only, de novo genes have a higher proportion of predicted disorder than conserved genes (fig. 3), suggesting contrasted evolutionary pressures (see Discussion section).
Okay so, this makes perfect sense in an evolutionary context. Imagine shooting blindly into protein sequence space to hit a functional gene. Regardless of how likely you think that is a priori, in so far as you manage to hit one - is it more or less likely that you’re going to hit the peak of some hill in the landscape, or just some place further down? Clearly, since the peak only occupies a tiny fraction of all sequences that make up the hill, it is more likely that randomly hitting a hill produces a sub-optimal sequence that doesn’t occupy the local, or global optimum.
De novo genes are further from the hill compared to older more conserved genes. A designer could have just made it optimal to begin with. Score one for evolution.
Aggregation propensity is usually selected against, since all proteins have some mutual affinity, it can interfere with protein function. Over time we expect evolution to reduce unwanted side effects on existing proteins that have been under selection for longer periods of time. What do we find? De novo genes are more aggregation prone. A designer could have just designed them without that. Score two for evolution.
Expression levels. Among all possible levels of expression, the most active is only a tiny fraction. A priori, again, we expect that a blind shot into sequence space does not produce the most active promoter. What do we find? De novo genes have overall lower expression levels. Score three for evolution.
Oh and they’re also generally shorter than older genes.
It gets better:
De Novo Genes Preferentially Emerge Next to Divergent Promoters in GC-Rich Intergenic Regions
We found that de novo genes are significantly enriched in opposing orientation with respect to their direct 5′ neighboring gene (fig. 4 A). Similar enrichment was already observed for mouse-specific genes (Neme and Tautz 2013). This suggests that de novo genes would benefit from the divergent transcription initiated from bidirectional promoters. In contrast, tandemly duplicated genes are significantly enriched in co-orientation with respect to their 5′ neighbor (69% and 74% in Saccharomyces and Lachancea , respectively) (not shown). Therefore, the bias toward opposing orientations strongly suggests that the de novo gene candidates do not actually correspond to tandemly duplicated genes that would have diverged beyond recognition. In addition, the bias towards divergent orientation is the strongest for the reliable de novo genes which correspond to the most recently emerged genes (see above), suggesting that divergent transcription from bidirectional promoters, which are widespread in eukaryotes (Core et al. 2008; Neil et al. 2009), is critical in the early stages of origination.
Okay so, again. How does a promoter function? To transcribe a region of DNA, supercoiled double-stranded DNA must be unwound and the double-strand “unzipped” so a transcriptional initiator can bind and recruit an RNA polymerase to read the DNA sequence and produce a complementary RNA transcript. That means DNA regions that are already more often unwound and unzipped are more frequently accessible to DNA binding proteins, such as transcriptional initiators. That implies we expect mutations near frequently transcribed regions to be more likely to produce novel promoters as transcription initiators have more opportunity to interact with exposed single-stranded DNA, and we are most likely to find frequently transcribed regions near existing promoters, leaving the DNA strand in the opposite direction where the sequence is more free to mutate as the most likely candidate region for a de novo gene. That’s what we find for novel genes, they are most typically found near existing promoters on the anti-parallel DNA strand going in the opposite direction. Score four for evolution.
Further down in the paper they also show de novo genes are more often found at recombination hotspots. Again, makes perfect sense in the context of evolution, both because of the accessibility again, and as recombination greatly facilitates the blind exploration of sequence space, as recombination can basically function in a way equivalent to multiple simultaneous mutations.
De Novo Genes Are Significantly Enriched at Recombination Hotspots
In multiple eukaryotic taxa, including yeasts and humans, heteroduplexes formed during meiotic recombination are repaired by gene conversion biased toward GC-alleles, thus increasing the GC content of recombination hotspots (RHS) (Lamb 1984; Jeffreys and Neumann 2002; Mancera et al. 2008; Duret and Galtier 2009). Furthermore, it provides a nucleosome-free region (Berchowitz et al. 2009; Pan et al. 2011) that promotes transcriptional activity. It follows then that RHS could be favorable locations for the emergence of de novo genes in yeasts.
We’re supposed to think these novel genes refute common ancestry, and that they couldn’t possibly evolve because there’s a lack of a plausible mechanism. That makes no sense whatsoever when we actually look at the data. Their pattern of distribution is how we can see their incremental accumulation over time, and their characteristics only make sense in light of gradual evolution from non-coding DNA. They begin short, with weak fitness effects, at low expression, near already existing genes and in recombination hotspots. They then grow in length over geological time, get expressed more strongly, climb to higher on the fitness peak and come unders stronger purifying selection, and are passed on to subsequent descendant species.
We aren’t “comparing the waiting time” for a sequence that binds a new ligand (what are we making a comparison of? - it’s word salad again).
What we are waiting for is the time for any possible adaptive function to evolve by any possible evolutionary mechanism. That’s it. We don’t know what kind of function new genes will have (we don’t even know what proportion of novel genes have functions that are strictly “new”), all we know is that in order for evolution to make sense of the observed patterns (such as the putatively novel genes in the Howe diagram), the process has to produce new protein sequences. Something only found in particular clades, or for truly orphan genes, something only found in one specific species(such as the yeast species Saccharomyces cerevisiae). Some of these new protein coding genes might even retain the old function but have just diverged in sequence. That is, they might just be duplications that drifted apart by each of them accumulating different mutations. For most novel genes we don’t actually know what functions they have.
Now, there are multiple ways evolution can produce new protein coding genes. One is, as mentioned, by sequence divergence of duplicates. A gene is duplicated, and then both continue to accumulate mutations becoming less and less similar over time. Whether they attain new functions or not, that is one way to get more genes that are not detected as orthologous. Another possible mechanism is that non-coding DNA regions accumulate mutations, resulting in a transcriptional promotor, and/or novel open reading frame. Another still is de novo from gain of a new ORF overlapping an already existing gene(either out-of-frame, or anti-sense on the opposite strand of DNA). Then there’s recombination/shuffling, and/or fusion of pieces of other already existing genes. All of these are ways to get more new genes.
So we just have to wait for any protein coding gene, whatever they may happen to be. It makes no sense to pick out some specific function that some new gene might have, after the fact that it originated (however it did), and ask what is the probability of that function evolving from the ancestral state? For the reason I explained in my analogy.
Texas sharpshooter fallacy again. Nobody is trying to hit an area of 13 nucleotides. Rather, mutations accumulate in lots of species, and some of them happen to produce new adaptive protein coding genes, and some of these happen to have new functions. The functions they have are just what happened to be in that area of sequence space, and those genes stuck around because they happened to be beneficial to that organism in that environment. Countless trillions of other organisms failed to adapt and went extinct instead.
Your entire problem with this stems from two completely wrong ways of looking at thing. First you seem to have a sort of tunnel vision, and you fail to comprehend evolution as an enormously parallel process happening to literally billions of different populations, each consisting of many hundreds of thousands to trillions of individuals, simultaneously. You focus on particular species and particular functions, rather than considering the question of new genes evolving in the context of all of life on Earth adapting to all current niches and environments there currently are.
The second problem, equally problematic, is you having an entirely imaginary axiom, a sort of assumption you apparently refuse to let go of, that functions are supposedly hyper-astronomically rare, and isolated from each other by vast areas of nonfunctional nonsense polymers, in protein sequence space.
So when we see in a comparison between some related species, that some species have genes not found in others, you now take this observation and interpret it in the light of your assumption, your imaginary axiom that functions are rare and isolated, and you appear to think something like “How could this have happened by just chance accumulation of mutations? - It looks like some sort of statistical miracle happened here”.
But the problem was your assumption to begin with. Rather than accept that the phylogeny should undermine your axiom, you just take the axiom to be, well axiomatic, and then reject the phylogeny. You’re doing he literal opposite of following the evidence. You reject the evidence because it doesn’t match what you already believe, and instead invoke miracles to explain why the observation can still be compatible with your axiom. All the different species were specially created with unique genes.
You were led to believe that almost all functions are incredibly rare and isolated from each other by what amounts to some combination of misrepresentations of existing studies, and misunderstandings of others. And by selective quotations of people who we now today know had wrong hunches, such as Francois Jacob’s quaint old line about evolution being a tinkerer. Yes, evolution is a tinkerer, but tinkering is all it takes to produce new protein coding genes. And one of the ways we know this is partly through phylogenies showing that novel genes have continuously evolved over the history of life.
We know today the assumption has no basis in fact. It is and always was imaginary. While any specific structure-function relationship is rare to varying degrees (particular structure X with particular function Y is relatively rare, particular structure X2 with particular function Y2 is incredibly rare), the majority of protein sequence space is actually capable of some sort of biochemical function, and you can get rudimentary and adaptive functions in protein sequences almost completely devoid of structure. And once you have simple functions, they’re usually connected through short mutational distances to more complex and more rare functions. Individual domains, that themselves began as simple RNA binding peptides, can polymerize and fuse, and gradually evolve into larger multi-domain proteins such as RNA polymerases, which themselves eventually evolved into DNA polymerases with proofreading activity.
Some peptide that sticks to the surface of some other protein molecule or nucleotide polymer can have a weakly protective effect, and that is enough for natural selection to preserve it. Some small peptides adopt a stucture that consists of basically nothing more than a short alpha helix, which can insert into the cell memrane and function as a channel for ions.
Most random protein sequences have some mutual affinity for each other, so much so that selection often has to reduce it by discarding binding-enhancing mutations because it can interfere with their other functions. And most of protein sequence space consists of overlapping functions in the same sequences. It is virtually impossible to find a protein sequence that is capable of only one specific function and has zero sort of activity or affinity to anything else. ALL protein sequences, without any exception known to human science, are capable of multiple types of biochemical interactions, many of which are potentially adaptive to the organism in the right circumstance. It’s essentially why all drugs and medications have some sort of side-effects(to whatever degree of undesirability). You put a new chemical in your body chances are it’s not just going to interact with that receptor molecule you designed it to stick on to, and it’s going to have some other effect too, and all you can hope for is some sort of modification or drug combination that reduces undesirable side-effects and that the benefits out-weight the negatives. You want to cure Alzheimers? Maybe you can live with that rash, or a headache, to get there.
Remember that study on enzyme promiscuity I showed you? Most enzymes are known to catalyze multiple reactions, with some being capable of hundreds. And it gets better, because essentially all proteins will exhibit some mutual affinity however weakly. The only question is - in an evolutionary context - whether this stickiness negatively affects the protein’s impact on organismal fitness. It is physically unavoidable that molecules made of multiple atoms with unequal charge distributions will show some sort of affinity or stickiness. Read about that here:
In light of what we now know, you have no basis for thinking new proteins with adaptive functions can’t evolve. Direct experimental biochemistry and phylogenetic inference confirms this. This axiomatic belief you were once convinced of just doesn’t make sense in light of what we know.
No, me explaining why doing post-fact probability calculations to argue against evolution commits the Texas sharpshooter fallacy - is not circular reasoning. I am explaining why the sort of argument you are trying doesn’t work, even in a case where we strictly don’t know how (or even whether) some gene evolved. Yes in my hypothetical example I begin by assuming some sequence evolves into a descendant because doing this shows why doing such calculations after the fact don’t have the potential to undermine what actually happened in history.
But in cases where we hypothetically don’t know, even the fact that the sequence could potentially have evolved, and you strictly don’t know that it didn’t, means the kind of argument you’re making is fallacious. Because we could be in the situation where the sequence actually evolved, and thus the kind of argument you’re making would contradict actual history. And then you’d be making an argument that contradicts actual history, and that can only happen if your argument commits some sort of fallacy, either through invalid logical leaps, or because it has false premises.
Now, it’s important for you to understand that me making that analogy to you is not meant to prove evolution. When I explain that your argument commits a fallacy, I am not thereby proving evolution, and you don’t have to end up accepting evolution just because you might realize an argument against evolution that you’ve been making commits a logical fallacy.
Obviously, from your perspective as one who doubts evolution, merely saying that evolution could hypothetically account for the novel gene would not suffice to convince you. You want to be given some reason to think evolution could produce new genes.
But logically speaking the issue is that you are the one doubting evolution in the first place, the reason you are rejecting the phylogeny is partly because you have a baseless assumption that to evolve new genes is basically miraculously rare. So when a phylogeny implies that one species has a collection of genes not found in another, that seems perplexing to you because you have this baseless axiom that such sequences are incredibly rare.
And rather than inferring from the phylogeny that, hey, maybe novel genes actually can evolve because they’re not as rare as you used to take as axiomatic, you just go back and reassert your axiom: novel genes are astronomically rare, then you find the idea that these genes evolved on the phylogeny conflicts with the axiom, and then reject both the phylogeny itself and that these genes evolved.
You could go the Michael Behe route and accept the phylogeny but posit miracles for each new gene. Rather than poofing new species, poof new genes. But you don’t do even that. You reject all of it because, well, why? Again I must ask, why not at least go the Behe route? In any case, neither of you seem able to accept what the phylogeny implies because you both seem to share this imaginary axiom: new genes must be statistically miraculously rare.
Now, as for why new genes aren’t statistically miraculously rare, I first invoke… the forking phylogeny. We just have no damned reason in hell to have a phylogeny in the first place if new genes can’t evolve. And I invoke MORE DETAIL about the phylogeny, the gradual sequence evolution of the novel genes, the substitution biases in their sequences, all the above mentioned the characteristics of the encoded proteins. The INNUMERABLE threads we have on protein biochemistry, enzyme promiscuity, de novo gene evolution (VPU1 in HIV, T-urf13, de novo peptides against antibiotics etc. etc.), ubiquituous biochemical activity in protein sequence space, and who the fork knows what else has been discussed on this and other forums for years and years.
(2)
(3)
(4)
(5)
. With the parameters used in analyses herein, this condition was only approached in a few extreme situations, and in any event the deviation between these two results is not great unless n is large. For example, with n =2, both the preceding formula and n /(20+ n ) yield an expected frequency of type-2 alleles of 0.091, and with n =10, the respective frequencies are 0.333 and 0.282. Comparison of the simulated results including this modification with the analytical approximation just noted shows that this added complication at large N is of minor effect.