Of “models” and “algorithms”

I was short with Joe Felsenstein in the comments section of “Stark Incompetence,” a post in which I address, well, um, the stark incompetence on display in a recent publication of Eric Holloway. I have apologized to Joe, and promised to make amends with a brief post on the topic that he wants to address. Now, the topic is a putative model that Eric introduced in “Mutual Algorithmic Information, Information Non-growth, and Allele Frequency” (or perhaps an improved version of the model). Here is a remark that I addressed to Joe:

Tom English: As you know, if a putative model is logically inconsistent, then it is not a model of anything. I claim that that EricMH’s putative model is logically inconsistent. You had better prove that it is consistent, or turn it into something that you can prove is consistent, before going on to discuss its biological relevance.

I will not have to go far into Eric’s post to identify inconsistencies. After explaining the inconsistencies, which I doubt can be eliminated, I will remark on why the “model” is not worth salvaging. The gist is that Eric’s attempted analysis puts a halting, output-generating simulator of a non-halting, non-output-generating evolutionary process in place of the process itself. An analysis of the simulator would not, in any case, be an analysis of the simuland.

Inconsistency

In the following passage from his post, Eric describes a randomized procedure, dubs it an evolutionary algorithm, and then asserts the existence of a halting program that implements the procedure.

The alleles are 1s and 0s, and the gene G a bitstring of N bits. A gene’s fitness is based on how many 1s it has, so fitness(G) = sum(G). The population consists of a single gene, and evolution proceeds by randomly flipping one bit, and if fitness is improved, it keeps that gene, otherwise it keeps the original. Once fitness(G) = N, the evolutionary algorithm stops and outputs G, which consists of N 1s. The bitstring that is N 1s will be denoted Y. We will denote the evolutionary algorithm E, and it is prefixed on an input bitstring X of length N that will be turned into the bitstring of N 1s, so executing the pair on a universal Turing machine outputs the bitstring of 1s: U(E,X) = Y.

The first thing to note is that the randomized procedure is not an algorithm: it halts with probability less than one. That is, by a simple inductive argument, for all natural numbers n, the probability is less than one that the procedure halts after n or fewer bit flips. Indeed, the probability is greater than zero that the procedure performs n bit flips without improving fitness. Thus if you were to turn the procedure into an algorithm by stipulating that it performs at most M bit flips, there would be a nonzero probability that gene G remains equal to input X \neq Y when the algorithm halts, no matter how large you make M. The problem is not the particular randomized procedure that Eric has chosen. Evolutionary procedures do not converge surely to local fitness maxima in discrete spaces (except in trivial cases).

It is gobsmacking for me, though probably not for you (I labored over “Stark Incompetence” in hope that everyone would be as astonished by something coming from Eric as I am by many of his claims), to see Eric flatly assert that the randomized “algorithm” is a program for a deterministic computer. To put it plainly, a universal Turing machine cannot flip bits randomly. Eric’s “model” is inconsistent, and thus is not a model. To get randomness, Eric must

  1. draw the deterministic bit-flipping program E randomly, or
  2. endow the deterministic bit-flipping program E with a pseudo-random number generator, and supply the program with a random seed as input (along with X).

However, this will not produce consistency, because Eric has predicated, with the expression U(E, X) = Y, that the program surely halts with an output that is maximal in fitness — no ifs, ands, or buts. His subsequent argument requires it. But his prior specification of the random bit-flipping procedure does not allow it.

The map is not the territory

Computer programs used by scientists to model evolutionary processes commonly signal the occurrence of events of interest to the scientists, and halt when the scientists are uninterested in gathering further data. An exceedingly naive response, most prominently on display in the “evolutionary informatics” of Marks, Dembski, and Ewert, is to analyze a program, and claim that the analysis applies to the modeled process — as though the evolutionary process itself signals the occurrence of events and halts.

I am not going to dig into Eric Holloway’s attempt at analysis. You should be able to see for yourself, if you have any business discussing what he has done, that it is literally the program E that enters into the analysis, and not the evolutionary process that is simulated by the program. It ought to be obvious that an evolutionary process does not “know” when fitness is maximized, let alone announce the genome for which fitness is maximal. The part of the program that detects and announces the event in which fitness is maximized, and subsequently halts, is not part of the (simulation of the) evolutionary process. It is a monitor of the simulated process, and can be decoupled from the simulation per se, even though it is usually tightly coupled with the simulation in practice. I advise against struggling to make Eric’s inconsistent “model” into one that is internally consistent, because the result would be a bogus, though consistent, “model” that mistakes the simulation software for the evolutionary process itself.

339 thoughts on “Of “models” and “algorithms”

  1. colewd: So can you generate the Weasel sentence without a target?

    I don’t have to, there are no targets in evolution. Just like there are no targets in geology. I also don’t have to reproduce the Mt. Everest in a model of plate tectonics to have good reason to think the Mt. Everest is the sort of thing that results from the processes that take place in the Earth’s crust and mantle.

  2. newton,

    Isn’t your position that the necessary attachments of a mind are the result of design? If so, isn’t that a potential problem for that hypothetical?

    Its not a problem at all. We are using humans to test the concept as humans have a mind plus necessary attachments. This is similar to using the sun plus measurement tools to test general relativity.

  3. Rumraket,

    I don’t have to, there are no targets in evolution.

    You do to show the above claim has any validity. If evolution can not create de novo information you then don’t have an overall theory.

  4. colewd: We are using humans to test the concept as humans have a mind plus necessary attachments

    Now all you have to do is show the necessary attachments used by your disembodied mind to physically create biological life, and explain how those necessary attachments were physically created.

    Any time today will do Bill.

  5. colewd: Its not a problem at all. We are using humans to test the concept as humans have a mind plus necessary attachments. This is similar to using the sun plus measurement tools to test general relativity.

    ROFL, wow. Wow!

    “Necessary attachments” to “human mind” is not at all analogous to “using sun plus measurement tools”. The sun is not causing there to be the physics of general relativity, and the “measurement tools” are not attached to the sun.

    Your analogy here, if one can even call it that, is so hopeless it’s hard to even know where to begin.

  6. Forget about that design theory, model or mechanism. We already know you don’t have one and you don’t even know what those things mean.
    Show us your scientific evidence that “the spliceosome” was a target, of evolution, design or whatever. Show your work, Billy

  7. colewd: If evolution can not create de novo information

    But it can, it just doesn’t have to create the exact information you want. We have been over articles that show that very thing. Remember the de novo proteins that give antibiotic resistance for example?

  8. colewd: If evolution can not create de novo information you then don’t have an overall theory

    Evolution can create de novo information as you’ve been shown ad nauseum. It just doesn’t have any pre-specified targets.

    Why is it so hard for you to understand such a simple concept?

  9. Adapa: Evolution can create de novo information as you’ve been shown ad nauseum.It just doesn’t have any pre-specified targets.

    Why is it so hard for you to understand such a simple concept?

    WEASEL showed that cumulative selection is far more powerful than random selection. But of course it was never intended to model anything like evolution, especially since it had a target and evolution does not.

    So let’s make a small modification here. Instead of having a target string, let’s simulate a “linguistic environment” by setting up a set of rules that the organization of letters should follow. Things like, maybe “keep instances of multiple consecutive consonants to a minimum”, or “make letter sequences without spaces less probable the longer they become.” You might also provide the relative frequency of each letter in normal prose in your environmental language.

    Once these rules are established, have the computer start generating sequences of six words, preserving each valid word as an “atomic letter” for future runs. After not too long, you will find valid short sentences being formed, no two alike. NOTE that there has never been a single target sentence, so none of these valid sentences could be said to have “hit the target.” If you have provided any semantic rules, you’ll get entire sensible paragraphs, no two alike.

    And every word sequence, valid or not, is new information. Valid sequences are information with meaning.

  10. Rumraket,

    But it can, it just doesn’t have to create the exact information you want. We have been over articles that show that very thing. Remember the de novo proteins that give antibiotic resistance for example?

    They are not de novo proteins. You continue to appeal to micro evolution. Where is your model that generates weasel without a target?

    Lets lower the bar a little. Generate a de novo English sentence of 50 characters without a target.

  11. Adapa: The Weasel program isn’t an evolution simulator.

    That’s a matter of interpretation. Some of us have used Weasel programs to simulate (a special case of) the Wright-Fisher model. See what I wrote to Faded Glory on the first page of comments.

  12. colewd: So can you generate the Weasel sentence without a target?

    I’m thinking of a length-28 sequence of uppercase letters and spaces. Can you generate the sequence I have in mind?

  13. colewd: They are not de novo proteins.

    Yes they are.

    Knopp M, Gudmundsdottir JS, Nilsson T, König F, Warsi O, Rajer F, Ädelroth P,
    Andersson DI. De Novo Emergence of Peptides That Confer Antibiotic resistance. MBio. 2019 Jun 4;10(3). pii: e00837-19. doi: 10.1128/mBio.00837-19.

    IMPORTANCE: De novo gene origination from nonfunctional DNA sequences was long assumed to be implausible. However, recent studies have shown that large fractions of genomic noncoding DNA are transcribed and translated, potentially generating new genes. Experimental validation of this process so far has been limited to comparative genomics, in vitro selections, or partial randomizations. Here, we describe selection of novel peptides in vivo using fully random synthetic expression libraries. The peptides confer aminoglycoside resistance by inserting into the bacterial membrane and thereby partly reducing membrane potential and decreasing drug uptake. Our results show that beneficial peptides can be selected from random sequence pools in vivo and support the idea that expression of noncoding sequences could spark the origination of new genes.”

    You continue to appeal to micro evolution.

    Uhm, you asked for de novo evolution of new information.

    Where is your model that generates weasel without a target?

    For reasons explained earlier, that demand is meaningless.

    Lets lower the bar a little. Generate a de novo English sentence of 50 characters without a target.

    Ironically, English evolved in part from latin, without a target. Nobody sat there with a template of how English was supposed to look. Yet it happened anyway.

  14. colewd: Where is your model that generates weasel without a target.

    Amazing Bill Cole is so clueless and slow he still can’t understand evolution doesn’t have any specific targets.

  15. colewd: Lets lower the bar a little. Generate a de novo English sentence of 50 characters without a target.

    Apparently Bill isn’t aware there are numerous random sentence generators online which produce new sentences without a target.

    random sentence generator

    Cue Bill whining “but they were intelligently designed with smuggled in information!!”

  16. In Billy’s world, nothing is de novo if it wasn’t popped into existence out of nothing. Lulz!

  17. colewd:
    T_aquaticus,

    This is the burden of evolution to show a model of a mechanism that can perform this task with the known species that exist.

    False. You said evolution can’t do it. It is now up to you to support that claim. Support your claim or withdraw it.

  18. colewd:

    Lets lower the bar a little.Generate a de novo English sentence of 50 characters without a target.

    There are no 50 character english sentences in any genome, therefore there is no information in any genome by the measure you are using.

  19. T_aquaticus,

    False. You said evolution can’t do it. It is now up to you to support that claim. Support your claim or withdraw it.

    I have shown at this point there is no evidence that evolution can do it as there is currently no evidence that weasel or any other english sentence of 50 characters or more can be obtained without a target. I have shown the mechanism is not up to the task as it fails the weasel challenge. You need to withdraw your claim that evolution can generate the necessary functional information to support the eukaryotic transition. A mind can be shown too easily support the weasel challenge.

    I have also shown exact sequence homology (mutual information) between species separated by 80 million years with the actin protein. I wonder what the cause of this is other then a designed sequence and strong purifying selection due to extreme functional constraint.

  20. T_aquaticus,

    There are no 50 character english sentences in any genome, therefore there is no information in any genome by the measure you are using.

    Look at the ubiquitin protein E2 D3 as gpuccio wrote about this system. If we align this between humans and mice the 141 AA’s perfectly align. With 20^141 possible arrangements this is remarkable. The sentence I am asking you to generate has only 50^28 possible arrangements. If you can create this algorithm and demonstrate how the cell and environment can perform this then you have come a long way from here explaining the mutual information between humans and mice contained in the ubiquitin protein E2 D3.

  21. colewd: strong purifying selection due to extreme functional constraint

    How does that work? Does “mind” come by sometimes to service the parts? Surely it doesn’t work through *gasp* differences in reproductive success does it?

  22. T_aquaticus: You fail right off the bat. All you need to do is create a mixture of antibiotic sensitive and resistance bacteria on an antibiotic plate, and then see which phenotype dominates.

    And that has what to do with “natural selection”?
    It is a very good thing “natural selection” is false, or else antibiotic resistant bacteria and other superbugs would have killed mankind by now as “evolution” falsely predicted.

    Tom English: I’ve not managed to find anything in your 23-point response that is relevant to my decomposition of evolutionary algorithms into two components, and explanation that only one of the two components is biologically inspired.

    My comment: “Yet your problem is that algorithms and models are not anchored in reality.” was in direct reply to yours.

    Are you not grasping that your “decomposition of evolutionary algorithms” is meaningless if said “evolutionary algorithms” are not based in reality?

    Also, did you not discuss “fitness” extensively in you essay? Well, why don’t you lead with your “fitness function” if there is such thing? But there isn’t. Nor is there a “natural selection”, “evolutionary processes”, and all the other mumbo-jumbo.

  23. colewd:
    T_aquaticus,
    I have shown at this point there is no evidence that evolution can do it as there is currently no evidence that weasel or any other english sentence of 50 characters or more can be obtained without a target. I have shown the mechanism is not up to the task as it fails the weasel challenge.You need to withdraw your claim that evolution can generate the necessary functional information to support the eukaryotic transition. A mind can be shown too easily support the weasel challenge.

    Wait. Let’s see the logic here: if the Weasel sentence cannot be generated without a target then evolutionary mechanisms could not have generated the functional information that resulted in the eukaryotic “transition”? I don’t see the connection Bill. Looks a lot like a non-sequitur. Have you examined your assumptions? No? Then let’s. What are you assuming in order to make what appears to me to be a nonsensical connection between Weasel and eukaryotic transitions?

    colewd:
    I have also shown exact sequence homology (mutual information) between species separated by 80 million years with the actin protein.

    This is a conceptual mess. Sequence identity is not the same as homology. Two very divergent proteins can be homologous and have low identity. Now, what you mean is sequence identity between the homologous proteins of species separated by 80 million years. Sure. let’s buy that. So?

    colewd:
    I wonder what the cause of this is other then a designed sequence and strong purifying selection due to extreme functional constraint.

    Why not evolved sequence and then strong purifying selection Bill? Evolution happens. Designers have actin. So, the designers designed the actin that allowed them to use tools and thus design actin?

  24. Nonlin.org: And that has what to do with “natural selection”?

    Everything. An allele came to dominate a population due to environmental pressures. That’s natural selection.

    It is a very good thing “natural selection” is false, or else antibiotic resistant bacteria and other superbugs would have killed mankind by now as “evolution” falsely predicted.

    Strawman. Bacteria didn’t drive mankind to extinction before antibiotics, so there is no reason to think the result would be different if antibiotics became ineffective.

    My comment: “Yet your problem is that algorithms and models are not anchored in reality.” was in direct reply to yours.

    There are many lab experiments where fitness is directly measured, such as the Lenski experiment.

    Also, did you not discuss “fitness” extensively in you essay? Well, why don’t you lead with your “fitness function” if there is such thing? But there isn’t. Nor is there a “natural selection”, “evolutionary processes”, and all the other mumbo-jumbo.

    You should really read up on population genetics which contains all the algorithms you need.

    http://blog.uvm.edu/cgoodnig/2013/06/14/relative-fitness/

  25. colewd:
    T_aquaticus,

    Look at the ubiquitin protein E2 D3 as gpuccio wrote about this system.

    Ok, let’s look at the protein sequence for human polyubiquitin-c:

    MQIFVKTLTGKTITLEVEPSDTIENVKAKIQDKEGIPPDQQRLIFAGKQLEDGRTLSDYN
    IQKESTLHLVLRLRGGMQIFVKTLTGKTITLEVEPSDTIENVKAKIQDKEGIPPDQQRLI
    FAGKQLEDGRTLSDYNIQKESTLHLVLRLRGGMQIFVKTLTGKTITLEVEPSDTIENVKA
    KIQDKEGIPPDQQRLIFAGKQLEDGRTLSDYNIQKESTLHLVLRLRGGMQIFVKTLTGKT
    ITLEVEPSDTIENVKAKIQDKEGIPPDQQRLIFAGKQLEDGRTLSDYNIQKESTLHLVLR
    LRGGMQIFVKTLTGKTITLEVEPSDTIENVKAKIQDKEGIPPDQQRLIFAGKQLEDGRTL
    SDYNIQKESTLHLVLRLRGGMQIFVKTLTGKTITLEVEPSDTIENVKAKIQDKEGIPPDQ
    QRLIFAGKQLEDGRTLSDYNIQKESTLHLVLRLRGGMQIFVKTLTGKTITLEVEPSDTIE
    NVKAKIQDKEGIPPDQQRLIFAGKQLEDGRTLSDYNIQKESTLHLVLRLRGGMQIFVKTL
    TGKTITLEVEPSDTIENVKAKIQDKEGIPPDQQRLIFAGKQLEDGRTLSDYNIQKESTLH
    LVLRLRGGMQIFVKTLTGKTITLEVEPSDTIENVKAKIQDKEGIPPDQQRLIFAGKQLED
    GRTLSDYNIQKESTLHLVLRLRGGV

    Do you see a 50 character english sentence in there anywhere? If not, it doesn’t contain information according to you.

    If we align this between humans and mice the 141 AA’s perfectly align.With 20^141 possible arrangements this is remarkable.

    That’s called inheritance. Ever heard of it? About half of your genome is identical to your father’s genome, and it has nothing to do with intelligent design.

  26. T_aquaticus:
    That’s called inheritance. Ever heard of it? About half of your genome is identical to your father’s genome, and it has nothing to do with intelligent design.

    That’s nothing. My genome is almost identical to yours! And that’s a probability of 1 in 4**3.3 billion! (haploid). The only explanation for this is that our genomes were each designed by some Designer who put them together in almost the very same order. Otherwise how do you explain such an astounding coincidence!? Unless you can prove that some model that tries to explain some aspect of inheritance can produce Weasel w/o a target, then inheritance cannot be the reason for our common genomes. Not a chance! But a mind can!

  27. colewd: I have shown at this point there is no evidence that evolution can do it as there is currently no evidence that weasel or any other english sentence of 50 characters or more can be obtained without a target.

    Bill why do you continue to bare faced lie about this? How many times has it been explained to you evolution doesn’t require a target? I even posted a NO TARGET random English sentence generator for you and you ignored it.

    Why should anyone think you’re not just another disingenuous liar for Jesus?

  28. colewd: The sentence I am asking you to generate has only 50^28 possible arrangements.

    The multiple different de novo proteins evolved in the antibiotic resistance in the experiments described in the paper I linked above, were selected from a library constrained to a sequence space of \sim 1.3\times10^{65}. That was the total size of sequence space allowed in the protocol, and thus the size of the “search space” to be sampled blindly. And yet multiple functional proteins were found. Your challenge has been met.

  29. Oh also, they only sampled about \sim 10^8 random sequences, which is 0.000000000000000000000000000000000000000000000000000000089 percent of the complete space.

    And yet, again, multiple functional sequences were found.

  30. Mutations finding function is analogous to the Birthday problem. What are the chances that someone’s birthday is March 17th? Most of would think there is a 1 in 365.25 chance, which is correct. When you have a specific target, those are the odds. You would need quite a few people in order to have a good chance of someone having a birthday on that date. However, it changes a bit if you have a moving target. If you randomly choose 70 people there is a 99.9% chance that two of them will have the same birthday.

    The same applies to evolution. There are tons of mutations, and there are tons of functional sequences. The odds of finding a specific functional sequence are low, but it is much, much easier to find a function. This is the simple concept that ID supporters just can’t seem to understand. They think that any match found is the only possible match, and then do the math wrong.

  31. T_aquaticus: They think that any match found is the only possible match, and then do the math wrong.

    How true.

    colewd: The sentence I am asking you to generate has only 50^28 possible arrangements.

    I think not Bill. The sentence you request has slightly under 27^50 possible arrangements. You’re off by ~10^23.
    What is it with IDists and exponentiation?

  32. DNA_Jock: I think not Bill. The sentence you request has slightly under 27^50 possible arrangements. You’re off by ~10^23.
    What is it with IDists and exponentiation?

    What does that amount of error equate to in Dembskis? 🙂

  33. Joe Felsenstein:
    […] However I think I will not worry about the incoherence of Holloway’s argument, but instead just be in “even if” mode and say that even if his result were true …

    I don’t either see anything wrong with that. A mathematical model is based on a conceptual model. And the validity (or invalidity) of that conceptual model does not depend on the internal consistency (or lack thereof) of anybody’s mathematical interpretation/implementation of it.

  34. T_aquaticus: It is a very good thing “natural selection” is false, or else antibiotic resistant bacteria and other superbugs would have killed mankind by now as “evolution” falsely predicted.

    Strawman. Bacteria didn’t drive mankind to extinction before antibiotics, so there is no reason to think the result would be different if antibiotics became ineffective.

    Right, bacteria didn’t drive mankind to extinction. But if we really were to believe the power of natural selection, with all the bacteria on the planet and all the generations they generate, they should be able to simple consume they rest of all life, long before the slow generations of all other living things can find some defense.

    That’s a problem evolutionists like to ignore (of the many!).

  35. Instead of using the word ‘target’ it would be much better to use the word ‘outcome’.

  36. T_aquaticus,

    Do you see a 50 character english sentence in there anywhere? If not, it doesn’t contain information according to you.

    It certainly contains information. Feel free to work in any language you choose including the language of human proteins which you chose above. Fell free to expand it to all vertebrate proteins.

    That’s called inheritance. Ever heard of it? About half of your genome is identical to your father’s genome, and it has nothing to do with intelligent design.

    It is called inheritance along with functional constraint. The example that contained 50 million years of separation is slightly more interesting then one that contained 20 years.

    Functional constraint has everything to do with intelligent design unless you can model how the cell creates this on its own with nature alone guiding this. Sexual reproduction also has everything to do with intelligent design unless you can model how nature created this process on its own. Notice that I am opening this up so you can find mechanisms that evolution has not yet identified.

    It is interesting that the law of information non growth is being tested here as we are seeing identical sequences that are not degrading even with animals of rapid generation rates and separated by millions of years yet the mutual information is staying the same.

  37. phoodoo: Right, bacteria didn’t drive mankind to extinction. But if we really were to believe the power of natural selection, with all the bacteria on the planet and all the generations they generate, they should be able to simple consume they rest of all life, long before the slow generations of all other living things can find some defense.

    That’s a problem evolutionists like to ignore (of the many!).

    https://en.wikipedia.org/wiki/Optimal_virulence

    They ignore it he says. Virulence evolution turns up 770.000 results on google scholar. In Denmark we have it’s very own institute (State Serum Institute) with entire sections employing literally hundreds of scientists dedicated to studying virulence evolution in pathogens that affect the population. Among other things because Denmark’s economy is heavily dependent on agricultural exports, we’d like to know if something is infecting and killing the livestock and crops.

    Is there a possible world in which you won’t write a post I will laugh at, phoodoo?

  38. colewd: Functional constraint has everything to do with intelligent design unless you can…

    colewd: Sexual reproduction also has everything to do with intelligent design unless you can…

  39. Rumraket,

    You are not questioning the supposition, which is what a real skeptic would do.

    You have an arms race where one side can make 10 million copies to every one on the other side (or is it ten billion to one?) and somehow they can come to a draw. . The math alone makes the premise ridiculous. We just accept this as the way it is, without questioning why that should be.

    How many of your silly Google hits deck with this contradiction? This is just more of your reference bluffing you guys are known for.

  40. phoodoo: How many of your silly Google hits deck with this contradiction? This is just more of your reference bluffing you guys are known for.

    Why don’t you do the search yourself and read the actual papers? Once again we are faced with an opportunity for you to prove that you are not deliberately deciding to remain ignorant and the laughing stock of this forum. And yet we both know that is what you will do.

    What you will do, at most, is go search for something you find disagreeable, declare that this single thing you find disagreeable disproves everything, fail to show how it does so(you will merely declare this to be the case, as you just did with the “math” above) then use that as an excuse to dismiss the remaining 769.999 results.

    We will not see you do any actual math, and we will not see you do anything but what I just described. Merely assert things, and act out your incredulity as if it constitutes an argument.

  41. phoodoo: 10 billion> 1.

    You get ten billion new infections each winter?

    Unlikely, the effective population size of any pathogen must be restricted by the number of available hosts.

    Adjust your math, please.

  42. Okay, I guess that was it. Phoodoo’s penetrating mathematical disproof of evolution.

    Ten billion is more than one.

    QED.

  43. Corneel: You get ten billion new infections each winter?

    Yea, I was being facetious with the 10 billion number.

    Its actually more like 39 trillion in one person’s body.

  44. Rumraket: Ten billion is more than one.

    It is a pity, because the point phoodoo brings up is in itself valid: The shorter generation time of a pathogen works to its advantage in an evolutionary arms race. That’s a lot better than “sexual reproduction has everything to do with intelligent design” (“notice that I am opening this up” 😳).

    But then he assumes that nobody ever thought of it before, and refuses to acknowledge the literature that actually deals with the issue.

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