Evolving complex features

The Lenski et al 2003 paper, The evolutionary origin of complex features, is really worth reading.  Here’s the abstract:

A long-standing challenge to evolutionary theory has been whether it can explain the origin of complex organismal features. We examined this issue using digital organisms—computer programs that self-replicate, mutate, compete and evolve. Populations of digital organisms often evolved the ability to perform complex logic functions requiring the coordinated execution of many genomic instructions. Complex functions evolved by building on simpler functions that had evolved earlier, provided that these were also selectively favoured. However, no particular intermediate stage was essential for evolving complex functions. The first genotypes able to perform complex functions differed from their non-performing parents by only one or two mutations, but differed from the ancestor by many mutations that were also crucial to the new functions. In some cases, mutations that were deleterious when they appeared served as stepping-stones in the evolution of complex features. These findings show how complex functions can originate by random mutation and natural selection.

The thing about a computer instantiation of evolution like AVIDA is that you can check back every lineage and examine the fitness of all precursors.  Not only that, but you can choose your own environment, and how much selecting it does.  There are some really key findings:

  • Irreducibly complex functions evolve, where IC is defined as “if you take something away, it breaks”
  • Functions evolve via Irreducibly Complex pathways, i.e. pathways in which there are several neutral, or even quite steeply deleterious steps.
  • The more complex functions do not evolve without selection.
  • All the functions evolve via at least some neutral steps
  • There are many pathways to each function
  • Not all the functions are achieved in the same way.

The AVIDA findings are very good evidence that there is no reason, in principle, why irreducibly complex things can’t evolve, that some degree of natural selection aka heritable variance in reproductive success in the current environment is necessary for for certain features to evolve, but that not all steps need be advantageous – because of the role of drift, even quite sharply deleterious steps can prove key to the emergence of a complex function.

Then there’s the Lenski lab e-coli experiments.  But let’s start with AVIDA, because it really does rebut the idea that Irreducible Complexity, whether defined as the property of a function or of a path to a function, is an in-principle bar to evolution by natural selection.

242 thoughts on “Evolving complex features

  1. Behe:

    Here’s something to ponder long and hard: Malaria was intentionally designed. The molecular machinery with which the parasite invades red blood cells is an exquisitely purposeful arrangement of parts. C-Eve’s children died in her arms partly because an intelligent agent deliberately made malaria, or at least something very similar to it. (p. 237)

    http://www.pandasthumb.org/archives/2012/04/behes-malevolen.html

  2. Allan Miller:
    CharlieM,

    Behe gets the argument wrong, because Plasmodium is squeezed through a tiny bottleneck during its life cycle. The effective population size of Plasmodium is much closer to that of its local humans than it is to the census of all cells. This ‘edge of evolution’ can therefore be reached in quite small populations, irrespective of other ‘multiple-pathway’ and ‘Texas sharpshooter’ arguments.

    Do you understand Behe’s argument? Plasmodium can achieve resistance without having to get anywhere near the “edge of evolution”.

    Do you dispute Behe’s figures that there are roughly one trillion parasites in an infected person and there are about one billion infected people in the world in a year?

  3. CharlieM,

    Do you understand Behe’s argument?

    Yep. Do you?

    Plasmodium can achieve resistance without having to get anywhere near the “edge of evolution”.

    I understood Behe to be saying that resistance in Plasmodium is operating near the “edge of evolution”. Otherwise why even mention it, in a book on the edge of evolution?

    Do you dispute Behe’s figures that there are roughly one trillion paracites in an infected person and there are about one billion infected people in the world in a year?

    Do you dispute my assertion that the Plasmodium cells in an infected person go through a very tiny bottleneck (to wit: a mosquito’s gob), and therefore large census numbers obtained by multiplying P x H (Plasmodium times Human) are irrelevant to the assumed number of events involved in getting Plasmodium to achieve 2 serial mutations? Bone up on effective population size

    Then take on board the fact that Pf is sexual, which also changes the probability of both mutations getting into the same individual.

  4. CharlieM: Maybe a more serious question would be, Have apes and monkeys de-evolved from us?

    “de-evolved” is not a term used, or relevant to, the theory of evolution.

    Evolved simply means that a lineage changed over time (genetically and phenotypically), often adaptively, but not necessarily.

    There isn’t such a thing as “de-evolved”.

    Modern monkeys and apes and humans (all “primates”) evolved from earlier primates, i.e. we are all descended from earlier primates Those earlier primates, if you go far back enough, would, according to the ToE have been a single population – in other words modern primates share a single primate ancestral population.

    That ancestral population probably looked a little more like modern monkeys than modern apes and humans do, in that they probably had tails.

  5. petrushka:
    Two things: first, malaria has moved on to have double drug resistance. This is the thing Behe said was statistically impossible. Double lotto winner. Behe is simply wrong. He’s wrong about AIDS also.

    CharlieM:
    From “The Edge of Evolution”:

    In a real-world experiment involving this basic principle, scientists from Catholic University in Washington, D.C., showed. that resistance to one drug (called 5-fluoroorotate) at a particular concentration was found in malaria cells at a frequency of about one in a million, Resistance to a second drug (atovaquone) was about one in a hundred thousand. Sure enough, resistance to both drugs was the multiplied odds for the two cases, about one in a hundred thousand limes a million, that is, one in a hundred billion.

    Petrushka:

    Regarding flagella, why would you expect to find inefficient versions in the current environment?

    The earth is not just one current environment. There are a multitude of environments.

  6. What is your point? The frequency of drug resistance was approximately zero when the drugs were first introduced. Resistance to both has evolved, and the combination of both is now spreading.

  7. http://www.evolutionnews.org/2014/07/a_key_inference087761.html

    The need for multiple mutations neatly accounts for why the development of spontaneous resistance to chloroquine is an event of extremely low probability — approximately one in a hundred billion billion (1 in 10^20) malarial cell replications — as the distinguished Oxford University malariologist Nicholas White deduced years ago. The bottom line is that the need for an organism to acquire multiple mutations in some situations before a relevant selectable function appears is now an established experimental fact.

  8. Charlie:

    The latest word from Behe are his articles at ENV. You will see there that he says development of chloroquine resistance is a 1 in 10^20 event. He says this is just barely possible.

    The odds of a second form of resistance have the same odds, and the odds of both occurring in the same population are 10^20 times 10^20.

    And yet it happened in one human generation. Clearly he doesn’t understand how evolution actually works. He is assuming a path that is not relevant, because evolution pursues many paths simultaneously.

  9. OMagain: In a similar way there is only one type of car, would you agree? Do you agree or disagree?

    Disagree. A car is more like a bacteria than a flagellum. Perhaps you could talk about what is common to all internal combustion engines. That might be a more apt analogy.

  10. OMagain: So, given that text existed before you wrote it, did you write it Mung or was the “potential” inbuilt by your designer?

    It would appear that the potential for language is common among humans everywhere.

  11. OMagain: If we evolved from monkeys, why are there still monkeys?

    Because they are cute and serve to remind us where we came from and where we could end up again.

  12. petrushka:
    The designer so loves killing children with dysentery and other diseases, that they are almost as diverse as beetles.

    Do you mean the designer looks for children with dysentery and other diseases and kills them?

  13. Mung: Do you mean the designer looks for children with dysentery and other diseases and kills them?

    No, I mean Behe’s stated position on malaria is that it was designed, so I assume his position is the same on the dysentery bug’s flagellum.

  14. Elizabeth: But in that case there’s nothing anti-Darwinian about your argument.

    Well if you think Darwinism is compatible with intentional design I can’t stop you.

    As a book I’m reading says:

    Unlike metaphysical naturalists, they [evolutionary theists] need not accept that evolution is a purely contingent process. … they can interpret the stochasticity of evolution as part of God’s plan. The role of chance in evolution does not necessarily entail a lack of purpose.

    Let me make that relevant for you:

    Unlike metaphysical naturalists, they [IDists] need not accept that the appearance of EQU is based on a purely contingent process. … they can interpret the stochasticity of Avida as part of the designers’ plan. The role of chance in Avida does not necessarily entail a lack of purpose.

    Avida is designed to do what it does. It evolves what it was programmed to evolve. If that’s Darwinian and if that’s what you mean by “natural selection” then yes, design can produce IC. Whoever thought otherwise.

  15. Mung

    Unlike metaphysical naturalists, they [IDists] need not accept that the appearance of EQU is based on a purely contingent process. … they can interpret the stochasticity of Avida as part of the designers’ plan. The role of chance in Avida does not necessarily entail a lack of purpose.

    Gamblers can interpret the stochasticity of dice rolls on the craps table as the invisible, undetectable Dice Manipulator fixing the outcomes too. Given the complete lack of evidence for either an Intelligent Designer of life or the Intelligent Dice Manipulator we have no reason to posit such things.

    Avida is designed to do what it does. It evolves what it was programmed to evolve.

    No Mung, it doesn’t. The rules for evolution were set up and allowed to run. What emerged from the process was not prespecified.

    IDiots love the dishonest equivocation “genetic algorithms on computers were designed by humans so the results were designed too!”

  16. petrushka,

    He is assuming a path that is not relevant, because evolution pursues many paths simultaneously.

    True, but also – I’ll say it again, since Charlie chose not to comment – census size is not the deciding factor, particularly in a sexual organism. If he is choosing to define his ‘edge’ by reference to an organism with many more individuals than there are people, but it has an effective population size equivalent to humans, then he has scored an own goal.

    He ought to compare like with like. There are trillions of cells in each person. Multiply that by a billion to get the census size of human cells in a billion people. This number of cells is exploring genetic space in exactly the same sense that 10^15 Plasmodium are. “Somatic cells are irrelevant because they are dead ends”, I hear Behe cry. Yeah, and so are the Plasmodium cells that do not get into a mosquito bite. The life cycle of the parasite is much closer to that of human gametes than to 10^15 free living cells. His calculation is wrong.

  17. Mung: It evolves what it was programmed to evolve.

    Ah, so you are claiming you can predict it’s output?

    Well, go on then. Predict away!

  18. Mung: It would appear that the potential for language is common among humans everywhere.

    Non-responsive to the point and irrelevant. But then again, for you that’s closer to the mark then usual.

  19. Creationist reasoning: Given that Design is all-pervasive within AVIDA, and also within the technological environment within which AVIDA exists, it’s obvious that any result of AVIDAn so-called “evolution” must necessarily be Designed.

    This line of reasoning can be applied to a number of areas unrelated to AVIDA, with highly interesting results. For instance:

    A deck of playing cards is a Designed entity.
    The procedure called “shuffling the deck” is a Designed procedure.
    The rules of bridge are Designed rules.
    In the game of bridge, the procedure called “dealing out the cards” is a Designed procedure.
    Since everything about a bridge hand (the deck, the cards in the deck, etc etc) is Designed, therefore every bridge hand must necessarily be Designed.

  20. cubist,

    And if we use Winston Ewert`s methodology, viz

    … the design inference requires that we calculate probabilities, not a probability. Each chance hypothesis will have its own probability, and will be rejected if that probability is too low.)

    We can confirm that any given bridge hand is designed.
    See! It really works!

    😀

  21. Allan Miller: but it has an effective population size equivalent to humans,

    Not fully understanding this. If the human in question happens to be taking the drug, selection should be fierce for resistance. Anything that survives has a better chance of being passed on.

    I would think of humans as cultures. Perhaps in a population where people are treated, the rate of transmission goes way down for a while. But is some individuals are not treated, there’s an opportunity for the trillions to arise, and possibly a favorable mutation.

  22. Remove the potential to evolve logic functions from Avida and you won’t get EQU. So yes, it’s built in.

    “The most complex function, EQU, evolved only when several simpler functions were also useful.”

    It didn’t evolve. That’s just silly talk.

  23. petrushka,

    Me: but it has an effective population size equivalent to humans,

    P: Not fully understanding this. If the human in question happens to be taking the drug, selection should be fierce for resistance. Anything that survives has a better chance of being passed on.

    It’s not a human in question, it’s the population in question. It makes a world of difference whether the population is a free-living one, or one that goes through severe host-constrained bottlenecks in its life cycle, as to how likely a particular variant is to be found. It’s the likelihood of the double mutant that’s he’s arguing on, not just selection of it once it happens.

    He’s arguing that P falciparum took a generation to evolve a double mutant, with vast numbers of cells at its disposal. This is his ‘edge of evolution’, and any population with a smaller size (eg humans) cannot transcend that edge. But he is not comparing them equally. He forgets that Pf is bottlenecked – ironically, by the very species he’d like to exclude from having evolved.

    Imagine first that the Pf population is free-living, in a vat about the size of one billion people. It is reasonably mobile and encounters chloroquine concentrations in human-sized patches varying from nil to the levels encountered in treated patients. The entire population’s genomes are ‘searching’ the space for chloroquine resistance. When one cell finds it, the mutant is unconstrained. Any cell anywhere can find it and sire a resistant lineage which the presence of chloroquine can promote. If it took a human generation to find it, then we could say that’s what a population of 10^15 over 30 years or so can do.

    But what actually happens is that each human-sized space above is actually encased in .. .well, a human. Instead of 10^15 Pf working on the problem, we have a set of subpopulations, one in each human. In the first scenario, if the mutant arises in any human-sized space, it has a good chance of getting into the broader population. But in the second, the human may die without being bitten again, it may recover and become free of the parasite, or the new mutant may not get into the blood drop extracted by a second mosquito, or into another victim.

    To model that in the first scenario, we would need massive and periodic extinction of entire blocks of cells. If you imagine doing it all at once, say there are 100 parasites in every bite of an infected person, and everyone infected supplies one mosquito which successfully passes them on, you’d need to cull the population down from 10^15 to 10^11 – that’s getting rid of 99.99% of the population every few weeks just to get it through the mosquito-bite bottleneck, and of course it then has to develop in another person. That person may already have a resident population, or have resistance, increasing the bottlenecking effect still further. All of this lottery has to be traversed by the single mutants, which are assumed to have no advantage, before choroquine resistance can arise by second mutation or recombination.

    So really, the effective population of Pf – the idealised population that has the same chance of gaining the double mutant as the real one – is vastly smaller than Behe’s 10^15. It is closer to the population size of its hosts than it is to that one might assume from counting cells at a moment. The double mutant is not what 10^15 cells can do, it’s what a few million can do. The mode of transmission of Pf genes is reminiscent of that of human genes, passed among few large, enclosed colonies rather than scattered about the countryside.

  24. Mung: It didn’t evolve. That’s just silly talk.

    That more or less sums up the anti position. Ner Ner Ner.

  25. OMagain: That more or less sums up the anti position. Ner Ner Ner.

    Are you saying that what constitutes an EQU function was not predetermined? You may be surprised that EQU appeared, but I am not. Do you people even read the paper?

    An exhaustive search shows that the minimum number of nand operations to perform EQU is five, which is greater than for any other one- or two-input logic function. Using the 26 available instructions, we wrote a program of length 19 that performs EQU but does not replicate (Supplementary Information). This program seems, but has not been proven, to be the shortest one to perform EQU.

    Avida is a great example though of convergent evolution. Surely we can all at least agree on that.

    OMagain: Ah, so you are claiming you can predict it’s output?

    Some readers might suggest that we ‘stacked the deck’ by studying the evolution of a complex feature that could be built on simpler functions that were also useful. However, that is precisely what evolutionary theory requires, and indeed, our experiments showed that the complex feature never evolved when simpler functions were not rewarded. Our experiments also show that many different genomic solutions produce the same complex function. Following any particular path is extremely unlikely, but the complex function evolved with a high probability, implying a very large number of potential paths.

  26. Allan Miller,

    First you misrepresent Behe as to where “the edge of evolution” lies.

    Behe wrote:

    So what should we conclude from all this? Miller grants for purposes of discussion that the likelihood of developing a new protein binding site is 1 in 10^20.

    Now, suppose that, in order to acquire some new, useful property, not just one but two new protein-binding sites had to develop. In that case the odds would be the multiple of the two separate events — about 1 in 10^40, which is somewhat more than the number of cells that have existed on earth in the history of life. That seems like a reasonable place to set the likely limit to Darwinism, to draw the edge of evolution.

    Secondly your talk of models, mosquito lifecycles and bottlenecks are totally irrelevent to Behe’s argument. In his argument he was using actual data and not speculation from models.

    Prof Nicholas J. White FRS

    Resistance to chloroquine in P. falciparum has arisen spontaneously less than ten times in the past fifty years (14). This suggests that the per-parasite probability of developing resistance de novo is on the order of 1 in 10^20 parasite multiplications.

    It doesn’t matter what happens to Plasmodium falciparum during its lifecycle. The data make transparent the resistance conferring mutations occurring and spreading during the cell division phase in the victims bloodstream.

  27. petrushka:
    I have not read the Edge. I have read all of Behe’s replies to his critics. His argument is simple and it is wrong. He sees a path that appears to be blocked and concludes there is no usable path.

    No. He sees a path and provides evidence as to the number of times that path is found in a given search.

  28. OMagain:
    Behe:

    Here’s something to ponder long and hard: Malaria was intentionally designed. The molecular machinery with which the parasite invades red blood cells is an exquisitely purposeful arrangement of parts. C-Eve’s children died in her arms partly because an intelligent agent deliberately made malaria, or at least something very similar to it. (p. 237)

    http://www.pandasthumb.org/archives/2012/04/behes-malevolen.html

    Maybe you should read the book instead of picking quotes from hostile sites.

    In the pages following the above quote, Behe writes:

    Whether on balance one thinks life was a worthwhile project or not – whether the designer of life was a dope, a demon, or a deity – that’s a topic on which opinions over the millenia have differed considerably. Each argument has some merit…

    Maybe the designer isn’t all that beneficient or omnipotent. Science can’t answer questions like that. But denying design simply because it can cause terrible pain is a failure of nerve, a failure to look the universe squarely in the face.

    This makes clear that Behe does not equate the designer with the God he worships. If the designer is a dope or a demon so be it.

  29. Elizabeth: “de-evolved” is not a term used, or relevant to, the theory of evolution.

    Evolved simply means that a lineage changed over time (genetically and phenotypically), often adaptively, but not necessarily.

    There isn’t such a thing as “de-evolved”.

    Well my statement was a bit tongue-in-cheek 🙂 But it does mean that there are features which put humans on the main branch of the evolutionary tree with apes diverging from this branch.

    Modern monkeys and apes and humans (all “primates”) evolved from earlier primates, i.e. we are all descended from earlier primatesThose earlier primates, if you go far back enough, would, according to the ToE have been a single population – in other words modern primates share a single primate ancestral population.

    That ancestral population probably looked a little more like modern monkeys than modern apes and humans do, in that they probably had tails.

    That suggests that modern monkeys have remained at an earlier stage of evolution. I can go along with that.

  30. petrushka:
    What is your point? The frequency of drug resistance was approximately zero when the drugs were first introduced. Resistance to both has evolved, and the combination of both is now spreading.

    My point is that Behe has put facts and numbers into his argument.

  31. CharlieM: My point is that Behe has put facts and numbers into his argument.

    Yes. He is the only IDist who argues actual science.

    Unfortunately for him, when you argue facts and numbers, people can tell when you are wrong.

  32. Charlie, the latest word from Behe is in his articles at ENV. That’s where he responds to Edge critics.

    And elsewhere he has unambiguously identified the designer as the god of the Bible.

  33. petrushka:
    Charlie:

    The latest word from Behe are his articles at ENV. You will see there that he says development of chloroquine resistance is a 1 in 10^20 event. He says this is just barely possible.

    The odds of a second form of resistance have the same odds, and the odds of both occurring in the same population are 10^20 times 10^20.

    And yet it happened in one human generation. Clearly he doesn’t understand how evolution actually works. He is assuming a path that is not relevant, because evolution pursues many paths simultaneously.

    You obviously don’t understand his argument.

    Atovaquone resistance can be achieved in 10^12 cell divisions, chloroquine resistance in 10^20. Behe speculated on this difference. According to him this was probably because atovaquone resistance only required one mutation while chloroquine resistance required at least two. This was confirmed in a recent paper

  34. I’m curious what the group’s thoughts are on Jonathan Bartlett’s (AKA “JohnnyB”) argument about open-loops in the AVIDA program?

  35. So both in one can be achieved in 10^12 times 10^20. That’s a big number.

    But the actual probabilities aren’t found by multiplying. No matter how many mutations are required for a function, they occur independently and in parallel with each other, not in a necessary sequence.

  36. We know that because all the proteins required for a flagellum exist for other reasons in microbes that do not have flagella.

  37. TristanM:
    I’m curious what the group’s thoughts are on Jonathan Bartlett’s argument about open-loops in the AVIDA program?

    I think your link doesn’t work.

  38. petrushka: No matter how many mutations are required for a function, they occur independently and in parallel with each other, not in a necessary sequence.

    Avida shows that a sequence is necessary.

  39. No, it doesn’ t. There are innumerable paths.

    But living populations show that large numbers of variant sequences coexist in populations. Combinations do not have to come into existence in a particular order.

  40. Avida is just a glorified version of the Dawkins weasel program. WEASEL++

    METHINKS IT IS LIKE A WEASEL is IC because if you remove the word WEASEL it ceases to have the same function.

  41. Mung: Avida shows that a sequence is necessary.

    petrushka: No, it doesn’ t.

    The paper says otherwise:

    …our experiments showed that the complex feature never evolved when simpler functions were not rewarded

    ETA: petrushka edited his post after I read it and commented. I quoted the full extent of the original comment. It wasn’t a “quote-mine.”

  42. I edited my post within a minute or two. I’m using a phone so it’s not easy to make a long post.

    Life is a bit richer than Avida, and Avida is richer than Weasel. In life, most varients have no obvious advantage over other variants. Or they have both advantages and disadvantages, which tend to be neutral in combination.

  43. petrushka: There are innumerable paths.

    This was an unsubstantiated assertion made in the original paper, which I already mentioned in my comment on how Avida demonstrates convergence. But it’s utterly irrelevant to my point.

    There are innumerable paths across the Atlantic to Calais. People who travel by air or by ship are rewarded by being given a higher probability of arrival as opposed to those who try to swim there from Canada.

    “…our experiments showed that the complex feature never evolved when simpler functions were not rewarded.”

    The fact that we can increase the probability of a specific outcome (the EQU function) by rewarding other necessary steps in the sequence is not a surprise.

  44. petrushka:
    I edited my post within a minute or two. I’m using a phone so it’s not easy to make a long post.

    Understood. Did not intend to imply any sort of nefarious behavior.

  45. petrushka: Life is a bit richer than Avida, and Avida is richer than Weasel.

    🙂 Agreed.

    But my question is why cannot the same claims be made for the Dawkins WEASEL program that are being made for the Avida program with respect to “refuting IC,” or whatever the point is that Elizabeth was trying to make.

    Avida more clearly defines what counts as a “function.” Dawkins could have done the same with WEASEL. What is the essential difference?

  46. TristanM:

    I’m curious what the group’s thoughts are on Jonathan Bartlett’s (AKA “JohnnyB”) argument about open-loops in the AVIDA program?

    Tristan,

    I started a thread on the topic.

  47. CharlieM,

    First you misrepresent Behe as to where “the edge of evolution” lies.

    No I bloody did not! Or rather, show me the exact quote of mine where I made that misrepresentation.

    Secondly your talk of models, mosquito lifecycles and bottlenecks are totally irrelevent to Behe’s argument. In his argument he was using actual data and not speculation from models.

    ‘Actual data’ includes the fact that the mosquito population goes through a severe bottleneck every time it travels from one human to another. This is not speculation. If you don’t understand the relevance of it, I can’t force you.

    It doesn’t matter what happens to Plasmodium falciparum during its lifecycle.

    Of course it bloody does! If 99.99% or 100% of the parasite cells in an individual die off, then all mutations that occur die off with them. Therefore they cannot be counted, any more than your somatic cells can be counted, towards the overall incidence of a variant in the future. The variation in P falciparum does not come from the entirety of its census size, but from the tiny fraction that survives to breed. This is why effective population size is so important, a fact that escapes you and Behe.

    Suppose, as a reductio ad absurdum, we replicated one P falciparum cell 10^100000000 times, with all the various mutations that occur during replication, but then killed all but one. Would we count the number of times the double mutant had occurred in the ones that died? Why? What difference do they make to evolution? They might as well not have existed. They only count if they get out. Most Plasmodium cells do not get out. And most are genetically identical to one of their founders, in any individual. The ‘trillions’ in an individual have only been through about 30 generations. The mutation needs to happen early on to increase its likelihood of being sampled, but is less likely due to smaller numbers at that stage. It’s a classic boom-bust population, not 10^15 cells all beavering away in genetic space.

    Behe is arguing about the visible incidence of the double mutant in the first instance, not merely its subsequent selection by chloroquine. Chloroquine does not act as a selective factor until the double mutant has occurred, so we are looking for sampling to keep the single mutants. The operation of that sampling is absolutely relevant.

    The data make transparent the resistance conferring mutations occurring and spreading during the cell division phase in the victims bloodstream.

    We are not talking about one individual nor, in the first instance, about resistance. The argument, and quoting of White without considering anything other than raw, flattened cell numbers, is painfully simplistic.

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