On the ‘Evolving Complex Adaptations’ thread, a side-discussion arose with CharlieM over Behe’s ‘CCC’ argument. In summary, Behe places an event of probability 
as the upper bound or ‘Edge of Evolution’. If a specific single mutation has a probability of 
of arising in any one replication event, a specific double mutation has a probability of 
, a triple 
, and a quadruple – that is, if four independent changes must happen simultaneously before a particular step is achievable, then that step cannot realistically have occurred in the history of life on earth. Behe thinks he has found a case with a probability in the resistance to chloroquine in the malaria parasite Plasmodium falciparum.
He cites as support for this this review by Professor Nicholas White, in which he makes the following statement:
Resistance to chloroquine in P. Falciparum has arisen spontaneously less than ten times in the past fifty years. This suggests that the per-parasite probability of developing resistance de novo is on the order of 1 in 1020 parasite multiplications.
According to Behe, given that this requires two specific mutations in the transport gene PfCRT in the first instance, we require two 
events to get one ‘CCC’ (a ‘Chloroquine Complexity Complex’). Two CCCs, ie 4 simultaneous changes, and you hit the edge of evolution. If it takes an organism with a population numbering in the trillions to gain a single CCC, how much less likely is it for populations numbering in the thousands or millions, such as multicellular eukaryotes?
Numerous blogosphere heavyweights have weighed in on this argument – Dawkins, Coyne, Myers, Ken Miller, Moran – and much of the discussion was done and dusted in 2007. But as late as 2014, Behe seemed still to be claiming to remain unrefuted (“show us your numbers”), and evolution critics continue to turn up and say the same. You explain why the argument doesn’t fly, and the response is always “… but you haven’t refuted him”.
There are several arguments that can be made against the analysis – the possibility of multiple pathways and the dubiousness of deriving universal principles from a single selective scenario in one organism, to name but two – but I wish to focus on the probabilistic argument, and its relationship to population factors.
White himself says that the per-parasite probability of developing resistance is 
. He doesn’t (AFAIK) explain how he derives this figure, but if he treats the two mutation probabilities as independent, he makes the same mistake as Behe. How those replications actually occur – serially, simultaneously or the combination of both – is crucial, and the raw number is insufficient. Pace White, I don’t even think a per-cell rate is really meaningful except for the unrealistic scenario of a single round of replication for a population of 
individuals (giving rise to 
in that step). To take other extreme possibilities, a lineage of populations each one cell in size replicating times, and another allowing unrestrained expansion until cells had existed – all would experience the same number of double mutants. But the likelihood of the double mutant existing in the final population would be substantially different, and that is what ultimately matters. Chloroquine changes the game somewhat, but let’s ignore selection for now.
There certainly is a per-cell probability of both mutations arising during the same genome-replication, and for all I know it is . But this is not the sum of all sources of that particular chloroquine resistance genotype except in two very restricted scenarios – either the single-step replication of a population of individuals referenced above, or a more realistic population in which the single mutants were lethal. Only if they are lethal can they not build to any frequency in the population, and so must both happen in the same round of replication. It is then an independent probability, that of sampling a DNA strand from a pool to experience mutation A, replacing it, then of sampling the same strand again to get mutation B. If you sample and mutate until you have one double mutant, you will have also generated 
dead singles. All other scenarios involve the complexities of dependent probability, and depend upon population considerations.
Real populations include drift, recombination and repeat mutation. Even if the single mutants were mildly deleterious, they can be promoted both by drift and mutation to an appreciable frequency within the current population – subpopulations A and B. The total size of this single-mutant population A+B will be the deciding factor in the probability of the second mutation existing in the same genome copy as the first. The relative sizes of the individual A and B subpopulations will also be a determining factor in the possibility of the double combination arising by recombination in meiosis, because these organisms are sexual.
The probabilities are therefore dependent. It is way beyond my mathematically-challenged brain to work out what the dependent probability is, but it will be the contributed to by the double-mutant-in-one-replication scenario, the probabilities that the single mutants will get to particular frequencies, the probability that the second mutant will occur given that frequency, the probability of recombination between alleles a specified chromosomal distance apart in these subpopulations, and the local selective environment wrt chloroquine and virulence. That is, the only probability Behe will allow is by far the most trivial of the lot. Do we find the single mutants in the population at any frequency? If we do, then even if the first mutant has probability , the double is clearly not , in that population.
What we can actually say is that the probability of developing chloroquine resistance in 50 years, on the evidence, is likely to approach 1. It happened c10 times in 50 years, so it’s a pretty safe bet the 5-year probability is more than 0.5. That or we’ve got at least 10 heads in a row. If we have, we wouldn’t want to start deriving universal evolutionary principles from it!
Effective Population Size.
Behe uses the high population sizes of this single-celled eukaryote to try and disbar smaller populations of larger organisms from evolving. He suggests you need big numbers to get Close to the Edge. But how big are they? Yes, they produce vast numbers of cells. But so do we – they just don’t all survive. And neither, it turns out, do most of the cells of Plasmodium falciparum. Essentially, an inoculum of about 10 sporozoites is injected to start the infection; these replicate asexually to produce numbers of the order of 
, and then a small sample – a few tens – is taken up by the next one or a few biting mosquitoes. Various things happen in the mosquito, but not much increase.
In any mature single infection, mutants A and B will both have been produced about 100 times each. In every billion mature infections, the double mutant will also have been produced once. But in neither case are they guaranteed to persist. First, they have to get out. Getting out depends on your host being bitten again before dying or recovering, and on your frequency in the local population – in the human in which you first arose. Without selection, if the mutation happens on the first division, it will be in 50% of late-stage cells, but will only happen on the first division in 
people. Second division, it will be in 25% of cells and this will happen in 
people. And so on. The earlier it happens, the more likely it is to get out – but the less likely it is to happen. Of course, this means that the single mutants are less likely than in an uncontained, non-bottlenecked population. But it also means that drift is stronger. The single mutants are more likely, at least periodically, to reach significant numbers, even if they crash again.
Much the same happens with the multicellular germ line. A series of mitotic replications rapidly amplifies the diploid genome, which then undergoes a reductive division (meiosis) to produce a gamete. In a human female, there are about 7 million; over the lifetime of a male, about 5 billion. During the course of this, a significant number of mutations is produced, but that larger set is effectively randomly culled. There is a ‘gamete population bottleneck’ in every individual. As luck would have it, one of the malaria population bottlenecks is also based upon human individuals. It is not legitimate to equate the census population size of Plasmodium cells and that of human individuals, due to the effect of bottlenecking. The correct parameter for comparison is effective population size. This is not a personal eccentricity; it was introduced by Sewall Wright in 1931, to try to discount those census individuals that do not contribute to evolution, and arrive at a more ‘correct’ value for population size than simply counting numbers. Plasmodium discovered a CCC 5-10 times in 50 years with an effective population size (something which can be approximately measured) of the order of 15,000-50,000, not LateStageCells * InfectedIndividuals = VeryBigNumber. Choosing an organism that is bottlenecked by humans to try to assert evolutionary limits on humans is a subtle way to shoot oneself in the foot.
But at least the effective population size might be substantial, due to selection against non-chloroquine resistant organisms within the human.
It was a very simplistic calculation that Behe made, partly due to effective population size, also because in the absence of chloroquine the resistant organisms are at a disadvantage.
Mostly, though, I thought it interesting that Behe could ascertain that the Designer didn’t affect the evolution chloroquine-resistance, and from that he determined that the Designer affected most of the rest of the evolution of P. falciparum. All we need now is for Behe to show us how he knew when the Designer wasn’t working, because otherwise it’s just his assumption. Oh yes, a reason for designing P. falciparum and human resistance to same would be helpful, since it appears to be nothing but evolutionary opportunism without that reason.
Glen Davidson
GlenDavidson,
Selection reduces effective population size. Although that’s not germane to the argument – it’s the effective population size before selection that determines the availability of the first double-mutant by mutation/drift/recombination.
The picture is a little complicated, because we have a population within a human, which starts small (founder effect) and gets large. There is also a population of populations. Selection has within-human and within-wider-population effects. There’s no doubt that, once CR arises, selection will grab hold of it. But my post was about getting to that starting gate.
Measured effective population sizes within Pf are pretty low, for their census size – not much more than 10^5, from a brief search. They have significant inbreeding within the sexual phase, to go with the bottlenecking..
Point is, they do the CCC thing despite having effective populations of the order of the eukaryotes whose evolution is supposed to be probabilistically curtailed. Which means that Behe’s assumptions must be off, and CCCs are likely routine in the world of larger eukaryotes (albeit more slowly due to generation times).
Not forgetting that the probability of something curious happening somewhere is exponentially increased with the number of species probing the probabilistic envelope.
A deleterious mutation that has selection coefficient s against it will exist in about 1/s copies before it disappears. So if, say, s = 0.01 there will be 100 copies in existence after the average mutational event. (This accounts for genetic drift as well as selection). If a second mutation occurs in one of those deleterious copies, and causes it to then have a selection coefficient s’ in its favor, it will then have probability of nearly 2s’ of becoming fixed. So if the mutation rate is u and the population size N, each generation there is a probability 2Nu(1/s)u(2s’) that a mutation arises that survives long enough to be “rescued” by a second mutation which then fixes.
(For the malaria case you actually need to discuss both the population of parasites in a person, and the population of people at risk).
Well, I meant that absolute numbers having the two mutations within the effective population size would be increased via selection, although it wasn’t what I wrote.
Glen Davidson
Absolutley agree. It’s ridiculous to extrapolate and generalize Peppered Moths and Finch Beak evolution to the feasibility of macroevolution.
Quite.
Good thing that’s just a bizarre creationist fantasy.
Glen Davidson
Perhaps Sal or Behe could address how the double mutation occurred ten times in 50 years.
Does Behe’s claim that malaria is designed apply here, or is there perhaps something wrong with the assumptions?
stcordova,
Mmmm! They are indeed the bottom Jenga bricks of the entire enterprise. So if only you could somehow discredit peppered moths and Galapagos finches, the entire evolutionary edifice would come crashing down.
petrushka,
Behe would say it was because there were 10^21 cellular replications, so probability.
He claims malaria must be designed, but resistance is all Darwinism can do.
Hi — some good thoughts, but a coupla things:
1. Malaria (well, one species of it) Is Plasmodium falciparum, not Paramecium falciparum.
2. White’s (2004) estimate was supposedly an a-theoretical, empirical estimate — number of originations of chloroquine-resistance, divided by number of cells throughout that time period.
Behe relies heavily on #2, to the point of blind faith almost. But White’s estimate is pretty shockingly informal, it’s just an offhand, back-of-the-envelop calculation.
My main point about #2 in my 2007 TREE review of Behe was that the “number of originations” was really the “number of originations that have swept to large enough frequencies and geographic extents to be detected”. The true number of originations is probably much higher. This is especially true if there are intermediate stages with partial resistance, which it appears there are (even though it looks like one mutation that confers very high resistance, is highly deleterious if it’s the only mutation in a wild-type background; this is what make chloroquine resistance harder to evolve than some other resistances, apparently).
<a href="mailto:nickmatzke.ncse@gmail.com">nickmatzke.ncse@gmail.com</a>,
Welcome Nick! How’s Oz?
nick matzke,
Oh, FFS! I was obviously only half concentrating – switched to something else then back … so much for proof reading. Consider it fixed!
Allan Miller,
Right, fixed. I can only say … what a fucking knobhead!
My excuse, should anyone care, is that I typed it once and then copy-pasted it to the other locations. A deleterious mutation that increased in frequency by drift, he said weakly …
<a href="mailto:nickmatzke.ncse@gmail.com">nickmatzke.ncse@gmail.com</a>,
Sure, that was how I read it in our original debate, as a frequency. But my case was somewhat undermined by the fact that he calls it a probability.
So if I’m following this correctly, the guy who calculated that the bumblebee can’t fly and is concluding that flying bumblebees are proof of divine miracle isn’t basing his conclusion on his calculation at all. He is constructing his calculation in the first place to create “mathematical support” for his preconviction of divine action.
What I can never figure out is why Behe’s god has to stick his thumb on the scales in any way we can notice. Is his god so incompetent that evolution needs an “edge” constraining it, so that the god can miracle things over the edge?
That’s what always puzzles me about creationists and ID proponents. They insist on a god who is a bumbling incompetent fool. The theistic evolutionists have a much grander conception of their god.
I want to know the probability of one thing happening.
Mung,
Before or after it happens?
Joe Felsenstein,
Presumably an approximation only applicable at significant s?
Thanks! Now we just need to factor in recombinational gains and losses! There are at least 3 codon positions implicated in resistance in PfCRT (don’t know how much intron lies between them), several more in PfMDR1. As far as I can tell, all resistance markers survive happily enough without the others, somewhere.
Depends on the thing, of course, but coincidentally (Design again???) somebody who frequents another board with me (and has an intense interest in bashing J.M. Keynes) wrote this a couple of hours ago regarding his own views of “objective probabilities”:
Do you mean “What is THE PROBABILITY?” In which case, let us know the probability distribution you are using for the event.
Or do you mean “What IS the probability”. In which case, you’d need to decide if you are a frequentist, Bayesian, or something else.
Is this an old mug question, or a new mung question?
Assuming you are asking for the probability of any particular single point mutation happening in a population of microorganisms, it is as close to one as anyone could ask. And if a mutation is not immediately fatal, the allele will exist at some level in the population.
At least that’s the conclusion of Lenski, who has a bunch of microbes bottled up for analysis.
Maye you are hinting Probability is 1 (or undefined) after the event?
But when we do hypothesis testing after an experiment, we do act as if the probabilty of what we actually observed is not 1.
I guess it is to do with your attitude towards counterfactuals, but I think we need to believe in these for science (though it gets dicey for QM experiments).
The fitnesses are in the ratio 1 : 1-s. The number 1/s is an approximation, but it holds for all values of s in the interval (0,1]. What it does require is that the population size N be sufficiently large that each mutant copy does not interact with other mutant copies: they have fitnesses
1-s relative to their competitors. In effect this is a requirement that
N >> 1/s, i.e., that Ns is much bigger than 1.
If this condition does not hold then there will on average be more copies of the mutant allele than 1/s. And even a nontrivial chance of the deleterious allele fixing as a result of genetic drift.
You’d have to work out how often the two different alleles, each individually deleterious, are present in the same diploid individual, and how often a gamete from that individual contains a recombination that puts them on the same haploid genotype.
Now we have an explanation for Bornagain77.
Behe’s conclusion is based on a false assumption. He is basing the probability on the number of observed chloroquine resistances over fifty years. But that is like trying to say that the number of flu infections in a year is equal to the number that are hospitalized. The number of mutation events that lead to chloroquine resistance are probably much greater than the number he used.
Secondly, using something that is observed to estimate a probability of it occurring is dangerous. The example I have seen, and used myself, is the probability of the DNA assemblage of any individual occurring. Obviously it is one, because we exist. But if you start adding the probabilities of the specific sperm cell from your father fertilizing the specific egg from your mother, and the probability of it becoming implanted in the uterus, and the probability of your parents meeting and getting married, and then doing the same calculations for your grandparents, and great grandparents, etc. it does not take too many generations to arrive at a probability that is effectively zero n
BruceS,
I was being facetious, but actually it is probable that the individual point mutations involved in the resistance genotype all existed in Pf populations somewhere long before chloroquine was even thought of. And, from time to time, a resistant phenotype will have been generated by double mutation, second mutation or recombination. It was just unremarkable when it did so, till chloroquine came along and we said “crikey – what were the chances of that!”
So if the ‘one thing’ was a single mutant of the CCC cluster, one would need to go back to a point at which there were none, and know that a CCC-relevant mutation was the target without even knowing that a CCC was a thing.
Joe Felsenstein,
I figured when s approaches 0, you’d end up with more copies than population members.
Acartia,
To apply it to evolution, in transpositional and many recombinational scenarios, events can often be regarded as pretty much unique. And in the latter, it includes the probability of partners meeting in the first place. These drive a significant amount of evolutionary change. There really isn’t much point in assessing the retrospective probability of a particular such event that happened to be beneficial – “what was the probability that this exact sequence of 14 bases would be inverted” – if inversions, but not this exact one, happen routinely.
Every human being is born with something on the order of about 100-150 mutations.
Let’s just say 100. What is the probability that those 100 particular mutations that actually happen, would have happened before they happened out of all the possible 100 mutations?
Notice that every generation, that’s 100 simultaneous mutations that happen. And four should be impossible.
Macroevolution is an observed fact. And nobody is operating under the inference you are erecting there. Nobody says “finch beaks can change a bit, therefore cows became whales”. That is a creationist strawman.
The feasibility of large-scale morphological change is testified by the fossil record and comparative genomics, not the mere observation of microevolutionary change. You creationists keep erecting this stupid strawman. Microevolution merely proves that the evolutionary change happens and studying it informs us about what the underlying mechanisms are.
Since I have now informed you that you have been wrong about how macroevolution is inferred, you will stop regurgitating this stupid creationist lie that microevolution is used to prove macroevolution, right? You will inform all your creationist friends that they should stop using this argument too, because this is actually not how any scientist operates, right?
By the way, you are probably operating under a creationist (aka irrelevant) definition of macroevolution. What you are are thinking about is large-scale morphological and adaptive change, such as the transition from fish to tetrapods.
But macroevolution is merely defined as evolution above the species level. So reproductive isolation, or even extinction, qualifies as macroevolutionary change.
It’s ridiculous to extrapolate that because human beings can design things, there must be invisible designers that designed everything.
Your OP makes good sense to me.
I had thought Mung was trying to re-open an old conversation on the role of probability in evolution and science in general.
But maybe his was just a drive-by comment.
CharlieM, Crossposted from ‘Evolving Complex Features’
Discussion starts about here
A frequency is not a probability. Even though White calls it a probability, I actually think that is wrong. It’s the number of something counted between incidences – ticks of a clock. It’s easy to get bamboozled, because each of those ticks really does have an associated probability of both the single and the double mutation. But that’s not the probability of either incidence or detection, as you can surely see from the list you then quote:
Which of these is related to cell replication – the probability of the factor arising in 10^20 cellular replications?
It’s actually wrong! But it doesn’t matter too much. In order to get 34 trillion cells from a zygote, you have to do a certain number of cellular replications. Likewise in order to get one trillion Plasmodium from one cell in an individual. If we are counting cellular replications in Plasmodium, that’s what we must count in people, for a like-for-like comparison. Human mutations happen in cells, just like Plasmodium, and the population of cells is bottlenecked by the number of people just like Plasmodium.
Well the probability isn’t 1. If you average one 6 every 6 rolls of a die, the probability of a 6 in a given 6 rolls isn’t 1. But no matter. Why do we count cell replications in the Plasmodium case, but not in the human? Why do we count human individuals rather than human gametes, or somatic cells, or something else? Why do we count Plasmodium cells rather than infected people? Or years?
The population characteristics of Plasmodium actually resemble those of human gametes, or all post-zygotic cells combined, much more closely than they do human individuals. Their cells do a boom-bust, and most don’t get past 1 human individual, just like ours.
It must appear in an individual cell first, surely? A cell in the germ line, better yet.
Sorry, only spotted this thread after my last post in the previous thread. It’ll take me some time to read through the comments before participating further.
Meanwhile here is a copy of my last post:
Allan,
Sorry for the delay, life just gets in the way sometimes. Anyway, back to the subject.
It takes an enormous amount of replication events to occur before a fairly simple genetic change enables a parasite to overcome the effects of chloroquine. You
argue that Behe cannot legitimately invoke such large numbers, but these are the numbers White estimated from actual events. He estimated that the frequency
of a single mutation change in atovoquone was {10^{-12}. Do you agree with this figure? The facts are out there, the parasite can find resistance requiring a single mutation with relative ease, but it is vastly more difficult to stumble across resistance requiring two or more mutations.
If Behe is not allowed to use the vast amount of replication events in his argument then why do proponents of unguided evolution site the vast amount of time, and thus replication events, in their argument for the appearance of complex structures in living organisms, many of which involve far more intricate changes than that required for chloroquine resistance?
You say that multiple pathways can be used as an argument against Behe, but the figures that are arrived at are there regardless of the pathways taken.
Behe:
Selection cannot be used to justify the spread of the single mutations involved in chloroquine resistance as on their own they are more than likely to be deleterious.
From The Journal of Infectious Diseases (2001):
Chloroquine resistance is difficult to initiate but spreads easily once achieved.
I keep asking, do you have a point?
You seem somehow to be opposed to mainstream evolution. Is there something in your posts that argues against evolution?
Edit to add:
I read this to mean that there may be unknown — otherwise neutral — mutations that insulate against the deleterious effects of a necessary mutation. This is suggested by the apparent ease of evolving resistance, despite the numeric odds against Behe’s two, simultaneous mutations.
Now which seems more likely to you, that we don’t know the whole story, or that God loves killing children and sees to it that malaria doesn’t go extinct.
Smallpox seems to have gone extinct in the wild, so survival isn’t guaranteed.
petrushka,
Well petrushka, I cannot make you see the very limited capability of Darwinian evolution.I see It as obvious from the data that are emerging through modern techniques, you don’t. I wouldn’t have thought that either of us are going to change the other’s views on the matter.
That is my point – Darwinian evolution really does occur, but what it has been shown to have been capable of falls very far short of what is required to build the complexity demonstrated by the natural world. As Behe says, it is very good at breaking things but not so good at building things up.
You haven’t even presented an argument for your point. Nothing.
Charlie, does it not bother you that Behe has spent his entire professional life searching for some feature or sequence that could not have evolved, and come up empty?
He has a handful of examples of things whose history is unknown.
But ignorance of history is not an argument for anything except for research.
petrushka,
Do you think that chloroquine resistance is an example of Darwinian evolution in action? If so do you think that it shows Darwinian evolution as being a powerful force for evolutionary change? If not what better examples would you say there are?
Is there some reason you insist of inserting the word Darwinian? I mean, is the orbit of Mercury a good example of Newtonian physics?
Yes, resistance is a good example of evolution.
A good example of a complex feature evolving might be the bones of the mammalian inner ear. We are also beginning to understand the evolution of the blood clotting system, an icon of ID.
But if you intend to make a case, please answer Darwin’s challenge. Name something that could not have evolved by small, incremental steps, and provide evidence for the actual history of the feature, in detail.
At one time, I shared that skepticism. It comes from putting too much emphasis on natural selection, and not understanding of the power of mutation to allow a new variant to show a spurt of rapid growth (expansion of population) that can take over.
Darwin knew nothing about genetics, but he was an observer, and he interviewed the very best observers — plant and animal breeders. He understood the prevalence of nearly neutral variation and how small changes can accumulate.
Now we are beginning to understand this at the molecular level, through experiments like Lenski’s (and by experiments in the wild, like drug resistance).
The one big thing that IDists are failing to grasp is the ubiquity of neutral mutations, and how they function like word ladders, enabling multi-mutation adaptations. Kariosfocus’ isolated islands are not.
On what basis do you extrapolate the case of the evolution of resistance to chloroqine to the complexity of all of life? It seems to me rather unwarranted to extrapolate this single case to the evolution of everything else.
I think Behe is making an unwarranted extrapolation. Obviously there is going to be examples of things that take a long time to evolve, huge populations, many many generations and so on. But why believe this is the case for everything? So CR takes multiple mutations, maybe in a specific order, before it evolves, and maybe that is the only way for CR to evolve.
Take the evolution of humans and chimps from their common ancestor, are you aware of any adaptations that would require passing through the same kinds of bottlenecks as chloroquine resistance?
Do you have some sort of measure of complexity? How complex is a Rhinoceros, a wasp and an Earth-worm?
Better yet, how much more complex is the code for a human brain vs a chimp brain? Show your math.
I mean, it’s all well and good to highlight that chloroquine resistance takes years to evolve.
But then there are resistance to other antibiotics that evolves in mere weeks, among other reasons because there seem to be smooth slopes for selection to climb every step of the way, and because there are multiple pathways to resistance. This signficantly increases the odds of randomly arising variation (mutations) to happen to produce those beneficial steps.
And they involve just as many mutational steps as chloroquine resistance. On what basis should we think the rest of life’s complexity is more like evolving chloroquine resistance, than some other microbial antibiotic that evolved in a few thousand bacterial generations?
CharlieM,
And the reason in part, as I have implacably been arguing, is because most of those replication events do not result in longer-term descendants. Counting all 10^20 new Plasmodium cells between detections of CR as the probability of it occurring is not legitimate. It doesn’t matter if it’s White doing it or Behe. If 10^12 parasites arise in an infected individual from the initial 10 sporozoites, and that individual dies along with all of its parasites, or recovers, or only a few dozen are taken up in the next bite, on what basis do we include them in the probability? It’s like throwing a many-sided die a trillion times but only looking once, and then concluding that the probability of what you saw is 1 in a trillion. There is an enormous amount of sampling going on, but you insist on treating it as a free-living population bathed in varying concentrations of chloroquine.
Yes, White estimated cell counts per appearance of CR. To repeat: this is not the probability of CR occurring, nor is it the probability of CR rising to detectable levels. If the probability of a single mutation is 10^-10, then yes, a double mutation in the same round of replication is 10^-20. But (as I explained in this very OP) this is only relevant if the single mutants are lethal. If they are not lethal, the single mutants can increase by drift, creating a larger sub population within which the second mutation can occur with greater probability, and generating pools that can generate the double mutant by recombination with still greater probability. Do you acknowledge or deny this?
They aren’t lethal, because you can find subpopulations with the single mutations. The very fact that you can do this requires that they increase to a pretty significant level, as they are hard to find when rare, for obvious reasons.
A frequency is not a probability. The mutation rate is actually about 10^-9 per base pair, so 10^12 replications will actually see 1000 incidences of any given single-base change. But of course most of these are lost because, well, bottlenecking. You seem determined not to see the significance of the parasite’s life cycle.
This is not news. But the probability of the double is not the probability of the single squared unless the singles are lethal. Nor is the incidence of detection the same as the probability of occurrence.
Everybody needs to take account of the constriction of populations through bottlenecks. You can’t just count replications. ‘Evolutionists’ are not demanding exemption from probabilistic limitations. But, if you would absorb and address my comparative argument, you would see that the effective population size of Pf is of the order of that of multicellular eukaryotes, not 10^20 or whatever number you feel like bigging up. The same phenotypic change appears 5-10 times in 50 years. Does that seem like something that would disbar significant evolutionary change over, say, a million years? Certainly doesn’t to me.
No, the point is that one is drawing a target round the arrow after it has landed. How many different pathways to CR are there? Bet you don’t know. This is relevant to the probability of one.
And do you think CR is the only evolutionary change that took place in Pf over the past 50 years?
Do you think any other species might have evolved in the meantime?
You have vast numbers of organisms on the planet. You want to stop them all evolving in any significant manner by saying that the probability of 1 particular thing is 10^-20. It isn’t, but let’s just pretend it is. If there are 2 species each with a probability-of-evolving of 10^-20 in 5 years, what’s the probability that neither of them will evolve in 5 years? What if you have 100 species? 1000? A million? You soon get to the stage when the probability of nothing evolving – what you’d love to see – is vanishingly small.
Evolution is a racing certainty. There is a reason Behe has never published this in an evolutionary journal: it’s a bogus argument.