I'm a big fan of Richard Lenski's long-term evolution experiment (LTEE) and of Zachary Blount's work in particular. [Strolling around slopes and valleys in the adaptive landscape] [On the unpredictability of evolution and potentiation in Lenski's long-term evolution experiment] [Lenski's long-term evolution experiment: the evolution of bacteria that can use citrate as a carbon source]
The results of the LTEE raise some interesting questions about evolution. The Lenski experiment began with 12 (almost) identical cultures and these have now "evolved" for 31 years and more than 65,000 generations. All of the cultures have diverged to some extent and one of them (and only one) has developed the ability to use citrate as a carbon source. Many of the cultures exhibit identical, or very similar, mutations that have reached significant frequencies, or even fixation, in the cultures.Several other laboratory evolution experiments have been completed or are underway in various labs around the world. The overall results are relevant to a discussion about the role of contingency and accident in the history of life [see Evolution by Accident]. Is it true that if you replay the tape of life the results will be quite different? [Replaying life's tape].
Blount, Z.D., Lenski, R.E., and Losos, J.B. (2018) Contingency and determinism in evolution: replaying life’s tape. Science, 362:655, eaam5979 1-10. [doi: 10.1126/science.aam597]The conclusion is consistent with earlier results: similar isolated populations/species tend to find similar solutions when put under pressure to adapt but over the long term the populations diverge considerably due to stochastic effects.
Abstract: Historical processes display some degree of “contingency,” meaning their outcomes are sensitive to seemingly inconsequential events that can fundamentally change the future. Contingency is what makes historical outcomes unpredictable. Unlike many other natural phenomena, evolution is a historical process. Evolutionary change is often driven by the deterministic force of natural selection, but natural selection works upon variation that arises unpredictably through time by random mutation, and even beneficial mutations can be lost by chance through genetic drift. Moreover, evolution has taken place within a planetary environment with a particular history of its own. This tension between determinism and contingency makes evolutionary biology a kind of hybrid between science and history. While philosophers of science examine the nuances of contingency, biologists have performed many empirical studies of evolutionary repeatability and contingency. Here, we review the experimental and comparative evidence from these studies. Replicate populations in evolutionary “replay” experiments often show parallel changes, especially in overall performance, although idiosyncratic outcomes show that the particulars of a lineage’s history can affect which of several evolutionary paths is taken. Comparative biologists have found many notable examples of convergent adaptation to similar conditions, but quantification of how frequently such convergence occurs is difficult. On balance, the evidence indicates that evolution tends to be surprisingly repeatable among closely related lineages, but disparate outcomes become more likely as the footprint of history grows deeper. Ongoing research on the structure of adaptive landscapes is providing additional insight into the interplay of fate and chance in the evolutionary process.
It's not the paper's conclusion that I want to highlight. I want to call attention to the style of the paper and the quality of the writing. The authors define a serious problem (contingency vs determinism); they present the historical background and put it in a modern context; they review the data; and they discuss various problems and issues of interpretation. Throughout the paper they take the time to present both sides of the issue and cover all the objections that make this such a controversial issue.
In an ideal world this paper would not merit particular attention because this is the way all literature reviews should be written. In an ideal world all scientific papers would be excellent examples of critical thinking. However, this is not an ideal world and that's why this paper is unusual. Read this paper if you want to see a model for how all papers should be written.
There are a couple of points in the paper that deserve special mention ....
When discussing the history of life, the word contingency usually means that the path of evolution is shaped by all of the events that occurred earlier. Stephen Jay Gould made the word popular in his book Wonderful Life, which was all about contingency in that sense. Here's what he said on page 283 ...
I am not speaking of randomness ... but of the central principle of all history—contingency. A historical explanation does not rest on direct deductions from laws of nature, but on an unpredictable sequence of antecedent states, where any major change in any step of the sequence would have altered the final result. This final result is therefore dependent, or contingent, upon everything that came before—the unerasable and determining signature of history.Unfortunately, Gould did not stick to this definition. He often used the word contingency as a synonym for an unpredictable event. Blount et al. deal with this confusion in their paper by saying ...
Gould also introduced confusion about the concept of contingency itself. Despite its centrality to his thinking, Gould never formally defined "contingency." He gave various informal descriptions, but these tended to be unfulfilling and circular. Moreover, he often conflated the two common meanings of the word "contingency": "dependence on something else" and "an accidental or chance event."
The role of mutation
Here's how Blount et al. explain the relationship between mutation and contingency.
... the stochastic processes of mutation and genetic drift virtually guarantee that different histories will occur even when populations start from the same state and evolve under identical conditions. Such differences, in turn, constitute the sort of unpredictable antecedent events that might preclude populations from evolving the same solutions when confronting the same selective circumstances or, at least, change the relative likelihoods of different outcomes. These effects arise from how mutations and the order in which they occur affect later evolution. Indeed, the particular mutations that occur, their effects, and their fates can alter the rates of occurrence, phenotypic and developmental effects, and fates of later mutations, thereby shifting the probabilities of alternative evolutionary paths.
Convergence
Convergence demonstrates that the possible types of organisms are not only limited, but may in fact be severely constrained. The underlying reason for convergence seems to be that all organisms are under constant scrutiny of natural selection and are also subject to the constraints of the physical and chemical factors that severely limit the action of all inhabitants of the biosphere. Put simply, convergence shows that in a real world not all things are possible.Conway Morris doubled down on this point in subsequent books. For example, in Life's Solution he argues that the numerous examples of convergence imply that contingency has been widely exaggerated and that the history of life is broadly deterministic. Here's how he puts it on page 106 ...
... rewind the tape of life, as S.J. Gould repeatedly claimed, and let it replay: assuredly next time round the world will be a very different place, with a vanishingly small prospect of anything like a human emerging. I have already argued forcibly against such a position, and the purpose of much of the rest of this book is to develop in more detail why the trajectories of evolution are much more severely constrained than is sometimes supposed.1
Another difficulty is that convergence is identified after the fact. The saber-toothed condition evolved at least three times in the Carnivora, as well as once each in creodonts and South American marsupials, presumably as an adaptation to a particular predatory strategy. But how many other taxa, faced with the same selective conditions, failed to evolve this adaptation? Knowing the denominator is key to determining how repeatable a convergent trend is, but rarely does one know how many other lineages experienced similar circumstances, yet failed to evolve the trait in question. Moreover, although recent compilations of convergence are impressive, one could just as easily compile lists of adaptive types lacking a convergent doppelgänger: the two-leaved Welwitschia mirabilis, the platypus, chameleons, kiwis, elephants, octopuses, and hominins—all adaptive types that have evolved just once—to name a few.They also come up with an excellent example of a real-life experiment to test convergence.
Some convergence proponents go so far as to say that if life has evolved on Earth-like exoplanets, it will look much like what we see here. But we need not look to the stars to test that hypothesis: All we need to do is go to New Zealand, an island lacking any native terrestrial mammals. In their absence, New Zealand’s flora and fauna evolved to bear little resemblance to any other ecosystem in the world. In addition to kiwis, there are both carnivorous and flightless parrots, adzebills, moas, giant eagles, and flightless wrens, as well as a semi-terrestrial bat ..., giant snails and orthopterans, and divaricating shrubs with leaves that grow in the interior of the bush. And going back in time, one would be hard-pressed to find many similarities between the Mesozoic world of the dinosaurs and today’s faunas.This is the kind of scientific reasoning I admire. It's a shame that there aren't more examples in papers on junk DNA, alternative splicing, and a host of other examples where only one side of the argument is presented.
In short, lineages adapting to similar environmental conditions in nature can be thought of as evolutionary replays, even if these “natural experiments” are not as precise as carefully designed and controlled laboratory experiments. Because the lineages will have different genetic constitutions and will have experienced different histories, these cases are analogous to the historical difference experiments in laboratory studies. Unfortunately, however, the evidence boils down to one list of cases in which convergence occurred and another where it did not, rendering quantitative conclusions unsatisfactory. Nonetheless, the many impressive cases of convergence show that repeated outcomes can arise from similar environmental challenges. Conversely, the many cases in which convergence did not occur suggest that contingent effects can play a strong role in shaping divergent adaptive responses.
1. Simon Conway Morris is mostly upset about one of the main implications of evolution by accident; namely, that under different circumstances humans might never have arisen. He believes that God set up evolution so that sentient beings like humans were inevitable.
Blount, Z.D., Borland, C.Z., and Lenski, R.E. (2008) Historical contingency and the evolution of a key innovation in an experimental population of Escherichia coli. Proceedings of the National Academy of Sciences, 105(23), 7899-7906. [doi: 10.1073/pnas.0803151105]
Blount, Z. D. (2016) A case study in evolutionary contingency. Studies in History and Philosophy of Science Part C: Studies in History and Philosophy of Biological and Biomedical Sciences. [doi: 10.1016/j.shpsc.2015.12.007]
Lenski, R.E. (2017) Convergence and divergence in a long-term experiment with bacteria. The American Naturalist, 190:S57-S68. [doi: 10.1086/691209]
Yedid, G., Ofria, C., and Lenski, R.E. (2008) Historical and contingent factors affect re‐evolution of a complex feature lost during mass extinction in communities of digital organisms. Journal of evolutionary biology, 21:1335-1357. [doi: 10.1111/j.1420-9101.2008.01564.x]
66 comments :
Why don't you try to do the mathematics of fixation and adaptation for the LTEE?
I copied your advice for what a paper should do, and pasted it to the top of a paper I have stalled on for 2 months. I think it might help.
Larry, I don't know if you're familiar with Dr. Dr. Kleinman, but he has a long history on talk.origins. You may find him briefly entertaining. His schtick is that he has explained "the mutation and selection phenomenon" mathematically in a way that's superior to the way population geneticists do, and he has managed to publish a couple of papers in inappropriate journals to that effect. He's also a stealth YEC.
John Harshman is a PhD evolutionary biologist who can't explain the simplest laboratory examples of evolutionary biology such as the Kishony experiment and the LTEE. His failure to understand the basic mechanisms of evolution is astounding. If you want to see the mathematics of fixation and adaptation for the LTEE, you can find it here:
https://www.researchgate.net/publication/335243441_Fixation_and_Adaptation_in_the_Lenski_E_coli_Long_Term_Evolution_Experiment
It is pathetic that a PhD evolutionary biologist can not do such a simple calculation. Dr. Harshman doesn't even understand that if you double population size, you do not double the probability of a beneficial mutation occurring. The field of evolutionary biology is in a sad state when a PhD evolutionary biologist can not correctly answer an undergraduate level principle of evolution. This failure on the part of people like John Harshman contributes to the failure to understand antimicrobial resistance and cancer treatment failure.
"Alan Kleinman, (MD, doctor of medicine and PhD, doctor of Mechanical Engineering, licensed in both fields) is a primary care physician. Before his interest in medicine, he worked in aerospace engineering on the Space Shuttle and taught mechanical engineering at California State University Los Angeles. He got his BS, MS and PhD degrees in Mechanical Engineering at the University of California, Santa Barbara, BS in Advanced Biological Science from Touro College, New York, and the MD degree from the American University of the Caribbean. Drug-resistance had been an increasing problem in his medical practice. He started research on this problem which led to the publication of three papers on drug-resistance, "The basic science and mathematics of random mutation and natural selection", "Random Recombination and evolution of drug resistance", and "The Mathematics of Random Mutation and Natural Selection for Multiple Simultaneous Selection Pressures" published in the Journal "Statistics in Medicine"."
World Conference on
Bacteriology and Infectious Diseases
His Ph.D. is in mechanical engineering. If he's been on talk.origins then he probably knows about the Salem Conjecture.
I was not familiar with the Salem Conjecture until you brought it up. I am not a creationist because I am an engineer, I'm a creationist because of the multiplication rule of probabilities (which I understood in elementary school) and I understand how evolution works and how to apply the correct mathematical principles to describe Darwinian evolution. I understand the mathematics of adaptation and fixation (which is a different process than adaptation). And I know how to apply these principles to the Kishony experiment, the LTEE, to the evolution of hiv to combination therapy, and these results are published and three of the papers are in the US National Library of Medicine. Dr. Moran, perhaps you want to try and explain why combination therapy works for the treatment of hiv? And perhaps you could explain to us why it takes a billion replications for each beneficial mutation in the Kishony experiment?
On convergence.
AMEN. I think also convergence is very unlikely in the randomness of mutations. Instead it shows definite boundaries suggesting a blueprint and no random mutations at all.
Yes the long teeth of numerous creatures is strinking. Yet its not a convergence but instead shows the marsupial, placental, creodint, etc cats are just the same cat. then the long teeth is a trivial abiility that comes from the blueprint. likewise the other traits they , wrongly, use to group these creatures.
Convergence is such a great example of how unlikely mutations would lead to such wonderful same results. its impossible. they do find convergence more and more and more in biology. everywhere its a dominant option.
new Zealand does not show mutations glory but a simple result of limited fauna and so niches are filled. Birds simply can be more diverse but its not from mutations but againg taking advantage of a existing blueprint for diversity.
by the way i think the dinosaur world is just like New zealand. thies creationist sees the theropd etc group of dinos as just flightless ground birds. Just even bigger moas etc with teeth. it looks the same as now with a spectrum of diversity.
If mutations could do anything there would be greater results of adapting to environments. Instead the facts are great likeness in results. So they invoke the concept of convergence.
Internal evidence suggests that was Robert Byers.
What we really would enjoy is a PhD evolutionary biologist like you explain correctly how the LTEE or the Kishony experiment works. But sadly, despite your PhD in evolutionary biology, you cannot explain the simplest laboratory examples of evolution.
He can go on like this for months.
@kleinman
I realize that your engineering degree doesn't help in understanding biological experiments. Here's a couple of posts that explain how the long-term evolution experiment works.
Lenski's long-term evolution experiment: the evolution of bacteria that can use citrate as a carbon source
On the unpredictability of evolution and potentiation in Lenski's long-term evolution experiment
Basically, here's how his lab does the experiment. They grow 12 cultures of bacteria and dilute them every day. The cultures are under selection for rapid growth. They examine the cultures frequently to see what's happening. This includes sequencing the genomes to see what mutations have occurred.
HTHHND
Is this the best you have to offer, doxing someone? Why don't you explain something about evolution? Try explaining why combination therapy works for the treatment of hiv. Why does the virus easily evolve to single drug therapy in a week but 3 effective drugs gives durable treatment for the disease? And please try to be serious and don't go into your Elmer Fudd imitation.
I realize that your biochemistry degree doesn't help you much in understanding how to apply mathematics to physical or biological phenomena. Here's a couple of posts that explain how mathematics is applied to evolutionary adaptation:
For a single selection pressure:
https://www.ncbi.nlm.nih.gov/pubmed/25244620
And for multiple simultaneous selection pressures:
https://www.ncbi.nlm.nih.gov/pubmed/27501057
And I am very familiar with the LTEE. That experiment has two evolutionary processes operating in that experiment, one process is competition and the other process is adaptation. Here's how you do the mathematics for that experiment:
https://www.researchgate.net/publication/335243441_Fixation_and_Adaptation_in_the_Lenski_E_coli_Long_Term_Evolution_Experiment
If you think you understand the LTEE, explain to us what will happen in the experiment if run in either 1ml volumes or 100ml volumes instead of 10ml volumes. How will that affect the competition and adaptation process?
Why combination therapy works so well is an exercise in population genetics. kleinman seems to be suggesting that there is no explanation. kleinman is wrong. See here
You don't appear to be "very familiar" with the LTEE because there's a lot more going on than just competition and adaptation. Mutation and random genetic drift are two obvious ones that you missed. In addition, there's a lot of synergy and cooperation since most (all?) of the cultures contain two or more distinct populations.
Additional complications in the LTEE include changes in the mutation rate (Wielgloss et al., 2013); various examples of evolvability (Barrick et al., 2010; Crozat et al., 2010; Woods et al., 2011); and some very nice examples of epistasis (khan et al., 2011).
A lot of the evolution that's happening in the LTEE involves neutral or nearly-neutral alleles whose frequencies are changing due to random genetic drift (Wielgloss et al., 2011). That process is independent of population size so it wouldn't matter if the culture was 1ml, 10ml, or 100ml.
Biology is a lot more complicated than mechanical engineering. You seem to think that the entire process can be modeled as a simple "binomial probability problem" where a single beneficial either occurs or it doesn't occur. This ignores the vast literature on the problem that has been developed by population geneticists over the past 100 years. It also ignores the data.
HTHHND
So you think the LTEE is inexplicable? Competition is is an example of the first law of thermodynamics. In the LTEE, energy (glucose, except for some variants which are able to metabolize citrate) is the limiting factor for growth. And replication is the random trial for adaptation because that's when the mutations occur. And the different variants in each culture must compete for that limited resource where the more fit variant drives the less fit variants in the culture to extinction. This competition slows the rate of adaptation.
The mutation rate is a minor factor in the adaptation process. Adaptation is a binomial probability process. Changes in the mutation rate only changes that distribution slightly. What drives the adaptation process is the multiplication rule of probabilities. That is what determines how many replications a variant has to do in order to have a reasonable probability of the next beneficial mutation occurring on that variant. Did you read the paper I linked to for single selection pressures? The math is not difficult if you understand introductory probability theory.
LTEE is not an example of evolutionary drift. There are hitchhiking mutations that are carried along with the beneficial mutations but this experiment is driven by the most fit users of the energy available. The LTEE is clearly an example of evolutionary adaptation in a competitive environment. If you want to see an example of evolutionary adaptation in a non-competitive environment, study the Kishony experiment.
Are you claiming that biology does not obey the laws of physics? You clearly don't understand the physics of the LTEE. Evolutionary competition is an example of the first law of thermodynamics and evolutionary adaptation is an example of the second law of thermodynamics. And I don't model all of biology with a binomial probability distribution, only evolutionary adaptation. And I'm not the only one who has done this, read this paper:
https://www.jstor.org/stable/44149038?read-now=1&seq=1#page_scan_tab_contents
And if more than a single selection pressure is acting at a time, evolutionary adaptation must be modeled with nested binomial probability distributions. This markedly drives down the probability that the evolutionary trajectory can occur. The number of replications necessary for a lineage to travel that evolutionary trajectory becomes exponentially larger. This is why combination therapy works for the treatment of hiv.
The error that population geneticists make is conflating competition with adaptation. Haldane, Kimura, Fisher,... have done plenty of mathematics for competition thinking that fixation is the critical step in evolution. That is incorrect physically and mathematically. Competition slows adaptation and Lenski knows this:
https://www.pnas.org/content/109/13/4950.long
If you have data which shows otherwise, show us.
Sure, combination therapy is an exercise in population genetics for evolutionary adaptation and the mathematics given in your link starts to do that mathematics. If you want to see the full derivation of the mathematics with multiple simultaneous selection pressures, read this paper:
https://www.ncbi.nlm.nih.gov/pubmed/27501057
Your link is doing the math for a single step on an evolutionary trajectory for a single selection pressure.
You can't actually talk to him. The only thing you can really do is ride him out. Incidentally, his math doesn't actually deal with selection at all, only with mutation.
Kleinman's math, of course, doesn't deal with selection at all. But you can't tell him that. You can't tell him anything.
John Harshman can't explain the simplest laboratory examples of evolution and yet he thinks he understands selection. His failure to correctly explain these simple experiments is the reason why physicians have such a severe problem with drug-resistant infections and failed cancer treatments. When will Harshman take a course in introductory probability theory and learn something about evolutionary adaptation?
John Harshman can't explain the simplest laboratory examples of evolution and yet he thinks he understands selection. His failure to correctly explain these simple experiments is the reason why physicians have such a severe problem with drug-resistant infections and failed cancer treatments. When will Harshman take a course in introductory probability theory and learn something about evolutionary adaptation? When he does take that course in introductory probability theory, then he might finally understand selection and evolutionary adaptation.
John Harshman. Your right. It was Robert byers. I don't know why its UNKNOWN but i have a new computer.
Now, one might think that Harshman is wrong, because he is a molecular phylogeneticist, and not a theoretical population geneticist. So I went to read some of Kleinman's papers. I have some credentials in theoretical population genetics, having taught it for 50 years, and produced a downloadable text of theoretical population genetics, and having been the only person to produce a bibliography of the field (for the years 1867-1981).
My conclusion is that John is absolutely correct. Kleinman does calculations of probabilities of a single favorable mutant, or of multiple favorable mutants, arising in a population. There is simply no mathematics there for the changes in gene frequency of the mutants. Perhaps Kleinman is assuming that once a mutant arises, it fixes instantly, but he does not discuss that. Furthermore he makes the bizarre assertion in one of his manuscripts that JBS Haldane and Motoo Kimura both did not understand the multiplication of probabilities of independent events. Which is weird since both of them used that multiplication all the time.
I knew Kimura. I even, as an undergraduate student. saw Haldane give a lecture. I have read many of their papers. I know the logic they used in them, and that included the multiplication of probabilities of independent events. I will take John's word that there is no talking to Kleinman on this issue, but just wanted to set forth my conclusions from his papers.
Joe, those probabilities I calculate are dependent on the number of replications of the particular variant that is the measure of the absolute fitness of that variant and that determines whether that step will be taken on the particular evolutionary trajectory. Natural selection for evolutionary adaptation is not measured by relative fitness of the different variants. It is measured by the absolute fitness of the particular variant. If you are doing the mathematics of competition, then natural selection is determined by the relative fitnesses of the different variants in the population.
Now if you are familiar with Haldane's mathematics of evolution, you should recognize a blunder in Haldane's understanding of evolution which is repeated in the link you posted yesterday. You linked to this paper:
https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1002527
From that paper, this quote:
"In most population genetics models, the focus is on the fixation probability, rather than the establishment probability of a mutation. And in many models, if a mutation becomes established, it will go to fixation."
And in Haldane's "Cost of Natural Selection" paper he writes:
"The principle unit process in evolution is the substitution of one gene for another at the same locus."
This is a blunder in the understanding of evolutionary adaptation. Fixation is neither necessary nor sufficient for evolutionary adaptation to occur.
If you want to see an empirical example of evolutionary adaptation without fixation, study the Kishony experiment:
https://www.youtube.com/watch?v=Irnc6w_Gsas&t=96s
None of Kishony's populations go to fixation. The carrying capacity of the Kishony experiment is much larger than the Lenski experiment. Because of this, the Kishony variants can multiply exponentially with minimal competition from other variants. If you think fixation is occurring in the Kishony experiment, show us your calculation. The Lenski experiment, on the other hand, is carried out in a much smaller carrying capacity environment which forces his populations to compete which in turn, slows the adaptation process.
If you think you understand the population genetics of the Lenski experiment, calculate the rate of fixation of his populations, the rate of adaptation, and tell us what would happen if Lenski were to use 1ml volumes or 100ml volumes for his experiment. And if you think Lenski has done the calculation for fixation for his experiment, show us the paper.
You may have taught population genetics for 50 years but you have failed to correctly explain the evolution of drug-resistance and why cancer treatments fail.
I am not going to do some long study of the LTEE, but I thought I should document my assertion that Alan Kleinman's work ignores natural selection. Let me concentrate on his 2014 paper in the journal Statistics in Medicine, which is his first on mutation and natural selection, and is grandly entitled "The basic science and mathematics of random mutation and natural selection". It turns out to be a lot narrower than that, analysing a model where 5 favorable mutations can occur at a locus, but only if they occur in a particular order, first A, then B, then C, then D, then E.
Kleinman starts out correctly, computing in his equations (4) through (9) the probability that mutation A will not occur in the first nGA generations in a population of size n. Then he goes on in equation (10) to mutation B, trying to compute the probability of it not occurring in a subsequent GB generations. There is where things go wrong. He assumes that the 'subpopulation size" of A-containing members of the population is nA. Although he later acknowledges that the numbers of those in the population will change, he does not allow that in his math, keeping nA constant in each of the subsequent nGB generations. There is the point where I first find an error. Perhaps Alan Kleinman can explain that one specific point, rather than demanding that we all discuss the LTEE in detail.
I conclude that John Harshman is fully justified in saying that Kleinmen does not take natural selection properly into account.
Joe wrote:
"I am not going to do some long study of the LTEE, but I thought I should document my assertion that Alan Kleinman's work ignores natural selection. Let me concentrate on his 2014 paper in the journal Statistics in Medicine, which is his first on mutation and natural selection, and is grandly entitled "The basic science and mathematics of random mutation and natural selection". It turns out to be a lot narrower than that, analysing a model where 5 favorable mutations can occur at a locus, but only if they occur in a particular order, first A, then B, then C, then D, then E."
In fact, this is what Weinreich and his co-authors wrote in their study:
Darwinian evolution can follow only very few mutational paths to fitter proteins.
https://www.ncbi.nlm.nih.gov/pubmed/16601193
But note that Weinreich makes the same error on modeling adaptation that you make. From his paper:
"Thus, the relative probability of realizing any particular mutational trajectory is the product of the relative probabilities of its constituent mutations, because under our assumption the choice of each subsequent fixation is statistically independent of all previous fixations (12)."
The probability of a particular evolutionary trajectory occurring is independent of fixation at each evolutionary step, the probability at that evolutionary step depends only on the number of replications that variant can do.
Joe wrote:
"Kleinman starts out correctly, computing in his equations (4) through (9) the probability that mutation A will not occur in the first nGA generations in a population of size n. Then he goes on in equation (10) to mutation B, trying to compute the probability of it not occurring in a subsequent GB generations. There is where things go wrong. He assumes that the 'subpopulation size" of A-containing members of the population is nA. Although he later acknowledges that the numbers of those in the population will change, he does not allow that in his math, keeping nA constant in each of the subsequent nGB generations. There is the point where I first find an error. Perhaps Alan Kleinman can explain that one specific point, rather than demanding that we all discuss the LTEE in detail."
Joe, you are not quite understanding the mathematics. The product of the population size times the number of generations (n*nG) is simply the total number of replications of that particular variant. That defines the sample space for that evolutionary step. It doesn't matter how the variant accumulates those replications. I could have written that term as the SUM of all replications over generations where there are a variable number of replications each generation but the total number of replications is the appropriate number to determine the sample space and the probability of at least one beneficial mutation occurring. If you look at the graphs for the derived equations, the probabilities are a function of the total number of replications. A simple analogy is the sample space for the roll of a single die three times is the same sample space of the roll of three dice once.
When it comes to doing the mathematics of fixation for the LTEE, you have to understand how to handle mathematical discontinuities. The reason is, Lenski introduces a discontinuity on a daily basis by bottlenecking his population, taking 1% of the previous day's growth as a starting population for his next day's growth. For this reason, you can't write a simple algebraic model for fixation under these condition. This fixation process has to be modeled numerically. As an interesting sidebar on this, I studied the Haldane model from his "Cost of Natural Selection" paper where he writes an approximate solution for his D summation. You can in fact do an exact numerical solution of Haldane's model by directly doing the summation numerically and you will find that his approximate solution is accurate over most of the range.
Joe wrote:
"I conclude that John Harshman is fully justified in saying that Kleinmen does not take natural selection properly into account."
The error you (and John) make here is that natural selection is measured by the relative frequencies of the different variants in a population. This definition is only applicable when modeling competition. When modeling adaptation, natural selection has to be modeled by the absolute fitness to reproduce of a particular variant. The reason is the total number of replications of that variant determines the probability of at least one beneficial mutation occurring on one of its members. This is a common error in the field of population genetics. Competition is being conflated with evolutionary adaptation as demonstrated by what Haldane has written, what your hiv reference does and what Weinreich does in his paper.
kleinman,
"failed cancer treatments"are mainly due to the predominantly accepted dogma that mutations drive evolution and cancer is just the side effect and the inability of natural selection to sift them...
It's pretty clear that the great majority of mutations found in cancer cells are the effect of metabolic disorders causing cancer.
As an example, many cancerous cells have no mutations...
https://nutritionandmetabolism.biomedcentral.com/articles/10.1186/1743-7075-7-7
Jmac, I'm not talking about the causes of cancer, I talking about how targeted therapy will have to be used to have more successful treatment of cancers. Cancers cells are not exact clones from the founder cell(s). For this reason, mutations in the cancer cell lines will give rise to resistant variants for targeted therapy. Several years ago when I presented one of my papers at an oncology conference, I had a discussion with an oncologist who specialized in treating malignant melanoma. He said he has a targeted therapy that would knock out the cancer even with extensive metastases but was only effective for about 6 weeks. The problem is that the cancer had a diversity of cells. His treatment could kill 99+% of the cancer cells but that 1-% caused treatment failure. Depending on the number of cells in the tumor and the mutation rate, you can predict the probability of resistant variants existing in that population which would determine the number of targeted treatments necessary to have a reasonable probability of success.
Kleiman,
If mutations are not the cause of cancer but the effect, how could targeting the effects, rather than the cause, work?
As an example, you can transplant healthy mitochondrias into cancer cells with so-called cancerous mutations and the great majority of cancerous cells will not metastasize. They will likely die.
Over 11.000 different mutations have been associated with colon cancer alone. How can you predict this type of cancer?
Melanoma could be one of the few cancers not related to metabolic disorders...However, I wouldn't be surprised if melanoma turned out to be correlated with uv radiation leading to metabolic dysfunction and Warburg Effect...
Joe, you are not quite understanding the mathematics. The product of the population size times the number of generations (n*nG) is simply the total number of replications of that particular variant. That defines the sample space for that evolutionary step
You wrote it as a quantity raised to a constant power, and that raised in turn to a constant power. The mathematical notation is clear. There was no statement accompanying that equation that said that nA was a random variable.
Joe, you still don't get it. If nA=10 and the number of generations or replication is 100, you get a total of 1000 replications gives the same probability if nA=100 and the number of generations of replication is 10. You will get the same probability no matter how the replications accumulate. If the population growth is exponential, as soon as there are 1000 replications the probability will be identical to either of the cases above. The peer reviewers of this paper who are experts in probability theory had no trouble understanding this. Each replication is a random trial for the beneficial mutation. It is the total number of replications that determine the probability of that beneficial mutation to occur. It doesn't matter if it is a constant population size where the child generation replaces the parent generation one for one or if the population is growing. It is the total number of replications of the particular variant which determines the probability of that particular mutation occurring. That's why the graphs are plotted as the probability as a function of the total number of replications, not nA, not the number of generations, the total number of replications. You do understand that n*nG is not a constant, it depends on the total number of generations that constant population size replicates.
Jmac, you are conflating two concepts. One concept is a mutation that causes an otherwise normal cell to start growing abnormally without control and the other concept is a cancerous cell line that mutates altering other genes in those cancer cells. Let's say you have a monoclonal antibody that targets a specific protein in a cancer cell. The cancer cells as they are replicating accumulates mutations in its daughter cells. If one of those mutations is in the gene that produces the protein targeted by that monoclonal antibody, the change in that protein may be sufficient to change the conformation of protein so that the monoclonal antibody will no longer bind to that protein and the targeted therapy will not work on that cell. And if you understand the math that I've presented, you can predict the probability that those variant exist in that tumor based on the number of cells in that tumor and the mutation rate of those cells.
"...Jmac, you are conflating two concepts..."
I am not...
"One concept is a mutation that causes an otherwise normal cell to start growing abnormally without control and the other concept is a cancerous cell line that mutates altering other genes in those cancer cells.
They are the same concepts in a way...The daughter cell often has a dysfunctional metabolism first, leading to mutations in "care-takers" of normal cell growth leading to abnormalities..
" Emerging evidence indicates that impaired cellular energy metabolism is the defining characteristic of nearly all cancers regardless of cellular or tissue origin. In contrast to normal cells, which derive most of their usable energy from oxidative phosphorylation, most cancer cells become heavily dependent on substrate level phosphorylation to meet energy demands. Evidence is reviewed supporting a general hypothesis that genomic instability and essentially all hallmarks of cancer, including aerobic glycolysis (Warburg effect), can be linked to impaired mitochondrial function and energy metabolism. A view of cancer as primarily a metabolic disease will impact approaches to cancer management and prevention."
https://nutritionandmetabolism.biomedcentral.com/articles/10.1186/1743-7075-7-7
BTW: Your trying to prove to Joe the math is pointless as soon the omnipotent natural selection will make its appearance with his famous math 2+2=5. You can't beat the belief in omnipotence of NS...ever...
Joe, you are not quite understanding the mathematics. The product of the population size times the number of generations (n*nG) is simply the total number of replications of that particular variant. That defines the sample space for that evolutionary step. It doesn't matter how the variant accumulates those replications. I could have written that term as the SUM of all replications over generations where there are a variable number of replications each generation but the total number of replications is the appropriate number to determine the sample space and the probability of at least one beneficial mutation occurring.
Yes, you could have written it as the sum of the nA over the nGB generations. But you didn't. You wrote it as the product nA*nGB, as if nA was a constant.
Even if you were to write it as a sum, equation (10) has no theory that shows what nA would be in various generations.
Exactly. It isn't that he doesn't take selection properly into account. It's that he doesn't take it into account at all. He provides a table of the probabilities of a mutation (or several) happening at least once in n generations of a constant population, and supposes he has taken selection into account by allowing you to choose for yourself an entry on that table. There is no parameter for change either in frequency of an allele or of the size of a population possessing that allele. One cannot speak meaningfully of differences in strength of selection, since he has no parameter for any of that.
... and in a paper that he entitled "The basic science and mathematics of random mutation and natural selection"! And there's no basic equation for natural selection presented. I am surprised that reviewers let the paper go through with that far-too-general title. Usually reviewers will insist on a title that actually corresponds to what was done.
And the omnipotent natural selection has made its appearance, again...
It's amazing how natural selection is able to solve the most outrageous ideas and mathematical equations, such as 2+2=5, but it is unable to stop "cancer causing mutations" and yet it was able to evolve a 5 pound land walking mammal into a 50 ton whale...A story like that has gotta be true...
Felsenstein and Harshman never fail to disappoint...
You will note that the reviewers of that paper would have been statisticians who probably knew nothing about population genetics. They were not equipped to judge the appropriateness of the title. I presume they checked to see if he had made any mathematical errors.
"You will note that the reviewers of that paper would have been statisticians who probably knew nothing about population genetics. They were not equipped to judge the appropriateness of the title. I presume they checked to see if he had made any mathematical errors.
Neither are you...
Joe might be qualified that is as long as the omnipotent natural selection is watching over him and his math... lol
Joe wrote:
"Yes, you could have written it as the sum of the nA over the nGB generations. But you didn't. You wrote it as the product nA*nGB, as if nA was a constant.
Even if you were to write it as a sum, equation (10) has no theory that shows what nA would be in various generations."
Joe you need to go back to your introductory probability concepts and study and understand the concept of a "sample space".
https://en.wikipedia.org/wiki/Sample_space
The sample space for evolutionary adaptation only depends on the total number of replications of the particular variant, not on the rate of accumulations of the random trials (replication).
You are failing to understand a fundamental concept of evolutionary adaptation.
John wrote:
"Exactly. It isn't that he doesn't take selection properly into account. It's that he doesn't take it into account at all. He provides a table of the probabilities of a mutation (or several) happening at least once in n generations of a constant population, and supposes he has taken selection into account by allowing you to choose for yourself an entry on that table. There is no parameter for change either in frequency of an allele or of the size of a population possessing that allele. One cannot speak meaningfully of differences in strength of selection, since he has no parameter for any of that."
Just because Joe duplicates your error doesn't make your error correct. Adaptation does not require a change in frequency in variants, it requires an absolute number of replications of the particular variant to improve the probability of the next beneficial mutation occurring. This is what is demonstrated in the Kishony experiment which you have already admitted that you don't understand this experiment on the TO forum. Here's another paper which explains how evolutionary adaptation occurs using the concept of a Markov Process (with binomial probabilities). I'm sure you won't understand this paper either.
https://www.jstor.org/stable/44149038?read-now=1&seq=1#page_scan_tab_contents
John, you have a limited understanding of natural selection and that limitation is to competition. You don't understand that evolutionary adaptation is dependent on the total number of replication of the particular variant, not on the relative frequencies of variants in a population.
Joe wrote:
"... and in a paper that he entitled "The basic science and mathematics of random mutation and natural selection"! And there's no basic equation for natural selection presented. I am surprised that reviewers let the paper go through with that far-too-general title. Usually reviewers will insist on a title that actually corresponds to what was done."
Joe, I'm surprised you have so little understanding of the mathematics considering your 50 years experience. The editors of "Statistics in Medicine" asked me to write a Layman's abstract for those not experienced in this mathematics to explain evolutionary adaptation. You can find that paper here:
https://www.statisticsviews.com/details/news/10604248/Laymans-abstract-Random-mutation-and-natural-selection-a-predictable-phenomenon.html
I give a simple (minimal mathematical) explanation of how evolutionary adaptation works. The explanation starts with the paragraph with "In order for a replicator to adapt..."
You might want to look at the bottom of the page and check out the list of scientists and mathematicians on the panel who reviewed this abstract. Then you might want to study the Kishony experiment and when you understand that experiment, you will understand why you have been wrong in your understanding of evolutionary adaptation.
Hi Dr. Moran,
I just saw this very kind write up. I am glad you enjoyed the review. It was a joy for the three of us to write, and we've been happy that it has been stimulating some interesting discussion and thinking. I'm glad, too, that the balance was appreciated. We tried to make sure we didn't give anyone short shrift. It's a big subject, both sides have good arguments that deserve consideration, both for reasons of basic courtesy and because both are no doubt right to some degree.
All the best,
Zack Blount
Keep up the good work. I look forward to more papers like this.
I'll stand by my statements, and presumably Alan Kleinman will stand by his. I'm happy to let the readers judge the matter.
One detail, though. Alan Kleinman declared that Motoo Kimura and JBS Haldane did not correctly multiply probabilities of independent events. Could he give us a citation of where those mistakes occurred? The one citation to a statement in a paper by Haldane was about a different issue.
Joe wrote:
"I'll stand by my statements, and presumably Alan Kleinman will stand by his. I'm happy to let the readers judge the matter."
Joe, I watched your video:
https://natureecoevocommunity.nature.com/users/24561-richard-buggs/posts/31896-is-there-a-more-fundamental-theorem-of-natural-selection
I think it would be worthwhile for you to study the Lenski and Kishony experiments carefully because they demonstrate how the first and second laws of thermodynamics play into the evolutionary process. Competition is governed by the first law and adaptation by the second law. In the Lenski experiment, the different variants are competing for the limited glucose with the most efficient user of the glucose being fixed at each evolutionary step with the less fit users being driven to extinction. Then one of the more fit variants has to get another beneficial mutation to start the next cycle of fixation and adaptation. On the other hand, the Kishony experiment with its much larger carrying capacity doesn't force fixation on its variants. Kishony's populations can achieve the necessary replications to have a reasonable probability of getting a beneficial mutation without having to drive the less fit variants to extinction. Until you understand that competition and fixation is a distinct process from adaptation, you will not correctly describe evolution. Competition is the energy process, adaptation is the ordering (2nd law) process.
And I hope you cough has improved, if not, you should get it checked out.
Joe wrote:
"One detail, though. Alan Kleinman declared that Motoo Kimura and JBS Haldane did not correctly multiply probabilities of independent events. Could he give us a citation of where those mistakes occurred? The one citation to a statement in a paper by Haldane was about a different issue."
I didn't say that. What I said was Haldane and the authors of the hiv paper you linked to earlier conflate competition and fixation with adaptation. Competition and fixation is neither necessary nor sufficient for evolutionary adaptation to occur. In fact, competition slows the evolutionary adaptation process. Until you understand this, you will not correctly describe the physics and mathematics of evolution.
This discussion is over. I will delete any additional comments. Readers can decide for themselves whether one of the world's leading experts on population genetics understands mutation and adaptation better than a creationist mechanical engineer.
I have never understood this debate about contingency vs. determinism. Compare it to chemistry. If I put some salt in a cup of water and stir, the salt dissolves and I quickly end up with a homogeneous solution whose properties (e.g., conductivity) can be predicted solely from the amount of salt and the amount of water, i.e., the components. I don't have to know the history, because the system has reached equilibrium. It would reach exactly the same state regardless of whether the solution is shaken or stirred, or whether the salt is added all at once, or one grain at a time. History is erased by fast kinetics. It becomes inaccessible but it is also irrelevant. For any given salt solution, there is an actual history of all the molecules, but it doesn't matter.
But for systems that change with slow kinetics, we have to know the initial state and the detailed dynamics. That is, to construct a causal narrative that accounts for the current state, we have to know some things that we do not have to know if the system had reached equilibrium. This is contingency. It is simply the absence of equilibration.
Evolution is clearly slow. This allows us to infer history by comparing characters, i.e., phylogenetic inference is possible, precisely because evolution is slow. If it were fast, history would be erased. There may be local fast kinetics, e.g., some quantitative trait reaching a local optimum and staying there, but these are like swirling eddies on the surface of a wide slow river.
The fact that this debate still goes on is pretty clear evidence for Welch's answer #1 to the question of what's wrong with evolutionary biology.
sorry, reference to Welch is https://link.springer.com/article/10.1007/s10539-016-9557-8
Welch says, "Living things evolved from one or a few common ancestors, but are now characterized by their enormous abundance, variety and complexity. Each is the result of historical processes involving contingencies of distinct kinds, sometimes including one-off events, which might have been highly improbable, but which had profound consequences."
This may seem obvious to you and me (and Welch) but it's not so obvious to ultra-Darwinists like Dawkins and certainly not obvious to theistic evolutionists like Francis Collins, Simon Conway Morris, and Ken Miller.
Contingency and accident take place at two levels: the long-term history of life; and short-term changes in allele frequencies. There's data supporting both of these types of non-deterministic change. (I'm using deterministic in the colloquial sense.)
I fully support those who want to advertise and document this property of evolution because there are a surprisingly large number of scientists who don't subscribe to it.
Arlin, I think you must be aware of these scientists who don't understand evolution. They are the same ones who resist the idea that mutation and mutation bias can play an important role in evolution.
Right but ultimately "contingency" is a crutch, for reasons explained earlier in What 'limits' adaptation. Contingency merely signals departure from the ideal of finalism or equilibration. It is not a cause.
Larry, you are a stupid, harmful, mathematically incompetent nitwit. It is people like you that is the reason we have drug-resistant infections and failed cancer treatments. You are a stupid, harmful ass. And tell Joe that I'm not going to buzz off. Stick with your biased and ignorant echo chamber.
HTHHND you stupid jackass.
Ladies and gentlemen I give you Alan Kleinman. What a professional!
Still, he gives good advice.
Anyone else check out Kleinman's ms? I find it amusing that he uses the royal "we" in the abstract.
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