Does Basener and Sanford’s model of mutation versus selection show that deleterious mutations are unstoppable?

by Joe Felsenstein and Michael Lynch

The blogs of creationists and advocates of ID have been abuzz lately about exciting new work by William Basener and John Sanford. In a peer-reviewed paper at Journal of Mathematical Biology, they have presented a mathematical model of mutation and natural selection in a haploid population, and they find in one realistic case that natural selection is unable to prevent the continual decline of fitness. This is presented as correcting R.A. Fisher’s 1930 “Fundamental Theorem of Natural Selection”, which they argue is the basis for all subsequent theory in population genetics. The blog postings on that will be found here, here, here, here, here, here, and here.

One of us (JF) has argued at The Skeptical Zone that they have misread the literature on population genetics. The theory of mutation and natural selection developed during the 1920s, was relatively fully developed before Fisher’s 1930 book. Fisher’s FTNS has been difficult to understand, and subsequent work has not depended on it. But that still leaves us with the issue of whether the B and S simulations show some startling behavior, with deleterious mutations seemingly unable to be prevented from continually rising in frequency. Let’s take a closer look at their simulations.

Basener and Sanford show equations, mostly mostly taken from a paper by Claus Wilke, for changes in genotype frequencies in a haploid, asexual species experiencing mutation and natural selection. They keep track of the distribution of the values of fitness on a continuous scale time scale. Genotypes at different values of the fitness scale have different birth rates. There is a distribution of fitness effects of mutations, as displacements on the fitness scale. An important detail is that the genotypes are haploid and asexual — they have no recombination, so they do not mate.

After giving the equations for this model, they present runs of a simulation program. In some runs with distributions of mutations that show equal numbers of beneficial and deleterious mutations all goes as expected — the genetic variance in the population rises, and as it does the mean fitness rises more and more. But in their final case, which they argue is more realistic, there are mostly deleterious mutations. The startling outcome in the simulation in that case is there absence of an equilibrium between mutation and selection. Instead the deleterious mutations go to fixation in the population, and the mean fitness of the population steadily declines.

Why does that happen? For deleterious mutations in large populations, we typically see them come to a low equilibrium frequency reflecting a balance between mutation and selection. But they’re not doing that at high mutation rates!

The key is the absence of recombination in these clonally-reproducing haploid organisms. In effect each haploid organism is passed on whole, as if it were a copy of a single gene. So the frequencies of the mutant alleles should reflect the balance between the selection coefficient against the mutant (which is said to be near 0.001 in their simulation) versus the mutation rate. But they have one mutation per generation per haploid individual. Thus the mutation rate is, in effect, 1000 times the selection coefficient against the mutant allele. The selection coefficient of 0.001 means about a 0.1% decline in the frequency of a deleterious allele per generation, which is overwhelmed when one new mutant per individual comes in each generation.

In the usual calculations of the balance between mutation and selection, the mutation rate is smaller than the selection coefficient against the mutant. With (say) 20,000 loci (genes) the mutation rate per locus would be 1/20,000 = 0.00005. That would predict an equilibrium frequency near 0.00005/0.001, or 0.05, at each locus. But if the mutation rate were 1, we predict no equilibrium, but rather that the mutant allele is driven to fixation because the selection is too weak to counteract that large a rate of mutation. So there is really nothing new here. In fact 91 years ago J.B.S. Haldane, in his 1927 paper on the balance between selection and mutation, wrote that “To sum up, if selection acts against mutation, it is ineffective provided that the rate of mutation is greater than the coefficient of selection.”

If Basener and Sanford’s simulation allowed recombination between the genes, the outcome would be very different — there would be an equilibrium gene frequency at each locus, with no tendency of the mutant alleles at the individual loci to rise to fixation.

If selection acted individually at each locus, with growth rates for each haploid genotype being added across loci, a similar result would be expected, even without recombination. But in the Basener/Stanford simulation the fitnesses do not add — instead they generate linkage disequilibrium, in this case negative associations that leave us with selection at the different loci opposing each other. Add in recombination, and there would be a dramatically different, and much more conventional, result.

Technical Oddities

Most readers may want to stop there. We add this section for those more familiar with population genetics theory, simply to point out some mysteries connected with the Basener/Stanford simulations:

1. One odd assumption that they make is that any fitness class that has a frequency below 1 part in a billion gets set to 0. This is not a reasonable way to take genetic drift into account, as all fitness classes are subject to random fluctuations. We imagine such a treatment is a minor issue, relative to the enormous mutation pressure imposed in their study. But someone should check this, which can be done as their Javascript source can be downloaded and then made comprehensible by a Javascript beautifier.

2. The behavior of their iterations in some cases is, well, weird. In the crucial final simulation, the genetic variance of fitness rises, reaches a limit, bounces sharply off it, and from then on decreases. We’re not sure why, and suspect a program bug, which we haven’t noticed. We have found that if we run the simulation for many more generations, such odd bouncings of the mean and variance off of upper and lower limits are ultimately seen. We don’t think that this has much to do with mutation overwhelming selection, though.

3. We note one mistake in the Basener and Sanford work. The organisms’ death rates are 0.1 per time step. That would suggest a generation time of about 10 time steps. But Basener and Stanford take there to be one generation per unit of time. That is incorrect. However the mutation rate and the selection coefficient are still 1 and 0.001 per generation, even if the generations are 10 units of time.

Joe Felsenstein, originally trained as a theoretical population geneticist, is an evolutionary biologist who is Professor Emeritus in the Department of Genome Sciences and the Department of Biology at the University of Washington, Seattle. He is the author of the books “Inferring Phylogenies” and “Theoretical Evolutionary Genetics”. He frequently posts and comments here.

and

Michael Lynch is the director of the Biodesign Center for Mechanisms of Evolution at Arizona State University, and author of “The Origins of Genome Architecture” and, with Bruce Walsh, of “Genetics and Analysis of Quantitative Traits”. Six of his papers are cited in the Basener/Stanford paper.

318 thoughts on “Does Basener and Sanford’s model of mutation versus selection show that deleterious mutations are unstoppable?

  1. phoodoo: What were they doing before they could fly, falling out of trees, and bumping into moths?

    Don’t argue with Adapa! He must’ve been there watching bats choosing to evolve echolocation over quantum coherence for navigation…

  2. phoodoo:
    Then they suddenly developed a hankering for mosquitoes? So flying was convenient.

    Flying must have been quite beneficial since there are currently more species in the order chiroptera than any other mammalian order.

    Why are you two ID geniuses afraid to tell me if evolving the ability to fly was a gain of function / gain of information?

  3. Adapa: Flying must have been quite beneficial since there are currently more species in the order chiroptera than any other mammalian order.

    Why are you two ID geniuses afraid to tell me if evolving the ability to fly was a gain of function / gain of information?

    Because we need still to figure out what the just so story is first.

    “It must have been, because it is…” is not that convincing.

  4. phoodoo: Because we need still to figure out what the just so story is first.

    “It must have been, because it is…” is not that convincing.

    Your vast ignorance of evolutionary theory and its evidence is showing again. Not to mention your ever present cowardice in refusing to commit to any ID position.

  5. Adapa: Your vast ignorance of evolutionary theory and its evidence is showing again. Not to mention your ever present cowardice in refusing to commit to any ID position.

    What does that have to do with them eating acorns?

  6. phoodoo: What does that have to do with them eating acorns?

    As a total non-biologist, I would speculate that bats’ ancestors were much like shrews and mice, with similar diets. I can imagine the ability to locate prey in the dark would be helpful, and selected for leading to a trend toward improvement.

    Seems to me you tend (in general) to regard organisms as having just kind of appeared, poof, in their present form and lifestyle. And you continually express amazement that “evolutionists” could believe such a thing. I suspect it’s a sort of timescale blindness.

  7. Flint: As a total non-biologist, I would speculate that bats’ ancestors were much like shrews and mice, with similar diets. I can imagine the ability to locate prey in the dark would be helpful, and selected for leading to a trend toward improvement.

    Seems to me you tend (in general) to regard organisms as having just kind of appeared, poof, in their present form and lifestyle. And you continually express amazement that “evolutionists” could believe such a thing. I suspect it’s a sort of timescale blindness.

    I am perfectly happy to have evolutionists try to explain what it means to slowly learn to fly, and slowly learn to echolocate and slowly learn to balance…

    What’s the first steps towards a mice flying look like? How much advantage would that be? I wonder how long flying squirrels have been around, when are they going to learn to actually fly? How long does it take?

  8. This might be off thread but its based on mutations being positive or negative so i’m not sure. the host of the thread should make a verdict.
    Anyways.
    flightlessness in birds has nothing to do with loss of fitness. flightlessness is so common in island fossil records, and common enough in large landmass fossil records that its clearly a positive thing for that creature.
    (In fact i speculate all “dino’ theropods/rapters etc were just big flightless ground birds. Not reptiles/dinos etc)
    I don’t see flightlessness as coming from mutations being selected on.
    Not on a few who create a new population.
    Its as if all of the population ,m after a time, atrophy in their wings unrelated to randome mutations.
    Mutations as a force for new populations I never see in real life natural history. yes genetic change but it must be triggered in some way.

  9. petrushka: Regarding small genomes: doesn’t that imply less junk and the relative risk that a mutation would be critical? Isn’t it the rate of mutation in functional sequences that counts, rather than the number?

    Bacteria have less junk, but also a smaller functional genome. This represents a smaller mutational target, so bacteria really acquire less deleterious mutations per individual per generation than eukaryotes.
    And it is the number of deleterious mutations that counts, not the rate. This can be easily seen when you realise that to prevent the accumulation of deleterious mutations, the number of introduced mutations needs to equal the number removed by purifying selection. If every individual acquires at least one deleterious mutation, this can only be accomplished when the total population perishes. Species with very large functional genomes will find themselves close to this limit.

  10. petrushka: How does the number of generations in LTEE compare with the number of generations in the OP simulation? How long will LTEE have to run in order to test meltdown?

    There have been experiments on mutational meltdown. Funnily enough, it was Sal who provided a link to such a study, performed by a former colleague of mine (Arjan de Visser). It’s in yeast, not bacteria but you should get a feel for the population sizes involed. Basically, population sizes in the LTEE are too large to result in mutational meltdown.

  11. phoodoo: You are unable to address his issue, but you want to be a good cheerleader? You can’t even reach the level of criticizing his post.

    Phoodoo, it has been explained to J-Mac why this is a nonsensical argument but he has proven himself incapable of understanding. To spell it out: Regressive evolution simply is not an examples of mutational meltdown.
    I do expect a bit more from you.

  12. phoodoo:

    “It must have been, because it is…” is not that convincing.

    As usual, this is all you have to argue with. It all comes down to “I don’t believe it”.

    Great, have fun with that.

  13. Rumraket: As usual, this is all you have to argue with. It all comes down to “I don’t believe it”.

    Great, have fun with that.

    But not you, because you believe! You need to believe, you must believe! Your worldview is at stake. Have faith!

  14. Corneel: There have been experiments on mutational meltdown. Funnily enough, it was Sal who provided a link to such a study, performed by a former colleague of mine (Arjan de Visser). It’s in yeast, not bacteria but you should get a feel for the population sizes involed. Basically,population sizes in the LTEE are too large to result in mutational meltdown.

    Oh goodness, I expected more from you. IDists don’t believe that mutational meltdown is inevitable, rather they believe that if life were not designed, we should expect meltdown, but since that is not what happens in real life, something must be preventing it.

    By showing that in fact life can sustain, you are not making the case for random, yes I said it, unguided evolution. Life strives to succeed, this is what real life experiments tend to show.

  15. phoodoo: But not you, because you believe!You need to believe, you must believe!Your worldview is at stake.Have faith!

    Thank you for another total non-argument.

  16. phoodoo: By showing that in fact life can sustain, you are not making the case for random, yes I said it, unguided evolution.

    That’s literally what it shows. That in fact, random, unguided evolution is up to the task. Your ability to just engage in denial is not an argument.

  17. phoodoo: IDists don’t believe that mutational meltdown is inevitable, rather they believe that if life were not designed, we should expect meltdown,

    You are going to have to explain precisely why “designed” life is not subject to the same mutational load and selective pressure as “random” life : how does being designed affect the math?

    but since that is not what happens in real life, something must be preventing it.

    or your math is wrong. Which is the topic of this thread.

  18. J-Mac: Aren’t flightless birds the perfect examples of deleterious mutations overpowering natural selection?

    Isn’t the loss of flight the realistic evidence that natural selection is unable to prevent the continual decline of fitness?

    Even better example:

    Aren’t blind cave fish the perfect examples of deleterious mutations overpowering natural selection?
    Isn’t the loss of sight the realistic evidence that natural selection is unable to prevent the continual decline of fitness?

    Yeah. If and only if it is perpetually dark out.
    That’s a puzzler.

  19. phoodoo: IDists don’t believe that mutational meltdown is inevitable, rather they believe that if life were not designed, we should expect meltdown, but since that is not what happens in real life, something must be preventing it.

    That is not what Sal has been telling me (I take it that he qualifies as an IDist). What I got from him is that all species (including humans) started out with perfect genomes, but have been accumulating genetic defects (Genetic Entropy he calls it)

    But please tell me. Why would species experience mutational meltdown if they were not designed? I would expect purifying selection to prevent such a thing. Also, what do you think is preventing mutational meltdown in populations of designed organisms, if not selection?

    ETA: correction

  20. DNA_Jock: You are going to have to explain precisely why “designed” life is not subject to the same mutational load and selective pressure as “random” life : how does being designed affect the math?

    You don’t the difference between math and reality? What a surprise.

    The study he referenced is about real life, not math Jock. You should try looking at it sometime.

  21. Corneel,

    Corneel: Why would species experience mutational meltdown if they were not designed?

    Cause of the math I guess, ask Jock.

    He’s the one who prefers numbers to observation. But he may be too busy with his calculator to look up.

  22. phoodoo: Corneel: Why would species experience mutational meltdown if they were not designed?

    Cause of the math I guess, ask Jock.

    I am asking you, phoodoo. Living organisms acquire deleterious mutations, regardless of whether they have been designed or not. In my book, the thing preventing the buildup of a critical mutational burden is natural selection of the purifying kind.

    Yet you tell us that life sustains, because it strives to succeed. So what happens to the deleterious mutants in your scenario, and why is that mysterious mechanism restricted to designed organisms?

  23. Corneel: I am asking you, phoodoo. Living organisms acquire deleterious mutations, regardless of whether they have been designed or not. In my book, the thing preventing the buildup of a critical mutational burden is natural selection of the purifying kind.

    Yet you tell us that life sustains, because it strives to succeed. So what happens to the deleterious mutants in your scenario, and why is that mysterious mechanism restricted to designed organisms?

    I don’t believe in natural selection, so it doesn’t make sense for me to speculate about what it could do.

    But when people talk about natural selection, in light of all the modern information about biology, what exactly are you talking about-natural selection working on random mutations? Does anyone really believe in random mutations as doing anything anymore? Do you think hox genes, and evo-devo came about through random mutations? That’s ridiculous in my opinion. Do you think the brain developed through random mutations? Again, preposterous and requires such an imaginative just so story as to be silly.

    There is no such thing as random mutations doing anything complex or meaning whatsoever. So if we don’t accept random mutations, what exactly is natural selection working on? Without that component, there really is nothing to argue about. Something besides random is at work.

  24. phoodoo: I don’t believe in natural selection, so it doesn’t make sense for me to speculate about what it could do.

    You’re not being asked to speculate about natural selection, you’re being asked to give an explanation IN PLACE OF natural selection.

    But when people talk about natural selection, in light of all the modern information about biology, what exactly are you talking about-natural selection working on random mutations? Does anyone really believe in random mutations as doing anything anymore?

    Yes, because that’s what the evidence shows.

    Do you think hox genes, and evo-devo came about through random mutations?

    Yes. Every single one of them. Because that’s what the evidence shows.

    That’s ridiculous in my opinion.

    Thank you for your opinion.

    Do you think the brain developed through random mutations?

    Yes.

    Again, preposterous and requires such an imaginative just so story as to be silly.

    Thank you for your opinion.

    There is no such thing as random mutations doing anything complex or meaning whatsoever.

    Thank you for your opinion.

    So if we don’t accept random mutations, what exactly is natural selection working on?

    I agree, if you reject all the established facts of biology, you can’t make sense of biology.

    So, what do you now use to explain biology?

    Without that component, there really is nothing to argue about. Something besides random is at work.

    What does that even mean?

    You’re saying mutations have no effect, right? And natural selection doesn’t happen, right?

    Cool, now what do you propose is what happens to people, or other organisms, who suffer debilitating heritable diseases? How do those disease happen, if not by mutations? How are they heritable, if not through genetics? What prevents these from accumulating over time, if not purifying selection?

    You didn’t answer his question. What is it that prevents deleterious mutations from accumulating in organisms that “strives to succeed”? What does that even mean? What are we supposed to imagine is going on here, on your account?

    So there’s this population, like Homo sapiens, and we suffer deleterious genetic mutations that cause all sorts of genetic diseases. Or maybe they’re not mutations, they’re something else, yet that something else causes diseases which are heritable. Yet we persist, how?

    Do people, or plants, or animals, or bacteria, just “want” to live and if they somehow want it hard enough, the mutations(or what you propose in their place) don’t happen, or have no effect, or what? Or if the organisms just “strive to succeed” hard enough then they don’t suffer heritable diseases? How does this striving to succeed-thing happen? Is it sheer force of will or what?

    Please explain how you propose to solve this issue.

  25. phoodoo: Do you think hox genes, and evo-devo came about through random mutations? That’s ridiculous in my opinion. Do you think the brain developed through random mutations? Again, preposterous and requires such an imaginative just so story as to be silly.

    Yes, I thought that was the problem, but you need to realise this is a different issue. Whether natural selection is incapable of promoting the emergence of complex features is a very different question from whether it can prevent genetic defects from spreading.

    phoodoo: There is no such thing as random mutations doing anything complex or meaning whatsoever. So if we don’t accept random mutations, what exactly is natural selection working on? Without that component, there really is nothing to argue about. Something besides random is at work.

    If we were to grant you that all life was designed and beneficial mutations do not exist, then I would expect that any random mutation to the genome would be destructive (this is what Sal is arguing). Those mutations impact fitness negatively, and hence provide a substrate for natural selection to work on. Of course, the only work that natural selection can do in this case is preventing a species from going extinct from the accrual of deleterious mutations. Species cannot adapt or evolve new features without the help of the Designer.

    Bottom line: Even the ID universe needs natural selection to do the dirty work. That, or accept that all species are en route to extinction. The latter is what is implied by the B&S paper.

  26. Corneel: But please tell me. Why would species experience mutational meltdown if they were not designed? I would expect purifying selection to prevent such a thing. Also, what do you think is preventing mutational meltdown in populations of designed organisms, if not selection?

    That’s one of the elephants in the creationist room. Intelligent Design proponents are touting Basener and Sanford’s study, but fail to acknowledge that Sandford’s agenda (I don’t know about Basener) is YEC. This is the paradigm that his “research” is trying to promote. It does not even attempt to support “design.”

  27. We don’t seem to be getting much in the way of relevant creationist responses to Joe Felsenstein and Mike Lynch’s article. Just clueless rants about bats and such. Even Sal, the local creationist math whiz, has deferred comment. I guess we’ll have to wait and see if Basener and Sanford deign to grace us with their presence.

  28. Corneel,

    Corneel: But please tell me. Why would species experience mutational meltdown if they were not designed? I would expect purifying selection to prevent such a thing. Also, what do you think is preventing mutational meltdown in populations of designed organisms, if not selection?

    DNA repair. A lot of mutations that start to break down sequences can sneak through prior to an organism losing reproductive capability unless a repair mechanism is constantly fixing these mutations.

  29. Alan Fox,

    No need to apologize. I don’t really expect creationists to have the mental wherewithal to respond meaningfully, nor the integrity to acknowledge that they can’t. Not much you can do about that.

  30. OP: ” There is a distribution of fitness effects of mutations, as displacements on the fitness scale.”
    A question:
    Does this distribution of effects change as organisms move down the fitness scale?
    Should it not?

    An observation:
    HGT works as a poor man’s recombination. I could imagine situations (for haploid asexual organisms) where they would be headed for mutational meltdown, if not for HGT.
    And the organisms that appear most permissive of HGT are…

  31. colewd:
    Corneel,

    DNA repair.A lot of mutations that start to break down sequences can sneak through prior to an organism losing reproductive capability unless a repair mechanism is constantly fixing these mutations.

    People keep telling you, and you keep forgetting, that observed mutation rates are post-repair.

  32. Joe Felsenstein: phoodoo doesn’t believe in natural selection but does acknowledge that genotypes can differ in viability and in fertility. Go figure.

    And phoodoo voices no objection to doophoo, who tells us not only that natural selection is a tautology, but also that her view is shared by all IDists.

  33. Joe Felsenstein:
    phoodoo doesn’t believe in natural selection but does acknowledge that genotypes can differ in viability and in fertility.Go figure.

    I wouldn’t go as far…
    But its obvious that phoodoo and many others have enough evidence to doubt the omnipotence and the creative powers of natural selection that Darwinists and population genetics bamboozled us with…

  34. John:

    People keep telling you, and you keep forgetting, that observed mutation rates are post-repair.

    colewd:

    Since repair is a continuous process how do you know?

    Bill seems to be under the impression that after a mutation is established, the repair mechanisms can go in there and revert the DNA to its original state.

    He made the same mistake in another thread, and I think it was Allan who corrected him.

  35. Rumraket,

    1. Mutations still demonstrably happens.
    2. Compare the mutation rates between normal and repair-pathway knockouts.

    Fair point, however this won’t show if they are accumulating or just appearing and then eventually corrected for. I agree that mutations happen that cannot be repaired the question is at what rate?

  36. colewd:

    I agree that mutations happen that cannot be repaired the question is at what rate?

    Christ, Bill. That’s exactly what John was talking about:

    People keep telling you, and you keep forgetting, that observed mutation rates are post-repair.

  37. colewd: Fair point, however this won’t show if they are accumulating or just appearing and then eventually corrected for.

    Bill, the error-correction happens WHEN mutations happen. One of the proofreading mechanisms works by detecting mispaired DNA sequences (they “stick out” so to speak), where for example T (which should be a G) is put opposite to C. But the repair mechanism can mistakenly change the sequence so it changes the C to an A, so it properly pairs with T. At that stage the DNA will look “normal” to the proofreading mechanism, so it can’t go back to a G-C basepair.

    When mutations slip through this proofreading, they can no longer be corrected, because the machinery responsible for correcting, for example mismatches, doesn’t “know” what the “correct” sequence used to be. To that machinery, it will just appear to be “normal” DNA. There’s a T there opposite to an A, where there used to be a G opposite to C.

  38. keiths,

    People keep telling you, and you keep forgetting, that observed mutation rates are post-repair.

    How do you propose he differentiate between mutation that is a guanine to uracil reaction which cannot be mismatched repaired to another type that can be repaired? At this point are these differences being accounted for when counting mutation rates?

    Since mutation and repair is continuous there is no such thing as post repair the genome is not static.

  39. Rumraket,

    Bill, the error-correction happens WHEN mutations happen. One of the proofreading mechanisms works by detecting mispaired DNA sequences (they “stick out” so to speak), where for example T (which should be a G) is put opposite to C. But the repair mechanism can mistakenly change the sequence so it changes the C to an A, so it properly pairs with T. At that stage the DNA will look “normal” to the proofreading mechanism, so it can’t go back to a G-C basepair.

    When mutations slip through this proofreading, they can no longer be corrected, because the machinery responsible for correcting, for example mismatches, doesn’t “know” what the “correct” sequence used to be. To that machinery, it will just appear to be “normal” DNA. There’s a T there opposite to an A, where there used to be a G opposite to C.

    I understand this. Look at my response to keiths. Are we measuring mutations that we know the machinery cannot repair?

  40. colewd: I understand this. Look at my response to keiths. Are we measuring mutations that we know the machinery cannot repair?

    We know a mutation has happened simply by comparing DNA sequences of individuals and seeing where they differ, or by having sequenced ancestors and descendants and seeing where they differ.

    If the ancestor was sequenced to have:
    AGCTAGCTGATGATGC
    and we sequence the descendant to be:
    CGCTAGCTGATGATGC
    Then we know the first A mutated to C at some point.

    And yes, once those mutations have slipped through, they can no longer be corrected, because the repair machinery in the descendant has no way of knowing what the DNA in the ancestor looks like. It can only make corrections to something that “looks wrong” (for example mismatches, or methylations, or single/double-strand breaks).

    It’s all explained here pretty well: An Introduction to Genetic Analysis. (7th edition): Spontaneous mutations

  41. colewd:

    I understand this. Look at my response to keiths. Are we measuring mutations that we know the machinery cannot repair?

    Jesus H. Christ, Bill. For the third time, look at John’s statement:

    People keep telling you, and you keep forgetting, that observed mutation rates are post-repair.

  42. Rumraket,

    If the ancestor was sequenced to have:
    AGCTAGCTGATGATGC
    and we sequence the descendant to be:
    CGCTAGCTGATGATGC
    Then we know the first A mutated to C at some point.

    In the case of human DNA comparison there are two ancestors to every child. How do we know this difference is not caused by genetic recombination?

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