Good Math, Bad Math

My friend Razib, who is one of my
fellow ScienceBloggers sent me href="http://blog.beliefnet.com/cityofbrass/2009/01/is-evolution-sufficient.html">a
link to an interest attempt by creationist at arguing why evolution can’t
possibly work.

I say interesting, because it’s at least a little bit unusual in
its approach. It’s not just the same old regurgitation of the same talking
points. It’s still not a great argument, but it’s at least not as boring as
staring at the same stupid arguments over and over again. Alas, it’s not entirely
new, either. It’s an argument that the mutation rates required for humans to have evolved from a primate ancestor would have to be impossibly high.

In this case, the guy starts off with a gambit that always annoys the heck
out of me. That is, he starts by claiming to be a scientific guy who doesn’t
believe in all that ID rubbish.

Partly because I just went to Africa and flew over (but did not have a chance to actually visit) the Great Rift Valley (also known as the Cradle of Mankind), I’ve been thinking a bit about evolutionary theory of late. I am a scientist, but not a biologist – my field is medical physics. Still, my background makes me biased towards the scientific establishment and I am an ardent believer in the scientific method. While technically as a deeply religious person I do believe in “intelligent design” (in the abstract) I don’t believe in Intelligent Design as promoted by the various evolution-denialists in the political arena. I am quite strictly against introducing religious theories such as ID into the science curriculum.

Of course, from that point, it’s straight into the
ID rubbish for the rest of the argument.

He tries to use a mathematical argument for why evolution can’t work. But before
he really gets to it, he leads into it by saying something that I find remarkably strange.

From an engineering and aesthetic perspective, I have trouble with the idea that a system so complex as DNA and gene expression can be so rigid. My intuition is that DNA does not posess enough degrees of freedom to “encode” life as we know it. But how can I test that intuition without getting a PhD in genetics? I think I’ve come up with a way, though of course it is crude and rife with bland layman assumptions. Still, bear with me (and I hope to attract some attention to this from experts so we can refine it).

I really don’t understand what he means by this.

Coming at it from an engineering viewpoint, it makes no sense. DNA is not a simple, rigid system. In fact, part of what makes it so fascinating is its very fluidity. When we look at real gene sequences, to see how things have changed,
we find some really amazing things that demonstrate just how fluid DNA is. For one example, there’s the regulatory DNA – that is, there are non-protein-coding sequences that act as regulators for turning on and off the production of
proteins by other, coding regions. The location of a regulating region relative to the coding region that it regulate isn’t fixed. – different regulating sequences appear different distances from what they regulate.

Looked at from a mathematical viewpoint, it doesn’t make sense either. In the context of the argument that he’s going to move on to make, DNA is mathematically an information carrier – and talking about its “rigidity” in that context is meaningless.

Looked at biologically, it doesn’t make sense either. DNA is not rigid, biologically – that’s why mutations happen. If DNA were rigid, if it were able to reliably copy without error or change, and it always expressed itself in exactly the same way, there wouldn’t be any mutation at all.

Anyway, moving on…

Let’s take some basic numbers. There are about 20,000 genes in the human genome, with an average size of 50 kilobases (ie, 50,000 base pairs. Remember DNA is a double-helix, unlike RNA). Also, we are often told that humans and chimpanzees differ in their genomes by only 1%. Actually, that figure is only for genes where humans and chimps totally differm but there are some genes where the variation between teh species might not be so absolute. I’ll use 5% instead. Finally, we know that according to best estimates, humand and chimpanzees diverged from their common ancestor about 5 million years ago.

This is already pretty bad. If you’re just speculating, pull rough guesstimates
out of thin air is reasonable. It’s never good, but if you’re playing
with ballpark estimates, and you’ve got no way of finding out what the correct numbers are, then estimates are fine. But that’s not the case here. This is a number that can be looked up with a google search. But he doesn’t bother – he just takes a
rough ballpark number that he vaguely remembers.

But it’s worse than that. If you’re being scientific, and you’re making an
honest scientific argument, then if you use wild-ass estimates, you use
conservative estimates. That is, you don’t skew anything in your
favor. If you’re not sure, you use the honest estimate that’s worst for
your argument. But instead, he takes his vague memory of human/chimp DNA similarity,
and then multiplies it by five based on flimsy handwaving, in a way that makes it more favorable for his argument.

Taking these bits of data, we can actually estimate the required rate of evolution in terms of point mutations in DNA needed to turn a chimp into an ape. Of course, humans did not evolve from chimps, so we would then halve the rate we calculate to get the change from the common ancestor of both to humans (or chimps). So, let’s do the math.

Actually, let’s not do the math yet. Before we do the math, we need to
make sure that we understand what we’re doing, in order to make sure that we
do the correct math.

And he’s not. The key phrase: “required rate of evolution in terms of point mutations“. He’s going to only consider point mutation – one very restrictive kind of mutation. And he’s only going to consider independent point mutations.

That’s another example of stacking the numbers to benefit his argument. In reality, there are simple point mutations. There are also copies,
transpositions, deletions, breaks. There are point mutations that effectively
produce large numbers of new point mutations – for example, a frame shift. But
he completely discards all of those.

Ok, so now that we know that he’s stacked his math to try to make things
work out the way that he wants them to, let’s look at his math. (Note: I’ve change the formatting a bit to make it easier to read in a blockquote. The original text used indents, rather than bullets.)

  • 20,000 genes x 50,000 base pairs = 1 billion base pairs
  • 5% difference between humans and chimps = 50 million base pairs
  • rate of change = 1/2 * 50 million base pairs / 5 million years = 5 base pairs per year

So, to go from the common ancestor of humans and chimps, to modern humans, the average rate of mutation required would be 5 base pairs per year. This seems like a very high rate to me; if we discretize into generations of 25 years each, then we are talking about 125 base pairs every generation.

125 base pairs per generation. Stacking things very much in his favor,
by increasing the magnitude of difference between human and chimp DNA; by limiting mutation to only independent point mutations; and by choosing an extremely long generation length (really, historically, when have primates averaged
25 year generations?), the worst he can make things is to require a population-change of 125 base pairs out of (by his own figures) one billion base pairs in the genome, per generation. In other words, he requires that
each generation’s genome differs from the last in approximately 0.0000125% of
its genome.

Skewing the numbers, that’s the best he can get.

Getting that rate of change to fix in a population is unlikely – but not impossible. So cheating left and right, skewing things in arbitrary
ways, making things up, limiting the mutation process, slowing down the
rate of reproduction, exaggerating the required amount of change – all that,
and he still can’t produce a scenario where it’s impossible.

The argument just doesn’t work.

Comments

  1. #1 James Brennan
    February 3, 2009

    Interestingly, an estimate of 175 mutations per diploid genome per generation is given by Michael W. Nachman and Susan L. Crowell, Estimate of the Mutation Rate per Nucleotide in Humans, Genetics, Vol. 156, 297-304, September 2000

  2. #2 Tex
    February 4, 2009

    Actually, for all of the hand waving and general cluelessness on display in his arguments, this guy somehow got the right answer on mutation rates, but his conclusion that it cannot happen that fast is very wrong.

    Alan Wilson showed 20 years ago that unselected mutations (including the vast majority of those that separate chimps and humans) accumulate at a rate of about 1% per million years. Given a 5 myr divergence between these primate lineages, 5% difference is very close to what real scientists predict (and what the genomes show).

    Ochman H, Wilson AC. 1987. “Evolution in bacteria: evidence for a universal substitution rate in cellular genomes”. J Mol Evol. 26: 74–86.

  3. #3 Lowk
    February 4, 2009

    Plus, that is 125 mutations per generation throughout the entire population, which makes it even less difficult to think of (you still require all the mutations to go to fixation, but that )

    The distressing thing is that he just gives this number, 5bp/year, with no real indication of how this compares to, well, anything. Human beings have a SNP (a site where at least 2 people have different base pairs) every 1000 base pairs. This means that, given his his 1Gb genome size (wtf?), there are 1 million sites at which people differ (conservatively, any two individuals may differ by 10,000 of these). So the diversity in the human population is already 1/50th of the required changes, as he has defined it, are already present in the current human population!

  4. #4 Noel Grandin
    February 4, 2009

    Mark, you’re being a little mean.

    This kind of ballpark estimating was encouraged in my physics studies so that students could get a feel for the magnitude of answers without requiring exhaustive investigation.

    Judging from the other comments, he seems to have be in the right neighborhood, so it can’t have been too bad.

  5. #5 jeff
    February 4, 2009

    I agree with Noel, these kind of calculations are useful. But you can’t misinterpret them. Getting 125 from a simple argument means the true number is probably somewhere between 10 and 1000. And as others have noted, 10-1000 is correct.

  6. #6 Uncle Al
    February 4, 2009

    How much mutation is required to significantly diverge bonobos (sex-obsessed chimps), 98.5 to 99% genetic homology, from humans (sex-obsessed Hugh Heffner)? Perhaps just one mutation.

    Sialic acid, N-glycolyl-neuraminic acid (Neu5Gc), is a modified form form Neu5Ac by addition of an oxygen atom (methylene to carbonyl). The human form lacks the oxygenation. That changes the shape of the molecule in a region that could alter how it is recognized by other molecules, whether pathogens or cellular messengers.

    Homo sapiens‘ membranes contain only the Neu5Ac form of sialic acid; all other great apes have a roughly 50%/50% mix of the Neu5Ac and Neu5Gc forms. Perhaps Neu5Gc absence was the tipping point.

  7. #7 Mark C. Chu-Carroll
    February 4, 2009

    Re #4, #5:

    I didn’t mean to say that back of the envelope estimate calculations are useless. What I was trying to say was that there are two important things that you should do when you’re playing with rough estimates.

    (1) Remember that it’s an estimate. You need to keep track of just how wild your estimate is. The article that I was critiquing used at most two significant figures in his guestimates, and arbitrarily bounced a number upwards by a factor of five, without justification. Then he used it to try to produce a very specific number – not a range, but a single number. And then he tried to use that number as the basis of an argument. But the imprecision of the input to his computation means that the actual number could easily differ by one or even two orders of magnitude – but he doesn’t acknowledge that. He treats his wild-ass estimate as if its the result of carefully measured data.

    (2) There’s no excuse for using wild guesses when actual concrete numbers are easily available. It’s fine to sketch out something to get an order-of-magnitude sense of whether it’s worth the trouble of doing a detailed computation. But if you’re going to publish an argument based on a computation, and the specific inputs to your computation are available in a matter of seconds, then using the wild guesses is not acceptable.

    I just hit up Google to get some numbers:
    (1) Human genome size: roughly 3 billion base pairs. Took a total of three seconds. He’s off by a factor of 3.

    (2) A complete, detailed analysis comparing a sequenced chimpanzee genome to the sequenced human genome, with an analysis of the types and frequency of differences, likely causes, carefully computed rates of genome change, etc. Took about 35 seconds to find. Included in the paper: single base-pair substitution rate between humans and chimpanzees is between 1.06 and 1.23 percent. (Totally divergence is somewhat higher; they tally point-substitutions separately from other mutations types.) http://www.nature.com/nature/journal/v437/n7055/full/nature04072.html

    So – under a minute with Google, and I was able to find better estimates, and precise numbers on the divergence and divergence rates between humans and chimpanzees – answering both the questions and problems posed by the original author.

    There’s no excuse for using a sloppy back-of-the-envelope guess when one minute of work can provide you with the real answers. In fact, getting the real data with divergence rates probably took me less time than it took him to create his estimate.

  8. #8 Michael Maguire
    February 5, 2009

    I personally do not believe it would be possible to prove creation or the existence of God from our human vantage point. That is an issue of faith and not one of science.

    I’m tired of the argument from both sides that seems to say evolution or creation are mutually exclusive viewpoints. If one believes in creation, it is perfectly reasonable to still accept scientific evidence of evolution as the method God uses to create.

  9. #9 Mu
    February 5, 2009

    I find his numbers very convincing – in favor of evolution. It only requires one mutation per 10,000,000 pairs copied. That’s one heck of an error correction.
    If you think about it, your body produces some 200 million sperm cells a day – you probably have some viable chimp sperm cell hiding somewhere in there already.

  10. #10 Stu
    February 5, 2009

    If one believes in creation, it is perfectly reasonable to still accept scientific evidence of evolution as the method God uses to create.

    Sure. But isn’t God completely redundant then?

  11. #11 Mu
    February 5, 2009

    Not really, you can have him place the earth just right orbit wise, drop in a couple of amino acids in the right stereoisomer at the right time, and voila, life.
    Most creationist are heavily thumping the “abiogenesis is not explained by evolution” line (which is absolutely correct since they are only tentatively related anyway), so you can have creation of life followed by evolution.
    The only ones with problems at that stand are the literalists (who categorically deny any deviation from the 6000 years and all species as they are today interpretation) and the pharyngula crowd (for whom any supernatural explanation, even in the absence of any evidence either way, is unacceptable).

  12. #12 Mark C. Chu-Carroll
    February 5, 2009

    Re #10:

    I don’t think so.

    As I’ve said, despite the fact that I spend so much time debunking sloppy theism, I remain a religious Jew. Absolutely not a literalist, but definitely religious, and serious about my religion.

    The fact that the universe appears as it does doesn’t imply anything about the existence of a deity one way or another. It’s entirely reasonable to believe in a deity who created a well-behaved universe – that is, a universe that behaves according to laws, and where everything that happens in that universe follows from those laws.

    In fact, I’d argue that if you had a being capable of creating a universe, they’d be more likely to create a consistent, well-behaved universe, than they would be to create one full of holes, inconsistencies, and special cases.

    It’s absolutely true that from the perspective of pure logic, there’s no reason to believe in anything beyond the universe – there’s no concrete, objective evidence. But religion isn’t based on concrete evidence. And I think that
    religion isn’t really based on faith – faith, to me, is nothing more than a word meaning “I believe in X” – so saying belief is based on faith is just a word-game. Religion is based on subjective experiences. Whether that subjective experience that created the belief is a result of how you’re educated, or of other experiences – that depends on the individual. But people who’ve made a deliberate decision to be religious do it on the basis of something subjective.

    PZ and his crowd will, no doubt, jump all over me for saying this. But I think that PZ’s brand of atheism is every bit as nutty as hard-core religion.

    My own belief is that the evils of religion, as constantly cited by PZ, aren’t the evils of religion. They’re the result of people being people. It’s part of our nature to form groups, and to develop very strong inter-group/extra-group relations. Those group-based dynamics very often develop into “extra-group is *bad*”. It doesn’t matter what the group is – you can find the same kind of insanity based on religious belief, skin color, nationality, geography, language, customs, food, education, philosophy.

    What cause that to move from insanity to violence is certainty. When one group is absolutely sure that they’re right, and the out-group is wrong, that’s when things get ugly. And that’s got nothing to do with religion.

  13. #13 Jud
    February 6, 2009

    OK, coupla things:

    1- Re the “rigidity” of DNA: Yah, if you think DNA is bad, look at binary code. Totally rigid, all you can have is ones and zeros. Never be able to get anything significant out of that….

    2- The “religion thing” – I do agree that each side (among those who feel that sides must be chosen) tends to ascribe what are very human failings to the presence or absence of religious belief, which I think is pretty tangential to said failings.

    OTOH – Crediting the laws that govern the Universe to a deity gets you to Spinoza’s God and away from a personal one really, *really* quickly. If you want (literally) the cartoon version, there’s an old Far Side cartoon you may have seen, with a laptop screen showing a hapless shmo walking along the sidewalk under a piano being lifted by a crane, and God sitting at the laptop has his finger poised above a button labeled “Smite.” That’s a personal God, smiting some, sparing others, certainly closer to the deity portrayed in all the popular holy books than some disinterested being who set things in motion with the physical properties we see around us, then sat back and let it all unfold.

    Spinoza’s God isn’t very helpful from a moral standpoint, which is mostly what we want a God for, now that folks pretty well understand lightning ain’t Thor hurling thunderbolts. And frankly, I can see the frustration it causes folks like PZ and Larry Moran when people insist on a vague idea of a “guy in the sky” without feeling called upon to follow through and think even a little about specifics.

  14. #14 Darek
    February 6, 2009

    What cause that to move from insanity to violence is certainty. When one group is absolutely sure that they’re right, and the out-group is wrong, that’s when things get ugly. And that’s got nothing to do with religion.

    I think this is demonstrably wrong. This is where I think there is a false dichotomy when comparing the ‘PZ crowd’ and religious fundamentalists. Religion is based on nothing but certainties. Religion is full of answers on any subject related to questions surrounding purpose (ie why am I here?) and questions surrounding practice (ie how to live life to obtain salvation).

    There is a difference between being absolutely certain (to which religious doctrines maintain answers) and rude (which the ‘PZ crowd’ can be to religious people and ideas). As Jud pointed out, there is a frustration on the part of the latter on matters of evidence.

  15. #15 Mu
    February 6, 2009

    Darek,

    there’s so much stuff for which we lack any evidence how it happened (abiogenesis) or have adequate models (big bang, in the last 30 years they added dark matter, dark energy and inflation to keep the theory in line with the observed facts)that the certainty displayed in atheist cycles isn’t any different from the certainty of the religious nuts. There is the same amount of faith involved in believing science explains it all as in science does not. I for myself know I don’t know. The number of people in the world that can fully understand the math behind the “creation” (pun intended) of the universe is probably less than the number of people claiming to have spoken to god (so the latter seem to be less likely to be convinced by a new theory about what happened, usually because it involves psychiatric analysis).
    But after years of discussions on PZs board and with some very good, but also very active atheist, friends I’ve learned that nothing infuriates atheists more than being called “religiously (or fundamentalist) atheist”. But absence of evidence, in my view, is not evidence of absence.

  16. #16 SteveM
    February 6, 2009

    But absence of evidence, in my view, is not evidence of absence.

    But neither is it evidence of existence. There are far too many “things” for which there is no evidence in order to believe in them all. Why is some non-evidence more believable than other non-evidence? It is far more parsimonious to only believe in that for which there is evidence.

  17. #17 Mu
    February 6, 2009

    only believe in that for which there is evidence

    Sorry, that leaves my world with far too many holes, at least if I used my usual scientific definition of what is evidence.

  18. #18 Jud
    February 6, 2009

    Mu wrote: (in the last 30 years they added dark matter, dark energy and inflation to keep the theory in line with the observed facts)

    I do not think this means what you think it means.

    Dark matter, dark energy and inflation were broached as hypotheses in order to account for observed facts. There is now sufficient observational evidence for dark matter and dark energy that I’d guess most scientists in the field would consider their existence proved. I don’t think inflation would fall into the category of proved, though it certainly hasn’t been disproved.

    Taking currently proved facts and reasoning from them to form hypotheses that are eventually themselves either proved or disproved via empirical observation is part of the scientific method. It is the opposite of faith in assertions regardless of empirical evidence of falsity – e.g., virgin birth of a male child, or resurrection. In fact it is the very impossibility of such occurrences in the natural world – in other words, their miraculous nature – that gives them cachet in the context of religion, and that makes faith in them the sign of the “true believer.”

  19. #19 Mu
    February 6, 2009

    Jud,

    in any field but cosmology, if I start a model to explain a given observation, and thirty years later my model needs 2500% fudge factors to still be applicable, people would be laughing their ass off.
    There are indications for unobserved matter, mainly in gravitational lensing, that might indicate dark matter. That this is the same stuff that glues the galaxies together remains to be shown.
    I’ve yet to see any observable evidence for dark energy, other than “it has to be there because the universe is expanding and our equations show it shouldn’t be”.
    Maybe the universe is just mean and the KISS principle doesn’t work. Or the FSM was thinking we wouldn’t notice that F=Gm1m1/r^2 doesn’t hold over large distances due to the invisible spaghetti strands. Who knows? I believe in a big bang – but I sure don’t know the evidence is there to call it a shut case.

  20. #20 John Marley
    February 7, 2009

    …and the pharyngula crowd (for whom any supernatural explanation, even in the absence of any evidence either way, is unacceptable)

    A supernatural explanation is unacceptable.
    1) A supernatural explanation actually explains nothing, since there is no reason to rule out any alternative.
    2) Every supernatural explanation that has ever become amenable to testing has been falsified. Every. Single. One. At this point, “supernatural” is pretty much synonymous with “bullplop”.

    Anyway, without evidence, even a natural explanation is met with “Interesting idea. Now go find some evidence.” Which, minus the “interesting” part, is how supernatural explanations are met, too. Except that the latter usually get a more hostile reception, due to the request for evidence being inevitably met with equivocations and lies.

  21. #21 John Marley
    February 7, 2009

    @Mu(#19)

    Google is your friend. That took about 5 seconds.

  22. #22 Mu
    February 9, 2009

    If you’d spent more than 5 sec, and actually followed the story, you’d find out that while we know “something” is out there, no one is sure what it is. The first article is a typical example; it describes white dwarfs, which are NOT what is usually described as dark matter (the exotic stuff that’s only interacting via gravity) but ordinary matter, just hard to see.

  23. #23 Nick
    February 15, 2009

    Not to beat a dead horse, but he also messed up when counting the # of base pairs. The haploid genome has around 3 billion base pairs. You can’t get that number from multiplying the number of genes coding for proteins times the average size of the gene (and I have no clue where he got that average size he used in his equations, its way off) since the vast majority of the genome doesn’t consist of protein genes (though that doesn’t mean they have no effect on the organism). Luckily its easy to look up the size of the human genome, so I have no idea why he bothered with that calculation. Not sure if that helps or hurts his argument, because I got tired of trying to make sense of it. If you only have a half-ass understanding of something, you are probably not going to be able to prove it wrong.

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