Of Mice and Men and John Sanford's Genetic Entropy

Faith & Science Conversation
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Here is a fuller reply to a recent post on GE.

Genetic Entropy [ GE ], the signature model of John Sanford, is incoherent with observed everyday reality. An aeronautical scientist can publish a book full of arcane math, intimidating physics, computer simulations, and overflowing bibliographies, to prove that “bumblebees cannot fly”, and a layperson who has little grasp of the technicalities can confidently pronounce that he is wrong. Flying bumblebees can readily be observed. Similarly, despite Sanford’s status as a geneticist, it is ridiculously apparent by the most basic observations that GE is a farce.

Photosynthetic algae can double in less than a day and serves as the base of the ocean’s food chain. Rats progress from pink little pups to parents in less than three months, mice a bit quicker. Houseflies go from eggs to laying eggs in a matter of a couple of weeks. Bacteria can double several times in an hour. Viruses hijack host cells to explosively multiply. The popular aquarium and research model zebrafish has a generation time of about three months. Such examples can be found endlessly, but suffice that a representative cross section of life, vertebrate and invertebrate, terrestrial and aquatic, plant and animal, microbial and complex, will have undergone at least several tens of thousands of replications even given the six thousand years allowed by YEC.

GE predicts that all these populations should have inescapably suffered error catastrophe and become extinct, as with each generation slightly deleterious mutations accumulate and permeate the gene pool. That is the whole idea. But far from these species being long gone, or even teetering on the brink, instead what we have are populations which are thriving and robust, often despite our best efforts at eradication. Anybody, scientist or layperson, can see for themself that the reality could not be more contrary to the expectation of GE.

As this contradiction is bound to be frequently raised, Sanford associate Robert Carter penned an article to allow the usual “if they read our literature, they would know we have already addressed those criticisms” line YEC’s love to spout. In it, Carter carves out an exception from GE for the uncooperative bacteria, because “their genomes are simpler, they have high population sizes and short generation times, and they have lower overall mutation rates.” Oddly, except for the mutation rate, the same can be said for influenza virus, which he and Sanford offered as their principle case study for GE wiping out a simple organism in a matter of a few decades.

It gets even better. Carter devotes a paragraph to consider mice, which have a similar genome size to humans - how do they escape the ravages of GE? He maintains they actually haven’t. The common house mouse has “much more genetic diversity than people do”, and is “certainly experiencing GE”. Now, the conclusion that any clear thinking individual would draw from a vigorous, fecund, thriving population displaying high genetic diversity is that mutation does not simply correlate with decline into extinction. Carter presents no evidence whatsoever that mice are experiencing GE; what they are actually experiencing is mutation, which is something everyone agrees on. This observation fits with the expectations of mainstream population genetics and natural selection. And if the rodents are doing fine, we humans who have undergone far fewer replications have nothing to worry about.

So it is not surprising that population geneticists, at least those who may be aware of Sanford’s existence given his paltry journal output, find glaring shortcomings in his understanding. Scientists who have done recognized work specifically in population genetics and soundly critique Sanford include Zach B. Hancock, Michael Lynch, Joe Felsenstein, and Dan Stern Cardinale; joining other biologists such as Joel Duff. There is plenty for those who want to get into the weeds of drift, selection, the distribution of fitness effects, and mathematical modeling. The point here, however, is that armed only with a rudimentary lay understanding of nature, it is apparent that the GE idea is absurd. Apply the bumblebee test. Remember that the next time you shoo away an annoying fly, whose genes have replicated one hundred thousand times from the one that buzzed Adam six thousand years ago.

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One of my immediate reactions is to consider the magnitude of these mutations with respect to fitness. Even if slightly deleterious mutations significantly outnumber beneficial mutations you can still have an overall increase in fitness. For example, if 100 slightly deleterious mutations lower fitness by an average of 0.0001% this can easily be overcome by a single beneficial mutation that increases fitness by 1%. There is also the assumption that slightly deleterious mutations outnumber slightly beneficial mutations, and I haven’t seen anything that supports that assumption.

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That was going to be my question. I run into the claim that deleterious mutations outnumber beneficial and don’t recall any decent explanation why that should be so.

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Bacteria and viruses have very high mutation rates, and there’s no reason that a simpler genome would be more resistant to damage than a more complex one.

Mutations that slightly increase or decrease an enzyme’s activity are about equally frequent in the study that I remember seeing. Of course, whether that is advantageous, disadvantageous, or irrelevant to the organism is a much more complex question, which depends on the exact situation. On the one hand, this allows every mutation to be dismissed as harmful, but on the other that means that the mutations that they are claiming can’t happen are also harmful and able to happen by their contrived definitions.

If a gene already has a particular function in place, then unsurprisingly large changes are more likely to be detrimental to that function - it’s the lesson rarely learned by management or administration of “if it ain’t broke, don’t fix it.” But large changes do have a chance of significantly increasing its functionality for doing something quite different.

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I immediately thought of the ranger whose experiment ended up with bacteria that could metabolize arsenic: it might be the case that those bacteria didn’t need arsenic but could use it, or it might be the case that the bacteria needed arsenic. In the first case the new ability would be beneficial when arsenic was present and neutral without it, but in the second it would be beneficial when arsenic was present but detrimental when arsenic was not available.

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While rooting around my hard drive for something else, I ran into something I sent John Sanford in 2009 as part of an email exchange. It outlines some of the many problems with his genetic entropy claims. (Broken up into blocks since I can’t figure out another way to get spaced paragraphs.)

Hi John,
Viewed from a high level, populations crash in your model because of several features in the model. First, it has a high rate of very slightly deleterious mutations, ones that have too weak an effect to be weeded out by selection. Second, the accumulation of these mutations reduces the absolute fitness of the entire population. Third, beneficial mutations (and in particular compensating mutations) are rare enough (and remain rare enough even as the fitness declines) and of weak enough effect that they do not counteract the deleterious mutations. As far as I can tell, any model of evolution that has these features will lead to eventual extinction – the details of the simulation shouldn’t matter at this level. (Indeed, Kondrashov pointed out this general problem in 1995; I wouldn’t be surprised if others have made the same point earlier.)

So, there is no question that if these premises of the model are correct, organisms with modest population sizes (including all mammals, for example) are doomed, and Darwinian evolution fails as an explanation for the diversity of life. If one wishes to conclude that evolution does fail, however, it is necessary to show that all of the premises are true – not merely that they are possible, but they reflect the real processes occurring in natural populations. From my perspective, that means you need to provide empirical evidence to support each of them, and I don’t think you have done so.

Turning specifically to issue of soft selection: it matters here becuase it severs the connection between relative fitness and absolute population fitness. The essence of soft selection is that the absolute fitness of the population does not change, regardless of the relative fitness effects of individual mutations that accumulate in the population. As Kimura put it, “Therefore, under soft selection, the average fitness of the population remains the same even if the genetic constitution of the population changes drastically. This type of selection does not apply to recessive lethals that unconditionally kill homozygotes. However, if we consider the fact that weak competitors could still survive if strong competitors are absent, soft selection may not be uncommon in nature.” (p. 126, The Neutral Theory of Evolution).

(An unimportant point: my understanding from reading Wallace is that he introduced the term “soft selection” in the context of accumulating deleterious mutations (especially concerns about them raised by Jim Crow), not in connection with Haldane’s dilemma or the rate of beneficial substitution. If you have a citation that provides evidence otherwise, I would be interested in seeing it. The basic model of soft selection actually goes back at least to Levene in 1953 (predating Haldane’s work by a few years), when he was considering the maintenance of varied alleles in a mixed environment. So, this is not a new idea, and it is (contra your suggestion) is a well-defined concept, and one that is in fact often considered in the context of deleterious mutations and genetic load. Are there any recent published discussions of genetic load that do not consider soft selection as a possibility?)

In your reply to me, you said that the default in your program is purely soft selection. I don’t know what the actual default is for deciding whether fitness affects fertility (since I have not run the program), but the online user manual says that an effect on fertility is in fact the default (“The default value is ‘Yes’, which means that fertility declines with fitness, especially as fitness approaches zero.”) Regardless of the direct effect on fertility, the use of an additive model of fitness means that deleterious selection in your program ultimately ceases to be soft, since accumulating additive fitness always ends up or below zero, at which point the relative fitness values no longer matter. In a model of soft selection, the magnitude of the populations’s fitness makes no difference at all; only the relative values of individuals have an effect. In your program, that is not the case. So in practice, your program does not seem to model long-term soft selection.

(As an aside, I’m afraid I don’t understand your comments about having tested a multiplicative model of fitness. You say that in such a model, as the mean fitness falls, you see increasing numbers of individuals inherit a set of mutations that give a fitness less than or equal to zero. Under a multiplicative model, the fitness is given by f = (1-s1) * (1-s2) * (1-s3) *…, where s1, s2, s3… are the selection coefficients for the different mutations. If the various s values are less than 1.0 (as they must be if the mutations have been inherited), then f must always be greater than 0. I don’t see how you can have a multiplicative model with the reported behavior. Perhaps you have a noise term that is still additive?)

The real question is whether or not soft selection is actually important and needs to be modeled. As you say, soft selection is a mental construct Рbut so is hard selection. You dismiss it as a real phenonenon, but do you have any evidence to support your point here? Your populations crash because of very slightly deleterious mutations, and as far as I know, virtually nothing is known about what kind of fitness effects these mutations have. In general, there has been very little empirical work distinguishing soft from hard selection (or equivalently, quantifying the difference between absolute and relative fitness). The only recent study I know of to attempt it looked only at plant defense traits in A. thaliana (Kelley et al, Evolutionary Ecology Research, 2005, 7: 287–302), and they found soft selection effects to be more powerful than hard effects. So I do not see good empirical grounds for rejecting an important role for soft selection.

This isn’t to suggest that all selection is soft, or that many mutations don’t have real effects on the population fitness – but there are good theoretical and empirical reasons to think that the net effect of many deleterious mutations is smaller when they are fixed in the population than their relative fitness would suggest. (Not that we actually know what the distribution of relative fitnesses looks like, either. You can pick a functional form for that distribution for the purpose of doing a simulation, but it based on no real experimental evidence. Are deleterious mutations really so highly weighted toward very slight effects? There are just no data available to decide.

If much selection actualy is soft, then humans (and other mammals) could have in their genome millions of deleterious mutations already, the result of hundreds of millions of years of evolution; this is the standard evolutionary model. These mutations would have accumulated as population sizes shrank slowly (relaxing selection) and functional genome sizes grew (increasing the deleterious mutation rate). Indeed, many functional parts of the genome may never have been optimized at all: the deleterious “mutations” were there from the start. The results of this process are organisms that are imperfect compared to a platonic ideal version of the species, but perfectly functional in their own right. In your response, you cite systems biology’s assessment that many organisms are highly optimized to counter this possibility. I do not find this persuasive, partly because systems biologists can also cite many features that are suboptimal, but mostly because no branch of biology has the ability to quantify the overall optimization of an organism, or to detect tiny individual imperfections in fitness.

Alternatively, beneficial mutations may be more common and of larger effect than in your default model. I pointed to one recent example of a beneficial mutation with a much larger selective advantage than your model would allow (lactase persistence in human adults). In turn you suggest that such large effects occur only in response to fatal environmental conditions, but the example I gave does not fall in that class. Do you have any empirical evidence that the selective advantage is restricted to such small values?

Michael Whitlock has a nice discussion of this kind of model in a paper from 2000 (“Fixation of new alleles and the extinction of small populations: drift load, beneficial alleles, and sexual selection.” (Evolution, 54(6), 2000, pp. 1855‚Äì1861.)) His model tries to answer very similar questions to yours. With the choice of parameters that he thinks is reasonable, he finds that only a few hundred individuals are needed to prevent genetic decline.

He also discusses many of the same issues that we’re discussing here. For example, on the subject of soft selection he writes, “We also have insufficient information about the relationship between the effects of alleles on relative fitness in segregating populations and their effects on absolute fitness when fixed. Whitlock and Bourguet (2000) have shown that for new mutations in Drosophila melanogaster, there is a positive correlation across alleles between the effects of alleles on productivity (a combined measure of the fecundity of adults and the survivorship of offspring) and male mating success. This productivity score should reflect effects of alleles on mean fitness, but the effects of male mating success are relative. Without choice, females will eventually mate with the males available, but given a choice the males with deleterious alleles have a low probability of mating. Other studies on the so-called good-genes hypothesis have confirmed that male mating success correlates with offspring fitness (e.g., Partridge 1980; Welch et al. 1998; see Andersson 1994).”

His conclusion about his own model strikes me as equally appropriate to yours: “We should not have great confidence in the quantitative values of the predictions made in this paper. In addition to the usual concern that the theoretical model may not include enough relevant properties of the system (e.g., this model neglects dominance and interlocus interactions, the Hill-Robertson effect, the effects of changing environments), the empirical measurements of many of the most important genetic parameters range from merely controversial to nearly nonexistent.”

Using this kind of model to explore what factors might be important in evolution is fine, but I think using them to draw conclusions about the viability of evolution as a theory is quite premature.

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Um, what??? That seems bizarre to me! The two are not necessarily linked.

Love the platonic reference! It brought to mind my philosophy professor who pointed out that no individual duck ever matches the ideal duck; it always lacks something in “duckness”.

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There’s nothing wrong with trying out a simplistic model of a complex process as a way to learn about it. But when your simplistic model predicts results that look highly implausible and that are manifestly not seen in nature, the obvious thing to do is to improve your model – even if you happen to like the model’s results and have a deep emotional need for them to be correct.

And then there are the parameters of Sanford’s model. Here’s what I’ve previously written on that topic:

Let’s look at Sanford’s numbers. A key bit of his paper is this: “We model 10% of all mutations as being perfectly neutral, with the remainder of mutations being 99% deleterious and 1% beneficial [35] […] We use the well-accepted Weibull distribution for mutation effects (a natural, exponential-type distribution [26]). In this type of distribution, low-impact mutations are much more abundant than high-impact mutations.”

Reference 35 is to this paper . In that paper, the authors report on 91 synthetic mutants of an RNA virus. They found 24 produced no virus and can be presumed lethal. If we ignore those, 31 (46%) had no statistically significant effect on fitness, 32 (48%) were deleterious, and 4 (6%) were beneficial. If we assume (without justification) that all mutants with lower measured fitness were deleterious, even if the value was not statistically significant, we have 76% deleterious and 18% neutral. They also found that the distribution of fitness effects of the detectably non-lethal deleterious mutations had a longer tail – more highly deleterious mutations – than could be fit well with an exponential-type distribution. Mean beneficial effect was 1%, mean/median deleterious effect (for non-lethals) was -13.9%/-9.2%

So let’s compare the Sanford model with the empirical results from the source they cite. Fraction neutral: 10% (model) vs 18-34% (empirical); fraction beneficial: 0.9% (model) vs 4-6% (empirical); fraction deleterious: 89% (model) vs 46-76% (empirical); size of beneficial effect: maximum of 1% (model) vs mean of 1% (empirical). Sanford’s paper doesn’t give the mean fitness effect of their deleterious mutations, but does report that 10% had an effect > 10%. The empirical median value for deleterious mutations (assuming all of the non-significant ones were actually deleterious) is just under 10% (9.2%), which means that Sanford’s distribution is weighted far more toward mutations of small effect than the empirical values, i.e. weighted toward mutations that can accumulate rather than be purged quickly by selection.

In summary, Sanford and colleagues took (and cited) a study of empirical values for the very thing they’re modeling, and then discarded every single one of the values and replaced it with one that suited their thesis.

The original discussion was here. Later in the thread, you can see that a third party contacted Sanford and pointed out these discrepencies. Sanford didn’t care.

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I don’t see linking fertility with fitness as just simplifying; I deal with plants that struggle to survive in the bare sand of coastal dunes yet are astoundingly fertile, producing thousands of seeds per plant.

No kidding.

Why am I not surprised.