Variable "Wi" and "Mutator genomes decay, despite sustained fitness gains, in a long-term experiment with bacteria"

W or w represents fitness in most conventional population genetic literature. From a variety of texts (such as Felsenstein’s Theoretical Evolutionary Genetics and Gillespie’s Population Genetics a Concise Guide, etc.) “w” is usually treated as CONSTANT. That is fitness associated with a trait, an allele, a mutation, etc. is treated as a CONSTANT. There is some notable deviation from this situation where Joe Felsenstein analyzed situations such as migration and he had to use Komogorov forward equations, and hence variable fitness associated with traits…

The following paper:

Shows the additive, multiplicative, and stickbreaker ways of computing overall fitness for a particular genotype. Again as far as I can tell each Wi is a constant value.

I argue the results of Lenski’s paper shows this idealization where each Wi is constant does not hold over time!

An important passage is here from Lenski’s paper:

the signature of selection is sufficiently weak that these adapted genomes are essentially indistinguishable from those derived from mutation accumulation experiments, which are designed to impede the action of selection.

Some of the mutations that create this situation are those that disrupt DNA repair – disabling mutS and GO, etc.

As an approximation, when one or a small number of traits are strongly selected FOR, what ever other traits there are should have their fitness contribution (delta-Wi) approach zero in the additive model. This is extensible with some revision to the multiplicative and stickbreaker models.

But if this happens, this implies each Wi, is NOT a constant over time, and a disruptive new trait or small set of traits (such as loss of DNA repair) might increase fitness of the overall population because of these traits, but the other traits become essentially neutral. That is, for whatever reason, the other delta-Wi’s approach zero in the additive model.

The question is Why? But the experiments seem to indicate this is the case, and if so the idealization of each delta-Wi being a constant does not hold in general, and may actually be an idealization that is rare enough as to invalidate its use in analysis of evolution. But if the change of Wi overtime uncertain, then to the extent the evolutionary enterprise depends on the idealization of Wi being constant over time, then the evolutionary enterprise rests on uncertainty and therefore rests on possibly unprovable speculations, and is therefore built on faith statements more than actual experiments.

As Gillespie said in the preface:
“Population genetics is concerned with the genetic basis of evolution. It differs from much of biology in that its important insights are theoretical rather than observational or experimental.”

Well, now we have experiments such as Lenski’s mutator genomes that may controvert theoretical ideas in population genetics. This evident in the fact the genomes are decaying in Lenski experiment even though there is large scale adaptation and fitness gains and worse, under intense selection for some traits, it seems the evolution of other traits goes strongly into neutral mode making the rest of the genome evolve as a random walk! Haldane, Kimura, et. al sort of anticipated the situation with most of the genome being neutral, but it is especially noteworthy this is happening under intense increase in fitness and adaptation! That outcome is not exactly obvious in the additive model (and I would expect similarly in the multiplicative model).

Doesn’t Sanford’s genetic entropy depend upon the fitness of each mutation being constant? Do you no longer accept his idea of genetic entropy?


Surely this comes as a surprise to nobody. The fitness of an allele depends on the environment, including both internal and external environment, notably genetic background. The fitness of a genotype depends on the genotypes of the rest of the population, among other things. And any aspect of environment can change over time. Simplifying assumptions are exactly that. And this is what’s supposed to make evolutionary biology collapse? This is a fine example of grasping at any straw that seems to provide the desired result.


Thank you for your comment.

Our later publications such as “Dynamical Systems and Fitness Maximization in Evolutionary Biology” (2021) put on the table an obvious revision to conceptions of fitness compared to Sanford’s 2004.

When I pointed out Lenski’s 2017 article where the genome decays while adaptation and fitness increases, this actually shows the 2004 Genetic entropy understated the problem since deleterious mutations (as in contributing decrease to reproductive) efficiency was the focus.

In light of Lenski’s experiments where disabling DNA repair is considered Beneficial, I’d say, the major change is that not only “deleteroius” but more importantly even “beneficials” can contribute to genetic decay.

So obviously, in answer to your question, Genetic Entropy does NOT depend on fitness of mutations being constant, although many of his computational models adopted it.

If we were to revise the computationl models, it would show decay is even worse, but what would be the point???

The dominant mode of evolution appears to be genome reduction. We even have the word “reductive evolution” that is experimentally observed.

BUT, Sanford’s work is NOT the subject of this discussion. The subject is the validity of modelling Wi as constant. I argue Lenski’s experiments, and for that matter many experiments and observations, such as in papers like “Evolution by Gene Loss” or “Selection driven gene loss” or “Adaptation by Gene Loss” or “Genome Reduction as the Dominant Mode of Evolution”, shows the shaky ground of theories which assume constant Wi are built.

That said, just as the square root of 2 was shown to be irrational by a proof by contradiction, I’m enthusiastic to assume Wi’s are constant in order to make a proof by contradiction (reductio ad absurbdum) regarding evolutionary claims.

What a confused and silly post, Sal.

A) What is “the evolutionary enterprise”?

B) What you call an “idealization” is really just a simplifying assumption to make modeling and calculation easier and more convenient.

C) Evoluionary biology isn’t in the business of predicting the radiative input to the planet from the sun, for example, so if temperatures suddenly drop or increase fast due to the sun, lots of mutations will have their fitness-effects changed. It’s really the same thing as with the DFE, which for convenience is assumed constant in various models, even though we know it isn’t in reality. The problem is it can’t be known a priori to what extent it will change with time as environments themselves change in response to organismal behavior and other factors.

But nobody thinks any single model or equation is able to capture all aspects of the evolutionary history of life.

D) All of science rests on uncertainty. Nothing is known for certain. That is the typical creationist “if you don’t know EVERYTHING then you don’t know ANYTHING” fallacy. If this is somehow a problem with evolution it’s a problem with all of the findings of modern science. You’re going to stop taking aspirin for headaches and shut off your computer now, right?


So nice to see you again John.

Thank you for affirming the most important points

The fitness of an allele depends on the environment, including both internal and external environment, notably genetic background.

Well, then what mechanism creates “Organs of Extreme Perfection and Complication” as Darwin said in Origin of Species chapter 6?

If you say, “we don’t know”, I’d say that’s progress, because we don’t know what environment can possibly make such organs of extreme perfection and complication. It’s a faith statment on the part of the evolutonary enterprise that such environments existed in the past, it’s hasn’t even been shown to be theoretically feasibly in adequate detail, much less experimental validation.

Lenski 2017 doesn’t exactly help matters, nor the abundant experimental evidence that the “preservations of favored races in the struggle for life” leads to evolving the simple to more complex.

So even assuming common descent is true, as far as the emergence of complexity being well within normal expectation from a theoretical and experimental standpoint, that hasn’t been demonstrated, and probably will be unprovable and untestable, and hence it’s not first rate science (compared to established sciences like Classical Electromagnetic Theory).

Welcome back, Sal :slight_smile:

As John already noted, it’s just a simplification. Who expects this to be constant in nature?

It light of this statement, I don’t think you have any basis for complaint about the use of constant Wi.

I don’t think that is true. You are glossing over an even bigger simplification - that Wi can be represented by single number. In nature fitness is multivariate, with many different aspects. If you allow variable fitness then there should also be variable “modes” of fitness. This gets complicated, which explains the simplification. But if we could model the complexity I would not expect the overall decay to be worse overall. (I would make an exception if we are modeling at a local maximum fitness, but it’s also harder to get stuck in local minimums in multivariate space.)

I think the best you can hope for is to show that “fuzzy” fitness only allows for fuzzy optimization. In a population with increasing variability some members of the population must inevitably become more fit than others, allowing selection for fitness to occur.

I think you are aware that Sanford’s Genetic Entropy is essentially a rehash of the old 2LoT argument. Your claim here is similar, that energy expended through variation and selection cannot overcome randomness.


You are exhibiting dichotomous thinking again.

It’s still the same mechanisms of evolution that produce adaptations and complexity. The fact that complexity is not ALWAYS favored doesn’t mean it’s not EVER favored by selection. The fact that SOME adaptations are too tiny to be visible to selection doesn’t mean ALL adaptation are too tiny to be visible to selection.

This shouldn’t be difficult to understand.


There seems to be no possibility of having a serious discussion with you. Your main purpose seems to be to show how very clever you are and how very clever evolutionary biologists are not. Why should anyone respond?

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You (We) should have led with that. :wink:


These sentences are saying “there’s no need to read anything that follows, since this statement is so preposterous.”

Those curious about fitness measurement, modeling, etc should IMO start with this excellent review by Allen Orr. If nothing else, it’s a welcome palate cleanser after unwisely consuming nonsense. Contrast this excerpt (the first part of which is already known to all who have actually read a tiny amount of population genetics) with the stuff I quoted from the OP above:

Alleles almost surely do not enjoy constant fitness through time. Instead the fitness, either absolute or relative, of most alleles likely fluctuates through time in response to physical and biological changes in the environment.

The consequences of temporal fluctuations in fitness have been well studied 12,1620 and the results are surprising. In particular, one might guess that the allele with the highest average fitness through time would ultimately predominate in a population. This turns out not to be right.


Hi Sal, hope you’re doing well.

That fitness (W) is treated as a constant in the most basic one-locus population genetic models of selection in introductory textbooks is not indicative of how we view fitness writ-large. In fact, in Charlesworth & Charleworth’s Elements of Evolutionary Genetics textbook, the second half of Chapter 2 is dedicated to variable fitness, including frequency-dependent selection, temporal variation in fitness, spatial variation in fitness, and even discusses biochemical causes of variable fitness.

Empirical studies have also considered this. Stroud et al. (2023; evaluated a fitness landscape for Anolis lizards in the Caribbean, noting that their temporal trends were dominated by fluctuating selection (i.e., temporally varying fitness with population trait means tracking a shifting local optimum). A meta-analysis of over 10,000 samples, including fossil time series, published this year ( came to the same conclusion – that evolutionary dynamics were dominated by fluctuating directional selection around local optimum.

Variable fitness is introduced fairly early in all population genetic courses and is a cornerstone of entire subfields in evolutionary quantitative genetics.

You have not carefully read the Couce et al. (2017), something I have accused you of previously. Their results are exactly what is predicted under the theory of genetic draft, which they discuss at length in the paper. They compare three different mutational distributions: those from a natural strain, those from mutation accumulation strains, and those from the LTEE mutator strain. In the natural strain, they find strong evidence of purifying selection, as expected. The mutation accumulation strains, where you purposefully bottleneck the population so remove the action of selection, predictably showed no sign of selection and mutations accumulated freely. It turns out, the LTEE mutator strain showed a remarkably similar mutational distribution to the mutation accumulation strain despite not being bottlenecked.

The reason for this is the flipside of the same coin. The mutation accumulation suffered from increased genetic drift, whereas the LTEE experienced genetic draft. By mutating the repair enzyme, you get an exponential increase in new mutations, most of which are harmful but are strongly linked (since there’s no recombination) to beneficial ones. As these beneficial ones increase in frequency they drag a large number of neutral and deleterious alleles to high frequency with them. This generates a pattern of virtually indistinguishable from genetic drift in the mutation accumulation lines.

Again, you have a drift-dominated mutational distribution in the mutation accumulation experiments and a mutation-dominated distribution in the LTEE mutator strains. Importantly, neither are what is observed in natural strains of bacteria, which show strong purifying selection.

TLDR: W is not treated universally as a constant and is not required to be a constant for the “evolutionary enterprise” to function, and Couce et al. (2017) presents empirical evidence supporting the theory of genetic draft, an idea that goes back decades and is a well understood part of evolutionary theory (which, again, they discuss in the paper if you’d bothered to read it thoroughly).


Not really, but look at casinos and the so-called house edge. An unskilled gambler can win a few rounds at the craps or roulette table, but if the expected value is negative for the gambler, the law of large numbers will dominate and he’ll be a net loser over time. That is his starting bank roll will evolve downward over time. A testable prediction is multicellular eukaryotes will likewise devolve over time. Does any one here think the human geneome is improving??

If the dominant mode of evolution is gene loss, then we would not expect organs of extreme perfection or complication over time. We would just reproductive success through simplicity of organism with simple replication cycles.

Obviously organs of extreme perfection and complication exist as William Bialek argued very well in his published works, and particularly well in his Hans Bethe memorial lecture.

The question is whether such levels of complication and perfection are well within normative expectation. Or is the outcome like the fine tuning of the universe – fine tuning exists, but it does seem un-naturally probable. Rather than say “supernatural”, we can use the term “un-natural” as is used regarding fine tuning (from a google search):

Theories requiring fine-tuning are regarded as problematic in the absence of a known mechanism to explain why the parameters happen to have precisely the observed values that they return. The heuristic rule that parameters in a fundamental physical theory should not be too fine-tuned is called naturalness.

In any case, how frequent and applicable should constant Wi be invoked.

In classical mechanics and classical electro magnetic theory, we can invoke the classical approximations in well-defined domains – hence we have space probes and electrical generators that are well described by classical approximations. For a lot of every physics, the approximations are quite valid.

But that doesn’t at all seem to be the case in evolutionary biology as far as population genetics is concerned. Where in pop gen did it really predict the abundant examples selection driven gene loss or functional which appears the dominant mode of adaptation (except for horizontal gene transfer).

Even Jerry Coyne in 2010, commenting on Behe’s paper acknowledged Behe was right about present day experiments showing abundant function loss, but then Coyne pointed to all the supposed examples of selection which were not empirically demonstrated but only in his imagination.

But now its 2024, and we have Lenski’s work. Does anyone think ducS, mutS, GO functions will spontaneously recover? Even after 80,000 generations did ducS recover according to Dawkins Weasel? That broken dcuS gene is only 5 measily base pairs away from recovering function. If it can’t recover 5 measily base pairs, why would we think Weasel-like evolution the way Blindwatchmaker advertises would actually work? It doesn’t even have to be those specific 5 measily base pairs, how about a single insertion mutation to get the ducS back in frame to give it at least fighting chance to evolve back to some semblance of its former self? Or how about the genes that were disabled by a single nucleotide change creating a premature stop codon? Will Weasel-like evolution help? No, becuase REAL selective pressure favored damage in Lenski’s lineages.

We can’t even imagine what sort environment would be needed to take these mutator genes and resurrect the 5 measily bases of ducS and how to generate the appropriate Wis needed to fix them into the population. And lets be genererous, assume its not specifically those 5 measily base pairs, but some easier transformation. Where is the theoretical justification for resurrecting ducS? If we can’t even resurrect a functioning ducS that is already 97% in place, why would we expect it to evolve in the first place?

One can’t just assume there were appropriate Wis that existed in the past and then declare a victory for science. One has to justify why such Wis are within normal expectation. That hasn’t been done, and it probably never will be done, and it will not be likely provable. That’s a testable claim on my part.

Ask a five year old. Aqueous environments lead to hydrofoils, such as found on sharks, whales, plesiosaurs, ichthyosaurs, and mosasaurs. Bats, birds, and pterosaurs come with wings and lower density or body size for aerodynamics. Not sure where YEC stands with their dragons.

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There seems to be no possibility of having a serious discussion with you. Your main purpose seems to be to show how very clever you are and how very clever evolutionary biologists are not. Why should anyone respond?

You don’t have to, so I thank you all the more for your responses.

As far as the purpose for todays discussion, I was soliciting reactions to the gist of some ideas that I was invited to talk about this summer before ID friendly professors and researchers in biochemistry and engineering, among whom have been some of my co-authors in secular and ID-friendly publications.

I’m happy to refer to them to this discussion so they can see you’re all’s comments, especially since some in the audience I address are peer-reviewers for secular science journals. I invite them to judge if my claims stand up to their qualified scrutiny.

Yet the casinos continue to thrive, at least so long as they give back just enough that people are willing to accept those losses. It’s not like the entire human population is going bankrupt at casinos either.

I can imagine just such an environment, just turn them loose in nature. That might not regenerate that specific configuration, but enough to allow fitness to hold relatively even with the environment. If you are right, then bacterial populations should be gone (extinct) already. Mosquitos too.

Again, you are rehashing a tired old 2LoT argument, and it hasn’t improved with age.


Sal, I will note in passing that in your pretension to science, you have violated a basic principle by failing to fully cite any of the publications you have mentioned or alluded to.

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I expected that result and I was heartened to see it confirmed experimentally. So don’t accuse me of not reading the paper, and I’m familiar with the Direct Coupling Analysis that showed this.

But the bottom line is Adaptation and Fitness increased at the expense of genomic decay and then reduction of selection on other loci. Which means Wi has changed, and for many loci it started to approach ZERO for practical purposes! Exactly as I claim is a problem, and exactly as expected.

And by the way, you can’t say this isn’t genomic decay can you? How many other times will this scenario play out elsewhere for other organisms where genomes decay as fitness increases and the other loci have selection relaxed on them as a result? This means for selection to create complex features that are the product of many gene loci, that selection for increased reproductive fitness might have to be relaxed – a way of saying this is that for selection to work it sort of doesn’t have to work too well.

So thank you for confirming Wi is easily made variable, which means we can’t extrapolate that much into the past of how selection worked, therefore assertions that complexity evolved via natural selection is mostly built on untestable unprovable assertions. That’s fine if that’s all you have, but lets not pretend this is a theory on par with operational theories like electromagnetism.

Thank you for responding to my discussion.

An established increase in fitness will in and of itself change the environment. Failing to recognize this is one of the many elementary flaws in Sanford’s H1N1 paper.


Of course it does. GE is logically impossible if fitness effects of mutations aren’t constant, and they aren’t, so it’s logically impossible. People have been trying to tell you this for some time.

To be fair, it’s logically impossible for lots of other reasons anyway, because it’s a bad idea put forward by someone who doesn’t understand population genetics and is bad at math, but this was one of the big ones.