What has actually been measured about mutations

"Given the importance of measuring microbial fitness in diverse fields, it is frustrating that we cannot measure fitness more precisely.  Reported precision remains capped at detecting fitness differences on the order of 0.1–1%." — Kinsler and colleagues, Petrov laboratory, 2023¹

Every argument about genetic entropy reduces to one curve: how many mutations are harmful, by how much, and how many help.  Population geneticists call it the distribution of fitness effects, or DFE.  Change its shape and every conclusion on this site moves.

This page catalogues what has been measured, and separates it carefully from what has been inferred.  Three distinctions run through all of it, and they are the reason this page exists rather than a single table.

First, most numbers are not measurements.  Human DFE estimates are produced by fitting a population history and a selection model to sequence data at the same time.  You cannot get one without assuming the other.  A laboratory assay in a flask is a measurement; an estimate from human polymorphism is a model output that inherits every assumption in the demographic history.

Second, no instrument reaches the range the argument is about.  The best precision ever achieved on a single selection coefficient is about 2 × 10⁻⁴.  The human drift barrier — the threshold below which selection cannot act — is about 5 × 10⁻⁵.  The measurements stop an order of magnitude above the zone in dispute, and the field says so.

Third, "beneficial" almost never means what a reader assumes.  When a paper reports that 5% of mutations raised fitness, it has measured growth in an assay.  It has not asked how.  A mutation that deletes a gene the organism was paying to maintain but does not currently need will read as beneficial, and in a simple laboratory environment a great many do.  Almost no study classifies mechanism, and the ones that try find destruction dominating.

Why the third point matters most

The genetic entropy argument is not a claim about fitness.  It is a claim about whether specific functional sequence is being built as fast as it is destroyed.  Those are different quantities, and a beneficial fraction cannot be converted into a construction rate without knowing what the beneficial mutations did.

The authors of these studies often say so themselves.  Joseph and Hall, whose 5.75% beneficial figure in yeast is among the most quoted, list four reasons their own number may be inflated, and every one runs the same way:

"the protocol for measuring fitness may cause mutations that are deleterious in nature to be beneficial in the lab.  In the complete medium of our growth assays, several metabolic pathways, such as those involved in amino acid synthesis, are not required. ...  Mutations that reduce or preclude production of proteins in these types of pathways might be beneficial to diploid mitotic growth rate, even though they represent deleterious mutations in nature."²

"the ancestral strain used in our experiment may have been poorly adapted to the experimental conditions.  If this is true, a higher proportion of mutations are expected to be beneficial because the ancestral genotype was far from its fitness optimum."²

"dominance may have biased our estimates.  If deleterious mutations are more likely than beneficials to be recessive, then they would appear underrepresented because we are measuring heterozygous fitness."²

That is a careful paper being honest about its own limits.  The problem is downstream: the 5.75% travels and the caveats do not.

The resolution problem, in the field's own words

This is the single most important fact on this page, and it is not disputed by anyone.

Kinsler and colleagues, working in Dmitri Petrov's laboratory on the highest-throughput fitness assays that exist, state the cap plainly: "Reported precision remains capped at detecting fitness differences on the order of 0.1–1%."¹  Four sentences later they state the consequence:

"natural selection can distinguish fitness differences that are orders of magnitude smaller than we can measure in the laboratory, depending on effective population size.  This creates a problem for scientists: how do we understand the fitness effects of mutations if many of these effects are too small for us to measure precisely?"¹

A related limitation appears in one inference from sequence data.  Johri, Pfeifer and Jensen tested how much positive selection human exome data can rule in or out and concluded that "weak to moderate positive selection is consistent but unidentifiable if rare."³

A scale, so the numbers mean something.

Everything the argument is about happens in the first row.  Everything anyone has measured happens in the rows below it.

And the newest tool in the field makes the gap structural rather than incidental.  fastDFE, released in 2024, fits a beneficial class as well as a deleterious one — a real advance.  Its finest discrete bin near zero runs from 2N_e s = −1 to +1.  The entire drift zone, the whole region where this argument lives, is one undivided lump in the software's own design.⁴

Measured, or fitted?

Tagging every number by provenance is not pedantry.  It decides who can use it.

Measured, model-free.  Sequencing parents and children and counting new mutations.  Site-directed mutagenesis followed by a competition assay.  Deep mutational scanning.  Mutation-accumulation lines.  These are observations.  They have their own problems — assay environment, limited resolution, non-native conditions — but they do not depend on when humans arose or how large the population was.

Fitted, and the fit contains a population history.  Every human DFE inferred from polymorphism.  Every constrained-fraction estimate from comparative genomics, which needs a phylogeny and divergence dates.  The effective population size of 10,000 itself, which is a harmonic mean recovered under an assumed demographic model.

Johri, Pfeifer and Jensen address this dependence in "Developing an Evolutionary Baseline Model for Humans: Jointly Inferring Purifying Selection with Population History."  Their method fits both together and accounts for the effects of selection at linked sites.³

And the coupling is worse than a one-way assumption.  Soni, Pfeifer and Jensen showed that background selection skews the site frequency spectrum, that the skew "may then be mis-inferred as population size changes using neutral demographic estimators, which may in turn result in a mis-inference of the DFE."⁵  Errors in the history and errors in the selection estimate feed each other.

Note the direction of their bias, because it runs against this article's convenience: with realistic variation in mutation and recombination rates they found "variable mutation and recombination rates resulting in the inference of an excess of effectively neutral mutations," and in one case "DFE-alpha inferred a completely neutral DFE for population contraction scenarios."⁵  The published effectively-neutral fractions may be too high, which is the direction that flatters the argument made on this site.

What follows.  Anyone who rejects the mainstream population history has to recompute the fitted numbers, not borrow them.  And anyone who accepts it should treat the published confidence intervals as narrower than the real uncertainty, because they condition on the model being right.

What the measurements say

Bacteria: the neutral class shrinks every time somebody looks harder

This is the most useful pattern in the whole literature, because it is a replication rather than an argument.

In 1998 Elena and colleagues measured 226 insertion mutations in E. coli and reported that at least 80% were deleterious and about 20% might be neutral.  Then they checked.  They took thirteen clones whose fitness had come out statistically indistinguishable from the ancestor and ran ten more competitions on each:

"In all 13 cases, the more extensive data indicated that the insertion mutation did indeed cause a significant fitness loss (in all cases between 1.2% and 2.2%) ...  Evidently, most of the mutations that appeared to be neutral based on the initial set of competitions are, in fact, slightly deleterious."⁶

Fourteen years later Gallet and colleagues built a flow-cytometry assay an order of magnitude more sensitive — "we were able to estimate mean selection coefficients to a precision of 2 × 10⁻⁴," the best figure anyone has achieved — and pointed it at three more of the same clones, chosen because they had been published as neutral.  All three were deleterious: −1.2%, −1.7% and −0.3%.⁷

Their conclusion is the sentence this entire page is organised around:

"mutations formerly considered as neutral ... actually confer small, but significant, fitness effects.  Importantly, even in an apparently constant environment, their effect is best understood as being distributed, which complicates straightforward application of discrete classifications (deleterious/neutral/beneficial)."⁷

The same lesson holds in Salmonella, where a more sensitive assay found 120 of 126 mutations in ribosomal protein genes weakly deleterious, including synonymous ones that change no amino acid.

What this does and does not license.  It does not show that every reported neutral mutation is really harmful — nobody has tested most of them, and the ones re-tested were chosen for re-testing.  What it shows is that the published neutral fraction is partly an instrument reading, and that it has moved in one direction every time the instrument improved.

The experiment that proves the assay sets the answer

If one result on this page deserves to be better known, it is this one.

Stiffler, Hekstra and Ranganathan took all 4,997 single amino-acid mutations of one bacterial gene and measured the fitness of every one of them at five different antibiotic concentrations.  Same mutations, same organism, same laboratory — only the strength of selection changed.

"The strength of ampicillin selection controls the fraction of mutations in these two modes; increasing antibiotic concentration causes the relative proportion of mutations in the mode with deleterious mutations to increase and in the mode with neutral/nearly neutral mutations to decrease."⁸

At low concentration "the vast majority of mutations are statistically neutral."  At high concentration most are deleterious.  Neither number is wrong.  Both are properties of the experiment as much as of the gene.

And the same gene has produced 0% and 7% beneficial in different hands.  A coarse resistance assay found none; a deep mutational scan at one concentration found 7.0%; Stiffler's scan across five concentrations found none at any of them.  The gene did not change.

That is the honest frame for every beneficial percentage quoted anywhere, including on this site.

Viruses, and the one study that asked why

Almost no study classifies why its beneficial mutations helped.  One did, and the answer is the one this page keeps arriving at.

Haddox, Dingens and Bloom scanned the HIV envelope protein and found three clusters of adaptive mutations.  All three destroyed features the virus uses to evade antibodies — glycan shields that "actually decrease viral fitness in the absence of immune selection," and which "would not be selected in nature because they expose conserved epitopes."⁹  In a dish with no immune system, throwing away immune defences is an improvement.  In a host it is suicide.

Bacterial and yeast counterparts point the same way.  Where mechanism was classified, adaptive mutations were overwhelmingly disruptive, and the resulting strains did worse under conditions the assay did not test.

The broadest measured number.  Across 32 bacterial species with genome-wide knockout libraries, deleting a gene was significantly beneficial in at least one condition for 18% of all genes tested.¹⁰  That is a large number, and it is a number about destruction: every mutation in that experiment is a gene knocked out.

And the authors of the clearest such study state the catch themselves: "most of the beneficial mutations studied here are neutral or deleterious in environments other than the one in which they were identified."¹¹

Plants and algae: the strongest measured counter-evidence

This section reports results that cut against this site's argument.  They are the best-measured DFEs in any multicellular or near-multicellular system, and in several of them about half of new mutations raise fitness.

Arabidopsis, seventeen generations, no detectable decline.  Shaw, Byers and Darmo ran 120 mutation-accumulation lines and assayed generations 0, 8 and 17 side by side.  "For three reproductive traits, mean number of seeds per fruit, number of fruits, and dry mass of the infructescence, the means did not differ significantly among generations."  Their conclusion was about shape, not just magnitude: "These findings suggest that the distribution of mutational effects for these traits is approximately symmetric, in contrast to the usual assumption that mutations have predominantly negative effects on traits directly related to fitness."¹²

A follow-up reanalysis fitted a gamma displaced from zero, so that it could admit fitness-enhancing mutations, and found "U approximately 0.1-0.2, with distributions of mutational effects broadly spanning zero, such that roughly half the mutations reduce reproductive fitness."¹³

And in the field it is stronger, not weaker.  Rutter, Shaw and Fenster took the lines outdoors: "Many of the mutation accumulation lines have increased fitness, counter to the expectation that nearly all mutations decrease fitness."¹⁴  Their broader finding is the one to keep: "mutation parameters are not fixed, but are variables whose values may reflect the specific environment in which mutations are tested."

The sign of s is not a property of the mutation.  A later paper sequenced the lines, so the mutations were individually known, then assayed them across environments: "We demonstrate that the effects are beneficial, deleterious, or neutral depending on the environmental context."  Including this, which is directly on point for the destruction argument — "a line with a major deletion spanning a transcription factor gene expressed lower fitness than the founder under most conditions but exceeded the founder's fitness in one environment."¹⁵

Chlamydomonas, mutations individually genotyped, twice.  Bondel and colleagues crossed mutation-accumulation lines back to the ancestor to make 1,526 recombinant haplotypes, genotyped 386 of 476 mutations, and assayed growth.  This is a direct measurement of individually known mutations, with no demographic model anywhere in it.  Fitted shape parameter beta = 0.32 (95% credible interval 0.26-0.70).  Headline: "Of mutations with absolute fitness effects exceeding 1%, about one-sixth increase fitness in the laboratory environment" — while the two-sided model puts "the proportion of positive-effect mutations ... surprisingly high (about 80%)."¹⁶  A second study on a different strain, using frequency change under selection rather than growth assay, reproduced it: "approximately equal proportions of mutations have positive and negative effects on fitness."¹⁷

Why this is not fatal to the argument, and why that answer is thin.  Every one of these numbers is conditioned on a resolution threshold of roughly |s| = 1%, and the authors say so: "Inferring the detailed shape of the DFE for mutations with very small effects is, however, limited by experimental resolutions."¹⁶  The two Chlamydomonas headline figures — one-sixth beneficial and 80% beneficial — are not a contradiction; they are the same data at two different thresholds, which is the resolution problem restated.  Genetic entropy is a claim about mutations one hundred to ten thousand times smaller than that threshold.  So these experiments do not measure the disputed class.

That is a real answer.  It is also unfalsifiable in the shape a skeptic will immediately notice: the argument survives by locating itself permanently below the resolution of every experiment that could test it.  Anyone advancing it should say so plainly rather than wait to be caught at it.

And the counter-evidence is not uniform.  The same laboratory, same organism, different ancestral strains: Kraemer and colleagues in 2017 found "MA lines were on average less fit than their ancestors" with a significant negative correlation between fitness change and mutation count — and reported that "the best-fitting mutational effects models were highly dependent on the genetic background of the ancestral strain."¹⁸  Chlamydomonas gives a mean fitness decline or it does not, depending which strain you start from.

Multicellular eukaryotes

The nematode Caenorhabditis elegans has the most complete record of any animal, because the same laboratory lines were both sequenced and fitness-assayed.  Setting those two accountings side by side produces the sharpest statement of the resolution problem in the literature.

The gap between what arrives and what is visible is about a hundredfold.  Denver and colleagues sequenced mutation-accumulation lines directly and found a total genomic rate of about 2.1 mutations per haploid genome per generation.  Fitness assays on the same lines had put the deleterious rate at about 0.015.  Their conclusion:

"our sequence-based estimate of U_t (~2.1 mutations per haploid genome per generation) is about two orders of magnitude higher than the haploid deleterious genomic mutation rate (U_d) estimated by laboratory fitness assays with the same set of C. elegans MA lines (U_d ≈ 0.015 mutations per haploid genome per generation), indicating that most mutations in the MA lines (more than 99%) might either be neutral or have deleterious effects too mild to be detected in laboratory fitness assays."¹⁹

Estes and colleagues reached the same place from the other direction, comparing about 864 expected nonsynonymous mutations per line against the two or three that showed up in fitness: "it is apparent that only a small fraction, perhaps ≪1%, of the mutations in complex sequence have detectable effects on laboratory fitness."²⁰

Both groups say the assay is the problem, not the mutations.  Denver's own resolution is that comparative data across Caenorhabditis species imply "the vast majority of nonsynonymous mutations (~94% on the basis of a between-species Ka/Ks ratio of 0.06) are sufficiently deleterious for selection to act against them in nature," and that a sequence-based deleterious rate is therefore about 0.48 — thirty times the fitness-assay figure.¹⁹  Estes puts it plainly: "it is likely that typical mutation-accumulation experiments vastly underestimate the rate of occurrence of mutations that would be detrimental in nature ... the laboratory serving as a poor substitute for natural environments."²⁰

Note what kind of claim that is.  The 94% is a between-species Ka/Ks inference, not a measurement of any mutation's effect.  So the honest statement is that the two figures — 99% invisible, 94% deleterious — are supported by different kinds of evidence, and the field currently cannot tell whether the missing damage is real and unmeasurable or simply absent.  That is the same gap this whole page is about, in the one animal where both accountings exist.

A caution about the standard estimator.  The mutation rates and effect sizes from these fitness experiments come from Bateman-Mukai moments, which cannot separate the two quantities.  Baer and colleagues state the limitation about as clearly as it can be stated:

"The Bateman–Mukai method depends on the unrealistic assumption that mutational effects are constant ...  To underestimate the number of mutations (U) means that their effects (ā) must be exaggerated or vice versa.  Negative sampling covariance between mutation rate and effect is not limited to the Bateman–Mukai method; rather, it is an inherent property of the exercise.  Likelihood methods suffer from the same limitation."²¹

So published U figures are lower bounds and published effect sizes are upper bounds, and they trade off against each other.  Estes's group tried to fit a gamma with variable effects instead and could not get it to converge on the data.²⁰  Rescaling their own experiment on the sequenced mutation count gives a mean effect of −0.016 rather than the −0.11 to −0.21 the fitness analysis implied — an order of magnitude apart, from the same lines.

And the decay rate is not a species constant.  Across six inbred strains in three rhabditid species, Baer's group found the two C. briggsae strains "declined in fitness about twice as fast as either C. elegans or O. myriophila," with mutation-rate estimates differing severalfold between congeners.²¹  Any argument that quotes a single nematode U or s is quoting one strain.

The estimator cannot tell you what you want to know

Almost every mutation-accumulation number in the literature comes from the Bateman-Mukai method, and it has a structural limitation that is stated in the papers and dropped in the citations.

It observes two things: how fast the mean declines, and how fast the variance between lines grows.  From those two numbers it solves for two unknowns — how many mutations arrived, and how big each one was.  That works only if every mutation has the same effect.  Real effects vary, and the algebra then guarantees a one-directional error: the mutation rate comes out too low and the effect size comes out too high, and the two errors trade off exactly against each other.

Published U figures are therefore lower bounds and published effect sizes are upper bounds.  Vassilieva's group is the only one that labels its table columns honestly — U_min and ā_max.

How much does this matter?  Keightley and Bataillon measured it.  Fitting the same C. elegans data under different distribution shapes, they found that the mutation rate could be twelve times higher and the mean effect twenty times smaller at essentially no cost in likelihood.²²  The data do not choose.  Their abstract says so:

"changes of mean and variance of genetic values of MA lines in both C. elegans experiments are dominated by mutations with large effects, but the analysis does not rule out the presence of a large class of deleterious mutations with very small effects."²²

That sentence is the whole problem in one line.  "Few mutations of large effect" and "few of large effect plus an enormous invisible class of tiny ones" fit the data equally well — and those two worlds have completely different implications for whether a genome degrades.

The one experiment that bounded the invisible class

If mutation-accumulation assays cannot see small effects, the obvious move is to count the mutations by some independent route and ask how many went missing.  Davies, Peters and Keightley did exactly that: they induced mutations chemically at a rate they could calibrate, then measured how many showed up in fitness.

"In fitness assays, only about 4 percent of the deleterious mutations fixed in each line were detectable.  The remaining 96 percent, though cryptic, are significant for mutation load, and, potentially, for the evolution of sex."²³

And because the total was known independently, they could put a ceiling on how large the invisible ones could be: below about 0.07% of fitness each.²³

Two things follow, and they point in opposite directions.  The invisible class is real and it is large — this is the strongest direct evidence for it in any animal.  And the same result caps its per-mutation effect at a level far too small to notice in any experiment anyone can run, which is why the argument about it is still going.

Their model comparison also killed the standard curve.  A gamma distribution could not fit both a spike of severe mutations and a mass of tiny ones at once; a two-class model beat it decisively.  Their words: "the underlying distribution of mutation effects may be multimodal, because the γ distribution does not simultaneously allow a high frequency of slightly deleterious mutations and a 'spike' of strongly deleterious mutations."²³  Nearly every calculation in this field, including the ones on this site, uses a gamma.

How stable are these numbers? Not very

Daphnia is the cleanest test of reproducibility, because the same laboratory ran mutation-accumulation experiments on the same species for three decades.

Across traits and populations within one species, the Bateman-Mukai mutation rate estimates span from 0.002 to 1.946 — three orders of magnitude — and several carry standard errors as large as the estimate itself.²⁴  The two published beneficial figures, both line-level rather than per-mutation, are 8.1% of lines showing a significant positive slope in competition²⁵ and "up to ∼14% of the lines" whose net mutational effect could have been unconditionally beneficial in a modern assay.²⁶

And in thirty years of work on the organism, nobody has ever fitted a distribution to the fitness effects.  There is no gamma, no shape parameter, and no confidence interval on a shape parameter anywhere in the Daphnia literature.  The distributions used in every simulation of this argument — including Drift Lab's — are borrowed from other organisms.

The one experiment that watched a damaged genome recover

This is the most directly relevant result in the animal literature, and it deserves its own treatment.

Denver's group took an C. elegans line that had been bottlenecked for 323 generations and lost nearly half its fitness, let five populations of about a thousand individuals recover for 60 generations, and sequenced everything.  Fitness came back.  The question is how.

No mutation reverted.  Not one:

"We identified 68 base-substitution changes between N2 and MA12; in all 68 cases, the mutation was also detected in each of the three MA12-derived recovery lines.  Thus, no reversions of MA12 mutations were detected in the recovery lines."²⁷

The recovery was entirely compensation, and entirely somewhere else in the genome:

"None of the recovery response is attributable to detectable reversion mutations, and no cases of putative intragenic compensatory mutations were identified.  Thus, intergenic compensatory mutations likely drive all of the change that we observe."²⁷

That is the distinction this site's accounting argument turns on, measured rather than argued: fitness restored, damage untouched, the repairs located at different loci from the breaks.  The endpoint is a genome that performs like the ancestor while carrying all 68 of the mutations that degraded it.

They also measured the beneficial rate, and it is the only such measurement in an animal:

"This leads to a lower-bound adaptive genomic mutation rate estimate (U_a) of 3.8 × 10⁻⁵ per nematode per generation ...  this suggests that as few as one mutation in 55,263 (U_a/U_t) is adaptive."²⁷

Four caveats, all theirs, and they matter.  They could not distinguish beneficial mutations from neutral ones that hitchhiked, because the worm self-fertilises and everything is linked.  They only detected base substitutions, so indels and rearrangements could have driven the recovery instead.  They never functionally validated a single fixed mutation — the crosses failed.  And their own strong-selection inference of s ≈ 0.7 to 0.9 applies to compensating a genome already carrying 50% fitness loss, which is the regime where compensation is cheapest and says nothing about an undamaged one.²⁷

Read carefully, the result cuts both ways and should be stated that way.  Compensation is real, fast, and effective — a population recovered from severe damage in sixty generations.  And it repaired nothing: every original break was still there at the end.

Humans

Nobody has ever measured a human distribution of fitness effects.  Not without a population history — not at all.  Every published human DFE is the output of a model in which a demographic history and a selection model are fitted together, or one that imports a history from another paper, or one that absorbs it into free parameters standing in for it.

That is a strong claim, so here is what would count as an exception and why none qualifies.

The one human method that escapes demography works only where the argument does not live.  Estimating a per-gene selection coefficient from deterministic mutation-selection balance needs no population history — but it needs selection strong enough to overwhelm drift.  Weghorn and colleagues tested where it breaks and put the answer in their own abstract: the model "is applicable to the majority of human genes, but not to genes under the weakest selection."²⁸  It fails below a heterozygous cost of about 0.01 — roughly two hundred times above the drift barrier.  So the demography-free method covers everything except the region in dispute.

The one fully model-free measurement in living humans returned two loci.  Mostafavi and colleagues compared allele frequencies across age groups in about 150,000 people, with no demographic model at all.  Across roughly nine million variants, the entire genome-wide-significant yield was the APOE ε4 tag and a variant near CHRNA3.  No selection coefficients were reported.²⁹  That is what demography-free human measurement can currently do: find an effect large enough to shift an allele's frequency within a single lifespan, and nothing smaller.

And deep mutational scanning of human genes measures something else.  A saturation screen of a human gene in a cell line measures whether cells survive in a dish.  It is a molecular-function assay, not a selection coefficient in a population, and it is blind to any function the assay does not interrogate.

What this means for every human number on this site.  The mutation rate is a measurement.  The distribution of fitness effects, the functional fraction, and the effective population size are not — they are model outputs, and they inherit the history assumed to produce them.  Anyone who rejects that history has to recompute them rather than borrow them; anyone who accepts it should treat the published intervals as narrower than the real uncertainty.  This is set out at greater length in the main article.

The beneficial side

Most published "beneficial" figures are not what a reader assumes.  There are three different quantities in circulation and they differ by orders of magnitude.

alpha is not a beneficial fraction.  alpha is the share of substitutions between species driven by positive selection — the proportion of changes that got fixed, not the proportion of mutations that arrive.  Published animal values run from 0.18 to 0.93.³⁰  Quoting alpha as though it were "X% of mutations are beneficial" inflates the number by three to four orders of magnitude, and it is a mistake made in both directions of this debate.

The beneficial fraction of new mutations, where anyone has actually fitted one.  Booker and Keightley did it for wild mice from the unfolded frequency spectrum, and got p_a = 0.0030 at nonsynonymous sites, 0.013 in untranslated regions and 0.0098 in conserved noncoding elements.³¹  They also flag that this class of estimate runs high: "the frequency of advantageous mutations (p_a) was overestimated" in their own simulation check.

The only direct animal measurement is far smaller still — Denver's nematode recovery experiment put a lower bound at one mutation in 55,263.²⁷

Nobody has classified the beneficial side by mechanism.  Not once, in any organism.  Every figure above answers "did fitness go up?" and none answers "did anything get built?"  That distinction is the one the argument actually needs, and it is missing from the literature rather than answered against us.  This is set out with the evidence in the main article.

Where the numbers came from in creationist models

The same audit applied to our own side.  Six intelligent-design and creationist modelling papers were checked against their cited primaries.  The result is mixed, and the failures are worth naming first.

The worst-sourced parameter is Axe's lambda = 15.  It appears in a footnote to Table 1 of his 2010 waiting-time paper: "With 75% of random base substitutions being non-silent (unpublished simulation) and 1.5 kcal/mol reduction in folding stability being typical for single amino acid substitutions ... 15 random base changes would be expected to destabilize most proteins."³²

The 75% is correct — of the 549 single-base substitutions available from the 61 sense codons, 415 are non-silent, or 75.6%.  It is a property of the genetic code that any reader can derive in ten lines of code.  Citing it to a private, undocumented simulation instead is a real failure of practice, even though the number survives.  The 1.5 kcal/mol figure is weaker: it is eyeballed off a method-validation scatter plot in Guerois et al. 2002, which never states a typical value, and the mainstream measurement is lower — Tokuriki and Tawfik give about 1.3 kcal/mol for an average enzyme mutation, 0.6 at surface residues.  A higher figure makes lambda smaller and waiting times longer, so the bias runs in Axe's favour.

In fairness, lambda is not load-bearing.  Doubling it to 30 shrinks the waiting time by 2.5x at d = 4 and 19x at d = 7, while waiting times rise roughly 500x per unit increase in d.  Axe's headline conclusion survives, and the maladaptive case does not use lambda at all.

Two other unsourced parameters.  Axe 2010's adaptive coefficient s+ = 0.01 has no reference, no footnote and no justification anywhere in the paper; it enters only linearly.  Gauger and Axe 2011's assumption A4, "an overall growth advantage of 1%", is its direct descendant and is likewise uncited.  Their duplication rates and the pyrD 4% fitness cost do check out against Reams et al. 2010 — but the argH cost is given as 16% where Reams' table reports 0.77 and 0.74 relative fitness, a 23-26% cost.

Three of the six deserve credit, and one of them makes this page's own argument.  Axe et al. 2023 does not input a distribution of fitness effects at all; it lets one emerge from a scoring engine, precisely to escape the circularity it names in its own paper: "Computer models offer an alternative that can be studied with statistical precision, but usually only because the distribution of mutation effects is a model input.  The statistics that come out of these models are dictated by the statistics that went in."³³  That is an ID paper making the criticism a skeptic would make, against ID-adjacent modelling, and then meeting it.  Hossjer, Bechly and Gauger 2021 states that its selection coefficients have no empirical source and explains why, rather than smuggling them in.  Ewert 2015 flags three separate assumptions that favour his opponents.

Two things to disclose alongside any use of these.  Every BIO-Complexity paper carries the line "A Critique of this paper, when available, will be assigned doi:...c."  All five such critique DOIs return 404; sixteen years on, none has been written, while the supplement DOI resolves fine — so the absence is not a registration failure.  And Axe et al. 2023 and Ewert 2015 both have zero citations in OpenAlex.

The one exchange that went the other way.  Behe and Snoke's 2004 waiting-time paper reached Protein Science, was attacked by Lynch, and was then tested by Durrett and Schmidt in Genetics.  Behe raised three numerical objections to their reply.  Durrett and Schmidt conceded one outright — "Behe is right on this point.  This divides our previously computed overestimate of 5 million by 30" — and rebutted the other two.³⁴  That is what the process looks like when it works, and both halves belong in any honest citation of it.

What is missing

Four measurements would settle most of this, and none of them exists.

1. A distribution of fitness effects with the beneficial side classified by mechanism — repair, regulatory retuning, deletion, duplication, genuinely novel function. Achievable with current sequencing and structural tools. Nobody has published it.
2. A human DFE that does not assume a population history. Whether this is even possible is an open question worth stating.
3. A fitness assay that reaches 10⁻⁵. This is an instrumentation problem, and the field names it as one.
4. Mutation-accumulation lines in an organism with a known 100% functional genome. The minimal cell JCVI-syn3B has 493 genes, every one essential. Nobody has assayed fitness in mutation-accumulation lines of it. That would be the cleanest test of this whole argument that current technology allows.

Until those exist, every headline number on this page is either a measurement in the wrong range or a model output conditioned on a history, and the honest position is that the shape of the curve where it matters is unknown.

Sources