Sanford's Genetic Entropy, audited

"According to Kimura, fitness has low heritability - even as low as .004 (Kimura, 1983, p.30-31)." — Genetic Entropy, 2nd edition, chapter 4.  Kimura's figure is a broad-sense heritability measured in fruit flies, and he deploys it against a conclusion Sanford is arguing for.

John Sanford's Genetic Entropy & the Mystery of the Genome is the book that put this argument into circulation.  Sanford is a real plant geneticist — he co-invented the gene gun at Cornell and holds the patents — and the book is the reason most people who have heard of genetic entropy have heard of it.

It is also the weakest link in the case.  This page audits it against the primary sources, because an argument that depends on a book nobody has checked is not worth making.

The short version.  The book's central mechanism is sound and is now mainstream.  Its three most-quoted numbers are all misused, in ways that take between thirty seconds and an hour to verify.  Four editions across nine years fixed none of them.  The same pattern shows up outside the book, in a 2013 chapter that cites the only measured RNA-virus distribution of fitness effects and then uses none of its four values.  The main article's case is built from the primary literature rather than from this book, and that is deliberate.

What the book gets right

This has to come first, because the errors below are easy to mistake for a verdict on the whole argument.  They are not.

The mechanism is real and is not disputed.  Mutations whose fitness effect is smaller than roughly 1/(2N_e) are invisible to selection and fix at close to the neutral rate.  That is Ohta's nearly neutral theory, and Ohta states it in her own review: "I propose that a substantial fraction of mutant substitutions at the molecular level are caused by random fixation of very slightly deleterious mutations."¹  Sanford did not invent this and does not claim to.

The direction is right.  Mutations that land in functional DNA are overwhelmingly more likely to break something than improve it.  Every measured distribution of fitness effects, in every organism, is skewed toward harm.

The load literature he cites is real.  Muller raised the problem in 1950, Kondrashov titled a 1995 paper "why have we not died 100 times over?", Crow called the mutation rate a health risk in 1997, and Lynch has been warning about it for two decades.  None of them are creationists.  Sanford did not manufacture a controversy; he entered one.

And a mainstream lab now counts the fixations.  The Masel group at Arizona simulated a human-scale population and counted 56,255 deleterious fixations against 6,387 beneficial ones, and they call the process Ohta's ratchet.  The main article's arithmetic, run on their stated parameters, lands 12–26% above their count, the direction expected when a simulation includes linkage and a single-site equation does not.

So the question is not whether the process exists.  It is whether the book's numbers about it can be trusted.

Error 1: the Eyre-Walker and Keightley quotation

What the book prints, in Appendix 1 of the 2005 edition:

"...deleterious mutations rate appears to be so high in humans and our close relatives that it is doubtful that such species could survive..."

What the paper says, verified against the authors' own PDF:

"The deleterious mutation rate appears to be so high in humans and our close relatives that it is doubtful that such species, which have low reproductive rates, could survive if mutational effects on fitness were to combine in a multiplicative way.  Our results instead indicate that synergistic epistasis may occur between deleterious mutations, in hominids at least."²

Two things are cut, and neither cut is marked.

The first is an unflagged internal deletion: "such species, which have low reproductive rates, could survive" becomes "such species could survive", with no ellipsis at the join.

The second matters more.  The sentence does not end at "survive."  It ends with a condition — if fitness effects combine multiplicatively — and the authors' next sentence says their results indicate they do not.  Eyre-Walker and Keightley are running a reductio: multiplicative fitness is the thing that fails, so the real world must not be multiplicative.  The terminal ellipsis converts a rejected premise into a bare declaration that hominids should not exist.

In Sanford's favour, and it should be said: on the same page he quotes Nachman and Crowell with their multiplicative conditional intact, and he names and argues against synergistic epistasis in his own commentary.  He is not concealing the escape hatch.  He cut it out of one particular quotation, and that quotation is the one that gets reproduced.

Error 2: Crow's 1–2% run backwards through history

What the book does.  Figure 4 takes James Crow's estimate of a 1% per generation fitness decline and projects it back over 300 generations.  The 2005 caption:

"Dr. Crow (1997) indicates that he believes the fitness of the human race is presently degenerating at 1-2% per generation, due to the accumulation of mutations.  A 1% decline in fitness per generation (beginning with a fitness of 1) is shown for a hypothetical human population - over a period of 300 generations (6,000 years)."

What Crow wrote, in PNAS, free to read:

"If we are like Drosophila, the decrease in viability from mutation accumulation is some 1 or 2% per generation.  This is more than compensated for by much more rapid environmental improvements, which are keeping well ahead of any decreased efficiency of selection."³

Three things are wrong with the extrapolation, and they compound.

It is a fruit fly number.  "If we are like Drosophila" is a conditional, not a measurement in humans.

It is a modern number.  Crow locates it explicitly in "the past few centuries" and in "the wealthy nations", where "natural selection for differential mortality is greatly reduced."  His stated cause is relaxed mortality selection under modern medicine and wealth.

So running it back 300 generations asserts the effect in 299 generations that lack the cause.  On Sanford's own young-earth chronology, 300 generations reaches back roughly 6,000 years — nearly all of it before the conditions Crow names.

Again, in fairness: Appendix 1 does quote Crow's compensation clause.  The qualifier is in the book.  It is absent from the figure that does the work, and the figure is what circulates.

Error 3: heritability of fitness = 0.004

This is the most consequential of the three, because three chapters rest on it.

What the book says, across the 2005 edition:

"According to Kimura, fitness has low heritability - even as low as .004 (Kimura, 1983, p.30-31)."

"For a very general phenotypic trait, such as 'reproductive fitness', additive variation can account for less than 1% of total phenotypic variation (Kimura, 1983, p.30-31).  Another way of saying this is that more than 99% of any selective elimination based upon phenotypic superiority is entirely wasted."

"If Kimura's estimate is correct that fitness typically has a heritability of only about .004, then only about 0.4% of phenotypic variation for fitness is selectable.  This represents a signal-to-noise ratio of about 1:250."

What Kimura's page actually says:

"There is the possibility, however, that the broad-sense heritability of fitness is very low.  In fact, Mukai, Schaffer and Cockerham (1972) showed in Drosophila melanogaster that the fitness of individuals as a quantitative character has an extremely low... heritability (H²) of about 0.004, so that threshold or truncation selection cannot work effectively without entailing very severe culling."⁴

Four things go wrong.

It is broad-sense H², not narrow-sense h².  Sanford renders it as h² and repeatedly treats it as the additive component, which is the quantity that determines the response to selection.  They are different numbers.  The words "broad-sense", "narrow-sense", "Mukai" and "Drosophila" do not appear anywhere near the claim in the 2005 edition.

It is one estimate, in one species of fly, from one laboratory, and Kimura hedges it — "There is the possibility, however."

Kimura's point is the opposite of the use made of it.  He raises the low figure as an objection to Maynard Smith's truncation-selection rescue of Haldane's dilemma.  It is deployed against a position, not asserted as a general law about fitness.

And the 250 is stated without saying what it measures.  The breeder's equation has three equivalent forms, and they scale differently with heritability.  The fraction of the selection differential that is passed on is R/S = h².  The shift in the mean, measured in phenotypic standard deviations, is R/σ_P = i·h², where i is the intensity of selection.  The same shift measured in additive-genetic standard deviations is R/σ_A = i·h, the square root.  At h² = 0.004 the first two cost a factor of 250 and the third a factor of about 16 (1/√0.004 = 15.8).  Sanford's "signal-to-noise ratio of about 1:250" is a statement about the fraction of phenotypic variation that is selectable, which is the R/S question, and for that question 250 is arithmetically right.  An earlier version of this audit said the response "scales with the square root of heritability" and that the true cost is 16, not 250;  that is true only when the response is measured against the genetic standard deviation.  The real defect is that neither Sanford nor his critics, this page included, named the currency.  Which one matters depends on whether the question is how much of the imposed culling is returned (250) or how fast the population moves through the genetic variation it actually has (16).  The low heritability is a real and large cost in both.

A direct measurement now exists and lands between the two positions.  Bonnet and colleagues analysed 249,430 individuals across nineteen wild bird and mammal populations and put the heritability of fitness near 3%.⁵  That is very low — far below the 20% Mendel's Accountant uses as a default, which its own manual calls "extremely generous" — and it is also about seven and a half times Sanford's figure (0.03 against 0.004).

Error 4: the "138 sites" figure

On the same two Kimura pages sits a fourth problem, which appears not to have been noticed before.

Sanford writes that Kimura "states that only 138 sites can undergo selection simultaneously."

The 138 is not Kimura's figure.  It is Maynard Smith's, calculated for the multiplicative model Maynard Smith was arguing against.  The number Maynard Smith actually advocates — on the same line of the same page — is 25,500, about 185 times larger.  The book does not mention it.

Error 5: Figure 3d assumes its own conclusion

Figure 3d is the image that has carried this argument further than any sentence in the book: a large deleterious hump, a mirrored beneficial hump, and a shaded box labelled "Kimura's 'no-selection zone'."

Two points of credit first.  The deleterious side really is adapted from Kimura 1979, and Sanford says so.  And he discloses that the beneficial side is drawn far too large — "I have shown the expected beneficial distribution, but very greatly exaggerated, so it can be seen" — which is more honest than the figure's usual reproduction, where that caption is missing.⁶

The problem is the shape, which is asserted:

"Their distribution would be a reverse image of Kimura's curve, but reduced in range and scale, by a factor of somewhere between one thousand to one million."⁶

No source is given for "reverse image," because there is not one.  Kimura's distribution is a gamma over deleterious effects, and gammas are one-sided by construction — there is no beneficial side to mirror.  And the mirror assumption is what produces the conclusion.  Reflect the deleterious curve and every beneficial mutation is tiny by construction, therefore inside the box, therefore unselectable.

Measured beneficial distributions are not mirror images.  They are roughly exponential, with mean effects far larger relative to their frequency than a scaled-down gamma allows — and the mean beneficial effect is precisely the parameter the modern mainstream resolution turns on.

The 1,000-to-1 through 1,000,000-to-1 ratio is also contradicted by direct measurement.  Deep mutational scans put the beneficial fraction between about 1% and 7%: Joseph and Hall's yeast measurement at 5.75%, Firnberg's β-lactamase scan at 7.0%, Couce's E. coli ancestor at 6.8%.  Those are ratios near 15:1.  Some of the gap is real — laboratory assays inflate the beneficial fraction — but none of it reaches 1,000,000:1.

Error 6: the long-term E. coli claim reverses the paper it cites

Christopher Rupe and John Sanford published a document in 2015 arguing that Lenski's long-term evolution experiment "is ironically one of the most powerful demonstrations of genetic entropy and de-evolution."⁷

That half is defensible and nobody disputes it: the adaptive mutations in the LTEE are overwhelmingly losses and deletions of function.  It is also this argument's Argument 3 — adaptation by subtraction.

The rest contains a factual reversal that takes one abstract to check.  Their Figure 1 reproduces the fitness trajectory from Wiser, Ribeck and Lenski's 2013 Science paper and captions it:

"The red line represents the best-fit curve using the power-law model, based on the complete data set over the course of 50,000 generations.  It shows fitness has reached a near maximum and is not expected to significantly increase.  The blue line represents an alternate way of interpreting the data (using the hyperbolic model) that is favored by Lenski and colleagues.  It suggests fitness will increase without bound."⁷

Both attributions are backwards.  The power law is the unbounded model, and it is the one Lenski's group concluded fits — their abstract reads "Mean fitness appears to increase without bound, consistent with a power law."⁸  The hyperbolic model is the one with an upper asymptote, and it is the model they rejected.

And the experiment kept running.  Fitness in the LTEE continued to rise past 50,000 generations, including in the mutator lines running at 10 to 100 times the normal mutation rate.⁹  If a raised mutation rate drove decline in an asexual population, the mutator lines are where it would appear, and they are the lines that improved.

There is a good reason the LTEE cannot show genetic entropy — enormous population, small genome, asexual reproduction, so the drift barrier barely bites.  That is a fair answer, and it is also a reason not to have claimed the experiment as a demonstration.

Four editions fixed none of it

The book has gone through four printings, and the publisher advertises the fourth as containing "updated references, author's updates, and a new chapter."

Checking the 4th edition's text directly, all five problems survive:⁶

• The Eyre-Walker ellipsis — unchanged, essentially verbatim.
• The Crow extrapolation — unchanged. The caption widened "(6,000 years)" to "(6,000-9,000 years)" and added a clause about a "classic biological decay curve." The extrapolation itself is untouched.
• h² = 0.004 — unchanged. The only edit is that "even as low as .004" became "perhaps as low as 0.004." The number, the citation, and the three chapters built on it are the same.
• The 138 figure — unchanged.
• Figure 3d — unchanged.

One genuine improvement is worth recording: the 4th edition adds citations to Merilä and Sheldon 2000 and Kruuk 2000 on the heritability of fitness, which the earlier editions lacked.

A note on checking this yourself.  The 2nd and 3rd editions can be borrowed through Internet Archive's controlled digital lending.  The 4th cannot — its lending status was removed on 7 February 2025, and it is now reachable only through a print-disabled account.  Its text can still be searched, without page numbers, through Open Library's cross-corpus search-inside.

Error 7: the beneficial ceiling is an information argument spent as a fitness parameter

This is the most consequential problem in the book, and it is visible only by reading Sanford's own defence of the parameter.

Every simulation in this literature caps how good a beneficial mutation is allowed to be.  Mendel's Accountant has a setting for it; the published runs set it at 0.001 or 0.01.  That ceiling does most of the work — where it is lifted, the models stop declining.

The one place the ceiling is argued for is Appendix 5, and the argument is entirely about information:

"In a genome with 3 billion units of information, the average beneficial mutation should only increase information by about one part in 3 billion.  Yes, some beneficials will have more benefit than others, creating a natural distribution, but it is entirely unreasonable to believe that any beneficial point mutation could add as much information as, say, 30 million functional nucleotides."⁶

"it is conceivable that a mistake could cause you to stumble up hill, but only by a few feet.  You will never stumble uphill by thousands of feet."⁶

But the parameter it justifies is a ceiling on fitness, and Sanford himself insists the two come apart.  In the same appendix, on antibiotic resistance:

"So fitness has not merely been doubled relative to the other bacteria, it has increased infinitely, going from zero to one."⁶

"Certainly the two examples above are both 'mega-beneficial mutations' in terms of adaptation to a specific environment.  But they are both loss-of-function mutations that reduce net information within the genome.  In terms of information content, they are both still deleterious mutations."⁶

Read those together.  By his own analysis, real beneficial mutations routinely have fitness effects far above any of the caps used — one, he says, is effectively infinite — while having negative information effects.  The argument therefore supports capping an information gain.  It gives no support to capping a fitness gain at 0.001, and it is the fitness number that goes into the simulator.

The empirical check is not close.  One part in three billion is 3 × 10⁻¹⁰.  Measured mean beneficial effects in E. coli run around 1%, and individual beneficial mutations in the long-term evolution experiment run from about 1% to 13%.  That is seven to eight orders of magnitude between the asserted average and the measured one.

And it explains a pattern that runs through the whole literature.  Wherever the fitness ceiling is raised, the models stop behaving the way the thesis requires — which is the same observation Douglas Axe makes from inside the intelligent-design camp, below.

Credit where it is due, because it matters.  The distinction Sanford is drawing — that a mutation can raise fitness while destroying information — is correct, and it is underappreciated.  It is the same point this site makes at length about beneficial mutations being mechanism-blind, and it is the strongest idea in the book.  The defect is not the distinction.  It is that he draws it and then spends it in the wrong currency.

One related overreach worth flagging.  Of the long-term E. coli experiment's beneficial mutations, the 4th edition says "they all involved loss-of-function events (either broken genes or broken promoters).  Genome size consistently shrank ... (manuscript in preparation)."⁶  The strongest form of the claim is sourced to an unpublished manuscript of his own, and "all" does not survive the published genomics, which include regulatory point mutations in topA, spoT and pykF, and the citrate innovation's promoter capture.

Beyond the book: a chapter cites the one measurement and uses none of its numbers

Everything above concerns the book.  This section does not, and it is included because it is the clearest documented case of the method the book is accused of.

In 2013 Wesley Brewer, Franzine Smith and John Sanford published "Information Loss: Potential for Accelerating Natural Genetic Attenuation of RNA Viruses" in Biological Information: New Perspectives.¹⁰  It simulates an RNA virus degenerating.  Its methods section states the distribution of fitness effects it assumed:

"We model 10% of all mutations as being perfectly neutral, with the remainder of mutations being 99% deleterious and 1% beneficial [35]."¹⁰

That works out to 10% neutral, 89.1% deleterious, 0.9% beneficial.  Reference 35 is Sanjuán, Moya and Elena 2004 - a study that measured an RNA-virus DFE by building 91 site-directed mutants of vesicular stomatitis virus and competing them.¹¹  Here is what that paper reports for random mutations, against what the chapter assumed:

The assumed categories differ from the measured sample.  The neutral and beneficial shares are 2.7-fold and 4.7-fold lower, respectively.  Those choices reduce the room for neutral changes and beneficial compensation; the net effect of omitting a separate lethal class cannot be inferred from those ratios alone.  Steve Schaffner of the Broad Institute drew attention to the mismatch on the BioLogos forum.¹²

The lethal class had an escape hatch, and it was switched off.  The chapter answers the missing 39.6% lethal fraction by saying such particles can be accounted for through a random-death setting.¹⁰  But the headline run — the one Figure 1 reports and the abstract's claim rests on — sets that parameter to zero: "we modeled zero random death (zero percent of the viral particles were randomly lost)."¹⁰  So in the run that produces the result, the lethal class appears neither in the distribution nor in the parameter offered to absorb it.

The measured sample does not settle the precise distribution.  The discussion says: "Our greatest reservation is that no one knows the precise shape of the distribution of mutation effects for a given virus."¹⁰  A finite sample with a detection threshold does not contradict that reservation.  The narrower question is why the chosen distribution departs from the empirical sample cited in its support.

The counterweights, because the criticism is unfair without them.  Sanjuán himself says his figures "have to be considered as lower bounds, because some of the mutations classified as neutrals could actually have a fitness effect too weak to be detected."¹³  So the true neutral share is probably under 27.1%, and adjusting it downward is defensible - although that does not establish the chapter's chosen 10%.  He also flags his own beneficial fraction as suspect and explains why: his template was a chimera of two virus strains, so "many different possible ways to optimize such genomes are available," and the ratio of beneficial to deleterious "depends on the degree of adaptation of the virus to the laboratory conditions, which in this case is minimal."¹⁴  A creationist can fairly argue 4.2% is a maladapted-chimera artefact.  The chapter also discloses the lethal shortfall in words rather than hiding it, and this is a symposium book chapter, not a refereed journal paper.

What survives all of that.  The chapter's assumed class shares differ substantially from the empirical sample it cites, and its first run omits the random-death setting offered to represent lethal mutations.  These are reasons to test the simulation's sensitivity to its inputs.  The experiment does not supply an exact universal distribution, and these discrepancies alone do not establish how much changing the inputs would alter the result.

The sharpest criticism comes from inside the intelligent-design camp

Douglas Axe is the intelligent-design movement's most prominent laboratory scientist.  In 2023 he published a genetic-entropy result of his own — a population of 1,000 computational organisms whose fitness "declines approximately as a two-phase exponential decay," ending in "substantial loss of function for all 223 genes."¹⁵  He is an ally of the conclusion.

He is not an ally of the method.  His introduction states, of digital models of this kind:

"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."¹⁵

And he names Sanford's group specifically, noting that when their own parameters allowed occasional large beneficial mutations, those mutations reliably appeared given enough time and "substantially increase the fitness of the population by offsetting the prior history of mildly harmful mutations."¹⁵  His stated aim is to escape that circularity: "Our aim here is to examine genomic information loss in a model system that does have an underlying genetic mechanism."

This is the same criticism this article makes of Figure 3d — assume a mirrored distribution and you have assumed the answer — arriving from an author who accepts the conclusion and is trying to establish it more honestly.  It should carry more weight with a skeptical reader than anything a critic says, and it is the reason Drift Lab exposes every parameter and reports the ones nobody has measured as unmeasured.

One thing about the venue should be disclosed rather than left for a critic.  BIO-Complexity attaches to every paper a note that "A Critique of this paper, when available, will be assigned" its own DOI.  In seventeen years and fifty-five articles it has published none.  A promised adversarial review that never arrives is not peer review, and that applies to this paper as much as to any other in the journal.

What a fair reader should conclude

Not that the argument is wrong.  The mechanism the book describes is real, mainstream, and currently being quantified by people who reject every theological conclusion Sanford draws from it.

But that the book is not a reliable source for the numbers.  Three of its most-reproduced figures — the Eyre-Walker quotation, the Crow decline rate, and the heritability of fitness — are misused in ways that a reader with the primary sources can catch in an afternoon.  A fourth misattributes a number to Kimura that belongs to Maynard Smith, and a fifth draws a distribution it then reads as evidence.  Nine years and three revisions changed a comma, a parenthesis, and one adverb.

That matters beyond this book.  A critic who finds one of these errors will reasonably assume the rest of the case is built the same way.  The main article is built from Kimura, Ohta, Haldane, Kondrashov, Charlesworth, Lynch and Masel instead — not because Sanford is a creationist, but because the numbers have to survive being checked.

Sources