Haldane's Dilemma and the Waiting-Time Problem

"It is suggested that, in horotelic evolution, the mean time taken for each gene substitution is about 300 generations. This accords with the observed slowness of evolution." — J. B. S. Haldane, the last two sentences of the paper that started this¹

"Population geneticists no longer exhibit obvious concern that Haldane's Dilemma poses a limitation to the speed of adaptation, even when e.g. reporting high rates of adaptive sweeps." — Matheson, Exposito-Alonso and Masel, Genetics, 2025²

"Remine is right about one thing — the 1970s discussion was left unresolved, a mess. It was not population genetics's finest hour." — Joe Felsenstein, population geneticist, on sci.bio.evolution, 2006³

Summary

In 1957 the British geneticist J. B. S. Haldane published a short paper asking a question nobody had made quantitative before: when natural selection replaces one gene with another, how many organisms have to die for it?

His answer was that the number is surprisingly large, surprisingly constant, and almost independent of how strong the selection is. Substituting one gene costs roughly thirty times the population's size in selective deaths. A species can only afford to spend so much of its reproductive capacity on this, so gene substitutions must be spaced out — Haldane guessed about one per 300 generations.

Creationists later turned that number into an argument. If the human lineage had 10 million years and a 20-year generation, it had 500,000 generations, which buys about 1,667 beneficial mutations. Is 1,667 enough to turn an ape into a human? Walter ReMine named this "Haldane's dilemma" in its modern form and built a book around it.⁴ John Sanford later added a second and different argument — the waiting-time problem — about how long a population must wait for a specific string of mutations to appear at all.⁵

This article works through both. The research behind every claim is in the literature review and the fourteen dossiers beside this article. The conclusions, in order of confidence:

Haldane did not think he had found a problem for evolution, and the word "dilemma" is not his. His paper's closing line is that his result "accords with the observed slowness of evolution," and on the Pleistocene mammal record he wrote "The agreement with the theory here developed is satisfactory."¹ The name was attached by Leigh Van Valen in 1963.⁶ Haldane called it a cost, treated it as an explanation of a known fact, and in his last year of life called it "one of the factors, perhaps the main one, determining the speed of evolution."⁷
The famous 300 is two judgment calls stacked on each other, and both are Haldane's own. The cost figure of 30 is padded up from his own typical range: "To allow for occasional high values I take 30 as a mean."¹ The 10% selection intensity is a guess — "I think n = 300, which would give I = 0.1, is a more probable figure"¹ — and the one intensity he actually measures in the paper is 0.03, which would give 1,000 generations instead.¹ He also sanctions a 23-fold exception for colonists in empty habitat, while calling such episodes "probably exceptional."¹
The 1,667 figure is the single most generous arithmetic available, and it is not Haldane's. It is 10 million years ÷ 20 years ÷ 300, and it first appears on page 217 of ReMine's book.⁴ Every input has since moved. The best complete-genome estimate of the human-chimpanzee split is 5.5 to 6.3 million years,⁸ and the measured human generation interval is 26.9 years, not 20.⁹ Run with each paper's own internally consistent pair, the budget is 682 to 781 substitutions, not 1,667.¹⁰ This cuts against the creationist case and the article states it first for that reason.
The standard mainstream rebuttal concedes a number the mainstream literature has since revised upward by roughly an order of magnitude. Ian Musgrave's 2007 reply, which nearly every later critic reuses, puts adaptive fixations on the human lineage at 238, stretches it to 480 "even if you say we missed half," and to 960 with regulatory changes added — then declares the matter closed because 960 is under 1,667.¹¹ But Uricchio, Petrov and Enard in 2019 counted 29,925 human-specific nonsynonymous fixations and estimated that 13.5% were adaptive, which is about 4,000 adaptive protein changes in coding DNA alone.¹² That is roughly three to seventeen times what the critics concede, more than twice ReMine's ceiling, and five to six times the ceiling once a modern generation time is used. The popular refutation and the current measurement are not consistent with each other — and the people who noticed are the Arizona group, who wrote in Genetics that "it is curious that the empirical collapse of historical arguments for neutral theory has not yet led to a re-evaluation of related arguments by Haldane," citing Uricchio by name.²
The dilemma was re-derived without the flaw everyone attacks, and the re-derivation survives. The standard refutation, from Ewens in 1970, attacks Haldane's assumption that an optimal genotype exists.¹³ But Nei and Felsenstein independently derived nearly the same speed limit in 1971 without that assumption, by comparing the reproductive excess a species actually has against the excess a sweep consumes.¹⁴ ¹⁵ At Haldane's own parameters that gives 97 generations per substitution rather than 300 — a factor of three, not a refutation.² A team at Arizona restated and tested this in Genetics in 2025 and wrote that the argument "has not yet been fully addressed."²
The measured coding count fits the corrected limit; the strain, if there is one, is in the non-coding count. Run back through the Nei-Felsenstein limit, about 4,000 adaptive protein changes, every one a sweep from a single new mutation, need roughly a fifth of all deaths in every generation to be selective: twice Haldane's guess and never measured in a mammal, but not impossible.¹⁶ Adding this site's own estimate of adaptive non-coding changes raises the requirement steeply, and at the top of that range every woman would need about 17 births with every extra death selective. The usual escape, that human adaptation avoided costly sweeps, is weaker than it is usually presented. Hernandez and colleagues found that classic sweeps were rare,¹⁷ and a start from standing variation is cheap in Haldane's units: an allele starting at 25% costs 2.77 units where a new mutation in a population of 10,000 costs 19.81.¹⁸ But most of the measured adaptive fraction is weakly selected new mutations that Hernandez's test could barely see,¹⁷ and Kimura and Maruyama's theory says such alleles cost as much as strong ones.¹⁹ For a change at a single site, soft-sweep theory limits the standing-variation discount to about twofold.²⁰
The waiting-time problem is a different argument, and Sanford's own paper says so. In his 2015 simulations the selective sweep — the part that is Haldane's dilemma — takes 720 to 860 generations and accounts for between 0.0001% and 1.1% of the reported waiting time.²¹ Essentially all of the headline number is time spent waiting for a pre-specified string to appear. Sanford states it himself: "the waiting time associated with Haldane's Dilemma is eclipsed by a much more profound waiting time problem."⁵ Anyone citing that paper as confirmation of Haldane is citing the wrong paper.
The waiting-time argument works against the origin of specific new sequence, and not against the speed of adaptation — and Sanford's own model of Adam and Eve is what shows this. His 2018 paper says designed alleles adapt fast "because no extended 'waiting time' is required. All the required genetic variants are present from the first generation, and are already present at high frequency."²² That sentence rescues rapid post-Flood diversification. It also rescues every mainstream soft-sweep scenario, for exactly the same reason. The argument cannot be used one way and refused the other.
In the one system where every substitution can be watched, the cost of selection is not the binding constraint. E. coli in the Long-Term Evolution Experiment discards 99% of its cells daily, giving a Haldane ceiling near one substitution per 23 generations. The observed rate is one per 1,660.²³ Averaged over 50,000 generations it runs about 70 times slower than its own ceiling, and slower than Haldane's horotelic 300 — though the rate decelerates, and over its first ~1,600 generations it ran faster than 300. What limits it is mutation supply and clonal interference, not reproductive excess.²⁴ ²⁵

The verdict: Haldane's dilemma is a real quantitative tension that was never cleanly resolved, and the professional literature says so in its own words. But it is not the argument the popular creationist versions make, and the 1,667 ceiling is the wrong test. On the corrected Nei-Felsenstein limit, the roughly 4,000 measured adaptive protein changes fit, at roughly a fifth of deaths being selective, even if every one swept from a new mutation. The budget is strained only if adaptive changes number in the tens of thousands, as this site's own non-coding estimate suggests, and most of them started as single new copies. Whether they did is open: strong classic sweeps were rare, but weak sweeps from new mutations cost as much as strong ones, and standing variation can cut the bill for a single-site change by about half at most. The waiting-time problem is a genuinely separate and unrebutted argument about pre-specified targets, and its force depends entirely on a premise nobody has established — that human-specific traits needed particular multi-nucleotide strings at particular addresses.

What survives

The arithmetic is honest on all sides. Every value in ReMine's tables reproduces when recomputed independently — his three-generation minimum of 297, his reproductive threshold of 16.3 offspring per female, his appendix cost table.²⁶ So does Haldane's, to within 1% for weak selection.²⁷ So does Sanford's extrapolation, to within 3%.²⁸ This is a dispute about premises, not about multiplication.

There is no peer-reviewed rebuttal of Sanford et al. 2015. Three citation databases were checked on 15 August 2026: OpenAlex lists 11 citing works, Europe PMC 3, Semantic Scholar 15, and not one is a critique.⁵ The paper was never retracted, corrected, or flagged; PubMed shows no comment.²⁹ Anyone claiming otherwise is wrong, and the absence is a real point in the creationists' favour.

ReMine's central formal move is a genuine clarification. Recasting "cost" as a required reproduction rate rather than as a body count is clearer than the original, and two of his four referees at Theoretical Population Biology said so in writing.³⁰ Felsenstein classifies ReMine's cost as the same type of quantity as Ewens' and Crow's.³¹

The professional literature really did leave this unresolved. Van Valen coined the phrase, proposed the first solution, and withdrew that solution two years later, calling the inter-locus interference "probably inexorable."³² Ewens' Mathematical Population Genetics says the load arguments of "Haldane, Dobzhansky and Kimura are all unjustified";³³ Nei's Mutation-Driven Evolution says Haldane's cost is reasonable and that "Ewens (2004) recently criticized Haldane's theory, but he seems to have misunderstandings about the theory."³⁴ These are two of the field's most authoritative texts contradicting each other head-on.

What Haldane actually calculated

Haldane's 1957 paper is fourteen pages in the Journal of Genetics, and it opens with animal breeding rather than with evolution:¹

"It is well known that breeders find difficulty in selecting simultaneously for all the qualities desired in a stock of animals or plants. ... In this paper I shall try to make quantitative the fairly obvious statement that natural selection cannot occur with great intensity for a number of characters at once unless they happen to be controlled by the same genes."

The worked example that gives the paper its shape is the peppered moth. If the environment had changed enough to select ten independent characters as hard as it selected moth colour, only one in 1,024 of the original genotypes would survive, and "the species would presumably have become extinct."¹ Selection must not be too intense, because intense selection kills the population it is improving.

The cost is a ratio, not a body count

The quantity Haldane computes, which he calls D, is the sum over all generations of the fraction of the population that dies selectively while one allele replaces another. "D = 30" means the total selective deaths equal thirty times the number of individuals alive in one generation. Because it is a ratio, it does not depend on population size at all.

His crispest definition is in the 1960 follow-up: the cost is "the total number of deaths, or their equivalents in reduced fertility, sometimes called 'genetical deaths', which must occur in a population of constant size before a gene is replaced by one of its allelomorphs."³⁵

The phrase "or their equivalents in reduced fertility" matters, and Haldane repeats it.¹ He is not claiming that evolution requires corpses. He is claiming it requires reproductive excess — the modern gloss, which comes from James Crow rather than from Haldane, is "the amount of reproductive excess required to carry out a gene substitution."³⁶

For the standard case of a semi-dominant allele the answer is

D = −2 ln(p₀)

where p₀ is the frequency of the favoured allele when selection starts. Two things about that formula decide the whole argument, and both are usually missed.

It is one row of a five-row table. −2 ln(p₀) is the additive case only. If the favoured allele is dominant the cost is −ln(p₀); if it is fully recessive it is 1/p₀ − ln(p₀), which for p₀ = 0.01 is about 105.¹ Anyone stating "Haldane's cost is 2 ln(1/p₀)" is quoting one line.

It depends on the starting frequency and on almost nothing else. This is the load-bearing fact of the entire article. Recomputed from Haldane's own equation:¹⁸

Starting frequency p₀	What that represents	Cost D (additive case)
5 × 10^-5	one copy in 10,000 diploids	19.8
0.01	a variant at 1%	9.2
0.1	a variant at 10%	4.6
0.25	a common variant	2.8
0.5	half the population	1.4

Standing variation is a real discount and a bounded one: raising p₀ two thousand-fold, from 5 × 10^-5 to 0.1, cuts the cost only 4.3-fold, because the dependence is logarithmic. But it is the only term in the formula that moves much, and every serious resolution of Haldane's dilemma in the last fifty years has gone through it.

Where 300 comes from, and how soft it is

Two separate judgments produce the number.

First, D = 30. Haldane's own typical range is lower, and he says so: the substitution "usually involves a number of deaths equal to about 10 or 20 times the number in a generation, always exceeding this number, and perhaps rarely being 100 times this number. To allow for occasional high values I take 30 as a mean."¹ Thirty is his padded figure. His own preferred parameters give 19.8.

Second, I = 0.1, the fraction of reproductive capacity a species can spend. Here is the passage in full:¹

"To be concrete, if a species had immigrated into an environment where its reproductive capacity was half that obtainable after selection had run its course, so that I = ln 2 = 0.69, n would be 43. ... I doubt if such high intensities of selection have been common in the course of evolution. I think n = 300, which would give I = 0.1, is a more probable figure."

That is a judgment about what a species can afford, offered in the first person, bracketed by two rejected alternatives. It is not measured. The one selection intensity Haldane actually measures in the paper — infant survival in a London district, from Karn and Penrose — is I = 0.03,¹ which on his own formula gives 1,000 generations per substitution rather than 300. He does not comment on the gap.

And he explicitly allows a fast lane:¹

"Evolution by natural selection can be very rapid if a species, like the first land vertebrates, or the first colonists of an island, finds itself in an environment to which it is very ill-adapted, but in which it has no competition, and perhaps no predators and few parasites. If so selection might be so intense as to reduce the capacity for increase to one-tenth of that of its adapted descendants, and it could yet hold its own. Such episodes have doubtless been important, and account for tachytelic (Simpson, 1953) evolution. But they are probably exceptional."

One-tenth means I = ln 10 = 2.303, which is 13 generations per substitution — a 23-fold speed-up, sanctioned by Haldane, for colonists in empty habitat. The last sentence is quoted here because an earlier draft of this article left it out and drew the opposite conclusion from it: Haldane offers the fast lane and then says it is exceptional. Emphasis mine. What the paragraph establishes is that 300 is not a physical ceiling and that Haldane knew of situations 23 times faster; what it does not establish is that such situations were common.

He thought it explained evolution, not that it refuted evolution

The four-sentence summary of the paper ends: "It is suggested that, in horotelic evolution, the mean time taken for each gene substitution is about 300 generations. This accords with the observed slowness of evolution."¹ "Horotelic" is Simpson's word for the standard middling rate, as against fast and slow — so the 300 is offered as a typical value, not a universal limit.

Against Zeuner's Pleistocene mammal data he wrote "The agreement with the theory here developed is satisfactory."¹ Of the eye: "The slowness of evolution of such an organ as the vertebrate eye is thus intelligible."¹ In 1964, the year he died: "I think it defines one of the factors, perhaps the main one, determining the speed of evolution."⁷

He did draw one hard limiting conclusion, and honesty requires quoting it. Against Fisher's theory of the evolution of dominance, which needs thousands of modifier genes selected in parallel, he wrote that "even the geological time scale is too short for such processes to go on in respect of thousands of loci."¹ The target is Fisher's dominance theory, not evolution at large.

And he closed the discussion by disclaiming finality: "To conclude, I am quite aware that my conclusions will probably need drastic revision."¹

The paper Haldane promised and never published

There is one loose thread in the primary sources that both sides should know about. In the 1960 follow-up, Haldane identified an escape from his own result: if a gene rises in frequency by recurrent mutation while still slightly deleterious, and only later becomes favoured, then by the time selection starts the allele is already common and p₀ is high. The mechanism is mutation-selection balance, not drift — Haldane is explicit about this and an earlier draft of this article got it wrong. His words:³⁵

"if the rate of increase of fitness were much slower than is likely to be the case, the substitution would occur with no 'cost' at all, in fact a slight negative cost. ... So by the time that selection begins to favour it, its frequency may be a great deal higher than the value of 10^-4, which I have taken as a maximum, in this paper."

He cited a forthcoming paper for the demonstration — "Haldane 1961b, Evolution under selection of slowly changing intensity, J. Genet., in press." That paper never appeared. A search of the complete Haldane bibliography finds no such paper in 1961 or in any year afterwards, nor the companion paper on iteration he cited for the underlying mathematics.³⁷ He died in December 1964.

This cuts both ways and should be reported as such. Creationists can say the escape route was announced but never demonstrated. Evolutionists can say Haldane himself identified the loophole and believed he had proved it. Neither should say he retracted, because he did not.

Where the "dilemma" came from

The word is not Haldane's. It appears nowhere in any of his four relevant papers.³⁸

Leigh Van Valen attached it in 1963, in a paper titled "Haldane's dilemma, evolutionary rates, and heterosis."⁶ Van Valen proposed the first solution — and two years later withdrew it, concluding that the interference between loci is "probably inexorable."³² The man who named the problem and offered the first answer took the answer back.

The modern creationist form is Walter ReMine's. His 1993 book The Biotic Message devotes a chapter to it, and the 1,667 figure first appears on page 217.⁴ Its provenance is exactly traceable and completely unoriginal: 10,000,000 years ÷ 20 years per generation ÷ 300 generations per substitution = 1,666.7. Every parameter is inherited.

ReMine's own framing of what the number means is a rhetorical question: "Is 1,667 selectively significant nucleotides enough to make a sapien out of a simian?"⁴ He never quantifies how many beneficial substitutions human evolution requires. The argument rests on the reader finding 1,667 obviously too few.

Two things ReMine says that his own popularisers get wrong. He insists the argument is about the total number of beneficial substitutions in one lineage, not about the genetic difference between living humans and living chimpanzees.³⁹ Don Batten's 2005 article for Creation Ministries International — the version most readers meet — leads with the human-chimp difference and attributes 1,667 to Haldane.⁴⁰ Both moves are things ReMine explicitly disowns. And in 2006 ReMine argued that Haldane's cost figure of 30 rests on an environmental-change scenario he rejects, so "we must seek a more realistic figure, which will surely be higher."⁴¹ If the cost is higher than 30, then 1,667 is not Haldane's limit and cannot be cited as his.

The sixties: four attacks, and the field never converged

Between 1963 and 1975 the professional literature mounted four distinct attacks on Haldane's result. They are different arguments with different verdicts, and the popular literature on both sides runs them together.

Attack	Who	Does it work?
The cost is real but the environment pays it	Van Valen 1963, Brues 1964, Felsenstein 1971	Partly. Van Valen retracted; Nei answered Felsenstein
Costs at different loci are not additive	Sved, Reed & Bodmer 1967; King 1967; Milkman 1967; Sved 1968; Maynard Smith 1968	Mathematically yes, under truncation selection. Empirically contested
There is no cost in a constant environment	Van Valen, Brues, Felsenstein	Contested; Nei 1971 answers it directly
Most substitutions are neutral, so there is no cost	Kimura 1968; King & Jukes 1969	Yes — and it is the answer the field actually took

The truncation argument is the strongest of the first three and deserves stating properly. Haldane's model treats loci as independent and adds their costs. If instead selection works by a threshold — everyone below a certain overall score fails to reproduce — then one death removes several disfavoured alleles at once, and the costs stop adding. Crow and Kimura put the efficiency gain at 5 to 20 fold.⁴² This is a genuine mathematical escape. The dispute is whether real populations select that way, and Nei's verdict in 2013 is that truncation "almost never occurs in nature."³⁴

A detail worth recording because it is often cited backwards: Kimura and Maruyama showed in 1969 that adding finite population size makes the substitutional load larger, not smaller, for genuinely selected alleles starting rare. The excess is an additive constant of 2 — in their own worked example 25.0 against Haldane's 23.0, about 8.7% larger.¹⁹ Drift reduces the load only where selection is already too weak to matter.

Where the field ended up is best shown by what its textbooks do. Hartl and Clark's Principles of Population Genetics contains zero occurrences of "cost of natural selection," "substitutional load," or "Haldane's dilemma."⁴³ Felsenstein's own 527-page Theoretical Evolutionary Genetics likewise contains none of those phrases, and its fifteen Haldane bibliography entries do not include 1957 — written by the author of one of the two modern derivations of the limit.⁴⁴ But the disappearance is datable rather than universal: Futuyma's Evolutionary Biology carried "Cost of selection, 176" in its printed index in the 2nd edition of 1986 and dropped it by the 3rd edition of 1998, while Ridley 1996 and Hamilton 2009 still teach it.⁴⁵

Meanwhile Haldane 1957 is still cited 16 to 32 times a year with no decline.¹ The topic did not get settled. It got dropped from teaching while staying alive in the journals.

Kimura's escape, and the price of it

The neutral theory of molecular evolution was founded on Haldane's arithmetic. This is not a creationist gloss; it is what Kimura's 1968 paper does.

Kimura computed a genome-wide nucleotide substitution rate for mammals of about one every two years, noticed that this is hundreds of times faster than one per 300 generations, and concluded that most substitutions must therefore be invisible to selection.⁴⁶ If they are neutral, nobody has to die for them, and the cost vanishes.

That is a clean escape, and it is the answer the field took. But it has a price and a weakness.

The price is that it concedes the dilemma for everything that is adaptive. Neutral theory does not refute Haldane's cost; it argues that the cost applies to a much smaller number of substitutions than anyone thought.

The weakness is that Kimura's arithmetic used the wrong denominator, and the criticism comes from inside. Masatoshi Nei pointed out that Kimura counted all four billion nucleotides as targets of selection when the real target is genes.⁴⁷ Kern and Hahn put the same point in one sentence in 2018: Kimura "overestimates the number of protein-coding sites in the genome by two orders of magnitude."⁴⁸ Nei's own recomputation, with genes as the unit, gives one gene substitution every 220,000 to 286,000 years against Haldane's ceiling of 1,200 years — and with amino acids as the unit, one every 636 years, about twice Haldane's ceiling.⁴⁷

So the cost argument was never refuted by showing the cost is fake. It was defused by showing the denominator was wrong. A factor of two, not a factor of a hundred thousand.

This matters now because the historical justification has weakened. The Arizona team put it plainly in Genetics in 2025:²

"The development of neutral theory resolved this apparent dilemma by suggesting that most amino acid substitutions are neutral and do not count against the speed limit. However, the basis for this historical argument is now on troubled ground, because recent literature argues that the fraction of amino acid substitutions explained by adaptation can be high. ... Nevertheless, it is curious that the empirical collapse of historical arguments for neutral theory has not yet led to a re-evaluation of related arguments by Haldane."

The limit was re-derived without its flaw

The standard refutation of Haldane, from Warren Ewens in 1970, attacks a specific weak point: Haldane's intensity of selection compares the population's mean fitness to an optimal genotype that may not exist in the population, or anywhere.¹³ If nobody has the perfect genome, comparing everyone to it is a bookkeeping fiction.

That criticism is correct, and it kills Haldane's route from cost to speed limit. It does not touch the first half of his argument — that a sweep requires 20 to 30 population-equivalents of selective deaths.

Nei and Felsenstein both saw this in 1971 and both built the limit a different way: compare the reproductive excess a population has against the reproductive excess a sweep consumes. No optimal genotype is needed. The result is a minimum spacing between substitutions of

n = −ln(p₀) / ln(k)

where k is the reproductive excess factor. At Haldane's own numbers — p₀ = 10^-4 and 10% of deaths selective, so k = 1.1 — this gives 97 generations per substitution against Haldane's 300.²

Nei's own conclusion on the whole dispute was "HALDANE's conclusion is essentially correct."¹⁴

The Arizona group's statement of why this version is harder to escape is worth quoting in full:²

"Importantly, this speed limit calculation is not subject to the same criticisms as Haldane's original argument. Where Haldane's calculation includes a comparison between the mean fitness of the population and an optimal genotype which may or may not exist, Nei's (1971) and Felsenstein's (1971) approach compares the available reproductive excess to the reproductive excess required to effect changes in allele frequencies. Even if no individual exists who possesses the beneficial allele at every segregating site, each sweep still requires a certain fraction of deaths to contribute to its selection. It is the finite nature of reproductive excess that directly produces this limit on the rate of adaptation."

They add a criticism of standard practice that a creationist could have written but did not: "The relative fitness models that dominate population genetics (e.g. Wright–Fisher and Moran) implicitly assume inexhaustible reproductive excess. ... However, real populations have a finite reproductive excess, e.g. human females do not easily give birth to more than 20 infants."²

And they name, unprompted, why they think it is worth settling: "The attention of 'creation science' to the question of Haldane's dilemma (Remine 2005, 2006) highlights the importance of clearly resolving it."²

The one simulation built to test it

Leonard Nunney's 2003 paper is the only modern simulation written specifically to test Haldane's cost, and it cuts both ways.⁴⁹

Against Haldane, costs do not simply add up locus by locus. "The intercept was positive in all cases, showing that the cost of simultaneously selecting on several traits is less than the summed cost of selecting on each trait separately in different generations." The maximum rate of evolution falls as more loci are involved, but "it is reduced much less than expected based on Haldane's (1957) result."⁴⁹ In a large population the speed-up is dramatic: with ten new mutations per locus per generation, his simulated population survives a substitution at seven loci every 40 generations.⁴⁹

For Haldane, the speed-up belongs to large populations only. In Nunney's words, "The finding that natural selection can drive evolution much faster than suggested by Haldane's result only applies to large populations with M ≥ 1," where M is the number of new mutations per locus per generation, and "The situation changes rather dramatically for the worse as M declines below 1." His worked example is a population of 10,000, the size usually given for human ancestors: "This relatively large population will become extinct if the environmental change requires allelic substitution faster than about every 300 generations, i.e. at the rate suggested by Haldane (1957)."⁴⁹

That 300 is easy to overstate, so read it carefully. In Nunney's model it is the interval at which each of several loci must change at once. On his own Table 1 it matches three or four loci changing together, so the spacing between substitutions is nearer one per 80 to 95 generations, and each extra locus adds 44 generations.⁵⁰ The measured human coding rate of one adaptive substitution per 51 to 58 generations sits near that 44-generation margin. Three cautions keep this from being oversold. Nunney ran only up to seven loci, so applying his fit to thousands is an extrapolation. His 10,000 is a census size in a model where the effective size is about the same, and human ancestors probably numbered more than their effective size of about 10,000, which would raise M. And it is a hard-selection model. Nunney defends that choice: soft selection "eliminates the cost of substitution," but it "is only important when natural selection is driven by intraspecific competition," while predators, competitors and climate pose challenges "unlikely to result in soft selection."⁴⁹

The 10% ceiling has now been measured once

Haldane's I = 0.1 sat unmeasured for 68 years. In 2025 the Masel lab measured it, in 517 genotypes of Arabidopsis thaliana across eight environments, and found the proportion of deaths that are selective ranges from 8.5% to 95%.²

That is a real empirical blow to Haldane's auxiliary assumption, and it should be granted. Two caveats belong with it, both from the authors. The 8.5% minimum came from the benign environment and falls below Haldane's guess. And they flag the species problem themselves: "future work under more natural conditions (e.g. with higher extrinsic mortality) and in different species (e.g. less fecund) remains necessary," noting that "Haldane (1957) originally used mammals as example."²

Arabidopsis is an annual selfer with enormous fecundity. Humans are the paradigm low-fecundity species. The measurement that would settle the hominin case has not been made.

The crux: the critics concede a smaller number than the field measures

This section is the reason the article exists, and it embarrasses both sides. An earlier draft called the comparison one "nobody in the debate appears to have made." That was wrong, and the correction matters: Matheson, Exposito-Alonso and Masel made exactly this point in Genetics in 2025, citing Uricchio et al. by name, and the current Wikipedia article makes the same α-versus-Haldane comparison for Drosophila.⁵¹ What follows is not new. What is still missing from the popular versions on both sides is the arithmetic.

What the critics concede. Ian Musgrave's 2007 post "Haldane's non-dilemma" is the standard reply. Nearly every later critic reuses it. His method is to count genes carrying a signature of positive selection between humans and chimpanzees, and his numbers are 238 adaptive fixations, stretched to 480 "even if you say we missed half," and to 960 by adding an equal allowance for regulatory changes.¹¹ Dan Stern Cardinale's 2021 video gives "between 240 and 780," then doubles the top figure to 1,560 to allow for what the scans miss.⁵² Both then observe that these fit under ReMine's 1,667 and conclude there is no dilemma. Note how little room either has: Musgrave's top figure of 960 sits 4% under the ceiling his own footnote concedes, and Cardinale's 1,560 sits 6% under ReMine's. Neither margin is comfortable.

Larry Moran, asked directly in 2014 how many of the differences between humans and chimpanzees were adaptive, answered: "We don't know how many of those were beneficial (adaptive) leading to ways in which modern chimps are better adapted than the common ancestor. (Same for humans.) My guess would be only a few thousand in each lineage."⁵³ It is a guess and he says so. Shown that figure two years later, Felsenstein replied "That may not be way off."⁵⁴

What the field now measures. Uricchio, Petrov and Enard published in 2019 the one paper that gives both an adaptive fraction and the raw count it applies to. They counted 29,925 human-specific nonsynonymous fixations and estimated α = 0.135, with a 95% credible interval of 0.096 to 0.17.¹² That is 4,040 adaptive amino-acid substitutions on the human lineage, range 2,900 to 5,100. Independent estimates bracket it: Zhen and colleagues give α = 0.16 for the human lineage;⁵⁵ Boyko and colleagues give 10 to 20%;⁵⁶ Galtier gives 0.24.⁵⁷ Eyre-Walker and Keightley's point estimate is the outlier at essentially zero, with an upper bound of 40%.⁵⁸

And that is coding DNA only. Regulatory DNA is not countable from any published paper, because nobody has multiplied a genome-wide extent of conserved non-coding sequence by an adaptive fraction. Built from Torgerson's own fixed-difference counts and the genome-wide conserved extent, this site's own arithmetic gives a further 6,000 to 10,000 adaptive non-coding substitutions on the conservative reading and 25,000 to 40,000 on the turnover-aware reading.⁵⁹ Those are ours, not anyone's published figure, and they carry six caveats set out in the dossier.

Put the three numbers side by side.

Quantity	Value	Source
Haldane budget, 10 Myr and 20-yr generations	1,667	ReMine 1993, from Haldane's 300⁴
Haldane budget, 5.5-6.3 Myr and 26.9-yr generations	682 to 781	this site's recomputation¹⁰
What the mainstream critics concede	238 to 1,560	Musgrave 2007; Stern Cardinale 2021¹¹ ⁵²
What the mainstream literature measures, coding only	~4,000	Uricchio, Petrov & Enard 2019¹²
Adding non-coding, this site's arithmetic	10,000 to 44,000	see dossier⁵⁹

The central measured figure of 4,040 exceeds the conceded number by roughly three to seventeen times, depending on which critic's figure is used. It exceeds ReMine's ceiling by more than twice, and the modern ceiling by five to six times.

Musgrave's own margin is 4%. His footnote 5 concedes that at a 6-million-year split the ceiling is 1,000, not 1,667. His top estimate is 960. Substituting the measured 26.9-year generation interval drops the ceiling to 682-781, which is below his own upper estimate.⁶⁰ His conclusion does not survive two parameter updates that both post-date him.

And his method was criticised in his own comment thread within hours. He converts a count of genes carrying a selection signature into a count of substitutions with no conversion factor. A commenter using the handle "p-ter" added that genome scans of that kind cannot detect weakly adaptive fixations at all — which Uricchio later found are 72% of human α.⁶¹

So the popular refutation of Haldane's dilemma rests on a number the field has since revised upward by roughly an order of magnitude. That is a real finding and it favours the creationist side of the ledger.

What the measured count would cost

Counting is half of the test. The other half is to run the measured count back through the speed limit and ask what it would have needed. The defensible form of the limit is the Nei-Felsenstein one given above, n = −ln(p₀)/ln(k). Turned around, S sweeps in G generations need ln(k) = S × −ln(p₀) / G. Take the hardest case for the mainstream, in which every adaptive substitution began as one new copy in a population of 10,000, and use the 204,000 to 234,000 generations since the split:¹⁶

Adaptive substitutions on the human line	One every	Reproductive excess spent on selection, k	Births per woman, at the very least
4,040: coding, Uricchio's central estimate	51 to 58 generations	1.19 to 1.22	2.4
2,900 to 5,100: coding, Uricchio's interval	40 to 82 generations	1.13 to 1.28	2.3 to 2.6
10,000 to 14,000: adding this site's conservative non-coding estimate	15 to 23 generations	1.5 to 2.0	3.1 to 3.9
29,000 to 44,000: adding this site's turnover-aware non-coding estimate	5 to 8 generations	3.4 to 8.4	6.8 to 17

The first row cuts against the creationist case, and it should be said plainly. On the field's own accounting, about 4,000 adaptive protein changes, every one of them a sweep from a single new mutation, need k ≈ 1.2 in every generation. On the Arizona group's own conversion, in which Haldane's 10% "is equivalent to 10% of deaths being selective, which corresponds to k = 1.1,"² that means roughly a fifth of all deaths being selective. That is twice Haldane's guess, and nobody has measured it in any mammal. But it is inside the 8.5% to 95% the same group measured in Arabidopsis, and it is not obviously beyond a species in which many children died young. In Haldane's original units the same count needs a selection intensity of about 0.4 per generation, four times his 0.1; most of the difference between the two answers is the correction Nei and Felsenstein made. So the coding count alone does not break the speed limit. It strains Haldane's version of it and fits inside the corrected one.

The last row cuts the other way. If the turnover-aware non-coding count is right, and those changes also swept from new mutations, every woman would have needed at least 7 to 17 births with every death beyond replacement a selective one. The Arizona group's own benchmark is that "human females do not easily give birth to more than 20 infants."² The top of that range leaves almost no room for a death that was not selective. That row rests on this site's own non-coding arithmetic, not on a published count, so it is a reason to want the non-coding count measured, not a refutation.

Why this is not the end of the story

Having said that plainly, the article must say the other half just as plainly, because the two numbers are not measured in the same units.

Haldane's 300 prices one specific trajectory: a new allele appearing at frequency 1/2N and sweeping to fixation. Almost the whole cost is incurred while the allele is rare, which is why D depends on ln(p₀) and on almost nothing else. α is something different — the fraction of fixed differences that exceed the neutral prediction. It commits to nothing about how they got there.

And the mode matters, because the mode was tested. Hernandez and colleagues used 179 resequenced human genomes to look for the diversity trough that classic sweeps leave behind. Their result: the trough around human-specific amino-acid substitutions is statistically indistinguishable from the trough around synonymous ones, p = 0.90.¹⁷ Their simulations say that even 10% strongly-favoured or 25% weakly-favoured amino-acid fixations would have been detectable. The conclusion: "classic sweeps were not a dominant mode of adaptation over the past ~250,000 years."

Creationists cite this as showing adaptation was rare. It does not say that, and the paper goes out of its way to say it does not:¹⁷

"This conclusion does not imply that humans have experienced few phenotypic adaptations. ... Comparisons of diversity and divergence levels at putatively functional versus neutral sites, for example, suggest that 10–15% (and possibly as many as 40%) of amino acid differences between humans and chimpanzees were adaptive ... Given the paucity of classic sweeps revealed by our findings, an excess of functional divergence would point to the importance of other modes of adaptation."

The modes they name are mostly the cheap ones: "selection on standing variation or on multiple beneficial alleles brings rare or intermediate frequency alleles to fixation; and other forms of adaptation, such as selection on polygenic traits, increase or decrease allele frequencies to a lesser extent."

Uricchio's own paper explains why the sweeps were not seen, but not why they would have been cheap. 72% of human α comes from weakly adaptive variants, with 2Ns = 10 rather than 500, and the model that produced the estimate treats both classes as new mutations.¹² An allele that weak rises slowly and leaves a narrow footprint. Hernandez's own supplement says of its weak case, a selection coefficient of 0.1%, that "the beneficial allele does not sweep through the population and consequently leaves a narrow footprint," and puts its 99% detection threshold for that case at more than 10% of amino-acid substitutions.¹⁷ Uricchio's weak class is 9.7%, at a smaller selection coefficient still. So Hernandez's null result says little about most of the measured α.

And weak does not mean cheap. Kimura and Maruyama's finite-population result, given earlier, is that a substitution starting from one new copy costs 2[1 + ln(1/p)] whenever 2N_es is well above 1, slightly more than Haldane's figure. The cost only falls toward zero when 2N_es is much less than 1.¹⁹ Their own table shows where the turn comes: for a haploid allele starting at 1%, the cost is 4.34 at N_es = 1, 5.47 at N_es = 5 and 5.50 at N_es = 10, against 4.605 when selection is strong.¹⁹ An allele with 2Ns = 10 pays full price. An earlier version of this article said such alleles cost "far less than Haldane's D." That was wrong, and "classic sweeps were rare" is a different claim from "adaptive substitutions were cheap."

So the resolution is not that there were only 240 adaptive substitutions. There were probably several thousand, and the critics' number is too low. The coding count is affordable on the Nei-Felsenstein accounting even if every one of them swept from a new mutation, at roughly a fifth of all deaths being selective. What would have to be cheap is anything much beyond that: adaptive non-coding changes in the tens of thousands. In Haldane's units only two things make a substitution cheap: starting from standing variation at an appreciable frequency, or selection so weak (2N_es below about 1) that it adds little to α.

That resolution has a cost of its own, and the article states it rather than waiting to be caught: it is unfalsifiable in the direction that matters. "The substitutions we cannot price were the cheap kind" is a claim about trajectories that mostly cannot be recovered from present-day sequence. Hernandez's null result constrains the last 250,000 years, not the last six million.

The one calculation nobody has done

Felsenstein, pressed on this in 2016, named the escape that actually scales: standing variation.⁵⁴ By Haldane's own logarithmic scaling, alleles starting at appreciable frequency rather than at 1/2N raise the budget by roughly fourfold — which is about the size of the gap between the modern ceiling of ~700 and the measured ~4,000 coding substitutions.

One published result limits how far that escape can go for a change at a single site. Joachim Hermisson and Pleuni Pennings worked out when adaptation draws on standing variation rather than on new mutations, by comparing the chance that a usable allele is already present when selection begins with the chance that a new one arrives afterwards. Per site, the hominin mutation supply is far below one new copy per generation; the soft-sweep criterion discussed below puts it near 2 × 10^-4. In that regime they find that "in a time span that an allele from the standing variation needs to reach fixation, it is at least as likely that the allele alternatively appears as a new mutation destined for fixation only after the environmental change."⁶² On this site's reading, that holds the standing-variation share of single-site substitutions to about half or less. Even if that half cost nothing, the total bill would fall by about twofold at most, short of the fourfold the escape was supposed to supply.²⁰

The skeptic's reply is fair. Their model is one change of environment acting on an allele that was neutral or harmful before it. Balancing or fluctuating selection can hold an allele at a middling frequency for a long time, and polygenic adaptation moves many alleles part of the way without fixing any. Neither has been counted for the human line.

Nobody appears to have done that calculation properly: taken a realistic distribution of starting frequencies for human adaptive alleles, integrated Haldane's cost over it, and compared the total to a measured reproductive excess. It is a well-posed problem and the inputs exist. After the Nei-Felsenstein arithmetic above, it matters less for the coding count, which fits the corrected limit even as hard sweeps, than for the non-coding count, where the bill only closes if most of those changes were cheap. This article flags it as the most useful open question in the subject.

The waiting-time problem is a different argument

Everything above is about rate: how fast can selection replace genes. The waiting-time problem is about chance: how long must a population wait for a particular combination of mutations to appear at all. They share a Haldane ancestor and they fail or succeed for different reasons.

Behe, Durrett and Schmidt

The mathematical core is not in dispute. If an adaptation needs two specific mutations and the intermediate is neutral, the population does not have to wait for the first to fix before the second arrives. A doomed lineage of first-step mutants can throw off a second-step mutant before it dies out. This is stochastic tunnelling, imported from cancer modelling, and Durrett and Schmidt's formula for the mean waiting time is⁶³

T = 1 / (2N · u₁ · √u₂)

The square root is the whole point. It makes two mutations roughly 1/√u₂ ≈ 10,000 times faster than a naive "both at once" calculation.

Michael Behe had argued in The Edge of Evolution that such multi-step adaptations are prohibitively rare, anchoring on chloroquine resistance in malaria at one in 10²⁰ parasites.⁶⁴ Durrett and Schmidt's 2008 paper in Genetics applied their formula to regulatory sequence and got 216 million years for one prespecified pair of mutations in a human-sized population — which they took as an argument against Behe, since the same maths gives short times for the far larger populations of malaria parasites.⁶³

Behe replied in Genetics in 2009. The exchange is worth citing whole rather than in halves.

Behe won one point outright, and Durrett and Schmidt conceded it in print: "Behe is right on this point. This divides our previously computed overestimate of 5 million by 30."⁶⁵

He lost two others, and the same reply says so. The article should not quote the concession without the rest.⁶⁵

The real fault line is neither of those. It is whether the target is one pre-specified pair or any of many. Durrett and Schmidt divide their answer by the number of alternative targets k and get something trivially short. Behe answers that the empirical rarity of chloroquine resistance already includes every alternative the parasite had, and asks for a number rather than a principle. Both moves are legitimate. Neither side has ever carried k through to a defensible value, and that unresolved quantity is where the whole dispute actually lives.

Two empirical results bear on it directly. Summers and colleagues confirmed in PNAS in 2014 that at least two specific mutations in PfCRT are needed before any chloroquine transport occurs — Behe's core empirical claim, verified.⁶⁶ And Meyer and colleagues watched a four-mutation, all-or-nothing switch arise in phage lambda independently in 24 of 96 replicate flasks, with a median of 12 days.⁶⁷ Multi-mutation adaptations with non-selectable intermediates are real, they have been observed forming, and how hard they are depends entirely on population size and target count.

Sanford's simulations

John Sanford's 2015 paper in Theoretical Biology and Medical Modelling is the creationist flagship. Using Mendel's Accountant, it reports that establishing a specific two-nucleotide string in a hominin population of 10,000 takes 84 million years, and a specific five-nucleotide string 2 billion years.⁵

Its full parameter set is in the dossier. The things that matter most:

Setting	Value
Population	10,000 (swept 1,000 to 1,000,000)
Generation time	20 years
Mutation rate	10^-8 per site, inflated 10,000-fold then corrected back proportionally
Fitness benefit of the completed target	0.1, i.e. a 10% increase
Starting string	differs from the target at every site
Intermediates	strictly neutral until the exact target appears
Rest of the genome	no other genetic variants arising or segregating
Recombination	suppressed

Three things count in Sanford's favour and should be said first. He reports that his own published numbers understate his extrapolation by roughly tenfold, and quotes the smaller figure anyway.⁵ His extrapolation reproduces to within 3% on independent recomputation.²⁸ And he lists the five relaxations that would shorten the answer, then writes: "In all these special circumstances the waiting time will certainly be shorter than this study indicates."⁵

Four things count against. The target must match a pre-specified string at a pre-specified location; the simulator's matching routine is a single string-equality test with no partial credit.⁶⁸ The rest of the genome is not merely disregarded — the fitness function has no other terms, and the simulated organism's genome is shrunk to the length of the target, so a five-nucleotide search runs in a five-base genome.⁶⁸ The paper's "we used the default settings" silently imports a heritability of 0.2 and a non-scaling noise of 0.05, so selection acts on a phenotype that is mostly environmental noise and the nominal 10% benefit is an upper bound on the realised advantage.⁶⁹ And the published pseudo-code contradicts both the paper's own Methods and the source code on the fixation criterion.⁵

But the decisive point is structural, and it is Sanford's own. His waiting time splits into two phases: waiting for the string to appear, and then sweeping it to fixation. The sweep is the part that is Haldane's dilemma. Recomputed from his own Table 2:²¹

String length	Sweep to fixation	Total waiting time	Sweep as share of total
1	16,500 yr	1.53 million yr	1.08%
2	17,200 yr	84.1 million yr	0.020%
5	14,400 yr	2.31 billion yr	0.0006%
8	16,900 yr	18.5 billion yr	0.0001%

The sweep takes 720 to 860 generations throughout — squarely in Haldane's own territory — and is irrelevant to the totals. Sanford says so himself: "Although significant, the waiting time associated with Haldane's Dilemma is eclipsed by a much more profound waiting time problem."⁵

So the two arguments in this article's title are not the same argument, and citing Sanford 2015 for Haldane's dilemma is a category error. The paper that does make the Haldane argument from Sanford's group is Rupe and Sanford 2013 — and its headline result was never simulated. The paper states that "deleterious mutation accumulation could not be simulated through such deep time, as it always either caused overflow of memory or premature termination due to extinction," and the 100,000 deleterious fixations in its conclusion are extrapolated from a figure.⁷⁰ Their own most favourable run also produced 1,476 selective fixations, more than the Haldane ceiling the same paper cites, and the paper does not remark on it.⁷⁰

The number Sanford reports against himself

The single most important source cited by Sanford against his own conclusion is Behrens and Vingron 2010. Sanford reports that dropping the requirement that the target sit at one specified address — letting it arise anywhere among 20,000 human promoters — brings the waiting time for a five-nucleotide string down to about 7,000 years, six orders of magnitude below his own figure.⁵

The paper was obtained and his characterisation of it is accurate to the digit: 83 to 338 million years for a 5-mer in one 1-kb promoter, 7,467 years averaged across 20,000 promoters.⁷¹ Sanford rejects it on biological rather than mathematical grounds — "biologically it is simply not reasonable to assume that a specific short string can be, by itself, beneficial almost anywhere in the genome, with minimal contextual constraint."

That is a fair objection and it is also the entire dispute. Behrens and Vingron's model contains no population, no selection and no fixation probability; the drift is folded into a substitution rate from a three-species alignment.⁷¹ Neither side has established how many addresses in a mammalian genome could host a given regulatory motif usefully.

What the technical answers are worth

The mainstream replies are real, quantitatively powerful, and narrower than they are usually presented as being.

Stochastic tunnelling is worth a factor of 1/√u₂, about 17,000-fold at realistic mutation rates — but it is a square root, not an escape, and Durrett and Schmidt still got 216 million years for one prespecified pair.⁶³

Soft sweeps and standing variation do not apply to the hominin case as modelled, and their own authors say so: Messer and Petrov's criterion is Θ = 2Nμ ≳ 1, and a hominin population sits at Θ ≈ 2 × 10^-4 per site.⁷²

The "many targets" answer is the strongest, and it is measured. Villar and colleagues fitted activity conservation across 20 mammals and report a mean lifetime of 427 million years for enhancers and 207 million years for CEBPA binding sites, which works out to roughly 50 to 100 regulatory-element gains and losses per million years per lineage.⁷³ Regulatory sequence turns over constantly in real genomes. Whether the specific elements human evolution needed are drawn from that pool is the unanswered question.

And there is no peer-reviewed rebuttal of Sanford et al. 2015. Concede it. The only peer-reviewed rebuttal anywhere in this literature targets Hössjer, Bechly and Gauger's 2021 paper, not Sanford's.⁷⁴

What has actually been measured

Argument is cheap. The following are cases where somebody measured how fast an adaptive allele really spread, put against Haldane's own accounting.

Lactase persistence is the fastest thoroughly documented human sweep from a new mutation. On Bersaglieri's own parameters it consumes an intensity of selection of about 0.07 to 0.14 per generation.⁷⁵ Haldane's assumed budget for the entire genome is 0.1. One locus eats the budget. It does not eat ten times the budget.

The peppered moth — Haldane's own example of unusually intense selection — comes out at about 0.16 to 0.22, one locus at roughly twice the whole-genome budget.⁷⁶ Haldane's own figure for Biston was far higher, I ≈ 0.69, and he used it to argue that such intensities are not common: "This represents, in my opinion, fairly intense selection, of the order of that found in Biston betularia ... I doubt if such high intensities of selection have been common in the course of evolution."¹ So this site's recomputation disagrees with Haldane by a factor of three to four, in the direction of a cheaper sweep. An earlier draft of this article claimed agreement where there is none.

The figure most often quoted as blowing past the ceiling was introduced by its own authors in order to refute it. Hawks and colleagues are routinely cited for a recent human adaptive substitution rate of 13.25 per generation. That number is derived under an explicitly labelled null hypothesis of constant rate and constant population size, and the very next section of their paper is headed "Predictions of Constant Rate," deriving four predictions "each of which refutes the null hypothesis of constant rate." Their own third prediction is the same reductio: the implied rate "predicts an implausible 6.4 million adaptive substitutions between humans and chimpanzees ... 100 times the observed number of amino acid substitutions," which they call "implausible."⁷⁷ Their preferred demographic model gives "a low long-term substitution rate." So Hawks is not a case of a measured rate exceeding Haldane's limit; it is a paper that constructs such a rate and then discards it. Anyone citing 13.25 against Haldane — in either direction — is quoting a number its authors rejected. Hernandez's 179 genomes independently found the sweep signature is not there.¹⁷

And the Long-Term Evolution Experiment runs slower than its own ceiling. E. coli in the LTEE is diluted 1:100 daily and regrows, so 99% of cells produced each day are discarded, giving a ceiling near one substitution per 23 generations. Averaged over 50,000 generations the observed rate is one adaptive substitution per 1,658 — about 70 times slower.²³

Two qualifications keep that from being oversold, and both cut against the way this article first stated it. The rate decelerates, because Tenaillon's fitted beneficial term goes as √t; at 500 generations the cumulative rate was one per 166, within a factor of seven of the ceiling, and the experiment only fell below Haldane's horotelic 300 after about 1,600 generations. And the LTEE does not have the largest reproductive excess ever studied, which is what an earlier draft claimed. Haldane's budget is denominated per generation, and a 100-fold daily dilution spread over 6.64 generations is a per-generation multiplication of exactly 2 — binary fission, the floor for any replicator. Its ceiling of one-per-23 is not unusually high; it sits inside the range this site computes for Stone Age humans.

The reason is in the papers and has nothing to do with cost: limited beneficial-mutation supply, diminishing-returns epistasis, and clonal interference. Good and colleagues, watching every allele-frequency trajectory: "many mutations in Fig. 1 persist at intermediate frequencies for long periods, often undergoing reversals in frequency that sometimes result in extinction. ... Part of this complexity is driven by clonal interference."²⁵

That result cuts against both sides, and both halves belong here. It refutes the claim that experiment has shown Haldane's limit to be routinely exceeded. It also shows the limit is not the operative constraint in the one system where every substitution can be watched.

A structural warning that both sides need. Most of the famous "rapid evolution in the wild" studies do not measure gene substitutions at all. Reznick's guppies, the Grants' finches, and the whole darwins-and-haldanes rate literature measure phenotypic change in quantitative traits drawn from standing variation. A polygenic shift of a tenth of a standard deviation in beak depth involves no fixation and costs essentially nothing in Haldane's units. Citing finch beaks against Haldane's dilemma is a category error, and so is citing Haldane's dilemma against finch beaks.

Does the same arithmetic destroy the young-earth model?

It should, and the interesting thing is that young-earth authors got there first and published the negative result themselves.

Answers in Genesis' Ark research puts 1,398 kinds on the Ark.⁷⁸ Jean Lightner's mammal survey gives 137 extant mammal kinds, including "14 genera and 40 species of cats" and "13 genera and 35 species of canids" descending from single pairs.⁷⁹ Getting from 137 mammal kinds to roughly 4,800 living mammal species in 4,350 years is a doubling of species number every 848 years, or about one new mammal species somewhere on earth every eleven months, sustained for four and a half millennia.⁸⁰ Todd Wood's own worst case is 150 horse species in about 400 years.⁸¹

Against that, 174 generations at Haldane's payment rate of 0.1 buys 17.4 cost-units — 0.58 substitutions at D = 30, or 0.88 for a single new mutation in a population of 10,000.⁸⁰

And the creationists ran the numbers on themselves. Kurt Wise in 1994: the required post-Flood change is "too rapid a change to have been produced by any traditional microevolutionary mechanisms (for example, mutations acted on by natural selection)."⁸² Jeanson and Lisle in 2016 computed that sequential selection of a million variants would need a population growth-and-crash cycle every 1.6 days, and concluded it "was not a plausible scenario."⁸³ Wood built an entire mechanism — designed transposable elements — to escape the rate problem.⁸¹

Their answer is to move the engine from selection to created variation plus drift. And it works, for a reason this article has already established: Haldane's cost turns on the starting frequency and on almost nothing else, scaling as −2 ln(p₀) in the additive case. A designed allele starting at 25% costs 2.77 units against 19.81 for a new mutation in a population of 10,000, and about 30 for Haldane's worked case — a seven-fold discount and an eleven-fold one. Drift pays no substitution cost at all. Sanford states the principle himself:²²

"Designed alleles represent the most effective and the most rapid way to cause selection-driven adaptation. This is because no extended 'waiting time' is required. All the required genetic variants are present from the first generation, and are already present at high frequency, enabling very rapid selective progress. There is no need to wait for just the right set of mutations to arise serendipitously and then slowly move from allelic near-extinction to allelic fixation."

That sentence is the hinge of this whole article. Every term in it — the serendipitous arising, the near-extinction starting frequency, the slow move to fixation — is a property of de novo mutation, not of adaptation as such. It rescues the Ark. It also rescues every mainstream soft-sweep and standing-variation scenario, for identical reasons. A creationist who invokes it cannot then deploy the waiting-time argument against measured human adaptation, and this article says so in those words.

The remaining creationist rejoinder is real and should be stated: designed variation is created, so the model owes no account of how the variation arose naturally, whereas an evolutionist's standing variation still has to come from somewhere. That is a legitimate difference. But it converts the dispute from an arithmetic one into a metaphysical one, and the arithmetic can no longer be presented as an independent test.

Where the objection survives every escape is uniparental DNA. Only one female of each unclean kind was aboard, so mitochondrial variation cannot be created heterozygosity. Wood says so in his own words: "any mitochondrial sequence variability must be attributed to real mutations instead of allelic diversity preserved from before the Flood."⁸⁴ He then measures up to 46 differences per 287 aligned positions within cats, and up to 62 per 493 within dogs, all of which must be generated in 4,350 years.⁸⁴ His answer is a post-Flood mutation-rate spike that later shut off — unmeasured, unexplained, and in direct tension with Sanford's genetic entropy, which says a raised mutation rate is what drives populations toward error catastrophe.

Note carefully that this last point is a mutation-rate argument, not a Haldane argument. Nothing has to be selected for drift and lineage sorting to produce those differences, so the cost of substitution is the wrong tool and this article does not apply it there.

No creationist appears to have applied Haldane's limit by name to their own model. Six targeted searches across creation.com, Answers in Genesis, ICR, the Creation Research Society and the ICC proceedings found the argument always pointed outward.⁸⁵ Report that as an absence of the label, not an absence of the reasoning: Wise and Jeanson and Lisle did the reasoning and published the negative result.

Common Objections

Objection 1: "Haldane refuted his own argument, so creationists are quoting a dead paper"

Not quite. Haldane never retracted. He confirmed the 1957 results in 1960 — "The main results of Haldane (1957) are confirmed"³⁵ — and was still describing the cost as a determinant of evolutionary speed in 1964. What is true is that he never intended it as an anti-evolutionary argument and said so in the paper's last sentence. What is also true is that he identified an escape route in 1960, said he had demonstrated it in a forthcoming paper, and that paper never appeared.

Objection 2: "Truncation selection solves it — many deaths can be shared"

It is a real mathematical escape and this article grants it. Crow and Kimura put the efficiency gain at 5 to 20 fold.⁴² The dispute is empirical: does selection in real populations work by a threshold? Nei's verdict is that truncation "almost never occurs in nature."³⁴ Rupe and Sanford call it "highly unrealistic and never happens even in artificial breeding experiments" — and then use 50% truncation in their own most favourable run.⁷⁰

Objection 3: "Neutral theory dissolved the problem in 1968"

It relocated the problem rather than dissolving it, and the relocation depended on a denominator error that Nei and later Kern and Hahn corrected — Kimura "overestimates the number of protein-coding sites in the genome by two orders of magnitude."⁴⁸ With the right units the gap is about a factor of two.⁴⁷ More importantly, the historical justification has weakened: the fraction of amino-acid substitutions attributed to adaptation is now estimated to be high in many species, and the Arizona group calls it "curious that the empirical collapse of historical arguments for neutral theory has not yet led to a re-evaluation of related arguments by Haldane."²

Objection 4: "In the LTEE the transfer is a random 1% sample, so most of the selection is random and that is why fixation is slow"

The premise is right and the conclusion does not follow. The protocol is a 1:100 daily dilution with regrowth at 6.64 generations per day, so 99% of cells are discarded blind to genotype.⁸⁶ But a proportional 1-in-100 draw preserves allele frequencies in expectation; drift acts only through the sampling variance, and roughly five million cells are transferred. The bottleneck is already priced into the effective population size of about 10⁷, which is some fifty-fold below the peak census. Good and colleagues did this calculation explicitly:²⁵

"With an effective population size of N_e ~10⁷, new mutations would require Δt ~ 0.1N_e ~10⁶ generations to reach the 10% detection threshold by genetic drift alone. Thus, the mutations in Fig. 1 must have reached observable frequencies through the direct or indirect action of natural selection."

Drift needs a million generations; the experiment has run 60,000 to 75,000. At N_e = 10⁷ and s = 0.01, 2N_e·s = 200,000, so selection is not competing with drift. What the daily discard does mean is that the LTEE's enormous reproductive excess is mostly unspent — which is why its Haldane ceiling is so high and its observed rate so far below it. One caveat this article has not resolved: serial-transfer regimes do reduce fixation probability relative to the textbook 2s, and the size of that correction has not been verified here.

Objection 5: "Sanford's waiting-time paper was published in a junk journal and quietly withdrawn"

False on the second half, and the first half needs care. Theoretical Biology and Medical Modelling was a BioMed Central journal that ceased publication at the end of 2021; Sanford's group had published in it twice before.⁸⁷ The paper has never been retracted, corrected, or flagged, and PubMed records no comment.²⁹ A separate Journal of Theoretical Biology editorial disclaimer that is sometimes cited in this connection attaches to a different paper by different authors, and its complaint is about undisclosed affiliation and keyword insertion after review, not about the mathematics.⁸⁸

Objection 6: "1,667 beneficial mutations is obviously far too few to build a human"

This is ReMine's actual argument, and he gives it a scale in his own words: 1,667 nucleotides "would have the information content of less than 10 lines of text in this book. It amounts to one three-hundredths of one one-hundredth of one-percent of the human genome." On the same page he asks: "Is 1,667 selectively significant nucleotides enough to make a sapien out of a simian?"⁴ That is the weakest link in his case. He measures the size of the budget but never the size of the requirement: he does not say how many beneficial substitutions human evolution needs, so there is no number to compare against, and the argument works only if the reader already finds 1,667 too few. Meanwhile the ceiling on modern parameters is 682-781, and the measured coding count is about 4,000. So a quantitative version of ReMine's point is available, and it is stronger than his rhetorical one, but it comes from the mainstream literature he was arguing against. It also has a limit he did not foresee: run through the corrected Nei-Felsenstein limit, the coding count needs roughly a fifth of all deaths to be selective, which is high but not impossible. The pressure point is the non-coding count, not the coding one.¹⁶

Objection 7: "Sex solves Haldane's dilemma"

A 2019 paper in Genome argues exactly this: recombination stops the costs at different loci from accumulating.⁸⁹ Three cautions. Its published parameters start the favoured allele at 5%, not at the 1/2N a new mutation would have, so a large part of the per-locus cost is removed by assumption before recombination does anything. Its source code renormalises fitness to the fittest individual each generation and truncates the population back to 100,000 — so it is a soft-selection model, which is precisely the modelling choice Matheson and colleagues identify as assuming inexhaustible reproductive excess.⁹⁰ And the authors themselves disclaim the strong reading: "the results presented in the current study should not be seen as a refutation of Haldane's ideas."

Sources

1.
Haldane, J. B. S. “The cost of natural selection.” Journal of Genetics 55:511–524. 1957. The founding paper on the cost, a theoretical work in which J. B. S. Haldane works out how many deaths a gene replacement costs a population. The main result is that, unless selection is very intense, the cost is often about 30 times the number of organisms in a generation, which at the middling rate of evolution that Simpson called horotelic means about 300 generations per gene substitution. Haldane himself warned that his conclusions would probably need drastic revision, and the article uses the paper as the source of the 300-generation figure.
1. 1a.
  Page 524: The paper's four-sentence Summary, in full: “Unless selection is very intense, the number of deaths needed to secure the substitution, by natural selection, of one gene for another at a locus, is independent of the intensity of selection. It is often about 30 times the number of organisms in a generation. It is suggested that, in horotelic evolution, the mean time taken for each gene substitution is about 300 generations. This accords with the observed slowness of evolution.” "Horotelic" is Simpson's term for the standard middling rate of evolution, as against tachytelic (fast) and bradytelic (slow). ↩ ↩
2. 1b.
  Page 511: The first and second paragraphs. ↩
3. 1c.
  Page 511: “Now if the change of environment had been so radical that ten other independently inherited characters had been subject to selection of the same intensity as that for colour, only (1/2)¹⁰, or one in 1024, of the original genotype would have survived. The species would presumably have become extinct. ... We see, then, that natural selection must not be too intense.” ↩
4. 1d.
  Page 514: “a number of deaths, or their equivalents in lowered fertility, have occurred.” Emphasis added. Page 520: Repeated on page 520: “If natural selection acts by diminished fertility the effect is equivalent.” ↩
5. 1e.
  Page 517: “If λ = 0 (A dominant), then from (7), D = -ln p0, if λ = 1/2, D = -2 ln p0, if λ = 3/4, D = -4 ln p0 - 3.3, and if λ = 0.9, D = -10 ln p0 - 19.8. ... Thus D usually lies between 10 and 100, with 30 as a representative value.” The full five-case result. λ is the dominance of the disfavoured allele. The commonly quoted -2 ln p0 is the λ = 1/2 row only. ↩
6. 1f.
  Page 520: “The unit process of evolution, the substitution of one allel by another, if carried out by natural selection based on juvenile deaths, usually involves a number of deaths equal to about 10 or 20 times the number in a generation, always exceeding this number, and perhaps rarely being 100 times this number. To allow for occasional high values I take 30 as a mean.”. Emphasis added. Haldane's own typical value is 10 to 20. ↩ ↩
7. 1g.
  Pages 520–521: The logical structure is I = 30/n, with I = 0.69 rejected as too intense and I = 4 rejected as lethal, leaving I = 0.1 asserted as "more probable." ↩ ↩ ↩
8. 1h.
  Page 512: Haldane's calibrating example, from Karn & Penrose 1951: “about 95.5% of all babies born in a London district and 98.5% of those weighing 7.5-8.5 lb. survived birth and the first month of life: s0 = 0.985, S = 0.955, I = 0.03.” This is the only measured intensity of selection anywhere in the paper, and it is a third of the value he then adopts. A caution: Karn and Penrose measured selection on birthweight over one month in one population, not the total lifetime selective mortality of a species, so the two quantities may not be strictly commensurable. The comparison is offered as a flag, not as a refutation. ↩ ↩
9. 1i.
  Page 523: "One-tenth" gives I = ln 10 = 2.303, hence n = 30 / 2.303 = 13 generations per substitution. The arithmetic is the article's own. The article quotes this passage in the body, including the sentence that follows it, which is Haldane's continuation: “Such episodes have doubtless been important, and account for tachytelic (Simpson, 1953) evolution. But they are probably exceptional.” ↩ ↩
10. 1j.
  Page 522: Haldane wrote, of Zeuner's 1945 analysis of the Pleistocene record: “He estimated the total duration of the Pleistocene at 600,000 years ... The agreement with the theory here developed is satisfactory.”. Emphasis added. ↩ ↩
11. 1k.
  Page 522: “In either case the cost is high and the process must, therefore, be slow. The slowness of evolution of such an organ as the vertebrate eye is thus intelligible.” ↩
12. 1l.
  Page 522: “Some writers, such as Fisher (1930, 1931), appear to assume that the number of loci at which 'modifiers' ... may be selected, is indefinitely large. ... even if enough modifiers were available, the selection of, say, ten modifiers which between them caused a previously dominant mutant to become recessive, would involve the death of a number of individuals equal to about 300 generations of the species concerned. Even the geological time scale is too short for such processes to go on in respect of thousands of loci.” ↩
13. 1m.
  Page 523: The last sentence of the Discussion. “To conclude, I am quite aware that my conclusions will probably need drastic revision. But I am convinced that quantitative arguments of the kind here put forward should play a part in all future discussions of evolution.” ↩
14. 1n.
  An image-only scan of the 1957 paper at about 157 dpi, with no text layer, so its text cannot be searched or copied. Its resolution drops characters, and the article warns readers about it because it is widely linked. Cited here as url https://blackwellpublishing.com/ridley/classictexts/haldane2.pdf. Page 520: On this scan, Haldane's relation on page 520 reads: “n = 30 Σδᵢ”. That is dimensionally wrong. The Garland facsimile of the same page reads: “n = 30/Σδᵢ, roughly”. which is what the surrounding algebra requires. ↩
15. 1o.
  OpenAlex's database record for the 1957 paper, which gives 760 lifetime citations and these counts by year: 2012: 24, 2013: 24, 2014: 21, 2015: 23, 2016: 24, 2017: 16, 2018: 21, 2019: 28, 2020: 22, 2021: 20, 2022: 20, 2023: 23 and 2024: 32. The series also carries 2025: 12 and 2026: 36, both partial years. The yearly range is 16 to 32, with a mean of 23.2 for 2012 to 2016 and 23.4 for 2020 to 2024, so the article can say the citations show no decline. Cited here as in OpenAlex. ↩
2.
Matheson, Joseph et al. “Substitution load revisited: a high proportion of deaths can be selective.” Genetics 229(4):iyaf011. Jan 25, 2025. A peer-reviewed paper in the journal Genetics, published as Advance Access on 25 January 2025, funded by the John Templeton Foundation, with its code deposited on GitHub at github.com/josephmatheson/selective_deaths. It measures reproductive excess, the surplus of offspring a population can produce beyond what it needs to replace itself, and the share of deaths that are selective, meaning they help change which gene versions are common. It does this for 517 genotypes of the plant Arabidopsis thaliana in eight environments and finds a much higher share of selective deaths than the 10% cap Haldane assumed; the article uses it for that finding and for its authors' point that the historical case for neutral theory has collapsed.
1. 2a.
  Section Discussion: The first sentence of the section. ↩
2. 2b.
  “Comparing this cost to the reproductive excess of the population produced the novel result that the minimum spacing n is −ln(p₀)/ln(k) (Felsenstein 1971; Nei 1971). For Haldane's estimates of p₀ = 10^-4 and k = 1.1, this yields n = 97 generations between selective sweeps.” The v1 preprint's summary of the same result is blunter: “This limit is more permissive than Haldane's, but much slower than the rosy limits predicted by variance- or lead-based arguments.” ↩ ↩ ↩
3. 2c.
  Page 4: “Haldane’s 10% selection intensity estimate is equivalent to 10% of deaths being selective, which corresponds to k = 1.1. Nei (1971) and Felsenstein (1971) retain this 10% cap for illustrative purposes, where k includes the fact that extrinsic mortality substantially reduces the fecundity available to be “used” for selective deaths.” ↩
4. 2d.
  “Nei (1971) and Felsenstein (1971) made a key advance building on just this first part of Haldane's argument. This advance has not received substantial attention, perhaps partially due to confusion about terminology, and also because growing acceptance of the neutral theory of molecular evolution had seemed to resolve the immediate issues posed by speed limits.” ↩
5. 2e.
  Quoted in full in the body. ↩
6. 2f.
  “The relative fitness models that dominate population genetics (e.g. Wright–Fisher and Moran) implicitly assume inexhaustible reproductive excess (Bertram and Masel 2019). ... However, real populations have a finite reproductive excess, e.g. human females do not easily give birth to more than 20 infants.” ↩ ↩
7. 2g.
  The published sentence is softer than its first draft, and its drafting history is itself a finding. In the 2021 bioRxiv v1 the same point appeared in body text: “discussion of the relevance of reproductive excess for Haldane's arguments has been so absent from the literature that a creationist author tried to reintroduce the concept of reproductive excess in 2005.” The softening happened before journal submission. ↩
8. 2h.
  Measured across 517 Arabidopsis thaliana genotypes in eight environments. The 8.5% minimum came from the benign environment and falls below Haldane's guessed 10%. ↩
9. 2i.
  “future work under more natural conditions (e.g. with higher extrinsic mortality) and in different species (e.g. less fecund) remains necessary.” The v1 preprint is blunter: “many species are less fecund than Arabidopsis, and Haldane (1957) originally used mammals as example.” ↩
10. 2j.
  Section Introduction: Quoted in the body. ↩ ↩ ↩
3.
Felsenstein, Joseph. “Post to sci.bio.evolution.” sci.bio.evolution. Jun 8, 2006. A Usenet post by Joe Felsenstein, a population geneticist, answering a Wikipedia editor who was complaining that "ReMine is rewriting the whole thing." He says the 1970s discussion of the cost was left unresolved and "a mess," and denies the inference ReMine draws from that, not the observation that the literature was left in a mess. He made the same point in different words on The Panda's Thumb on 26 February 2008: "So shortly after I published my 1971 paper which I thought cleared things up ... the whole discussion died and everyone forgot about it. The mess was left in the literature. Remine complains that it is an unresolved mess and in that he is quite right." The article cites it for the 1970s mess.
1. 3a.
  “Remine is right about one thing — the 1970s discussion was left unresolved, a mess. It was not population genetics's finest hour.” ↩
4.
ReMine, Walter J. The Biotic Message: Evolution Versus Message Theory. St. Paul Science. 1993. A 1993 book by Walter ReMine. Its chapter 8, Haldane's Dilemma, argues that a human-like lineage with a 20-year generation time could substitute at most about 500,000 traits in ten million years at one per generation, and that it could replace at most 1,667 nucleotides. The book concludes that this is not nearly enough to account for human evolution. The article uses it as the modern form of the argument, and as the source of the 1,667 figure. ↩
1. 4a.
  Page 217: The provenance is 10,000,000 years ÷ 20 years per generation ÷ 300 generations per substitution = 1,666.7. Every parameter is inherited from Haldane; ReMine performed no new calculation to obtain it. ↩ ↩ ↩
2. 4b.
  Page 217: “Given 10 million years, the population could selectively replace a maximum of 1,667 nucleotides. This would have the information content of less than 10 lines of text in this book. It amounts to one three-hundredths of one one-hundredth of one-percent of the human genome.” “Is 1,667 selectively significant nucleotides enough to make a sapien out of a simian?” ReMine gives the size of the budget as a fraction of the genome and as lines of text. He nowhere quantifies how many beneficial substitutions human evolution requires, which is the weakest link in his case. ↩ ↩
5.
Sanford, John et al. “The waiting time problem in a model hominin population.” Theoretical Biology and Medical Modelling 12:18. 2015. A computer simulation of how long a hominin population needs to fix a short, specific string of DNA letters. It modified Mendel's Accountant so that a starting string and a target string could be set, simulated a population of at least 10,000 with 20-year generations and very strong selection, and found that a two-nucleotide string takes on average 84 million years and a five-nucleotide string 2 billion years. Sanford runs the creationist FMS Foundation, which the paper does not mention; the paper gives his affiliation as Cornell and Baumgardner's as Los Alamos (retired), and it was received on 8 July 2015 and accepted on 7 September 2015, a 61-day turnaround. The article uses it as the creationist flagship for the waiting-time argument, and shows that the paper's headline number is about waiting for a specific string, not about Haldane's sweep. ↩ ↩
1. 5a.
  Page 2: “Although significant, the waiting time associated with Haldane's Dilemma is eclipsed by a much more profound waiting time problem. Haldane assumed a continuous supply of high-impact beneficial mutations, and did not realize that such mutations occur very rarely.” ↩ ↩
2. 5b.
  Pages 4–5: The whole passage, in full. “We expect dialog regarding the details of our formulation. Some may say the string should be able to arise anywhere (genetic context does not matter). Some may say that the rewarded sequence should not have to match the specified target sequence exactly. Some may say that in a specified location, the string might already be there – perhaps lacking only a single new nucleotide. Some may say that each nucleotide in the string should be independently rewarded. In all these special circumstances the waiting time will certainly be shorter than this study indicates.”. Emphasis added. This sentence is the entire debate in one line. ↩
3. 5c.
  Page 11: “Because we used the more conservative method of simple proportional correction for mutation rate, all of our reported waiting times in this paper actually underestimate waiting time by roughly a factor of ten (Table 1).” By his own Table 1 the honest five-nucleotide figure is 39.5 billion years rather than the 2.31 billion quoted in the abstract. He quotes the smaller number, which is conservatism against his own thesis and should be reported as such. ↩
4. 5d.
  Pages 24–25: Sanford reports Behrens & Vingron's result that dropping the location constraint yields waiting times "about 7,000 years," six orders of magnitude below his own, and rejects it on biological grounds: “biologically it is simply not reasonable to assume that a specific short string can be, by itself, beneficial almost anywhere in the genome, with minimal contextual constraint.” ↩
5. 5e.
  OpenAlex lists 11 citing works for doi:10.1186/s12976-015-0016-z, Europe PMC lists 3, and Semantic Scholar lists 15. Not one is a critique. There is no peer-reviewed rebuttal of Sanford et al. 2015. ↩
6. 5f.
  The 2015 waiting-time simulation paper, read here for its published pseudo-code, which states the program's termination criterion. The article cites it beside the simulator's source code, because the published pseudo-code and the code disagree on whether the 99% threshold counts homozygous individuals or allele frequency. Page 8: The published pseudo-code gives the termination criterion as: “if portion of population with homozygous target match exceeds 99 %.” Minor for the numbers, but a real error in the published methods. The paper's own Methods (p. 6) and the source code both use allele frequency. ↩
6.
Van Valen, Leigh. “Haldane's dilemma, evolutionary rates, and heterosis.” American Naturalist 97:185–190. 1963. The coinage sentence is attributed to Van Valen in Dronamraju (2017), page 110: “I like to think of it as a dilemma for the population: for most organisms, rapid turnover in a few genes precludes rapid turnover in the others”. The one loose thread on the name is Dodson (1962), "Note on the Cost of Natural Selection," American Naturalist 96:123–126, the only item in Van Valen's reference list that could have supplied it. A short paper that proposes general adaptations and other changes that raise mean population fitness as a solution to Haldane's dilemma, the cost to the population of natural selection. It also builds a simple model of the genetic load caused by heterosis, and concludes that interaction between loci that is not simply additive is the most probable way to keep that load from becoming excessive. The article uses it as the source of the name and of Van Valen's first solution to the problem. ↩ ↩
7.
Haldane, J. B. S. “A defence of beanbag genetics.” Perspectives in Biology and Medicine 7:343–359. 1964. Page 351: His last published word on the cost, in the year he died: “posterity may or may not think that my concept of the cost of natural selection — that is to say, the number of genetic deaths required to bring about an evolutionary change — is important. I think it defines one of the factors, perhaps the main one, determining the speed of evolution. It has been accepted by some and criticized by others. If it is shown to be false, the demonstration of its falsity will probably reveal the truth, or at least a closer approximation to the truth.” A reply by Haldane to Professor Ernst Mayr of Harvard University, who had asked what the mathematical school of population genetics had contributed to evolutionary theory. Its mathematics rests on six stated simplifying assumptions, such as an infinite population and random mating, which Haldane admits are simplifications. The article quotes it for Haldane's final statement that the cost is one of the main factors determining the speed of evolution. ↩ ↩
8.
Yoo, DongAhn et al. “Complete sequencing of ape genomes.” Nature 641:401–418. 2025. A Nature paper by a large consortium that completely sequenced six ape genomes (chimpanzee, bonobo, gorilla, two orangutans and siamang), including regions that earlier reference genomes left out. It gives the newest and best split-time estimate for the human-chimpanzee divergence: 5.5 to 6.3 million years. The article uses it for that split time. ↩
9.
Wang, Richard J. et al. “Human generation times across the past 250,000 years.” Science Advances 9:eabm7047. 2023. A measurement paper that gives the mean human generation interval as 26.9 years over the past 250,000 years. For comparison, see Fenner 2005 (American Journal of Physical Anthropology 128:415–423), and Langergraber et al. 2012 (PNAS 109:15716–15721), who measured 24.6 years directly from parentage data in eight wild chimpanzee communities. The article uses it for the 26.9-year figure, which it sets against the 20 years in the arithmetic behind 1,667. ↩
10.
Berean Archive. This site's own arithmetic. n.d. The site's own calculation, using each source's internally consistent pair of split time and generation interval, with Haldane's ceiling equal to generations ÷ 300: Yoo 2025 (5.5–6.3 million years) with Wang 2023 (26.9 years) gives 204,000–234,000 generations and a ceiling of 682–781; Moorjani 2016 (7.9 million years) with 26.9 years gives 293,700 generations and 979; and Langergraber 2012 (7–13 million years) with 29 years gives 241,000–448,000 and 805–1,494. The classic 1,667 requires a 10-million-year split and 20-year generations simultaneously, and no paper in the current literature supports both, because the only studies putting the split beyond 10 million years get there by assuming a 29-year generation; the best current range for generations available is roughly 200,000–350,000. The article uses it for the 682–781 figure. ↩ ↩ ↩
11.
Musgrave, Ian. “Haldane's non-dilemma.” The Panda's Thumb. Jul 1, 2007. A post on The Panda's Thumb by Ian Musgrave, a senior lecturer in pharmacology at the University of Adelaide, not a population geneticist. His counts are 238 adaptive fixations on the human lineage, 480 "even if you say we missed half," and 960 with an equal allowance for regulatory change. The article uses it as the standard mainstream reply, which nearly every later critic reuses. ↩ ↩ ↩
12.
Uricchio, Lawrence H. et al. “Exploiting selection at linked sites to infer the rate and strength of adaptation.” Nature Ecology & Evolution 3(6):977–984. 2019. A population-genetics paper by researchers at Stanford University and the University of Arizona. It is the one paper that publishes both an adaptive fraction and the raw fixation count it applies to: 29,925 human-specific nonsynonymous fixations, with α = 0.135 (95% credible interval 0.096 to 0.17). Multiplying gives 4,040 adaptive amino-acid substitutions, range 2,873–5,087. The article uses it for the measured number of adaptive protein changes on the human lineage. ↩ ↩ ↩ ↩
1. 12a.
  Section Results: “We find strong posterior support for a substantial component of α driven by weakly-beneficial alleles”. Table 1: First row, all genes: α = 0.135, of which 0.097 is from weakly beneficial and 0.041 from strongly beneficial alleles. 0.097 of 0.135 is 72%. Section Methods: “is the component of α due to weakly-beneficial mutations (2 N s = 10) and α S represents strongly-beneficial alleles (2 N s = 500)”. “We sampled parameters from prior distributions corresponding to the shape and scale of deleterious selection coefficients (assumed to be Gamma-distributed) and the rate of mutation of weakly and strongly-beneficial mutations.” Both classes enter the model as new mutations, so the estimate gives no support to the idea that the adaptive alleles began at high frequency. ↩
13.
Ewens, Warren J. “Remarks on the substitutional load.” Theoretical Population Biology 1:129–139. 1970. The standard refutation of Haldane's cost. Its target is Haldane's use of an optimal genotype that may not exist, and Ewens' lead-based reformulation gives roughly 20 generations between substitutions for s = 0.01, against Haldane's 300. The article cites it for that objection to the optimal genotype. ↩ ↩
14.
Nei, Masatoshi. “Fertility excess necessary for gene substitution in regulated populations.” Genetics 68:169–184. 1971. A theory paper on how fast gene substitution, the takeover of a population by a new version of a gene, can happen when the population size is held steady by competition. It asks how much spare reproduction a species needs for a given rate of substitution, and concludes that competition does not create threshold selection, in which only individuals above a cutoff reproduce. The article uses it as one of two independent re-derivations of Haldane's speed limit that rest on finite reproductive excess rather than on an optimal genotype. ↩
1. 14a.
  Page 169: Nei's own verdict on the dispute: “HALDANE's conclusion is essentially correct.” ↩
15.
Felsenstein, Joseph. “On the biological significance of the cost of gene substitution.” American Naturalist 105:1–11. 1971. A 1971 theory paper that re-derives the speed limit from finite reproductive excess rather than from an optimal genotype. Felsenstein's own emphasis is that a population lacking sufficient reproductive excess, even at low density, goes extinct, while Nei's is that a strongly density-regulated population of constant size is constrained in rate but not threatened with extinction; the formula is the same and the interpretation differs. The article uses it as the second of two independent re-derivations. ↩
16.
This site's own arithmetic, in research/measured-count-cost.ts, which anyone can rerun. It takes the Nei-Felsenstein spacing as Matheson, Exposito-Alonso and Masel state it, n = −ln(p₀)/ln(k), and reproduces their 97 generations at p₀ = 10^-4 and k = 1.1.² It then solves for k: ln(k) = S × ln(2N) / G, with N = 10,000 so that p₀ = 1/20,000, and G = 204,461 to 234,201 generations from the Yoo and Wang pairing.¹⁰ The coding counts are Uricchio's 29,925 human-specific nonsynonymous fixations times α = 0.096, 0.135 and 0.17.¹² The non-coding additions, 6,000 to 10,000 and 25,000 to 40,000, are this site's own estimate, not a published figure.⁵⁹ Births per woman is 2k, the floor if every death beyond replacement were selective; any death that was not selective raises it. In Haldane's units, with Kimura and Maruyama's load of 2[1 + ln(2N)] = 21.8 per substitution, the central coding count needs a load of 0.38 to 0.43 per generation.¹⁹ A larger population raises every figure slightly, because −ln(p₀) grows with the logarithm of N. ↩ ↩ ↩
17.
Hernandez, Ryan D. et al. “Classic selective sweeps were rare in recent human evolution.” Science 331(6019):920–924. 2011. “the trough in diversity around human-specific amino acid substitutions is no more pronounced than around synonymous substitutions”. A Science paper by researchers at the University of Chicago, Oxford and Hebrew University, among others, that tests whether classic sweeps (a single new, strongly beneficial mutation rising to fixation and dragging nearby variation with it) drove human adaptation. Using sequence data from 179 human genomes, it found the dip in diversity around human-specific amino-acid substitutions no more pronounced than around synonymous ones (p = 0.90), and its simulations indicate that 10% strongly-favoured or 25% weakly-favoured amino-acid fixations would have been detectable. The article uses it for the finding that classic sweeps were not the dominant mode of adaptation over the past ~250,000 years. ↩ ↩ ↩
1. 17a.
  The article quotes it at length in its body. The paper explicitly disclaims the reading that adaptation was rare, and names standing variation, multiple beneficial alleles, and polygenic frequency shifts as the alternative modes. ↩
2. 17b.
  Section Supplement: Power simulations: “In the fourth set of simulations, 25% of substitutions were favored, with a much weaker selection coefficient of 0.1%. When selection is as weak as 0.1%, the beneficial allele does not sweep through the population and consequently leaves a narrow footprint (on average ~10 kb in humans (S16)), so this case is not what is envisaged by classic sweep models”. Section Supplement: The effects of clustering of amino acid substitutions on power: “Assuming a selection coefficient of 1%, we estimated that there is 99% power to detect the signature of classic sweeps if they constitute more than 4.5% of amino acid substitutions; assuming a selection coefficient of 0.1%, there is 99% power for a fraction above 10%.” The selection coefficients are those behind the main text's "strongly favored" (1%) and "weak effects" (0.1%) cases. ↩ ↩
18.
Berean Archive. This site's own arithmetic. n.d. A calculation of Haldane's cost of substitution, D, from his 1957 equation (7), for the additive case where D = −2 ln(p₀) and p₀ is the starting frequency of the new allele. It gives 19.81 at p₀ = 5 × 10^-5, 9.21 at p₀ = 0.01, 4.61 at p₀ = 0.1, 2.77 at p₀ = 0.25 and 1.39 at p₀ = 0.5. The article uses it because the cost depends on the starting frequency and on almost nothing else. ↩ ↩
19.
Kimura, Motoo, and Takeo Maruyama. “The substitutional load in a finite population.” Heredity 24:101–114. 1969. Page 113: For near-neutral alleles, with 2N_e s much less than 1, the load. “may become indefinitely small”. Drift reduces the cost only where selection is already too weak to matter. A 1969 theory paper on the substitutional load, the total selective deaths needed to replace one gene version with another, when the population is finite. Their result is L(p) = 2[1 + loge(1/p)], against Haldane's 2 loge(1/p): an additive excess of 2, not a multiplicative factor, so their worked example gives 25.0 where Haldane gives 23.0, 8.7% larger. The article uses it because the finite-population effect is often cited backwards: for alleles that start rare it makes the load larger, not smaller. ↩
1. 19a.
  Page 112: “First, if the selective advantage is sufficiently large such that 2N_es ≫ 1 while the initial frequency is very low so that 2N_esp ≪ 1, we have approximately u(p) = 2N_esp and L(p) = 2[1+log_e(1/p)]. Namely, the load for one gene substitution is larger by about two as compared with the corresponding value derived by Haldane (1957) who used a deterministic treatment.” Page 113: “Secondly, if the mutant gene is almost neutral such that |2N_es| ≪ 1, we have approximately u(p) = p+N_esp(1−p) and L(p) = 4N_es log_e(1/p).” ↩ ↩ ↩
2. 19b.
  Page 108: “The value of L at N_es = ∞ is 4·605.” Page 109, table 1: Theory column, haploid population, initial frequency p = 0.01, N_e = 100: s = 0.01 gives 4·34, s = 0.02 gives 5·17, s = 0.05 gives 5·47 and s = 0.10 gives 5·50, so N_es = 1, 2, 5 and 10. The load passes the strong-selection value by N_es = 2 and stays above it. ↩
20.
This site's reading of Hermisson and Pennings. They define G_sgv as the time after selection begins at which the chance that a new mutation destined for fixation has arrived equals the chance that the allele fixes from standing variation, and they show that G_sgv is shorter than the time a standing-variation allele needs to fix.⁶² So among completed substitutions at one site, standing variation supplies about half or less when the mutation supply per site is well below one, and less the longer selection lasts. If that share cost nothing and the rest paid the new-mutation price, the total cost would fall by at most about half. The bound is for one site and one bout of selection; it says nothing about traits built from many small shifts that never fix. ↩ ↩
21.
Berean Archive. This site's own arithmetic. n.d. A calculation by this site from the amplification column of Sanford et al. 2015's Table 2, divided by its total column. In those simulations the sweep phase takes 720–860 generations throughout, which is squarely in Haldane's territory, and is 1.08%, 0.020%, 0.0006% and 0.0001% of the total for string lengths 1, 2, 5 and 8. The article uses it to show how little of Sanford's headline waiting time is the sweep that Haldane's dilemma concerns. ↩ ↩
22.
Sanford, John et al. “Adam and Eve, designed diversity, and allele frequencies.” Proceedings of the Eighth International Conference on Creationism, 200–216. 2018. A creationist simulation paper by six authors, most of them from the FMS Foundation, with Computational Solutions and Logos Research Associates also listed, presented at the 2018 International Conference on Creationism. It asks whether two people could have produced today's allele frequency patterns if they were created with designed alleles, variants built in from the start rather than made by mutation, and finds that they could. The article uses it because the argument that designed alleles need no waiting time also rescues fast post-Flood diversification, and the same reasoning rescues every mainstream soft-sweep scenario.
1. 22a.
  Page 212: Quoted in the body. Page 203: The methods admission: “we have made all mutations effectively neutral, as is commonly assumed. This is essential for longer runs over many generations, or the population will go extinct due to slightly deleterious mutations, long before the simulation is complete.”. Emphasis added. This means the designed-diversity simulations and the genetic-entropy simulations have never been run in the same model at the same parameter settings. ↩ ↩
23.
This site. Haldane ceiling and observed rate in the Long-Term Evolution Experiment. n.d. The arithmetic is the site's own, on the published figures. E. coli in the LTEE is diluted 1:100 daily and regrows at 6.64 generations per day, so 99% of cells produced each day are discarded; if every discarded cell were discarded selectively, the maximum supportable intensity gives a ceiling near one substitution per 23 generations. Observed: 30.2 beneficial substitutions in 50,000 generations from Tenaillon's fitted driver term, i.e. one per 1,658 generations; or one detected mutation per 500-1,000 generations from Good et al. Averaged over 50,000 generations the LTEE therefore runs about 70 times slower than its own ceiling and 5.5 times slower than Haldane's horotelic 300, but the rate decelerates, so the average hides it. Tenaillon's beneficial term is b√t with b = 0.134856, so the cumulative rate is √t/b: one per 166 generations at t = 500, one per 235 at t = 1,000, one per 524 at t = 5,000 and one per 1,658 at t = 50,000. Setting √t/b = 300 gives t = 1,637, so for its first roughly 1,600 generations the LTEE ran faster than Haldane's horotelic figure, and at 500 generations it was within a factor of seven of its own ceiling rather than seventy. The LTEE does not have the largest reproductive excess ever studied: Haldane's budget is per generation, and 100-fold dilution over 6.64 generations is a per-generation factor of exactly 2, the floor for any replicator, giving I_max = ln 2 = 0.693. The peppered moth's physical ceiling is roughly ln(1000) ≈ 6.9, ten times higher. The article cites it to show that mutation supply and clonal interference, not reproductive excess, limit the LTEE. ↩ ↩
24.
Tenaillon, Olivier et al. “Tempo and mode of genome evolution in a 50,000-generation experiment.” Nature 536(7615):165–170. 2016. “many mutations in Fig. 1 persist at intermediate frequencies for long periods, often undergoing reversals in frequency that sometimes result in extinction. Part of this complexity is driven by clonal interference.” This passage is not this paper's wording. It is the wording of Good, McDonald, Barrick, Lenski and Desai's 2017 paper, and the article's quotation of it belongs to that paper. A genome study of the E. coli Long-Term Evolution Experiment. It sequenced 264 complete genomes from 12 populations over 50,000 generations, and its abstract says that most fixed mutations in the populations that kept the ancestral mutation rate are beneficial, and that the fraction of beneficial mutations declines as fitness rises. The article cites it beside Good et al. 2017 for the claim that mutation supply and clonal interference, not reproductive excess, limit the experiment. ↩
25.
Good, Benjamin H. et al. “The dynamics of molecular evolution over 60,000 generations.” Nature 551(7678):45–50. 2017. A genome study of the Long-Term Evolution Experiment's 12 E. coli populations, sequenced as mixed populations every 500 generations through 60,000 generations. It found that even as the rate of fitness gain declines, the populations show signs of rapid adaptation, with several beneficial mutations competing for dominance in each population at once. The article cites it for that competition, which the paper calls clonal interference. ↩
1. 25a.
  Section Emergence of quasi-stable coexistence: “many mutations in Fig. 1 persist at intermediate frequencies for long periods, often undergoing reversals in frequency that sometimes result in extinction. ... Part of this complexity is driven by clonal interference.” The two sentences are separate paragraphs in the original and the ellipsis marks the join. An earlier draft of this article attributed this quotation to Tenaillon et al. 2016; it is Good et al. 2017, and "Fig. 1" is Good's allele-frequency-trajectory figure, not Tenaillon's mutation-count figure. ↩
2. 25b.
  This is the direct answer to the objection that the Long-Term Evolution Experiment's daily 1% sampling makes selection random: drift needs about 10⁶ generations to move a mutation to detectable frequency, and the experiment has run 60,000–75,000 generations. The article's body cites Good and colleagues for this calculation. ↩
26.
Berean Archive. This site's own arithmetic. n.d. A check, made by this site, that every value in ReMine's Table 2, his three-generation minimum of 297, his reproductive threshold of 16.3 offspring per female, his 25,000 neutral substitutions and his appendix cost table reproduces exactly. The article uses it to show that the dispute with ReMine is about premises, not arithmetic. ↩
27.
Berean Archive. This site's own arithmetic. n.d. A check of Haldane's claim that D does not depend on the selection coefficient. The independence is exact to better than 1% up to K ≈ 0.01, within 7% at K = 0.1, and 23% short at Haldane's own stated threshold of K = 1/3 and 35% short at K = 1/2. The article uses it to show that Haldane's claim is honest and that his stated caveat sits where the numbers say it should. ↩
28.
This site. Recalculation of Sanford's extrapolation from his own Table 1. n.d. The ratios between successive corrected waiting times in Sanford's Table 1, as the mutation rate falls by a decade, are 1.34, 2.64 and 1.82, with a geometric mean of 1.86. Extrapolating two further decades from 10^-5 to the biological 10^-7 gives 3.85 × 10¹⁰ years against Sanford's printed 3.95 × 10¹⁰, agreement to within 3%, so his stated extrapolation is arithmetically sound and honestly reported. A caution he does not state: the three measured ratios span 1.34 to 2.64, and the extrapolation runs two decades past the data across a regime change (2Nμ falls from 200 to 0.2), so the figure carries roughly a factor-of-4 uncertainty in each direction. The article cites it because the arithmetic reproduces, which makes the dispute one about premises rather than multiplication. ↩ ↩
29.
PubMed. PubMed record for PMID 26376851. n.d. The database entry that the article uses for the Sanford et al. 2015 paper. Its only PublicationType is "Journal Article," and it has no comments-and-corrections section: no comment, no erratum, no expression of concern and no retraction. The article uses it to show that the paper has never been retracted, corrected or flagged. ↩ ↩
30.
ReMine. Referee reports on ReMine's paper for Theoretical Population Biology. n.d. The referee reports on ReMine's paper for Theoretical Population Biology, as he reproduced them, including Joe Felsenstein's report and James Crow's public reply. Two of the four referees credited the clarification. These are ReMine's transcriptions, not the journal's, and should be cited as such. The article cites it for two of his four referees saying in writing that his clarification was genuine. ↩
31.
Felsenstein. Classification of ReMine's cost (citation to be confirmed). n.d. Felsenstein, the population geneticist, classifies ReMine's cost as the same type of quantity as Ewens' and Crow's, a legitimate formulation whatever he thinks of the inference drawn from it. The article cites it for that classification. ↩
32.
Van Valen. Van Valen's 1965 withdrawal of his 1963 solution. 1965. “probably inexorable”. Van Valen withdrew his own 1963 solution two years later, describing the interference between loci as "probably inexorable." The withdrawal is the single most damaging fact for the narrative that the dilemma was solved in the 1960s. The article cites it to show that the professional literature really did leave the dilemma unresolved: Van Valen coined the phrase, proposed the first solution, and withdrew that solution two years later, calling the inter-locus interference "probably inexorable." ↩ ↩
33.
Ewens, Warren J. Mathematical Population Genetics. Springer. 2nd edition. 2004. Page 79: The passage says that the (implicit) arguments of Haldane, Dobzhansky and Kimura are all unjustified: “Haldane, Dobzhansky and Kimura are all unjustified.” The first volume of a planned two-volume work on the mathematics of population genetics, in its second edition. Ewens holds that the load arguments of Haldane, Dobzhansky and Kimura are unjustified, and the article sets this against Nei 2013, which reaches the opposite verdict on the same literature. ↩
34.
Nei, Masatoshi. Mutation-Driven Evolution. Oxford University Press. 2013. “Ewens (2004) recently criticized Haldane's theory, but he seems to have misunderstandings about the theory.” A 2013 book in which Nei accepts Haldane's cost as reasonable and rejects the truncation-selection rescue, the claim that selection which culls only individuals below a cutoff avoids the cost. The article uses it as one of two leading texts that contradict each other, and quotes Nei on Ewens. ↩
1. 34a.
  Nei's verdict is that truncation selection. “almost never occurs in nature.” ↩ ↩
35.
Haldane, J. B. S. “More precise expressions for the cost of natural selection.” Journal of Genetics 57:351–360. 1960. A mathematical follow-up to Haldane's 1957 paper that gives more exact formulas for the cost, because the 1957 formulas were accurate only when selection is weak. It treats a gene that is harmful at a frequency of 10^-4 or less and then becomes favoured, and it finds that the cost falls by nearly 30% when one genotype is twice as fit as another. The article uses it for Haldane's clearest definition of the cost and for the escape route he identified in it.
1. 35a.
  Page 351: The opening paragraph, which gives the crispest definition of the cost anywhere in Haldane's work. The paper also widens the assumed starting frequency from a single value to a range of 10^-4 down to 10^-8. ↩
2. 35b.
  Page 359: “The main results of Haldane (1957) are confirmed.” The 1960 Summary is two sentences and does not revisit the 300: “More precise expressions are given for the cost of natural selection. It is reduced by nearly 30% if one genotype is twice as fit as another.” ↩
3. 35c.
  Pages 359–360: The exact haploid correction factor is K/(-ln(1-K)), which is 1 as K approaches 0 and 0.7213 at K = 1/2, the "nearly 30%" of his Summary. ↩
36.
Crow, James F. “Foreword.” Selected Genetic Papers of J. B. S. Haldane, xi–xii. Garland. Edited by Krishna R. Dronamraju. 1990. Pages xi–xii: “In the second, he showed that the amount of reproductive excess required to carry out a gene substitution depends mainly on its initial frequency and not on the magnitude of its effect.” The phrase "reproductive excess" is Crow's gloss; Haldane's own wording is "deaths, or their equivalents in reduced fertility." An article using "reproductive excess" should attribute the framing to Crow, Felsenstein or ReMine, not to Haldane. The foreword to a 1990 collection of Haldane's genetics papers, edited by Krishna Dronamraju. The article uses it for Crow's own gloss on the cost, the phrase "reproductive excess." ↩
37.
Haldane, J. B. S. Bibliography of J. B. S. Haldane, maintained at jbshaldane.org. n.d. The 1960 paper's reference list gives the two forthcoming papers as: “HALDANE, J. B. S. (1961a). The theory of iteration, with special reference to population genetics., Proc. Nat. Inst. Sci. India (in press)”. “HALDANE, J. B. S. (1961b). Evolution under selection of slowly changing intensity, Journ Genet. (in press).” An online list of Haldane's publications whose entries for 1961 to 1965 contain neither of the two forthcoming papers his 1960 paper cites. Its six 1961 entries are on artificial selection, natural selection in man, J. S. Haldane's scientific work, probability integrals, evolution as a test for ethics, and stable polymorphism. The article uses it to show that the promised demonstration was never published. ↩
38.
Haldane, J. B. S. Four papers, 1937 to 1964. 1964. The word "dilemma" appears in none of the four papers, and Haldane consistently calls the quantity a cost. The article uses this to show that the name is not Haldane's. ↩
39.
ReMine. Later writing on Haldane's dilemma [citation to be supplied]. n.d. ReMine insists in his later writing that the argument concerns the total number of beneficial substitutions in one lineage, not the genetic difference between living humans and living chimpanzees. TalkOrigins CB121 and Batten's popular article both make the move he disowns. The article uses it to separate what ReMine says from what his popularisers say. ↩
40.
Batten, Don. “Haldane's dilemma has not been solved.” Journal of Creation 19(1):20–21. 2005. A Creation Ministries International article, the popular version of the creationist argument that most readers meet. It leads with the human-chimpanzee difference and attributes 1,667 to Haldane, both moves that ReMine explicitly disowns. ↩
41.
ReMine, Walter J. “Cost theory and the cost of substitution — more precise calculations.” Creation Research Society Quarterly 43(2):111–120. 2006. A theory paper that restates Haldane's cost of substitution as the reproduction rate a scenario requires, meaning the offspring per parent a population must produce for a new trait to spread through it. The article uses it for ReMine's 2006 reply on Haldane's figure of 30.
1. 41a.
  ReMine argues that Haldane's figure of 30 rests on an environmental-change scenario he rejects, so he writes: “we must seek a more realistic figure, which will surely be higher.” This cuts in his favour numerically and against the attribution of 1,667 to Haldane, on which every popular version depends. ↩
42.
Crow, James F., and Motoo Kimura. “Efficiency of truncation selection.” PNAS 76(1):396–399. 1979. Page 399: “the relative efficiency of truncation selection ranges from 5 to 20”. A 1979 theory paper on truncation selection, a form of selection in which only individuals above a cutoff reproduce. For mutations that reduce viability in Drosophila, the authors argue that it can hold the mutation load low despite a high mutation rate, and their scenario culls 10% of the population, Haldane's own budget, so the claim is that truncation lets a low-fecundity species pay a load that multiplicative arithmetic says it cannot. The article uses it as a real mathematical escape from that arithmetic, and quotes the authors' efficiency figure for their Drosophila case. ↩ ↩
43.
Hartl, Daniel L., and Andrew G. Clark. Principles of Population Genetics. n.d. A population-genetics textbook. It never uses the terms "cost of natural selection", "substitutional load", "segregational load", "mutational load" or "Haldane's dilemma", and uses "genetic load" once, in passing. The article uses it as an example of how the field's textbooks stopped teaching the cost of selection. ↩
44.
Felsenstein, Joseph. Theoretical Evolutionary Genetics. University of Washington. 2016. A textbook of theoretical evolutionary genetics, 527 pages in its 2016 edition, written by the author of one of the two 1971 re-derivations of the reproductive-excess limit. It contains none of the terms "substitutional load", "cost of natural selection", "cost of selection", "Haldane's dilemma", "soft selection" or "hard selection", and its fifteen Haldane bibliography entries run from 1924 to 1963, with no 1957 entry. It covers mutational load at length, including a section titled "Why we aren't all dead," and the article uses it to show that the field's textbooks dropped the cost of selection. ↩
45.
Thirteen textbooks checked for substitutional load and Haldane's dilemma. n.d. A survey of thirteen textbooks for those two phrases. Futuyma's Evolutionary Biology, 2nd edition (1986), has "Cost of selection, 176" in its printed index and drops it by the 3rd edition (1998), so the disappearance is datable. Ridley (1996, Table 7.3, index entry "Substitutional load, 160") and Hamilton (2009) still teach it, and "Haldane's dilemma" occurs in none of the thirteen. The article uses the survey to date the field's loss of the topic. ↩
46.
Kimura, Motoo. “Evolutionary rate at the molecular level.” Nature 217:624–626. Feb 17, 1968. A 1968 Nature article, the founding paper of the neutral theory, the idea that most DNA changes are neutral, meaning selection neither helps nor harms them. It is built directly on Haldane's arithmetic: Kimura computes a mammalian nucleotide substitution rate of roughly one every two years, compares it with Haldane's one per 300 generations, and concludes that most substitutions must be invisible to selection. The article cites it because if most substitutions are neutral, nobody has to die for them, and the cost vanishes. ↩
47.
Nei, Masatoshi. “Selectionism and neutralism in molecular evolution.” Molecular Biology and Evolution 22(12):2318–2342. 2005. A 2005 paper on the long dispute between selectionism, the view that natural selection drives most molecular change, and neutralism, the view that most of it is neutral. Nei argues that Kimura's calculation of the cost of selection treated all four billion nucleotides in the genome as targets of selection, when the unit of selection should be a gene or an amino acid, because noncoding DNA is largely irrelevant to the evolution of proteins. The article uses it for that criticism of Kimura's arithmetic. ↩
1. 47a.
  Nei's own recomputation, with the corrected unit of selection, gives one gene substitution every 286,000 years (or 220,000 years in his 2013 book), against Haldane's ceiling of 1,200 years. With amino acids as the unit, the rate is one every 636 years, about twice Haldane's ceiling. The article uses it to show that with the right units the gap is about a factor of two. ↩ ↩
48.
Kern, Andrew D., and Matthew W. Hahn. “The neutral theory in light of natural selection.” Molecular Biology and Evolution 35(6):1366–1371. May 2, 2018. “overestimates the number of protein-coding sites in the genome by two orders of magnitude.” The article uses it for that criticism. The broader thesis is contested: Jensen et al. (2019, Evolution 73:111–114) reply to it. A 2018 article by two population geneticists arguing that the neutral theory, the idea that most DNA changes are neutral, has been undermined by genomic data. Its main criticism of Kimura is a counting error, which the authors state in one sentence about Kimura: ↩ ↩
49.
Nunney, Leonard. “The cost of natural selection revisited.” Annales Zoologici Fennici 40:185–194. 2003. A simulation study by an evolutionary geneticist at the University of California, Riverside, of a density-regulated population in a steadily changing environment, with one to seven survival traits each controlled by one locus. The cost is measured as the shortest interval between substitutions at all selected loci that the population survives; it falls steeply as the supply of new beneficial mutations per locus rises, and costs across loci add up to less than Haldane assumed. It is the one modern test written for Haldane's cost, and its hard-selection model favours neither side outright. ↩
1. 49a.
  Page 189: “The intercept was positive in all cases, showing that the cost of simultaneously selecting on several traits is less than the summed cost of selecting on each trait separately in different generations.” Page 190: “As a result, the maximum rate of evolution is reduced when the adaptive response is spread across several loci; however, it is reduced much less than expected based on Haldaneʼs (1957) result”. ↩
2. 49b.
  Page 193: “Thus, a simulated population with M = 10 can tolerate environmental change that requires allelic substitution at 7 loci (determining 7 independent traits) every 40 generations.” ↩
3. 49c.
  Page 193: “The finding that natural selection can drive evolution much faster than suggested by Haldaneʼs result only applies to large populations with M ≥ 1. The situation changes rather dramatically for the worse as M declines below 1 (Fig. 3). … For example, a population of K = 10 000 … has a value of M = 0.1. This relatively large population will become extinct if the environmental change requires allelic substitution faster than about every 300 generations, i.e. at the rate suggested by Haldane (1957).” M = 2Ku, the number of new mutations per locus per generation, where K is the carrying capacity and u the mutation rate per locus; Nunney's example takes u = 5 × 10^-6 per gamete. ↩
4. 49d.
  Page 194: “It is clear that soft selection, whereby all genotypes have equal fitness under low density, eliminates the cost of substitution (see Wallace 1970, Mather 1973). … Unfortunately, soft selection is only important when natural selection is driven by intraspecific competition. … Such challenges are unlikely to result in soft selection, and those species that cannot tolerate the cost of selection will go extinct.” ↩
5. 49e.
  Page 185: “The cost of selection (C) was measured as the shortest number of generations between an allelic substitution at all loci under selection that was consistent with population persistence.” ↩
6. 49f.
  Page 190, table 1: Fixed cost and additional cost per locus at K = 5000: 429.0 and 68.6 at M = 0.05; 150.2 and 44.4 at M = 0.1; 43.6 and 25.8 at M = 0.25; 4.8 and 11.8 at M = 1.0; 3.7 and 4.5 at M = 10. “Indeed, the costs were frequently statistically indistinguishable despite the 10-fold difference in the K and u (see Table 1).” Page 193: “Moreover, if the carrying capacity is reduced to 5000, the population could only tolerate an environment changing at less than half of this rate, i.e. about every 700 generations.” ↩
50.
This site's arithmetic on Nunney's Table 1. Nunney measures cost as "the shortest number of generations between an allelic substitution at all loci under selection that was consistent with population persistence,"⁴⁹ and fits it as a fixed cost plus a cost per locus. At M = 0.1 his Table 1 gives 150.2 + 44.4 generations per locus, so the interval is about 283 generations for three loci and 328 for four: Haldane's 300 is matched by three or four loci each changing once in that time, which is one substitution per 82 to 94 generations. At M = 0.05, which is what halving the population to 5,000 does, the fit is 429.0 + 68.6 per locus, giving 635 to 703 generations for three or four loci, which matches his "about every 700 generations". His Table 1 was fitted at a carrying capacity of 5,000; he applies it to 10,000 because at equal M the costs "were frequently statistically indistinguishable despite the 10-fold difference in the K and u".⁴⁹ ↩
51.
This site. Priority note. n.d. Introduction: “the fraction of amino acid substitutions explained by adaptation can be high ... it is curious that the empirical collapse of historical arguments for neutral theory has not yet led to a re-evaluation of related arguments by Haldane”. Discussion: “Population geneticists no longer exhibit obvious concern that Haldane's Dilemma poses a limitation to the speed of adaptation, even when e.g. reporting high rates of adaptive sweeps”. Wikipedia: “if divergence between Drosophila species was as adaptive as the alpha parameter suggests, then it would exceed Haldane's limit.” The owner of this project also put Moran's "a few thousand" against the Haldane ceiling to Felsenstein directly at The Skeptical Zone in 2016. What this article adds is the arithmetic and the side-by-side table, not the observation. An earlier draft of this article claimed the comparison was new, which was false. Matheson, Exposito-Alonso & Masel 2025 make the point in Genetics, citing Uricchio et al. 2019 by name in both the Introduction and the Discussion. The current Wikipedia article on Haldane's dilemma makes the same comparison for flies. ↩
52.
Stern Cardinale, Dan. Video treatment of Haldane's dilemma. 2021. At 00:09:08–00:09:40: “we found that between 240 and 780 beneficial alleles have fixed in the human genome ... but even if we double the highest estimate here to account for that ... we still come in under the erroneous limit.” His conceded top figure is therefore 1,560, not 780 — 93.6% of ReMine's 1,667, a 6% margin. Like Musgrave, he compares against ReMine's 10-million-year figure rather than against the ceiling his own split date implies. A video on Haldane's dilemma by Dan Stern Cardinale. The article uses it as a second mainstream critic who puts the number of adaptive fixations under ReMine's ceiling and concludes there is no dilemma. ↩ ↩
53.
Moran, Laurence A. Comment on Sandwalk. 2014. “We don't know how many of those were beneficial (adaptive) leading to ways in which modern chimps are better adapted than the common ancestor. (Same for humans.) My guess would be only a few thousand in each lineage.” It is a guess and he says so; it should not be reported as a measurement. A comment by Laurence Moran, a biochemist at the University of Toronto and a prominent critic of intelligent design, on his blog Sandwalk. The article uses it because Moran was asked directly how many human-chimpanzee differences were adaptive and answered with a guess. ↩
54.
Felsenstein. “Comment on Larry Moran's estimate (citation to be confirmed).” The Skeptical Zone. 2016. “That may not be way off.” Felsenstein, responding to Larry Moran's "a few thousand" estimate of adaptive differences between humans and chimpanzees, answered that the figure may not be far off. He then names standing variation as the escape that actually scales. The article cites it for both points. ↩ ↩
55.
Zhen, Ying et al. “Greater strength of selection and higher proportion of beneficial amino acid changing mutations in humans compared with mice and Drosophila melanogaster.” Genome Research 31:110–120. 2021. A genome comparison by researchers at the University of California, Los Angeles and Westlake University that estimates how much adaptive evolution happened in humans, mice and fruit flies, by comparing variation within each species with differences between species; it finds that humans have a higher proportion and strength of beneficial mutations than the other two, and that at least 20% of nonsynonymous substitutions between humans and an outgroup species were fixed by positive selection. Its α (the share of substitutions attributed to positive selection) is 0.16 for the human lineage and 0.25 for human-chimpanzee, under its complex demographic model, yet the same data give α from −0.70 to +0.25 depending on the model. The article uses it for the 0.16 figure, as one of the independent estimates for the human lineage. ↩
56.
Boyko, Adam R. et al. “Assessing the evolutionary impact of amino acid mutations in the human genome.” PLoS Genetics 4(5):e1000083. 2008. A method paper that estimates how the fitness effects of new mutations are distributed in humans, using 47,576 coding SNPs from 11,404 genes sequenced in 35 people (20 European Americans and 15 African Americans). It finds that 10–20% of amino-acid differences between humans and chimpanzees were fixed by positive selection. The same paper gives the fraction of new nonsynonymous mutations that is beneficial as 0.05% to 1.86%, a different quantity that is routinely confused with α, and the confusion inflates numbers by three or four orders of magnitude; the article uses the 10–20% figure. ↩
57.
Galtier, Nicolas. “Adaptive protein evolution in animals and the effective population size hypothesis.” PLoS Genetics 12(1):e1005774. 2016. A research article by Nicolas Galtier of the Institut des Sciences de l'Evolution in Montpellier. It surveys 44 pairs of non-model animal species, from insects to mammals, and finds that adaptive evolution drives amino-acid change in most of them, with humans and primates the notable exception. Its human estimate is α = 0.24 [0.18, 0.29], which rests on four individuals and 1,204 nonsynonymous divergent sites, so the confidence interval understates the real uncertainty; the article uses the 0.24 figure. ↩
58.
Eyre-Walker, Adam, and Peter D. Keightley. “Estimating the rate of adaptive molecular evolution in the presence of slightly deleterious mutations and population size change.” Molecular Biology and Evolution 26:2097–2108. 2009. A population-genetics paper that gives the low end of the estimates: its point estimate is essentially zero, with 95% confidence limits of −0.30 to 0.24. Their widely quoted "could be as high as 40%" comes entirely from assuming N_D = 10 N_P. The article uses it as the outlier among the independent estimates for humans. ↩
59.
Berean Archive. This site's own arithmetic. n.d. A count made by this site, not a published figure, of adaptive substitutions in non-coding DNA, which no paper reports: papers that count constrained sites define constraint as substitution removal, so few substitutions occur there by construction, while Torgerson et al. 2009 measures the adaptive fraction of conserved elements, which mix constrained and free sites. It starts from Torgerson's 50,249 human-chimpanzee fixed differences in 6.9 Mb of conserved non-coding sequence (7,282 per Mb), which reports fixed differences only within its own 6.9 Mb panel, and scales them by a genome-wide extent, the human-lineage share and a pooled α of 4.67%. The result is 6,000–10,000 adaptive non-coding substitutions on the conservative reading and 25,000–40,000 on the turnover-aware reading, with per-class adaptive fractions from 2.22% (intronic conserved non-coding) to 23.3% (3′ UTRs); six caveats apply, and the article uses it to add non-coding substitutions to its coding-only figures. ↩ ↩ ↩
60.
Musgrave. Musgrave's footnote 5 (citation to be confirmed). n.d. Musgrave's footnote 5 concedes that at a 6-million-year split the ceiling is 1,000 rather than 1,667. His own top estimate is 960, a 4% margin. Substituting the measured 26.9-year generation interval drops the ceiling to 682-781, below his own upper estimate. The article cites it for Musgrave's own margin. ↩
61.
“Comments on Haldane's non-dilemma.” The Panda's Thumb. 2007. Two mainstream commenters, among the 66 comments under Musgrave's 2007 post, identified the method error within hours. Musgrave converts a count of genes carrying a selection signature (Bakewell's 154 of 13,888) into a count of substitutions with no conversion factor, and the commenter "p-ter" added that genome scans of this kind cannot detect weakly adaptive fixations, which Uricchio et al. 2019 later found constitute 72% of human α. The article cites it to show that Musgrave's method was criticised in his own comment thread within hours. ↩
62.
Hermisson, Joachim, and Pleuni S. Pennings. “Soft sweeps: molecular population genetics of adaptation from standing genetic variation.” Genetics 169(4):2335–2352. 2005. A diffusion-theory paper, checked against simulations, on whether a population adapts from alleles already present when the environment changes or from new mutations that arrive afterwards. It finds standing variation favoured when selection is weak or when both the selection coefficient and the mutation rate are high. The article uses its comparison of the two routes to bound how much standing variation can lower Haldane's cost for a change at one site.
1. 62a.
  Page 2339: “This result means that in a time span that an allele from the standing variation needs to reach fixation, it is at least as likely that the allele alternatively appears as a new mutation destined for fixation only after the environmental change.” "The time span" is the time an allele from standing variation needs to fix; the comparison, set up on page 2338, is with the time at which a new mutation destined for fixation becomes as likely as a fixation from standing variation. The approximation behind it holds when the scaled mutation rate to the allele, Θ = 4N_eu, is below 1. ↩ ↩
63.
Durrett, Rick, and Deena Schmidt. “Waiting for two mutations: with applications to regulatory sequence evolution and the limits of Darwinian evolution.” Genetics 180(3):1501–1509. 2008. A mathematical paper from Cornell that works out how long a population waits for two specific mutations, using a stochastic-tunnelling treatment derived from the cancer-modelling work of Iwasa, Michor, Komarova and Nowak. It applies this to regulatory DNA and finds 216 million years for one prespecified pair of mutations in a human-sized population. The article uses its formula for the mean waiting time and its result, which the authors set against Behe. ↩
1. 63a.
  216 million years for one prespecified pair of regulatory mutations in a human-sized population. Their argument against Behe is that the same mathematics gives short times for the vastly larger populations of malaria parasites. ↩ ↩
64.
Behe, Michael J. The Edge of Evolution. Free Press. 2007. A book arguing that adaptations needing several specific mutations are too rare to arise, illustrated by the "chloroquine complexity cluster" in malaria and a 1-in-10²⁰ figure for the chloroquine case. That figure comes from Nicholas White's 2004 review in the Journal of Clinical Investigation 113:1084–1092, and it is an establishment probability, not a mutation probability. Behe's defence is that both of his figures carry the same discount, so the ratio between them still measures the cost of the second mutation, and that defence is not obviously wrong. The article uses it for the claim that Durrett and Schmidt's 2008 paper tests. ↩
65.
Durrett, Rick, and Deena Schmidt. “Reply to Michael Behe.” Genetics 181(2):821–822. 2009. A two-page reply by the same authors to Michael Behe's piece in the same journal, Genetics 181:819–820. Cite this exchange whole or not at all. Behe wins one point and loses two, and quoting only the concession misrepresents the exchange, so the article quotes the concession only alongside the two points Behe lost. ↩
1. 65a.
  “Behe is right on this point. This divides our previously computed overestimate of 5 million by 30.” ↩
66.
Summers, Robert L. et al. “Diverse mutational pathways converge on saturable chloroquine transport by the malaria parasite PfCRT.” PNAS 111(17):E1759–E1767. 2014. A research paper on how different sets of mutations in the malaria parasite's chloroquine resistance transporter (PfCRT) converge on the same chloroquine transport. It confirms Behe's core empirical claim that at least two specific mutations in PfCRT are needed before any chloroquine transport occurs. It does not settle whether the intermediate is deleterious, which is the load-bearing unresolved fact in the dispute: the deleterious case multiplies the waiting time by a factor that can reach 1,000. The article uses it as the empirical test of Behe's claim. ↩
67.
Meyer, Justin R. et al. “Repeatability and contingency in the evolution of a key innovation in phage lambda.” Science 335(6067):428–432. 2012. A laboratory experiment with phage lambda, a virus that infects bacteria, run in 96 replicate flasks. A four-mutation, all-or-nothing switch to the OmpF receptor arose independently in 24 of the 96 flasks, with a median of 12 days. The article uses it as the watched case of a multi-mutation adaptation with non-selectable intermediates, which the paper shows forming. ↩
68.
Mendel's Accountant source code. n.d. The public source code of the population-genetics simulator that Sanford's 2015 waiting-time paper uses. The target-matching routine poly_match in polygenic.f90 is a single string equality, if(str1==str2), with no partial credit, no mismatch tolerance, no alternative targets and no sliding window, so the article uses it to show how narrow the search is. ↩
1. 68a.
  selection.f90 computes fitness in two mutually exclusive branches; when waiting-time mode is on, the entire linkage-block fitness calculation is never executed, so individual fitness is baseline plus the target bonus and nothing else. init.f90 sets num_linkage_subunits = poly_str_len and haploid_chromosome_number = 1, replacing the 989-block, 23-chromosome default human genome with a single chromosome as long as the target, so a five-nucleotide search runs in a five-base genome. mendel.js forces fraction_neutral = 1.0 and frac_fav_mutn = 0.0. ↩
69.
Mendel's Accountant default settings. n.d. The simulator's default settings, which the paper leaves unlisted, include heritability = 0.2 and non_scaling_noise = 0.05, as the file mendel.in and the user manual show. The manual's own comment reads: "For a very general character such as reproductive fitness, 0.2 is an extremely generous heritability value. In most field contexts, it is in fact usually lower than this." So selection acts on a phenotype that is mostly environmental noise, and the nominal 10% fitness benefit is an upper bound on the realised advantage. The paper's Methods say only, on page 6: "Unless otherwise specified, we used the default settings of Mendel's Accountant." The article cites it for the defaults the paper relies on without saying so, and for an unresolved tension on dominance: Mendel's default is co-dominance, while the paper claims full dominance and never reports changing it. ↩
70.
Rupe, Christopher L., and John C. Sanford. “Using numerical simulation to better understand fixation rates, and establishment of a new principle: Haldane's Ratchet.” Proceedings of the Seventh International Conference on Creationism 7. 2013. “Deleterious mutation accumulation could not be simulated through such deep time, as it always either caused overflow of memory or premature termination due to extinction.” The paper's own statement. Its conclusion's "at least 100,000 low-impact deleterious fixations" is extrapolated from a 20,000-generation run at N = 1,000 out to 300,000 generations at N = 10,000. Each table row is a single run; there are no replicates and no error bars anywhere in the paper. “at least 100,000 low-impact deleterious fixations”. A computer simulation paper, article 32 in volume 7, by Rupe of the FMS Foundation and Sanford of Cornell, which follows each new mutation until drift loses it or it becomes fixed. With realistic settings it sees only a few hundred beneficial fixations after 300,000 generations (6 million years), and a few thousand under optimal settings, where the ape-to-man scenario needs tens of millions of substitutions in the human lineage. The paper names "Haldane's Ratchet" for the finding that deleterious fixations outnumber beneficial ones. The article uses it as the paper that makes the Haldane argument from Sanford's group, which Sanford et al. 2015 does not. ↩
1. 70a.
  Their optimised run qrtoju produced 1,476 selective fixations, against the roughly 1,000 the same paper's introduction gives as Haldane's ceiling for 300,000 generations. The paper does not remark on this. ↩
2. 70b.
  Section Methods: Their Methods declare truncation selection: “highly unrealistic and never happens even in artificial breeding experiments, let alone in nature.” Their most favourable run then employs 50% truncation selection. Labelling it a best case is fair, but it means the most evolution-friendly number they report was obtained under a regime they say does not exist. ↩
71.
Behrens, Sarah, and Martin Vingron. “Studying the evolution of promoter sequences: a waiting time problem.” Journal of Computational Biology 17(12):1591–1606. 2010. A computer model of how long it takes for a given short binding site for a regulatory protein to appear at random in a promoter, the stretch of DNA that switches a gene on. It uses two probability models and a three-species alignment of human, chimpanzee and macaque to set the substitution rates, and it gives 83–338 million years for a 5-mer in one 1-kb promoter and 7,467 years averaged across 20,000 promoters. The article uses it because Sanford rejects its result on biological grounds. ↩
1. 71a.
  Their model contains no population, no selection and no fixation probability; the drift is folded into a substitution rate estimated from a human/chimp/macaque alignment. Both sides should note this: it is not a population-genetic calculation, and comparing it directly to a Mendel simulation is comparing unlike things. ↩
72.
Messer, Philipp W., and Dmitri A. Petrov. “Population genomics of rapid adaptation by soft selective sweeps.” Trends in Ecology & Evolution 28:659–669. 2013. A review of how populations adapt quickly. A soft sweep is one in which several adaptive alleles spread through the population at the same time, either because they were already present as standing variation or because they arose independently by new mutation. Their own criterion for soft sweeps is Θ = 2Nμ ≳ 1, and a hominin population sits at Θ ≈ 2 × 10^-4 per site, so the soft-sweep literature does not rescue the specific case Sanford modelled, and its authors do not claim it does. The article uses it for that criterion. ↩
73.
Villar, Diego et al. “Enhancer evolution across 20 mammalian species.” Cell 160:554–566. 2015. A comparative study that mapped the active enhancers (DNA switches that turn genes on from a distance) and promoters in the liver of 20 mammal species, using two chemical marks on histone proteins that flag active regions, and found 30–45,000 active regions per species. It found that enhancers are rarely conserved between these species while almost all liver promoters are conserved, and its fitted exponential decay of activity conservation gives a mean lifetime of 427 million years for enhancers and 207 million years for CEBPA binding sites (places where the CEBPA protein attaches to DNA), which works out to roughly 50–100 regulatory-element gains and losses per million years per lineage. The article takes these figures as the empirical form of its "many targets" answer. ↩
74.
Traulsen et al. “On the misuse of evolutionary theory to bolster the 'scientific' case for intelligent design: A cautionary note.” Journal of Theoretical Biology 596:111985. 2024. The only peer-reviewed rebuttal anywhere in this literature. It targets Hössjer, Bechly & Gauger 2021, not the Sanford paper. The article cites it to concede that the Sanford paper has no peer-reviewed rebuttal, because this one answers a different paper. ↩
75.
Bersaglieri, Todd et al. “Genetic signatures of strong recent positive selection at the lactase gene.” American Journal of Human Genetics 74:1111–1120. 2004. A genetic study that typed 101 single-nucleotide polymorphisms (single-letter differences in DNA) across 3.2 million bases around the lactase gene in several human populations, looking for signs of recent selection. It estimates that strong selection occurred within the past 5,000–10,000 years, consistent with an advantage to lactase persistence in dairy farming, and its authors say the signals are among the strongest yet seen for any gene in the genome. The article cites it for lactase persistence, which it calls the fastest thoroughly documented human sweep from a new mutation. On the paper's own parameters the sweep consumes an intensity of selection of about 0.07–0.14 per generation, so one locus consumes Haldane's whole-genome budget of 0.1. ↩
76.
Cook, L. M. et al. “Selective bird predation on the peppered moth: the last experiment of Michael Majerus.” Biology Letters 8:609–612. 2012. This site's own calculation, combining van't Hof's dating of the carbonaria mutation to about 1819 and high frequency in Manchester by roughly 1895 (n = 76 generations at one per year), gives an implied intensity of −ln(1/2N_e)/76. For N_e of 10⁵ to 10⁷ this gives 0.161 to 0.221. An earlier draft printed an upper bound of 0.24, which would need N_e ≈ 1.5 × 10⁸ and does not reproduce. The 1895 date is this site's working figure and is not tightly sourced, so treat the whole calculation as an order-of-magnitude check. Haldane's own Biston intensity was I ≈ 0.69, three to four times higher, so this recomputation does not agree with him. A reanalysis of the last field experiment of Michael Majerus, who released 4,864 peppered moths in a six-year test of bird predation, the largest such experiment ever attempted. The authors found strong differential predation against the dark (melanic) moths, with daily selection against them of about 0.1, enough to explain the decline of melanism in post-industrial Britain. Majerus died before publishing, so the authors present his results from a keynote talk in 2007. The article uses it for the peppered moth's intensity of selection, a case it calls Haldane's own example of unusually intense selection. ↩
77.
Hawks, John et al. “Recent acceleration of human adaptive evolution.” PNAS 104(52):20753–20758. 2007. Section Methods: The 13.25 figure appears once, under the Methods heading "Estimating the Rate of Adaptive Substitutions," whose first sentence begins: “Under the null hypothesis of a constant rate of adaptive substitution”. The same paragraph adds: “Under the null hypothesis, the population size N_t is constant across all generations.” Section Predictions of Constant Rate: The next Results heading, with its first sentence, reads: “Predictions of Constant Rate. We can derive four predictions from the rate of adaptive substitution, each of which refutes the null hypothesis of constant rate.” Their third prediction states the reductio themselves: the implied annual rate: “predicts an implausible 6.4 million adaptive substitutions between humans and chimpanzees ... or 100 times the observed number of amino acid substitutions, is implausible.” Their preferred demographic model: “predicts a low long-term substitution rate.” Emphasis in the original headings. An earlier draft of this article presented 13.25 as a claim to be refuted, which is a straw man: Hawks constructed it in order to refute it. A population-genetics paper that used the 3.9-million-SNP HapMap dataset (a catalogue of common single-letter DNA differences between human populations) to date recently selected stretches of the genome, and found that selection has accelerated greatly during the last 40,000 years. The article cites it because the 13.25 figure is routinely quoted from it as a recent human rate, though the authors derive that figure under a null hypothesis they set out to refute. ↩
78.
Belknap, Michael, and Tim Chaffey. “How could all the animals fit on the Ark?” Answers in Genesis. 2019. An Answers in Genesis web article on how its Ark Encounter researchers estimated the kinds of animals on Noah's Ark, using hybrid data, the cognitum method (judging kinds by appearance) and statistical baraminology (statistical tests of physical traits). Their worst case multiplies clean animals and flying animals by fourteen instead of seven. It gives 1,398 kinds and 6,744 individual animals, of which 136 are living mammal kinds and 195 living bird kinds, and the article cites it for the 1,398-kind figure from Answers in Genesis's ark research. ↩
79.
Lightner, Jean K. “Mammalian Ark Kinds.” Answers Research Journal 5:151–204. 2012. “Examining information on extant species ... it was estimated that they represent 137 created kinds.” Within that: “There are 14 genera and 40 species of cats”. “There are 13 genera and 35 species of canids”. “a single genus with eight species of equids.” A survey of the living mammal species by an independent scholar, published in the research journal of Answers in Genesis, which counts them into 137 created kinds. The author adds that, counting extinct mammal families, the actual number on the Ark "could easily have been well over 300." The article uses the 137 figure as the creationist count of mammal kinds. ↩
80.
This site. Mammal kinds, species growth and the Haldane budget over the post-Flood interval. n.d. The calculation uses creationist species counts and a 4,350-year post-Flood interval at 25 years per generation, which is 174 generations. 137 mammal kinds growing to roughly 4,800 living mammal species is a doubling every 848 years. The budget is 174 generations × 0.1 payment per generation = 17.4 cost-units, which buys 0.58 substitutions at D = 30, 0.88 at D = 19.81 (a new mutation in a population of 10,000, additive case), 6.3 at p₀ = 0.25 and 12.5 at p₀ = 0.5. Haldane's 0.1 payment rate was chosen for a slow-breeding vertebrate; for a murid with a reproductive excess of 3, a designed allele at p₀ = 0.25 fixes in about one generation. The article sets the doubling rate against the substitution budget, which buys only 0.58 substitutions at D = 30. ↩ ↩
81.
Wood, Todd C. “Perspectives on AGEing, A Young-Earth Creation Diversification Model.” Proceedings of the Fifth International Conference on Creationism, 479–489. 2003. Page 479: “a new report places all fossil equids in a single monobaramin ... This would require the origin of 150 species of horse prior to the gift of donkeys (Equus asinus) from Pharaoh to Abram (Gen. 12:16), which took place ~400 years after the Flood. ... Since we see no 'speciation' like this today or in historical times, we can infer that the mechanism of intrabaraminic diversification is qualitatively different from modern speciation.”. Emphasis mine. That is one new horse species every 2.7 years. A young-earth creationist's review of his AGEing model, which proposes that transposable elements (DNA segments that move around a genome), designed by God, drove the diversification of created kinds after the Flood. It reviews evidence gathered since the model was proposed in 1999 and argues that the model needs significant revision. The article cites it for the 150-horse estimate and for the model's mechanism. ↩
1. 81a.
  Pages 480–481: His proposed mechanism is Altruistic Genetic Elements — transposable elements designed by God with high insertional specificity. “Obviously, the most important prediction of the AGEing model is that AGEs can induce beneficial genetic changes at a rate higher than random mutations.” That is a bare rate claim with no independent measurement behind it. ↩
82.
Wise, Kurt P. “Australopithecus ramidus and the Fossil Record.” Creation Ex Nihilo Technical Journal 8(2):160–165. 1994. Page 162: “This means that there would of necessity have been an explosive amount of biological change in the few centuries after the Flood. Since this is too rapid a change to have been produced by any traditional microevolutionary mechanisms (for example, mutations acted on by natural selection), it seems that this change must have come from within the genome of the organisms themselves.”. Emphasis mine. His footnote 36 is still unanswered thirty years on: “What mechanism caused such a proliferation of form and then shut it down is perhaps the most exciting unsolved mystery of creationist biology.” A paper by the creationist Kurt Wise on Australopithecus ramidus, a fossil species dated conventionally to about 4.4 million years ago that evolutionists treat as a human ancestor. Wise argues it fits the creationist model of the fossil record better than the evolutionary one, because it shares six features with other fossil species: lack of transitional forms, species stasis, high homoplasy (similar features arising independently), rarity of stratomorphic intermediates and of stratomorphic series (fossils intermediate in both time and form), and the commonness of high species diversity in those series. The article cites it for Wise's own statement that the post-Flood change was too rapid for ordinary mutation and selection. ↩
83.
Jeanson, Nathaniel T., and Jason Lisle. “On the Origin of Eukaryotic Species' Genotypic and Phenotypic Diversity.” Answers Research Journal 9:81–122. 2016. Page 114: “If selection were to act on individual variants, one-at-a-time, in a sequential manner, then millions of growth-crash cycles would be required. For just 1 million homozygous variants to be selected, a growth-crash cycle would be required once every ~1.6 days ... In all the mammal species for which we had data, none of them could produce more than three individuals in this space of time. Hence, sequential selection of millions of DNA variants was not a plausible scenario by which to reduce heterozygosity on the YEC timescale.” Emphasis mine. This is the closest thing that exists to a creationist applying a reproductive-excess argument to the young-earth model, and it reaches a negative result. A creationist paper by Nathaniel Jeanson, of Answers in Genesis, and Jason Lisle, of the Institute for Creation Research. It compares mitochondrial and nuclear DNA clocks and proposes a model it calls created heterozygosity (genetic variety built in at creation) plus natural processes, which it says can account for the diversity of species. The article cites it for the calculation of how often growth-and-crash cycles would be needed to select many variants one at a time. ↩
84.
Wood, Todd C. “Mitochondrial DNA Analysis of Three Terrestrial Mammal Baramins (Equidae, Felidae, and Canidae) Implies an Accelerated Mutation Rate Near the Time of the Flood.” Proceedings of the Seventh International Conference on Creationism. 2013. Section Introduction: “As terrestrial baramins, we may hypothesize that they have descended from a single pair preserved by Noah on the Ark. Consequently, any mitochondrial sequence variability must be attributed to real mutations instead of allelic diversity preserved from before the Flood.”. Emphasis mine. He considers and rejects the heteroplasmy escape. A conference paper by the young-earth creationist Todd Wood, who compared published ancient and modern mitochondrial DNA sequences (the small circular genome inherited from the mother) from horses, cats and dogs. He argues that the ancient sequences already show the modern diversity, which implies that the diversity was established soon after the Flood. The article cites it for Wood's answer to the uniparental-DNA objection: a post-Flood mutation-rate spike that later shut off. ↩
1. 84a.
  Felid-felid cytochrome-b comparisons run to 2–46 single-nucleotide differences over 287 aligned positions; extant canid-canid control-region comparisons 0–62 over 493 positions; extant equid-equid 5–29 over 423 positions. His conclusion: “these results imply a period of rapid genetic divergence after the Flood that quickly decreased to the low mutation rates characteristic of the present.” ↩
85.
This site. Six targeted searches of creationist sources. n.d. The site's own search of creation.com, answersingenesis.org, icr.org, creationresearch.org, creationwiki.org and the ICC proceedings indexes for 1994, 2003, 2013 and 2018 found no creationist source that applies Haldane's cost of substitution by name to post-Flood diversification. The article cites it to report this as an absence of the label rather than an absence of the reasoning, since Wise 1994 and Jeanson & Lisle 2016 do the reasoning without the label. ↩
86.
Blount, Zachary D. et al. “Historical contingency and the evolution of a key innovation in an experimental population of Escherichia coli.” PNAS 105(23):7899–7906. 2008. “Given 1:100 dilution and regrowth, the populations achieve ≈6.64 generations per day.” A laboratory evolution experiment with E. coli bacteria. The article uses it for the protocol's numbers, the daily dilution and regrowth that set the rate of generations. ↩
87.
Theoretical Biology and Medical Modelling. BioMed Central. n.d. A small BioMed Central journal, eISSN 1742-4682, established in 2004, that ceased publication at the end of 2021; its archive remains live. Sanford's group had published in it twice before, in 2011 and 2012. BMC did not publish peer-review histories or handling-editor names in 2015, so who handled the Sanford paper cannot be established from the published record. The article cites it for the closure and for Sanford's earlier papers in the journal. ↩
88.
Kirschner, Denise et al. “Disclaimer.” Journal of Theoretical Biology 506:110456. 2020. An editorial disclaimer by the journal's editors, about a paper by other authors. It was written about Thorvaldsen & Hössjer 2020, a fine-tuning paper, though Elsevier's metadata also links it to Hössjer, Bechly & Gauger's 2021 waiting-time paper. The editors' complaint is that the authors' creationist affiliation was undisclosed and that the keywords "intelligent design" were added after review; they identify no error in the mathematics. The article cites it because a disclaimer sometimes cited against the waiting-time argument attaches to that different paper, and conflating the two criticisms would be unfair to Hössjer, who is a professor of mathematical statistics at Stockholm University. ↩
89.
Hickey, Donal A., and G. Brian Golding. “Sex solves Haldane's dilemma.” Genome 62(11):761–768. 2019. The paper carries a Correction in Genome 63(2):131 that reads in full: “This manuscript was mistakenly published as a Comment, but in fact it is an Article.” It is a typesetting fix and carries no scientific content. The authors disclaim the strong reading themselves: “the results presented in the current study should not be seen as a refutation of Haldane's ideas.” A 2019 paper that argues that sex solves Haldane's dilemma. The article cites it for the claim that recombination stops the costs at different loci from accumulating, and quotes the authors' own disclaimer of the strong reading. ↩
90.
Published simulation source code for Sex solves Haldane's dilemma. n.d. The published version changed the preprint's parameters, initial frequency from 0.01 to 0.05 and selection coefficient from 0.05 to 0.02, so any figure quoted from the preprint needs recomputing. The published simulation code behind the 2019 paper. The authors' published source file, sexual7.c, renormalises fitness to the fittest individual each generation and truncates the population back to 100,000 by random sampling, so it is a soft-selection, fixed-N model. That is the modelling choice Matheson et al. identify as assuming inexhaustible reproductive excess, and the paper never reports the number of selective deaths its simulation spends. The article uses it to show that the authors' own code is a soft-selection model, the modelling choice that Matheson and colleagues identify as assuming inexhaustible reproductive excess. ↩