How These Numbers Get Misused

"One puzzle remains unsolved.  The basic fact — that [N_e] is an average, not a minimum — is uncontroversial, uncontested, and widely known by biologists.  In direct conflict with established consensus science, it is difficult to understand why evolutionary creationists so frequently claimed [N_e] was a minimum.  It is unclear how, for more than a decade, they did so without correction." — Joshua Swamidass¹

What this page is

Companion to the population-genetics reference.  Every case below quotes the offending passage verbatim, names the venue honestly, says how large the error is, and gives a verdict on whether it is load-bearing — meaning the argument collapses without it — or incidental.

Cases from both camps are included, and the mainstream cases come first, because a page like this from a creationist site will be assumed to be one-sided until it demonstrates otherwise.  Section 5 lists the technical points creationists get right, which is the same exercise run the other way.

Where an error has already been audited elsewhere on this site, this page links rather than repeats.

1. Effective population size read as a headcount

This is the most common error in the whole subject and it appears in every venue, up to and including Science.

1.1 Science, 2023, corrected in GENETICS in December 2024

A 2023 paper inferring a severe Early-to-Middle-Pleistocene human bottleneck described its result as "about 1280 breeding individuals."²  Deng, Nielsen and Song replied:

"they argued for a bottleneck size of 1,280 individuals, but we note that their estimate actually corresponds to an effective population size of N_e = 1,280.  Effective population sizes can be substantially smaller than the actual number of individuals, especially when there is a high variance in offspring numbers among individuals."³

Verdict:  load-bearing for the paper's public framing, not for its statistics.  Print this case first whenever somebody suggests the confusion is a layman's problem.  It is not.

1.2 Adam and the Genome, and a decade without correction

Dennis Venema, then BioLogos's Fellow of Biology and chair of biology at Trinity Western, writes in Adam and the Genome (Brazos Press, 2017 — a trade religious publisher, not peer reviewed) that the human population "never dipped below about 10,000 individuals."⁴

His earlier peer-reviewed version is page-verified and says the same thing more precisely:

"…any bottlenecks our lineage did experience were a reduction only to a population of several thousand breeding individuals."⁵

What is wrong.  Every method he cites — linkage disequilibrium, incomplete lineage sorting, PSMC — estimates N_e, which is an average with no resolution at the scale of one or a few generations.  "A reduction only to" is the headcount reading in a single clause.

Who caught it.  Not creationists.  Richard Buggs, professor of evolutionary genomics at Queen Mary University of London and Kew:

"It is easy to have misleading intuitions about the population genetic effects of a short, sudden bottleneck. […] When two individuals are taken at random from an existing large population, they will on average carry 75% of its heterozygosity."⁶

Buggs caught a second, independent defect as well:  Venema adds African and non-African N_e estimates together to reach 10,000, when the non-African estimate is a subset of the African variation, not an addition to it.

And Swamidass documented the institutional history:  a theologian, Vern Poythress, objected in 2014 that N_e was an average rather than a minimum;  Venema conceded the point in his response;  and the claim then reappeared in the 2017 book.¹

Verdict:  load-bearing, completely.  Chapter 3's thesis is that a two-person bottleneck is excluded with the certainty of heliocentrism.  Remove the average-as-minimum step and the linkage-disequilibrium and lineage-sorting evidence contributes nothing to that thesis.  The conclusion may still be true — see §1.4 — but not by this route.

1.3 The creationist version of the same error

Robert Carter, in Journal of Creation 32(2) — a creationist journal, and Carter has a PhD in marine biology from Miami and does original population-genetic modelling, which should be said — writes:

"The maximum effective population size of the Ark-borne population was calculated to be 4.75 individuals (carrying the equivalent of 9.5 haploid genomes)."⁷

His own endnote defines the term:

"Technically, effective population size is defined as the number of individuals in a population that contribute offspring to the next generation."⁷

What is wrong.  That definition is the exact misconception Waples names and demonstrates is false in both directions.⁸  Carter's 4.75 is a count of surviving independent genome equivalents — a perfectly sensible quantity, and his arithmetic checks:  3 + 2 − 2(½)³ = 4.75.  But it is not variance N_e, not inbreeding N_e, and not any other N_e.

Verdict:  rhetorically load-bearing, technically not.  The article's punch comes from putting "4.75" beside the literature's "10,000" and inviting the reader to see how close they are.  They are not the same quantity and a skeptic will notice.  Carter did disclose the deviation in a note, which is more than most writers do;  the disclosure states the wrong definition.

A related pattern worth one sentence:  Sanford's waiting-time simulations run "a human population size consistent with human evolutionary theory (10,000)" as a census size, when 10,000 is the literature's effective size and the corresponding census is four to five times larger.  Waiting time scales as 1/(2Nμ), so this inflates every waiting time by the same factor.  Not load-bearing — a factor of four or five does not rescue a result reported in millions of years — but it should be disclosed, because it is the kind of thing a hostile reviewer finds and then uses against everything else.

1.4 What does exclude a two-person bottleneck, and when

Since this page dismantles the usual argument, it owes the reader the one that works.

N_e-based methods cannot rule out a brief bottleneck even in principle.  The statistic that does the work is TMR4A — the time to the most recent four alleles — whose median is about 495,000 years.  Swamidass, who is the person who narrowed the mainstream claim, states the corrected version:

"The genetic evidence only rules out a single-couple bottleneck (2, not 10,000) going back about 500,000 years (not 18 million)."¹

And the direction of detectability matters:  recent bottlenecks are the easy case, not the hard one.  A 4,500-year-old bottleneck of eight people sits in the visible part of the detection window.

2. Fixation probability waved off

2.1 PNAS, 2010

Wilf and Ewens — a mathematician and one of population genetics' senior theoreticians, both at Penn — published a rebuttal of the "tornado in a junkyard" argument.  Their model:

"After guessing each of the letters, we are told which (if any) of the guessed letters are correct, and then those letters are retained."⁹

And, in the same column:

"In practice further modifications are needed to the calculations since, because of stochastic events, only a proportion of selectively favored new mutations become fixed in a population.  However, the force of our result does not depend on the numerical values that one assigns to K and L."⁹

What is wrong, in two separate ways.  First, "we are told which of the guessed letters are correct" is an oracle:  it supplies information natural selection does not have, because selection sees a variant's current fitness effect, not whether it matches a distant target.  Second, the fixation probability is dismissed in a sentence — but the answer to "how long" scales as 1/(probability of fixation), and that probability is of order 2s, a percent or less.  The disclaimer is about K and L, not about the omitted factor.

Who caught it.  Ewert, Dembski, Gauger and Marks, in BIO-Complexity — the intelligent-design movement's own journal, and it must be labelled as such:

"within their model are implicit information sources, including the equivalent of a highly informed oracle that prophesies when a mutation is 'correct' […] They neglect the effects of genetic drift on the probability of fixation."¹⁰

Both sides are partly right, and this page says so.  Wilf and Ewens' central point is correct and important:  the K^L argument really is wrong, because independent loci evolve in parallel and a fixed favourable allele is not thrown away when the next one arises.  Ewert and colleagues are also right that the specific model latches, and that omitting the fixation probability is not free.

Verdict:  partly load-bearing.  The parallel-versus-serial point survives without the oracle.  The headline figure — 390 rounds for a 20,000-locus genome — does not;  that is the oracle's answer, not selection's.

3. Load arithmetic

3.1 A corrigendum that made it worse

Dan Graur is one of the most prominent critics of the ENCODE project.  His 2017 paper in Genome Biology and Evolution, peer reviewed and open access, concludes:

"Mutational load considerations lead to the conclusion that the functional fraction within the human genome cannot exceed 15%."¹¹

The defect.  Table 1 was not computed from the equation as printed.  Fitting all 176 cells recovers the model F = (1 − 2μ)^(−fg) — 2U in the exponent where U belongs.  A 2019 corrigendum then added the "2" to the equation and stated that the numerical values "have also been corrected."¹²

But the reprinted Table 1 is bit-for-bit identical to the 2017 table — all sixteen rows, all eleven columns, verified cell by cell.  Nothing was recalculated.  The corrigendum aligned the equation with an already-wrong table.

Galeota-Sprung, Sniegowski and Ewens reach the same place by the other route:

"The factor-of-two difference in f is due to the fact that Graur, erroneously in our view, treats the total number of sites as the number of haploid sites, not the number of diploid sites."¹³

Size of the error:  exactly a factor of two in the functional fraction.  At Graur's own most permissive deleterious rate, the ceiling at a fertility of 2 moves from 14.2% to 28.3%.  "Cannot exceed 15%" should read "cannot exceed about 28%" — which is above the 15% upper end of the divergence-based estimates he says his result agrees with.

Verdict:  load-bearing for the headline number, not for the argument against ENCODE.  At ENCODE's 80% the corrected fertility requirement is still about seven children per adult, which is still absurd.  But "15%" is what gets quoted, including on this site, and it is wrong.

Two further things a fair reader should know.  Graur's 15% comes from the most permissive corner of his own grid;  at his central empirical deleterious rate his own table already demands 12 to 466 children per adult.  As an upper bound that is logically fine.  Quoted as an estimate it misleads.  And Galeota-Sprung and colleagues' substantive verdict is the sentence a skeptic will find:  "an argument from mutational load does not appear to be particularly limiting on f."

3.2 The load formula run backwards to prove junk DNA

Larry Moran, biochemist, on his blog Sandwalk (not peer reviewed):

"If there are 100 new mutations per genome and 4% are deleterious then this means that each individual in each generation will acquire 4 deleterious mutations.  That's an intolerable genetic load;  it suggests that most of our genome is not a target (i.e. not functional)."¹⁴

What is wrong.  "Intolerable" is doing all the work, and it is precisely the premise that Charlesworth, Lesecque and Galeota-Sprung reject.  Under a relative-fitness model, Lesecque and colleagues conclude that "a species could tolerate 10's or even 100's of new deleterious mutations per genome each generation."¹⁵

Verdict:  load-bearing, and symmetrically so.  This is the cleanest observation on the page:  mainstream and creationist writers are running the same calculation in opposite directions, and each is confident it settles a different question.  Whoever takes the relative-fitness escape has to give up the junk-DNA ceiling with it.  Our own genetic entropy article makes the same point and takes the first horn explicitly.

3.3 Creationist load errors — audited elsewhere

Seven are documented with primaries in Sanford's Genetic Entropy, audited.  Three belong to this page's subject:

• Crow's 1–2% per generation run back 300 generations. Crow's figure is conditional ("if we are like Drosophila"), modern, and caused by relaxed mortality selection in wealthy nations — a cause absent for 299 of the 300 generations.
• Heritability of fitness reported as h² when Kimura wrote H². Re-checked here: the truncation-selection penalty at 0.004 is 1/√0.004 = 15.81, so "a factor of about 16, not 250" is right — but see the correction to our own page below.
• A terminal ellipsis that converts Eyre-Walker and Keightley's rejected premise into a bare declaration.

4. Selection coefficients quoted without their model

A selection coefficient with no convention attached can be off by a factor of two, and with no environment attached can be off by more.

Lactase persistence is the standard example, and it is our own site's example too.  Bersaglieri and colleagues define the model in their methods:¹⁶  "We assumed a dominant model for lactase persistence—that is, w11 = w12 = 1 and w22 = 1 − s."  So s is the penalty on the non-persister.  Their results sentence glosses it as "the coefficient of selection associated with carrying at least one copy," which reads like a carrier bonus and is not one.  Re-based on the ancestral genotype, 0.19 becomes 0.2346 — a 23% inflation from nothing but the convention.

Ayala 1995's bottleneck floor is quoted five different ways in the literature, all from the same paper.¹⁷  Whoever prints one without the others invites the charge of cherry-picking, so here are all five:

Print "at least 4,000" as the bottleneck floor and 100,000 as the long-term figure.  Never cite 16 as Ayala's number, because he rejects it on the same page.  His own census conversion is on p. 1935:  "we can conclude that N is about two-ninths of the census population."

5. Where creationists are right about a technical point

Running the exercise the other way.  These are cases where the technical claim survives, whatever one thinks of the conclusions drawn from it.

The drift barrier.  Mutations below about 1/(2N_e) fix at close to the neutral rate, so a population accumulates slightly deleterious changes that selection cannot remove.  This is right, it is not original to creationists — it is Ohta's nearly-neutral theory — and the fixation counts are not disputed.  What is disputed is what follows from it.

Fitness assays cannot detect a function that is no longer being used.  Deep mutational scanning measures one function at a time in one environment.  A mutation that helps the assayed function while breaking an overlapping signal registers as beneficial.  This is a real limitation, it is under-appreciated, and it undercuts the beneficial-fraction estimates that get quoted against genetic-entropy arguments.

Basener and Sanford's 2018 mathematics.  Published in the Journal of Mathematical Biology, peer reviewed.¹⁸  Their formal point about mutation-selection balance under Fisher's theorem is correct;  what is in dispute is the historical target and whether Fisher ever claimed what they say he claimed.  Their result also depends on a hand-imposed truncation rule the authors describe in their own §5.4, which must be disclosed whenever the paper is cited.

ReMine's reformulation of Haldane's cost.  Recasting "cost" as a required reproduction rate rather than a body count is clearer than the original, and two of his four referees at Theoretical Population Biology said so in writing.  Every value in his tables reproduces on independent recomputation.  The detail is in Haldane's dilemma.

6. Corrections to this site's own pages

The rule this page applies to others applies to it.  Four errors found in our own published material while assembling the reference article:

1. The U bracket in genetic entropy uses an element-level constraint figure as though it were a per-base one. Zoonomia's 10.7% is the fraction of the genome covered by constrained elements; its single-base figure is 3.3%, which gives U = 2.25 rather than 7.3. The element-level reading inflates U by about 3.2×.
2. The "8% apart" claim in the same article does not hold on its source's own parameters. Feeding Masel's published values into Kimura's integral reproduces 60,780 only with a gamma shape of 0.2, whereas the paper states 0.169, and only by reading their 0.009 as a homozygote coefficient when they call it the heterozygote effect. On the paper's own two readings the answer is 63,212 or 71,056 — 12% to 26% above their simulation, not 8%. The direction holds and the argument survives; the sentence does not.
3. Graur's 15% is quoted on this site and, per §3.1, should be about 28%.
4. Our audit of Sanford's heritability error was itself imprecise. Sanford's book, audited says the 1-in-250 figure has "the wrong functional form" because response scales with √h². That is true in one currency and false in two others: R/S = h², R/σ_P = ih², R/σ_A = ih. Sanford's 250 is arithmetically right for R/S; the 16 is right for R/σ_A. Neither side of that exchange named its currency, which is the actual defect.

All four have been corrected on the genetic entropy pages (26 September 2026).

Sources

Entries without an inline marker are the sources of the tables above;  each is named in its row or caption.