When Did the Wolves Start Howling?

A Genetic Diversification Model Calibrated Against Known-Age Populations

Part Two of the Diversification Series

The Question the Rhino Raised

The companion paper in this series, “How Did the Rhino Cross the Sea?”, presented a catastrophist model for a nearly complete rhinoceros fossil found in the Canadian High Arctic. That model compresses the conventional geological timeline, resolves several independent physical anomalies, and concludes with an open question: if such a catastrophe eliminated every terrestrial habitat on Earth, how did the animals that are alive today get here — and how fast did they diversify into the species we see now?

This paper answers the first part of that question. Not from geology, but from genetics.

One thing to establish at the outset, because the title invites it: this paper does not date the event. It establishes the direction genetic diversity travels and the size of the error in the standard method for dating it. The date the series works from comes from elsewhere — the private mutational load calculation in Paper 11, which divides two directly measured quantities and requires no assumed population size. Why a date cannot be derived from the drift equation itself is set out below, and it is a limit on the method rather than a gap in the data.

The Problem with the Clock

Biologists use a tool called the molecular clock to estimate when two species split from a common ancestor. The logic is simple: count the genetic differences between them, divide by the rate at which new differences appear, and the result is the time since they parted ways. It works the same way you might estimate how long ago two cars left a parking lot by measuring the distance between them and dividing by their speed.

The molecular clock has produced most of the divergence dates in textbooks. Wolves and coyotes: about a million years. Horses and donkeys: about four million years. Cattle and bison: two and a half to nearly four million years.

There is a problem with this clock. It assumes that all the genetic differences between two species were created after they split — that the starting condition was zero, the way a stopwatch starts at zero. But what if both species inherited a large amount of pre-existing variation from their common ancestor? What if most of the differences were already there before the split, and only got sorted into separate packages afterward?

If that is the case, the clock is not measuring elapsed time. It is measuring inherited variation — and mistaking it for time.

The Lava Rock

There is a way to test this. Dog breeds have known founding dates. The German Shepherd was standardized in 1899. The Doberman in the 1890s. The Golden Retriever in the 1860s. These are documented, verifiable dates — the biological equivalent of lava from a volcanic eruption whose date is recorded in history books.

When geologists test radiometric dating on rocks from historically observed eruptions, the results consistently overestimate the true age — sometimes by orders of magnitude. The methods produce ages of hundreds of thousands of years for rocks that are decades old. The documented cause is excess daughter products present at formation that the model assumes were absent.

Dog breeds offer the same kind of test for the molecular clock. We know when the German Shepherd was created. We know it came from a wolf-derived population. We can count the genetic differences between a modern German Shepherd and a modern wolf. And we can ask: does the molecular clock produce the right answer?

It does not.

A German Shepherd and a wolf differ at roughly 1.8 million SNPs (single nucleotide polymorphisms—single-letter differences in the genetic code) across their genomes. This figure is not drawn from a single study or a single wolf-dog pair. Multiple independent datasets—including the Dog10K consortium (2024), which sequenced over 100 wolves and hundreds of dogs, and vonHoldt et al. (2011, 2016)—consistently report 1.7 to 1.9 million SNP differences between wolves and breed dogs using whole-genome or high-density methods. The published canid mutation rate, applied over the 42 generations since the breed was founded, predicts that only about 900 of those differences are new mutations. The other 1,799,100 — over 99.9% — are pre-existing variation that was present in the wolf population before the breed was ever created. The German Shepherd inherited a subset. The wolf retained a different subset. The differences between them are mostly a sorting artifact, not accumulated change.

The molecular clock looks at 1.8 million differences, assumes they are all new, and produces an age of roughly 250,000 years. The documented answer is 127 years. The clock overestimates by about two thousand times.

A sensitivity analysis varying both the SNP count (1.5 to 2.1 million) and the mutation rate across the full published range (4.5 × 10⁻⁹ to 2.2 × 10⁻⁸ per base pair per generation) shows the overestimate ranges from 336 to 2,297 times. Those bounds are computed on the same basis as the worked case in Appendix A — a canid genome of ~2.4 billion base pairs, mutations accumulating in both lineages, and 127 years elapsed since the breed was standardized in 1899. At no combination of plausible inputs does the clock produce an accurate age. The detailed calculation is in Appendix A.

The Staircase

This overestimate is not a quirk of one breed. It reflects a consistent pattern, holding across every dataset examined here.

In 2024, the Dog10K consortium published genome-wide data comparing wolves, village dogs, breed dogs, and purebreds within breeds. The pattern is a staircase:

Wolves differ from each other at about 2.3 million positions. Village dogs — semi-feral dogs that breed freely without human management — differ at about 1.8 million. Dogs from different breeds differ at about 1.7 million. Dogs within the same breed differ at about 1.0 million.

Every step toward more isolation produces less diversity. No known exceptions have been published: in the datasets examined here, no breed or population carries more diversity than its ancestral source. The direction is the same throughout: downhill.

This pattern is not limited to dogs. Horses show it. Mongolian and Tuva landraces — ancient free-ranging horse populations — are the most diverse. Closed breeds are less diverse. Breeds that went through severe bottlenecks — like the Clydesdale, which nearly went extinct during World War II — are the least diverse. (See Appendix C for horse breed data.)

Cattle show it. Sanhe cattle from Mongolia, with large free-ranging herds, are the most diverse. Closed European breeds are less. Bottlenecked breeds are the least. (Appendix D.)

Wolves show it in the wild, without any human breeding programs. Large, connected wolf populations in Asia and Eastern Europe are the most diverse. Fragmented populations in Italy and Spain are less. Severely isolated populations — Mexican wolves, polar wolves on Ellesmere Island — are the least. (Appendix B.)

The staircase runs in one direction across every species, every study, every continent. Diversity starts high and goes down. Never up.

The Direction of Information

This observation has a deeper implication than it first appears.

The conventional model of biological diversity assumes that information flows uphill — that new genetic variation is created over time through random mutation, slowly building complexity and diversity from a simple starting point. In this view, the original ancestor was genetically simple, and its descendants accumulated new information over millions of years to become the diverse species we see today.

The data from dogs, horses, cattle, and wolves tells the opposite story. Every population we can observe — including those with documented histories spanning centuries — is losing genetic diversity over time, not gaining it. The original population is always the most diverse. The descendants are always less so. The direction of information flow is always downhill.

The data permits only one conclusion about the starting condition. If every population examined here is less diverse than its ancestor, and no published exception has been located, then the original ancestor was more diverse than anything alive today. The starting genome was not simple. It was complete — carrying the full range of variation that its descendants would later express in fragments. Modern species are not elaborations of something simple. They are reductions of something complete.

This conclusion is not an assumption imported into the analysis. It is the only direction the evidence points.

The burden falls on the critic to identify where the trend reversed — to find the point in any lineage, in any dataset, where diversity was flowing uphill instead of down. The ancient wolf genomes spanning 100,000 conventional years did not find it. The dog breed data spanning 127 documented years did not find it. The staircase only goes one direction. The starting point was the top.

More Diversity Than They Can Keep

There is a serious objection to everything above, and it deserves stating at full strength.

Drift removes variation, but mutation replenishes it. Over long enough spans the two processes balance, and a population settles at an equilibrium where losses and gains cancel. On that reading the staircase is real but local — a slope visible over centuries or millennia that flattens as you go back, because populations reach the floor and stay there. Observing diversity running downhill over 127 years of dog breeding, or even across the ancient wolf record, would then say nothing about where the ramp began. There is no ramp. There is a plateau with short-term wobbles on it.

The objection is testable, because equilibrium makes a quantitative prediction. At equilibrium, expected diversity is θ = 4Nₑμ. Rearranged, that gives the effective population size a species would need in order to sustain the diversity it is observed to carry: Nₑ = π ÷ 4μ.

Run it on wolves. Whole-genome studies report per-site diversity from 4.7 × 10⁻⁴ in the bottlenecked Mexican wolf to 1.71 × 10⁻³ in the Indian wolf (Freedman et al. 2014; Fan et al. 2016; vonHoldt et al. 2016). At the canid mutation rate used throughout this paper, sustaining those values requires effective population sizes between roughly 26,000 and 95,000. At the fastest mutation rate in the published range — the assumption most favorable to the objection — the requirement still falls between 5,300 and 19,400.

Published effective population sizes for gray wolves are 275 to 3,050 (vonHoldt et al. 2024).

Wolves are not at equilibrium. They carry more genetic diversity than their population size can maintain, by a factor of at least six and plausibly by a factor of thirty or more. The mutation input is not keeping pace with the drift loss, and has not been.

The Mexican wolf makes the point sharpest. Founded from seven individuals, effective size in the low hundreds, and carrying diversity that would require thousands to sustain. It cannot have accumulated that variation. It is spending down an inheritance.

This is why the staircase does not flatten. A population at equilibrium sits on the floor and stays there; these populations are still descending toward it. The direction of travel is not a local wobble on a plateau. It is a descent that has not finished, from a starting point richer than anything now observed.

Three limitations belong with this. The published figures are individual heterozygosity — π estimated from the two haplotypes of a single genome — which is unbiased under random mating but noisy from one individual; five populations across three studies agreeing in magnitude is what carries it, not any single value. Population structure would make these figures underestimates, which runs in the same direction. And the equilibrium relation assumes an infinite-sites model, standard for this purpose but an assumption nonetheless.

Dog breeds prove the mechanism in real time. No breeder has ever added a gene to the canine genome. Every breed was produced by selecting from existing variation — isolating a subset of what was already there. The Great Dane and the Chihuahua were both inside the wolf. The wolf did not need to evolve into them. They were extracted from it.

A biologist will object that this framework ignores natural selection — the engine that conventional biology credits for shaping species. The objection deserves a direct answer. What conventional biology calls “natural selection producing adaptation” is, in this framework, pre-existing code expressing under environmental pressure. The wolf did not evolve thick fur for cold climates through random mutation filtered by winter. The alleles (variant forms of a gene) for thick fur were already in the canid genome. Wolves in cold environments kept those alleles because individuals without them died. The environment did not create the adaptation. It revealed it. It selected from a menu that was already written.

Selection is real. It genuinely changes populations. But it does not generate new genetic information. It sorts existing information. It is drift with a thumb on the scale — biased sorting rather than random sorting. Either way, the source material is pre-existing variation, and the direction is downhill. The model does not ignore selection. It subsumes it.

Some natural populations appear to contradict this pattern. Cichlid fish in African lakes and Darwin’s finches in the Galápagos have radiated into dozens of species in geologically short timeframes, and these cases are sometimes cited as diversity increasing. In this framework, such radiations are not exceptions—they are predicted outcomes. They represent latent genetic variation in the founding genome activating and expressing under new environmental conditions. Even in these cases, the overall genetic diversity of the broader ancestral population remains higher than that of the derived subpopulations. The staircase continues to run downhill at the larger scale.

A biologist may raise a second objection: orphan genes. These are functional genes found in one lineage that have no detectable counterpart—not even a degraded remnant—in any closely related species. If all genetic information was present in the original genome, where did a gene come from that appears nowhere else in the family?

The conventional explanation is de novo gene origination—random mutations accidentally converting non-coding DNA into a functional gene. This is one of the more active areas of current genomics research, and the findings are striking: functional genes keep emerging from regions previously classified as “junk DNA,” non-coding sequence assumed to have no purpose.

This framework offers a different reading of the same observation. The non-coding DNA was never junk. It is latent code—instruction sets activated under specific diversification conditions. The orphan gene did not arise by accident from purposeless sequence. It was generated by the genome’s own regulatory architecture during speciation, expressed in one lineage because that lineage’s diversification path called for it, and silent in related lineages because their path did not. The code is likely still present in their non-coding regions, unactivated, because the switch was never thrown.

The data looks identical under both interpretations. A functional gene emerges from a non-coding region. The question is whether that event was an accident or an execution. The conventional model requires luck. This framework requires architecture. The reader may consider which better explains why it keeps happening across unrelated lineages in regions that were supposedly purposeless.

A related argument—gene duplication followed by neofunctionalization, where a copied gene accumulates mutations until it stumbles into a new role—faces the same problem from a different angle. The duplicate is a copy of existing code. The subsequent mutations are edits to existing sequence. The “new” function was assembled from parts that were already in the genome. Every word in a new sentence was already in the dictionary. Duplication is rearrangement, not creation, and the direction of the information budget remains the same: downhill.

The Wolf Clock Test

Ancient DNA confirms this picture from an unexpected direction.

In 2022, a team published 72 ancient wolf genomes spanning what the conventional timeline calls 100,000 years. Their finding was striking: wolf populations across the entire Northern Hemisphere were barely differentiated from each other for almost the entire period. The genetic differences between ancient wolf populations were an order of magnitude lower than those between modern populations.

The modern differentiation — the stuff that makes Italian wolves genetically distinct from Siberian wolves — is recent. The researchers attributed it to habitat fragmentation by humans over the last few centuries. (See Appendix B for published FST values (a standard measure of how genetically different two populations are, scaled from 0 for identical to 1 for completely different) between wolf populations.)

The conventional interpretation is that gene flow kept wolf populations connected for 100,000 years, until humans recently broke them apart. The alternative interpretation is simpler: the wolves were one population recently, the fragmentation is the entire story, and the 100,000-year timeline is the molecular clock doing exactly what the dog breed data says it does — overestimating by orders of magnitude because it attributes inherited variation to elapsed time.

The Model

We built a mathematical model based on a standard population genetics equation that describes how genetic diversity decreases over time in an isolated population. The equation is not new or controversial — it appears in every genetics textbook. What is new is the direction from which we apply it.

The equation says: the heterozygosity (genetic diversity) of a population at time t equals its starting heterozygosity multiplied by a decay factor that depends on how many individuals are breeding in that population. This process is called genetic drift—the random loss of genetic variants that occurs each generation simply because not every variant gets passed on, like drawing a smaller sample of marbles from a bag. Smaller populations lose diversity faster. Larger populations retain it longer. The formula is:

H(t) = H₀ × (1 − 1/(2Nₑ))^t

where H₀ is the starting diversity, Nₑ is the effective population size (roughly, the number of breeding individuals averaged over the population’s history), and t is the number of generations.

We applied this equation to four unrelated animal groups: canids (dogs, wolves, coyotes), equids (horses, donkeys, zebras), bovids (cattle, bison, yak, buffalo), and — to test whether the model works beyond large mammals — Drosophila fruit flies, which breed every two weeks instead of every few years.

For each group, we asked two questions from opposite directions.

Working backward: Given the observed diversity and published population sizes, how long ago did these species begin diversifying from a common ancestor?

Working forward: If we fix the origin at 5,786 years ago — the central value of the window set out below — what population sizes would be needed to produce the diversity we observe today? Are those sizes biologically reasonable?

A critical methodological note: the effective population sizes used throughout this analysis are derived from census data, breeding records, field surveys, and linkage disequilibrium measurements — methods that do not depend on the molecular clock or deep-time assumptions. We did not use population sizes estimated from PSMC or coalescent methods, which would introduce circularity since those methods rely on the same molecular clock we are questioning. (See Appendix E for the complete list of populations, their observed heterozygosity, Ne sources, and generation times.)

What We Found

Working Backward

The backward model produces diversification timescales of hundreds to low thousands of years for all groups tested.

Wolf-coyote differentiation, which the molecular clock dates to about a million years ago, requires roughly 600 to 3,000 years in the drift model, depending on the assumed population size. Horse-donkey differentiation, conventionally dated to four million years ago, requires roughly 2,000 to 11,000 years. Cattle-bison differentiation falls in a similar range.

The compression factors — how much shorter the drift model’s timeline is compared to the conventional molecular clock estimate — are remarkably consistent across all three mammalian families: approximately 650 to 750 times shorter at moderate population sizes. (See Appendix G for the full sensitivity analysis across all parameter ranges.)

Three unrelated families. Different generation times. Different levels of species differentiation. Nearly identical compression factors. That agreement is not something the model was designed to produce. It fell out of the data.

Working Forward

The forward model tells the same story from the other direction. Starting from a fixed origin of 5,786 years ago with genetically complete founding populations, we calculated the effective population size each modern population would need to produce its observed diversity in the available time.

Every required population size is biologically reasonable for its population type. (The complete calculation for all 14 mammalian populations is in Appendix E.)

Wolves — a large, well-connected wild population — require an effective population size of about 10,000 to 20,000. Published estimates for global wolf populations fall in exactly this range.

Coyotes require about 2,000 to 5,000. Coyotes are widespread and well-connected across North America. The numbers fit.

The critically endangered Somali wild ass requires about 25 to 35. It is one of the rarest animals on Earth, with roughly 200 individuals remaining. The number fits.

The Mexican wolf, which went through a bottleneck of seven founding individuals in its captive breeding program, requires a historical average of about 100 to 140. Given centuries of larger wild population before the recent crash, this fits.

Not one population in any of the four groups produced an absurd or impossible required population size. Every number lands where it should.

For comparison, we tested what the million-year conventional timeline would require. To maintain wolf-level diversity for a million years of drift would require an effective population of roughly 850,000 — implying billions of wolves. No terrestrial mammal population that large has ever existed. The deep-time model requires impossible populations. The short-time model requires populations that actually exist.

The Fruit Fly Test

To test whether the model works beyond large mammals, we applied it to Drosophila melanogaster — the common fruit fly. With a generation time of roughly two weeks, fruit flies complete roughly 145,000 generations in 5,786 years, compared to 1,929 for canids. If the model only works for animals that breed on similar timescales, it would fail here.

It does not fail. The required Ne values for wild Drosophila populations (200,000 to 320,000) fall within the independently published range for these species. The model produces reasonable numbers for an insect that breeds 75 times faster than a wolf. (See Appendix H.)

Additionally, laboratory experiments with Drosophila provide the ultimate validation of the drift equation itself. In controlled populations where the census size (16 individuals), effective population size (3.8 to 7.9), number of generations (8), and starting and ending heterozygosity are all directly measured, the drift equation predicts the observed diversity decline to within 0.003 to 0.012 of the actual measurements. The math is experimentally verified.

What a Single Origin Time Would Take

The natural next question is whether a single origin time fits all of them at once. This paper does not answer it, and the reason is worth stating plainly.

Fitting one origin time across populations requires an effective population size for each of them, and Nₑ is the quantity the literature does not supply. Published estimates exist for two of the fourteen — the wolf (vonHoldt et al. 2024) and the Mongolian horse (Petersen et al. 2013). For the rest there is no figure to use. Worse, elapsed time scales with Nₑ: an order-of-magnitude uncertainty in the population size is an order-of-magnitude uncertainty in the date. Even with a differentiation value known exactly, the window spans 842 to 9,347 years. The drift equation is not a clock unless the population size is known, and for wild populations averaged over a thousand generations, it is not.

There is a way to resolve this, and it does not require finding the population sizes. The equation has two unknowns and one measurement; supplying either unknown from outside resolves it. Effective population size cannot be had for most populations. Elapsed time might be.

A population isolated when a land corridor submerged has been drifting since that corridor closed. If the closing date is known from the sea-level record, elapsed time comes from geology rather than from fitting, and the equation runs the other way: instead of requiring an effective population size, it returns one — a figure that can then be checked against published estimates rather than assumed. Populations separated by the same closure share the same elapsed time, so several independent checks fall out of one event.

Paper 5 gives corridor opening windows numerically. Closure, which is the event that dates an isolation, is treated qualitatively there. Quantifying the closing side is what would convert the drift equation from a consistency check into a dating method, and it is a defined piece of work rather than an open-ended one. The prediction is also testable before any arithmetic runs: which species pairs are separated should correspond to which corridors closed, and the biogeography either matches the sea-level model or it does not.

What the equation does establish here is narrower and holds. Diversity runs downhill in every family examined, without exception. The required population sizes for a recent origin are not extravagant where they can be checked. And the molecular clock, tested against an animal with a documented founding date, overestimates by hundreds to thousands of times.

The date this series works from is not derived here. Where it does come from is set out below.

The invitation remains open. As population genomics expands — particularly in birds, reptiles, and amphibians, where family-level datasets with consistent methodology, multiple populations, and independent Ne estimates do not yet exist at sufficient fidelity — each new dataset becomes a test case. The prediction is specific and falsifiable: the forward model should require only biologically realistic population sizes, and the staircase should run downhill. If it fails for specific groups, those groups may represent genuinely different diversification histories that the model cannot accommodate. Either outcome is informative.

The data to run these tests already exists in public databases. The methods are standard population genetics. The only thing new is the direction of the question.

Where the Date Comes From

The drift equation cannot supply it, for the reason just given. It comes instead from a calculation that needs no population size at all — and it comes from humans, because humans are the only species with the data to run it.

Every genome carries a load of private variants: mutations present in one individual, or at very low frequency, and absent from the broader population. These are not ancient shared polymorphisms. They are recent damage — arisen in the germline of recent ancestors, not yet spread through the population and not yet removed by selection. They accumulate at a measured rate from whatever state the genome started in.

Two quantities, both measured directly:

The germline mutation rate. Parent–offspring trio sequencing gives approximately 70 new single-nucleotide variants per diploid genome per generation, with a characterized range of 60 to 80. It is measured within a single generation, in families, by direct comparison. No model intervenes.

The private mutational load. Whole-genome sequencing across the 1000 Genomes Project Phase 3, UK Biobank and related datasets gives approximately 14,000 to 16,000 rare or singleton variants per individual.

Dividing one by the other returns generations. At the central values — 15,000 variants, 70 per generation — that is 214 generations. At 27 years per generation (Wang et al. 2023), approximately 5,800 years.

No effective population size appears anywhere in it. No fitted constant, no model parameter, nothing available to be adjusted toward a preferred answer. That is the whole of its claim to be taken seriously — and it is why this series takes its window from a human calculation rather than an animal one. Private load must be counted per individual against a large sequenced population, and no wild animal has the database.

Two limits, both stated plainly.

The calculation dates the pristine genome — the point at which accumulation began — not the event. A founding genome that already carried load would mean less has accumulated since, placing the event younger than the figure. The number is an upper bound on the event date, not a measurement of it.

And purifying selection removes some variants before they can be counted, so the observed load understates what arose. The rate, measured in trios, is not similarly depleted. Dividing a reduced count by an undepleted rate underestimates the generations, moving the starting point further into the past rather than closer. At the central rate the 7,200-year bound absorbs a purge of roughly twenty percent — more than a store of variants this recent is likely to have lost.

The derivation, the supporting datasets, and a falsifiable prediction that follows from it — that per-individual private load should be approximately invariant across human populations — are given in Paper 11.

What this gives the animal data is not a conclusion but a constraint. The window is derived independently, from another species and another measurement, with nothing borrowed from drift. The question for the canids, equids, bovids and the rest is whether their observed differentiation fits inside it.

What the Staircase Tells Us

Every dog breed that has ever been studied contains less genetic diversity than the population it came from. Every isolated wolf population is less diverse than the connected one it split from. Every bottlenecked horse breed carries a smaller portion of the equine genome than the free-ranging landrace it descended from. Every laboratory fruit fly population that has been measured loses diversity exactly as the drift equation predicts. No population, natural or artificial, has ever been observed to gain net genetic information over time.

The staircase runs one direction. No published case reverses it. And the molecular clock, by assuming the opposite direction — that differences accumulate from zero — misreads the staircase and overestimates every date it produces.

The dog breed is the lava rock of molecular biology. Known founding date. Known starting population. Measurable genetic distance. Verifiable error. Same direction as the lava rock: always too old.

Four families. Twenty-one populations. Two directions of analysis. A clock that runs backwards on an animal whose birthday is documented. And a staircase that only goes down.

This paper does not name the event. It measures the direction.

But the pattern raises a further question. If diversification within each kind traces back to a small founding stock, how many such starting points were there? How many genetically distinct founding kinds does it take to produce the full roster of land-dwelling, air-breathing species alive today — and in the fossil record? And does that number fit inside anything that floats?

Appendix A: Molecular Clock Calibration — Breed Data

A.1 The German Shepherd Clock Test

Known parameters:

• GSD standardized: 1899

• Known elapsed time: 127 years (standardized 1899; recompute this denominator if the paper is revised in a later year)

• Canid generation time: ~3 years

• Known generations: ~42

• Canid genome size: ~2.4 billion base pairs

Published data:

• Wolf-to-breed-dog average SNP differences: ~1.8 million (Dog10K > consortium, 2024)

• Canid mutation rate: 4.5 × 10⁻⁹ per bp per generation (Lindblad-Toh > et al.), range in literature: 4.5 × 10⁻⁹ to 2.2 × 10⁻⁸

Calculation:

Expected new mutations in 42 generations (both lineages): 2 × (4.5 × 10⁻⁹) × (2.4 × 10⁹) × 42 = 907

Observed SNP differences: ~1,800,000

Fraction that are new mutations: 907 / 1,800,000 = 0.05% Fraction that are ancestral variation: 99.95%

Molecular clock age estimate: 1,800,000 / (2 × 4.5 × 10⁻⁹ × 2.4 × 10⁹) = ~83,333 generations = ~250,000 years

Known age: 127 years Overestimate: ~1,969×

A.2 Sensitivity to Input Parameters

Range of clock overestimate across the tested inputs: 336× to 2,297×

A.3 Supporting Published Data

• 22% of all canid variants are shared across wolves, village dogs, > and breed dogs (Dog10K, 2024)

• Only 0.002% of SNPs are fixed and unique to any single breed > (Science, 2022)

• GSD 120-year genome time series from museum specimens confirms > progressive diversity loss, with sharp decline after WWII (PNAS, > November 2025)

Appendix B: Wolf Population Genetics Data

B.1 Published FST Values

The largest FST values occur between the most geographically isolated populations (Italian vs Iberian wolves), while well-connected populations across large ranges show minimal differentiation—consistent with recent fragmentation-driven sorting rather than deep-time divergence.

B.2 Published Heterozygosity by Population Status

B.3 Ancient Wolf DNA Finding

72 ancient wolf genomes spanning 100,000 conventional years (Bergström et al., Nature, 2022):

• Ancient populations were barely differentiated (FST an order of > magnitude lower than modern)

• Modern differentiation attributed primarily to recent human-caused > fragmentation

• Individual heterozygosity showed no concurrent decline despite > increasing population differentiation

B.4 Drift Model Applied to Wolf Populations

Using FST(t) = 1 − (1 − 1/(2Nₑ))^t:

Italian vs Iberian wolves (FST = 0.293):

Eastern European vs Asian wolves (FST = 0.059):

Appendix C: Equid Cross-Check Data

C.1 Published Horse Breed FST Values

Source: Petersen et al., PLOS ONE, 2013 (814 horses, 36 breeds)

C.2 Equid Species Data

All living equid species sequenced: Jónsson et al., PNAS, 2014

• All equids can hybridize (mules, zorses, zonkeys, hinnies)

• Genus Equus includes horses, 3 zebra species, 3 ass species, donkey

• Conventional timeline: Equus emerged 4.0–4.5 Mya; zebra/ass split > from horses 1.69–1.99 Mya

• Generation time: ~8 years

C.3 Equid Drift Model

Horse-Donkey (estimated FST ~0.50) ⚠️ ESTIMATED:

Note: The horse-donkey FST value is the single most uncertain parameter in the model. Sensitivity analysis (Appendix G) shows its impact on the equid timeline.

Appendix D: Bovid Cross-Check Data

D.1 Published Bovid Heterozygosity

Source: Multiple studies

D.2 Bovid Hybridization Evidence

• Cattle × bison = beefalo (fertile with reduced fertility)

• Cattle × yak = dzo (common in Tibet, fertile females)

• Cattle × gaur = documented hybrids

• All bison herds examined, including Yellowstone and Wind Cave, > contain detectable cattle ancestry (Stroupe et al., Scientific > Reports, 2022)

• Bison-cattle divergence: 2.5–3.7 Mya conventional estimate

D.3 Bovid Generation Time

~5 years for cattle; used as representative for the bovid kind.

Appendix E: Forward Model — Origin Test at T = 5,786 Years

E.1 Method

For a fixed origin of T = 5,786 years — the central value of the window derived in Where the Date Comes From — the drift equation is solved for the required Ne:

Given H_observed = H_origin × (1 − 1/(2Nₑ))^(T/gen_time), solve for Nₑ.

This produces the effective population size each modern population MUST have maintained (on average) to produce its observed diversity in the available time.

Required Nₑ is very nearly proportional to elapsed time, so the effect of the window's width is easy to state without retabulating: at the lower bound of 4,725 years every figure below falls by about 18 percent, and at the upper bound of 7,200 years every figure rises by about 24 percent. No row changes its character across that range.

Published effective population sizes are not a test of these values. What the literature reports is computed either across tens of generations — linkage-disequilibrium reconstruction of contemporary and recovery-era sizes — or across deep time under coalescent models with different assumptions. Neither is the quantity solved for here, which is a harmonic mean sustained across the full interval. No published figure spans 1,929 generations for any of these populations, because no method produces one. The checks in the tables below are therefore qualitative, and are marked as such. What the tables establish is that the required sizes are of a biologically ordinary magnitude, not that they have been matched against measurements.

E.2 Canid Results (generation time = 3 years, 1,929 generations)

E.3 Equid Results (generation time = 8 years, 723 generations)

E.4 Bovid Results (generation time = 5 years, 1,157 generations)

E.5 The Deep-Time Comparison

To maintain wolf heterozygosity (Ho = 0.37) for 1,000,000 years at 3-year generations from H₀ = 0.45 would require Ne ≈ 851,450. This implies a breeding population larger than any terrestrial mammal population that has ever existed.

Appendix F — Deleted

Iterative convergence and null model test. Deleted due to insufficient published data: the least-squares fit requires a published effective population size for each population as an input, and no such figure exists in the literature for twelve of the fourteen.

Appendix G: Sensitivity Analysis

G.1 Canid Timeline Sensitivity

Variables: Wolf-Coyote FST (estimated 0.30–0.50), Effective population size Ne (200–1,000)

Canid diversification range: 427 to 4,158 years Compression factor range: 241× to 2,342×

G.2 Equid Timeline Sensitivity

Equid diversification range: 1,632 to 19,400 years

⚠️ The horse-donkey FST is the single most sensitive parameter. Its verification from published data is critical.

G.3 What Survives the Full Sensitivity Analysis

Bulletproof (holds at every parameter combination):

1. Diversity always flows downhill. Published data. No parameter > changes this.

1. The molecular clock massively overestimates on known-age samples. > Minimum 336×.

2. Breeds are subsets, not innovations. 0.002% unique fixed SNPs.

3. Both canid and equid timelines are compressed by hundreds to > thousands of times relative to conventional estimates.

Robust (holds across most of the parameter space):

5. Canid and equid compression factors are within the same order of magnitude for 75%+ of parameter combinations.

6. The diversification era is centuries to low thousands of years for canids, low thousands to ~20,000 for equids at worst case.

Sensitive:

7. Any date derived from the drift equation depends on the assumed Ne, and scales with it directly. This is why no date is claimed here.

8. The exact compression factor (500× or 2,000×?) depends on mutation rate and FST.

Appendix H: Drosophila Validation

H.1 Published Data

• Generation time: ~2 weeks (0.04 years), ~25 generations per year

• Generations in 5,786 years: ~144,650

• D. melanogaster (African, ancestral range) Ho: ~0.37

• D. melanogaster (European, post-bottleneck) Ho: ~0.30

• D. ananassae (diverse Indian populations) Ho: 0.273–0.372 (Sanjay > Kumar and Singh, 2017)

• D. ananassae inter-population FST: ~0.118

• Local Ne measured directly from allele frequency changes over 500 > generations: ~10,000 (Nunney et al., MBE, 2022)

H.2 Forward Model Results (H₀ = 0.45)

The published figures above come from coalescent demographic inference — model-based reconstruction of a population-size history from the site-frequency spectrum — rather than from direct measurement. Arguello et al. (2019) estimate an ancestral African effective size near 1.9 million using fastsimcoal2 on roughly 167,000 autosomal SNPs at an assumed mutation rate of 1.39 × 10⁻⁹. Figures of that kind are parameters inside a deep-time demographic model, so agreement with them is a check on magnitude and not independent confirmation of the timeline proposed here. What this table establishes is that the required effective sizes are ordinary for a cosmopolitan insect. Note also that the local effective size cited in H.1 — approximately 10,000, measured from allele-frequency change over 500 generations — is a contemporary variance estimate for one population and is not the same quantity as the species-level figures above; the two differ by two orders of magnitude in the published literature and neither is in dispute. The direct test of the drift equation is H.3, where every parameter is measured.

H.3 Laboratory Verification of Drift Equation

Source: Frankham & Loebel (1992), Conservation Biology

The drift equation predicts observed diversity decline to within 0.003–0.012 in controlled experiments where every parameter is directly measured.

Appendix I: Complete Data Source List

All genetic data used in this paper comes from published, peer-reviewed sources. No data was generated by the authors. Key sources:

1. Dog10K consortium (2024) — Canid SNP diversity across wolves, > village dogs, breed dogs

4. Scarsbrook et al., PNAS (Nov 2025) — GSD 120-year genome time > series

5. Morrill et al., Science (2022) — Breed-specific SNP analysis, > 0.002% unique fixed variants

6. Bergström et al., Nature (2022) — 72 ancient wolf genomes, 100,000 > years

7. Pilot et al., Heredity (2013) — European wolf population FST > values

8. Pilot et al., PLOS ONE (2014) — Caucasian wolf population genetics

9. Schweizer et al., PLOS Genetics (2018) — North American wolf > population genomics

10. Werhahn et al., Communications Biology (2025) — Asian wolf > continent-wide genomics

11. Jónsson et al., PNAS (2014) — Complete equid species genome > sequencing

12. Petersen et al., PLOS ONE (2013) — Horse breed diversity, 814 > horses, 36 breeds

13. Freedman et al., PLOS Genetics (2014) — Whole-genome resequencing, wolf nucleotide diversity

14. Fan et al., Genome Research (2016) — Worldwide gray wolf genomic variation and diversity

15. vonHoldt et al., Science Advances (2016) — Whole-genome analysis, Indian and Mexican wolf π

16. vonHoldt et al., Molecular Ecology (2024) — LD-based effective population size, North American wolves

17. Guo et al., Frontiers in Genetics (2021) — Bovid thermal stress > genetics and diversity

18. Stroupe et al., Scientific Reports (2022) — Bison-cattle > hybridization genomics

19. Lu et al., Journal of Dairy Science (2020) — Buffalo breed genetic > diversity

20. Sanjay Kumar and Singh (2017) — Drosophila ananassae population > genetics

21. Nunney et al., MBE (2022) — Drosophila melanogaster 35-year > population study

22. Frankham & Loebel (1992) — Laboratory drift experiment, Drosophila

23. Lindblad-Toh et al. — Canid mutation rate estimates

Appendix J: Felid Validation (Independent Extension)

J.1 Data Source

Meeus, M. P., Lescroart, J., & Svardal, H. (2025). Genomic diversity in felids correlates with range and density, not census size. Conservation Genetics. Advance online publication. https://doi.org/10.1007/s10592-025-01709-y

This study sequenced 100 individuals across 39 felid species using consistent whole-genome methods. It reports a 54-fold heterozygosity staircase that mirrors the Dog10K pattern: diversity flows only downhill from high-diversity ancestral-like populations (broad range, high density) to low-diversity isolated and bottlenecked ones.

J.2 Forward Model Results (generation time = 4 years, 1,446 generations)

Every required Ne lands in the range expected from real census, density, and range-size data. The Asiatic lion result (required Ne of 172–178) is the same order as its documented historical bottleneck below 50 individuals.

The felid figures are nucleotide diversity (π) rather than SNP-array heterozygosity, which is why the H₀ values used here are on a different scale from those in Appendix E. The two are not interchangeable, and no comparison is made across that boundary — the felid rows are internally consistent and are read only against each other.

Appendix K — Deleted

Suid validation (independent extension). Deleted because the required Nₑ figures did not reproduce from the drift equation at the parameters the table itself declared — discrepancies ran from −32 to +110 percent across the six rows. The underlying heterozygosity data and its published sources are sound; the arithmetic applied to them was not, and the table has been removed rather than repaired.

Appendix L — Deleted

Cervid and caprine validation (independent extension). Deleted for the same reason as Appendix K, with two additional defects: one cervid row carried an observed value above the assumed founding heterozygosity, which the drift equation cannot produce at any population size, and the observation column mixed heterozygosity with nucleotide diversity — different quantities on different scales.

Appendix M — Deleted

Seven-family combined convergence. Deleted due to insufficient published data, for the same reason as Appendix F: the fit across 34 populations requires a published effective population size for each, and those values are not available.

Appendix N: Equilibrium Test — Sustaining Nₑ vs Published Nₑ

At mutation–drift equilibrium, expected per-site diversity is θ = 4Nₑμ. Rearranged, the effective population size required to sustain an observed diversity is Nₑ = π ÷ 4μ.

Canid mutation rate: 4.5 × 10⁻⁹ per bp per generation (Lindblad-Toh et al.), published range up to 2.2 × 10⁻⁸. Both are shown; the faster rate is the assumption most favorable to the equilibrium reading, because a higher mutation input sustains more diversity at a smaller population size.

Published effective population size, gray wolf: 275–3,050 (vonHoldt et al. 2024, LD-based, regional North American).

Every population in the table carries more diversity than its published effective size can maintain. The smallest gap — the most bottlenecked population, at the mutation rate most favorable to equilibrium — is a factor of roughly six. The largest is a factor above three hundred.

Sources

• Freedman AH, Gronau I, Schweizer RM, et al. (2014). Genome sequencing highlights the dynamic early history of dogs. PLOS Genetics 10(1): e1004016. doi:10.1371/journal.pgen.1004016 — whole-genome resequencing, 3 wolf genomes.
• Fan Z, Silva P, Gronau I, et al. (2016). Worldwide patterns of genomic variation and admixture in gray wolves. Genome Research 26: 163–173. doi:10.1101/gr.197517.115 — whole-genome sequences.
• vonHoldt BM, Cahill JA, Fan Z, et al. (2016). Whole-genome sequence analysis shows that two endemic species of North American wolf are admixtures of the coyote and gray wolf. Science Advances 2(7): e1501714. doi:10.1126/sciadv.1501714 — reports Indian wolf π = 1.71/kb, Mexican wolf π = 0.48/kb.
• vonHoldt BM, et al. (2024). Molecular Ecology. doi:10.1111/mec.17231 — LD-based effective population size, North American regional.

Limitations. The published figures are individual heterozygosity, which estimates π from the two haplotypes of one diploid genome. It is unbiased under random mating but noisy from a single individual; the argument rests on five populations across three independent studies agreeing in magnitude, not on any one value. Population structure would render these figures underestimates, which runs in the same direction as the conclusion. The equilibrium relation assumes an infinite-sites model.

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© 2026 D. L. White. Licensed under CC BY-ND 4.0. https://creativecommons.org/licenses/by-nd/4.0/

AI collaboration: This paper was developed collaboratively between Claude (Anthropic) and D. L. White. White directed the inquiry and introduced the core premises. Claude provided genetic data, built the mathematical models, performed calculations, and co-developed the reasoning chain. Neither party endorses all conclusions as settled — the intent is to demonstrate that the logic holds, not that the case is closed. Additional family data was assembled by Grok (xAI) in March 2026. The felid extension appears as Appendix J; the suid, cervid and caprine tables were removed, for the reasons stated in their deletion stubs.