Can a tiny number of living founders, equipped with a temporary generative inheritance system, become theinit()
function for an entire genetically robust population?
Imagine sending life to another world.
The obvious way to preserve a species is to bring as much of it as possible: many individuals, embryos, gametes, seed banks, genome libraries, carefully preserved diversity.
But there is another possibility.
What if the smallest viable founding population did not need to carry all of the diversity a future population would require?
What if it carried the ability to generate it?
A handful of living founders could contain not merely genomes, but a temporary biological initialization system: a compact set of rules capable of producing controlled genetic diversity during the dangerous first generations of a new population. As that population grows, recombines and becomes genetically stable, the mechanism fades away and eventually disappears, leaving behind an ordinary evolving population.
In that picture, the founders are not an archive.
They are a seed for a population-generating process.
For future biological colonization, conservation, or long-duration propagation of life, this raises an information question: must we transport many finished genomes, or could some of that burden be replaced by generative biological machinery?
For theoretical biology, it asks how much population-level genetic structure must be explicitly stored and how much can arise from rules, randomness, recombination and ordinary inheritance.
Looking backward, it also exposes a boundary in demographic inference. Population history is reconstructed from genetic data under assumptions about how inheritance, mutation and recombination work. If an early inheritance mechanism fell outside that model class, the demographic history inferred from descendants need not be identical to the literal history that produced them.
None of this establishes that such a mechanism exists, has existed, or is biologically practical.
This repository asks a narrower question and tries to break it experimentally:
Can temporary generative inheritance substantially change the neutral population-genetic consequences of an extreme founder event, without simply hiding a large archive of donor genomes inside the model?
Prefer a visual walkthrough first? ▶ Watch the video explainer on Youtube (generated with notebooklm)
A visual introduction to the core idea, the founder-bottleneck problem, the FounderCode hypothesis, and the experimental path leading to the final 006.2 simulation. The explainer walks through the core idea, the population-genetics problem behind extreme founder events, the FounderCode hypothesis, and the experimental path that led to the final
006.2
simulation.It is an accessible companion to the project. The source code, result files, experiment READMEs, and this README remain the authoritative research record.
For the current reproducible model, go directly to experiments/006.2_frequency_calibration/.
Two ordinary diploid founders begin with only four chromosome copies at each locus. Population growth can reshuffle those copies, and ordinary mutation can slowly add new variants, but growth does not magically restore all of the standing variation lost at the founding event.
Founder Population Init adds a temporary third ingredient:
few living founders
+
ordinary inheritance
+
temporary generative germline
↓
structured early diversity
↓
population grows
↓
generator shuts down
↓
ordinary evolution only
The hypothetical mechanism is called FounderCode or FounderProgram.
It should not be imagined as "mutation turned up very high" or as a secret library of hundreds of complete genomes.
The research question is whether generative rules can create useful population-level statistical diversity without explicitly storing all of the examples they can produce.
If you want to understand or try one simulation, use:
experiments/006.2_frequency_calibration/
This is the current integrated experiment and the main implementation to inspect, run, modify and challenge.
It includes the important pieces developed across the earlier experiments:
- a neutral sequence-derived source population generated with
msprime
; - a 32-founder ordinary reference;
- an ordinary two-founder control;
- the same exact two founders plus FounderProgram; - ordinary mutation and recombination;
- no external donor-haplotype bank;
- no source allele-frequency table;
- no source polymorphic-position list;
- procedural per-rewrite haplotypes;
- a neutral-theory
1/k
frequency grammar; - a marginal-preserving correlation model for generated haplotypes;
- feedback shutdown of FounderProgram;
- blind
dadi
inference from descendant SFS only.
The earlier experiments are important because they show how we got here, including the failed v4 inference experiment. But they are research history, not the recommended starting implementation.
From the 006.2 directory:
mamba activate founder-v6
chmod +x run_v6_2.sh
./run_v6_2.sh --export-only
./run_v6_2.sh
Main outputs are written under:
founder_v6_2_out/
├── v6_2_preflight.json
└── v6_2_dadi_results.json
If you are reviewing the project rather than reproducing its history, read the root README, then 006.2, then go backward only when you want to understand why a design choice exists.
The current computational evidence supports the following limited claim:
In simulation, a temporary embedded generative inheritance mechanism can substantially reduce the neutral population-genetic signature of an extreme two-founder bottleneck. This remains true after removing an explicit donor-genome reservoir and replacing it with procedural rules, although a detectable demographic and frequency-spectrum signature remains.
The completed v6.2 experiment strengthens the mechanism side of that claim:
A meaningful part of neutral population-level diversity structure can be generated from general rules rather than copied from an empirical donor-genome archive. Blind demographic inference still detects a severe bottleneck/recovery signature, so the result is substantial repair and partial masking, not demographic invisibility.
This is a theoretical / computational proof of principle.
It is not evidence that:
- a real biological germline could implement FounderCode;
- generated neutral variants would preserve functional species viability;
- two real humans could found a healthy human population this way;
- such a mechanism existed in human history;
- the 52-byte parameter payload is a complete biological genome generator.
The project did not begin with the final mechanism.
Instead, each experiment removes a shortcut or attacks a weakness exposed by the previous one.
| Experiment | Main question | Outcome |
|---|---|---|
001_bootstrap |
||
| Can temporary diversity generation rescue a two-founder toy population at all? | Positive toy proof of concept | |
002_linked_genomes |
||
| Does the effect survive linkage, recombination, haplotypes and simple viability constraints? | Positive; 2 + init resembles a much larger ordinary founding population |
|
003_blind_inference |
||
| Does the effect remain when the observer does not see FounderCode internals? | Positive direction; exact "equivalent founder count" shown to be poorly identifiable | |
004_dadi |
||
| Will an external demographic inference tool see the same effect? | Negative / invalid substrate; retained as a failure | |
005_sequence_dadi |
||
| Does the effect survive on sequence variation generated by standard ancestry/mutation machinery? | Strong positive, but uses a donor haplotype bank | |
006_embedded_generator |
||
| Can we delete the donor bank and procedurally generate variation? | Positive; substantial repair, visible SFS scar | |
006.1_generator_frequency |
||
| Does fresh procedural haplotype generation reduce the scar caused by template reuse? | Strong improvement | |
006.2_frequency_calibration |
||
| Can neutral-theory frequency rules improve the result without reading the target SFS? | Final positive proof-of-principle: strong direct SFS repair; blind dadi still detects a finite severe bottleneck/recovery scar |
The failures matter as much as the successes. In particular, v4 demonstrated that a sophisticated inference tool cannot make an invalid genetic substrate scientifically meaningful.
Later experiments compare four arms:
source_equilibrium
A neutral source population generated withmsprime
. This is the long-run reference. -
many_founder_reference
Ordinary descent from 32 diploid founders. -
ordinary_2
Ordinary descent from exactly two diploid founders. -
two_plus_generator
Thesame exact two founders asordinary_2
, plus temporary FounderProgram activity.
The later v6-series uses matched random streams for ordinary mating, recombination, mutation and population sampling in the ordinary-two and generator arms. FounderProgram receives a separate random stream.
The intended comparison is therefore:
same founders
same ordinary stochastic biology
same growth schedule
-------------------------------
difference = FounderProgram
v6.2 changes only the FounderProgram's frequency / LD generation law relative to v6.1.
It does not read:
- the source SFS;
- source allele frequencies;
- source polymorphic positions;
- donor haplotypes;
- the 32-founder reference.
Instead it uses a theoretical neutral 1/k
frequency grammar and a marginal-preserving Gaussian-copula construction for short-range correlation.
| Metric | Source | 32 founders | Ordinary 2 | 2 + FounderProgram |
|---|---|---|---|---|
| Segregating sites | 16,755 | 14,467 | 7,256 | 14,208 |
| Singleton fraction | 23.58% | 17.98% | 0.85% | 11.69% |
| Doubleton fraction | 12.83% | 12.23% | 0.07% | 7.85% |
| Common variants, MAF ≥ 0.25 | 26.91% | 31.09% | 64.58% | 39.58% |
Nucleotide diversity π |
||||
| 0.000488 | 0.000470 | 0.000363 | 0.000540 |
Folded-SFS Jensen-Shannon divergence:
ordinary 2 → source 0.31225
generator → source 0.06158
ordinary 2 → 32 founders 0.24372
generator → 32 founders 0.03135
On this metric, the v6.2 generator population is roughly 5× closer to the source and roughly 7.8× closer to the 32-founder reference than ordinary two-founder descendants.
The result is not a perfect match. Rare variants remain underrepresented, common variants remain overrepresented, and π
remains somewhat high.
That residual scar is part of the result, not something to tune away after seeing it.
With the current controller:
generation 1 FounderProgram active
generation 2 FounderProgram active
generation 3 inactive
generation 4 permanently silenced
generations 5–19 ordinary inheritance only
The special mechanism therefore acts during the bootstrap and then leaves the population to ordinary inheritance.
dadi
receives only the folded descendant SFS. It is not told founder count, pedigree, FounderProgram state, generated positions/haplotypes, controller history or source haplotypes.
The four arms behave differently:
| Population | Best AIC model | Best AIC | Boundary behavior | Reading |
|---|---|---|---|---|
| Source equilibrium | snm |
|||
| 256.39 | none | Correct calibration: equilibrium looks like equilibrium | ||
| 32-founder reference | two_epoch |
|||
| 311.42 | none | Ordinary finite size-change signal | ||
| Ordinary 2 | three_epoch |
|||
| 3687.77 | best fit hits lower bounds | |||
| Extreme bottleneck magnitude is effectively unresolved | ||||
| 2 + FounderProgram | three_epoch |
|||
| 2034.84 | no best-fit boundary hits | |||
| Strong bottleneck/recovery remains detectable, but as a finite conventional history |
For ordinary two-founder descent, three_epoch
and two_epoch
are essentially tied (ΔAIC ≈ 0.05
) and their best fits push bottleneck parameters to the optimization floor. The useful conclusion is therefore not the literal fitted magnitude; it is that the SFS demands an extreme contraction beyond what these simple models resolve cleanly.
For the FounderProgram descendants, three_epoch
is preferred. Its best fit is interior:
nuB ≈ 0.00103
nuF ≈ 0.949
recovery factor nuF/nuB ≈ 918
Those are effective-size ratios inside the fitted model, not literal founder counts.
The important contrast is:
ordinary two founders
→ pathological / boundary-limited extreme-bottleneck fit
same two founders + temporary FounderProgram
→ finite, stable bottleneck/recovery fit
This is partial demographic masking, not erasure of the founding event.
The direct SFS result and the blind inference result therefore tell a consistent but nuanced story:
FounderProgram reconstructs a large amount of neutral population-level diversity and moves the descendants strongly toward ordinary many-founder/source populations, while a demographic observer can still detect that something like a severe bottleneck/recovery occurred.
The project uses several population-genetic summaries.
Average pairwise sequence difference per base pair.
It measures total diversity, but two populations can have similar π
and very different frequency structures.
The distribution of allele counts across segregating sites.
Founder bottlenecks strongly distort the SFS, especially by removing rare variants and leaving surviving variants at unusually high frequencies.
Variants observed once or twice in the sampled chromosomes.
These are useful indicators of the rare-variant end of the SFS.
Here, the fraction of segregating variants with minor allele frequency at least 0.25.
Extreme founder populations tend to overrepresent common surviving variants.
A symmetric measure of how different two normalized SFS shapes are.
Lower is closer.
dadi
receives only the descendant folded SFS and fits ordinary demographic models such as equilibrium, population-size change, bottleneck/growth and three-epoch histories.
It is deliberately not told that FounderProgram exists.
Its interpretation is model-dependent. A fitted bottleneck is not a literal founder count.
The information-theory motivation is simple:
archive
stores many explicit examples
generator
stores rules capable of producing a distribution of examples
v5 still used an archive-like donor haplotype bank.
v6 removed that bank.
The v6-series stores a 52-byte parameter payload, but that number must not be misrepresented. The generative algorithm itself is additional information. Current experiments report implementation source size as a crude reminder of this cost.
Therefore:
52 bytes of parameters
is not52 bytes for a species
.
The deeper open question is the total irreducible information cost of:
founder genomes
+ algorithm
+ parameters
+ implementation machinery
+ any required functional priors
compared with transporting a conventional genetic archive.
If biological implementation were ever possible, a colonization or conservation architecture might trade some explicit archive size for generative machinery:
many stored genomes
versus
few living genomes + generator
This repository does not establish which architecture would be safer or smaller in reality.
Demographic inference is conditional on its model of inheritance.
The project demonstrates the general model-boundary point computationally: if the true data-generating process includes an inheritance mechanism outside an ordinary-demography model, an observer can infer a conventional demographic history that is only the best explanation inside the observer's allowed model family.
This is not evidence for alternative human history.
The project asks whether preserving the rules of a population distribution can ever substitute for preserving a large collection of realized genomes.
That question survives even if the current biological mechanism remains fictional.
The current experiments focus primarily on neutral/statistical genetic variation.
A real species also requires:
- functional alleles;
- essential conserved regions;
- regulation and development;
- deleterious and recessive-load management;
- epistasis;
- structural variation;
- immune-system diversity;
- fertility;
- environmental adaptation.
A generator that reproduces neutral population statistics is not automatically a generator for a viable organism or species.
Those questions belong to future work.
.
├── README.md
├── experiments/
│ ├── 001_bootstrap/
│ ├── 002_linked_genomes/
│ ├── 003_blind_inference/
│ ├── 004_dadi/
│ ├── 005_sequence_dadi/
│ ├── 006_embedded_generator/
│ ├── 006.1_generator_frequency/
│ └── 006.2_frequency_calibration/
└── docs/
└── learning-ledger/
Each experiment should remain reproducible and self-contained where practical. Negative results are retained.
For the scientific argument:
001 → 002 → 003 → 004 → 005 → 006 → 006.1 → 006.2
Do not skip 004_dadi
.
It is the point where the project learned that a flattering inference result is worthless when the synthetic data do not satisfy the assumptions of the measuring instrument.
For concepts rather than chronology, read the project learning ledger first.
**Keep controls visible.****Change one important mechanism at a time when possible.****Define the desired direction before looking at downstream inference.****Separate direct measurements from model-dependent interpretation.****Do not interpret optimizer boundary hits literally.****Do not call effective population size a census founder count.****Do not confuse neutral diversity with functional biological viability.****Count algorithmic machinery when making information/compression claims.****Preserve negative results.**Prefer an ugly result that survives scrutiny to a beautiful result produced by hidden assumptions.
Research state: completed proof-of-principle research pass / exploratory computational biology.
Current endpoint: v6.2 is complete, including blind dadi
inference. This is the intended stopping point for the current research pass.
The main implementation to inspect and reproduce is:
experiments/006.2_frequency_calibration/
The project is intentionally allowed to stop here.
Future work could attack replication across many seeds, LD/IBD/ROH observables, functional viability, stronger forward-genetic models, biological implementation and information limits if there is a reason to reopen it. Those are extensions of the present result, not prerequisites for understanding what this research pass demonstrated.
Treat the founders not merely as genomes, but asinit()
for a population.