# Historical Adaptive — exploratory global calculation (v0.2)

The page now answers: **under the selected assumptions, what share of the living world population is a genealogical descendant of the stipulated founder?** It opens with a completed, reproducible 96-run central ensemble through AD 2026. Changing the scenario runs a new ensemble in the browser; changing the displayed year reads the completed trajectories.

This is an **uncalibrated aggregate extension of the original site's Rohde-style simulator**. It is not the individual-pedigree computational model in Rohde–Olson–Chang Supplement B and is not the completed 28-region historical model. It must not be used to assert a historically established percentage. The detailed research register retains null for unestimated rates; the runnable scenario uses a separate, explicit grade-D assumption set.

## Meaning of the output

For run r and year t, let q[r,i,p,s,t] be the fraction descended from the founder in macroregion i, subpopulation p and social state s. Let w[i,t] be the normalized regional population weight inherited from the original simulator, and a[s] the state population share. The world percentage is:

`100 × sum_i w[i,t] × (sum_p sum_s a[s] × q[r,i,p,s,t]) / 4`.

The headline is the arithmetic mean across the selected run sample, **not a probability that a randomly specified historical individual was Jacob**. The displayed range is the empirical 10th–90th percentile of run-level world percentages. It mixes numerical-prior uncertainty and stochastic simulation variation within one scenario; it is not a confidence or credible interval for historical reality. It does not span all scenarios or missing mechanisms.

The default sample contains only runs whose lineage remains alive in AD 2026. That same final-survival sample is used throughout the timeline, including earlier years. Selecting “Include extinct lines” instead uses all 96 runs. Runs that eventually go extinct may have descendants at earlier dates, but contribute zero after extinction. If no runs survive, the conditional result is unavailable rather than reported as zero. The founder survival count is a simulated outcome of the assumed reproduction process, not a historical probability estimate.

Regional results are means from the same sample. Their population-weighted average equals the headline. Approximate headcounts multiply the headline by the original simulator's world-population scaffold; they are rounded. The terminal date is exactly AD 2026. Internally the calendar is astronomical: 1800 BC = −1799, 1 BC = 0. Historical dates in the original simulator's demographic function are converted when called.

## Connection to Rohde–Olson–Chang

The calculation preserves geographically structured populations, predominantly within-population reproduction, weaker local and long-distance connectivity, dated ports, opening pulses, destination clustering, demographic weights, stochastic rare-lineage events, and Monte Carlo ensembles. It separates migration, settlement, successful reproduction, crossing out of an endogamous community, and participation in the receiving host population.

It approximates local mating with four patches per macroregion; these are computational subpopulations, **not four literal ancient towns**. There are twelve macroregions inherited from the original simulator, each with three participation compartments: community/enclave E, newcomer/boundary B, and host H. The proposed 28-region research architecture is not silently treated as a calibrated numerical dataset.

The early E state means the founder's social community; it does not impose a Jewish identity in 1800 BC. Later E route candidates approximate diaspora networks. Descendants in H use H behavior independently of ancestral origin. The ancestry tag confers neither religious membership nor a permanent “Jewish migration rate.”

## Mechanics and numerical choices

Every run begins with one tagged adult in one Levantine community patch. No all-Israelite initial tagging, household of 70, or Exodus population injection occurs.

The local child prevalence approximation is `q_child = q + m × q × (1 − q)`. For m = 1 this is the two-independent-parent OR rule `1 − (1 − q)^2`; m below 1 approximates assortative and local mating. A fraction dt/generation of the population turns over per time step, with a maximum ten-year step and exact route/regime boundaries. This is an overlapping-cohort approximation, **not explicit lifetimes, sex-specific ages, marriages, or stored parents**.

For cells with 1–63 expected descendants, births and deaths are sampled with a Poisson/tau-leap approximation (deaths capped at the current count), allowing extinction. At larger counts the within-cell dynamics become deterministic. This is a hybrid numerical approximation: late extinction, family-correlated reproduction, and bottlenecks are not fully captured. The detailed synthetic pedigree diagnostic remains available separately to test explicit parent links.

Small migrant totals and tagged arrivals are sampled discretely so a tiny expected flux does not automatically plant a fractional founder in every destination. Settlement and successful reproduction thin the migration flow. Host-network migrants initially enter B, while community migrants enter E. A sampled clustering probability puts arrivals in one port patch; other arrivals select among four patches. Within-region migration is weak exchange between neighboring patches.

E-to-B descendant births depend on the cross-group reproduction coefficient and parental ancestry; conversion by itself does not tag anyone. B-to-H integration exchanges participation at a separate rate and conserves tagged counts within each same-region exchange, subject to cell capacity. Background regional populations are exogenous; interregional migration is a population-normalized composition update, **not a fully mass-balanced migration/demography model**.

### Scenario priors — all grade D

Draw once per run; keep that draw through time. These are illustrative scenario assumptions, not scholarly estimates of ancient rates. “Central” denotes the middle numerical scenario, not a scholarly consensus. Scenarios have no assigned historical probabilities.

| Quantity | Conservative | Central | Higher connectivity | Distribution / unit |
|---|---:|---:|---:|---|
| Local independent-parent mixing coefficient | 0.18–0.32 | 0.30–0.50 | 0.45–0.70 | Uniform, before geographic/state modifiers |
| Baseline interregional movement | 0.0001–0.0005 | 0.0004–0.0015 | 0.001–0.004 | Log-uniform, fraction of source compartment per generation before route modifiers |
| Community cross-group reproduction | 0.00002–0.0005 | 0.0002–0.004 | 0.001–0.015 | Log-uniform, per-generation opportunity coefficient before regime modifier |
| Boundary-to-host participation exchange | 0.015–0.05 | 0.04–0.15 | 0.10–0.35 | Uniform, per generation |

Common priors are generation interval 26–32 years (uniform), settlement probability 0.3–0.8 (uniform), successful reproduction after settlement 0.4–0.85 (uniform), community compartment fraction 0.002–0.02 (log-uniform), and port-patch clustering probability 0.70–0.95 (uniform). B is 4% of each patch, and H is the remainder. **Compartment fractions are computational capacities, not estimates of historical Jewish population shares**, and need sensitivity testing/calibration before substantive demographic use. Assumptions are independent in this first implementation; empirical correlations have not been calibrated.

Host mixing is reduced by each inherited region's barrier; the E mixing coefficient is additionally multiplied by 0.8. Local patch exchange is eight times the baseline interregional coefficient before time scaling. Distance decay uses power 1.5, original route strengths and reverse-direction factors. Non-land movement has a 0.12 multiplier. All are D-grade computational choices. No ancient annual migration rate has been inferred.

### Time dependence

| Regime (astronomical years, start inclusive) | Movement multiplier | Boundary multiplier | Local / integration multiplier |
|---|---:|---:|---:|
| Before −721 | 0.7 | 1 | 1 |
| −721 to −332 | 1.3 | 0.8 | 1 |
| −332 to 300 | 1.8 | 1 | 1 |
| 300 to 1500 | 1 | 0.5 | 1 |
| 1500 to 1800 | 2 | 0.8 | 1.1 |
| 1800 to 1950 | 4 | 1.5 | 1.25 |
| 1950 onward | 7 | 3 | 1.5 |

These are **coarse assumption windows, not empirically fitted rates**. The 70 and 135 crises are not converted into a universal expulsion or automatic genealogical seed. Their local demographic effects, separate ancient eastern subregions, and multiple medieval boundaries still require calibrated research.

Host routes and population series use the existing simulator's rough scaffold, including weak early Pacific/Bering alternatives and dated Atlantic/modern ports. It is not a replacement for the evidence ledger. New E-route candidates are eastern Levantine displacement (opening choice 721 BC), Egypt (600 BC), Mediterranean Europe (332 BC), North Africa–Europe (300 BC), an uncertain eastern–South Asian route (AD 500), and Atlantic routes (AD 1500/1650). These are deliberately approximate numerical activation choices, **not dates of first presence**. The eastern destination combines Mesopotamian/Iranian pathways within the inherited “Central Asia” macroregion: its coarse boundaries and weights are a known limitation. E routes use two directions with equal baseline rates pending better evidence; early eastern and Mediterranean pulses last one generation. Presence abroad does not imply host intermarriage.

## Evidence, inference, and assumptions

Historical context is supported by the research bibliography and separate route ledger. The numerical coefficients above have no direct empirical calibration. In particular, none of these works establishes the percentages on the page:

- [Rohde, Olson & Chang (2004), Nature](https://doi.org/10.1038/nature02842) and [Supplement B](https://www.stat.yale.edu/~jtc5/papers/CommonAncestors/NatureCommonAncestors-SupplementB.pdf): computational foundation and why structure/connectivity matter. Their global MRCA finding does not prove descent from this stipulated founder.
- [Radner, Assyrian resettlement](https://epub.ub.uni-muenchen.de/58863/) and [Alstola, Judeans in Babylonia](https://doi.org/10.1163/9789004365421): evidence motivating eastern displacement and continuing settlement, not a measured cross-group marriage probability.
- [Corpus Papyrorum Judaicarum IV](https://cris.huji.ac.il/en/publications/the-ptolemaic-period-323-bce30-bce/) and [Smallwood, pre-70 diaspora](https://www.cambridge.org/core/books/abs/cambridge-history-of-judaism/diaspora-in-the-roman-period-before-ce-70/AD1E5333322627A5BD5063DB966A0813): evidence motivating pre-Roman-destruction Mediterranean diaspora routes.
- [Satlow, Jewish Marriage in Antiquity](https://www.jstor.org/stable/j.ctv346sfv): social boundaries and marriage practices; no representative universal rate follows from this scholarship.

The original research registry and its unknown numerical fields remain intact. Genetic evidence does not directly supply a Jacob-descendant fraction. Sources motivate the possible connectivity structure; assumptions make this exploratory calculation runnable.

## Reproduction and limitations

“Download this run” exports the model version, seed, options, each numerical prior draw, all-run and survival-conditional trajectories, and regional outputs. The default seed is 20260930; “Run again” increments it. Results are reproducible for the same version and settings. Three scenario choices let users inspect assumption dependence; they do not constitute a completed global sensitivity analysis.

Critical uncalibrated quantities include ancient cross-group reproductive leakage, permanent settlement, integration lags, historical Jewish/community headcounts, mating substructure, reproductive inequality, correlated households, detailed growth/collapse histories, isolated-community barriers and extremely rare ports. Coarse averages cannot establish that every living person is descended from the founder, even if the displayed value approaches 100%.

Next refinement should first vary compartment capacities, local patch resolution, rare-event cutoffs and missing reproductive barriers, then extract evidence for parameters that materially move the output. Do not tune assumptions to obtain a desired modern percentage.