L1 ⚛ L1-408 ⊙ Testnet

Wright-Fisher Population Genetics

Computational Biology · Population genetics

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⬇ L1-408.md

# ⚛ L1 Principle — Wright-Fisher Population Genetics **ID:** `L1-408` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Computational Biology — *Population genetics* > **🎯 Problem class:** parameter estimation · **🧮 Solution space:** population genetic parameter vector > **📡 Carrier:** N/A · **🌫 Noise:** multinomial > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41555219 --- ## 🧠 1. Introduction **Wright-Fisher Population Genetics** is a **parameter-estimation problem** whose unknown lives in **population genetic parameter vector** space, within the **Population genetics** sub-domain of **Computational Biology**. Measurements consist of N/A via a **allele frequency sequencing** sensing mechanism. The forward operator applies, in order: applies a smooth nonlinear function element-wise; O · likelihood · allele frequency operator; S · mcmc · popgen posterior operator. Observations are corrupted by multinomial counting noise across categories. Existence of the recovered population_genetic_parameter_vector is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 100); population_structure_subdivision dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Multinomial sets the irreducible data-fidelity floor. ## ⚙ 2. Forward Model Physical chain: **x** → Pointwise nonlinearity → O · likelihood · allele frequency → S · mcmc · popgen posterior → **y** (detector). ``` y = `S.mcmc.popgen_posterior` `O.likelihood.allele_frequency` f(·) x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `N.pointwise` | Applies a smooth nonlinear function element-wise | | `O.likelihood.allele_frequency` | O · likelihood · allele frequency operator | | `S.mcmc.popgen_posterior` | S · mcmc · popgen posterior operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Computational Biology | | Sub domain | Population genetics | | Carrier | N/A | | Problem class | parameter_estimation | | Solution space | population_genetic_parameter_vector | | Noise model | multinomial | | Integration axis | generations | | Difficulty delta | 5 | | L dag | 3 | ## 📡 4. Measurement Model Existence of the recovered population_genetic_parameter_vector is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 100); population_structure_subdivision dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Multinomial sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | Ne_estimation_RMSE_log | | Secondary | selection_coefficient_RMSE | ## 📏 5. Operating Range (Ω) **Center problem class:** `parameter_estimation` · **Forward operator:** `allele_frequency_sequencing` **Center point:** | Parameter | Unit | Value | |---|---|---| | S selection | — | 0 | | Ne effective | — | 1000 | | N generations | — | 20 | | N sampled alleles | — | 100 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | S selection | — | -0.1 – 0.1 | | Ne effective | — | 10 – 100000 | | N generations | — | 5 – 100 | | N sampled alleles | — | 10 – 1000 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 0.3 Ne_estimation_RMSE_log | Metric | Range | |---|---| | Ne estimation rmse log | 0.05 – 1.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **Ne_estimation_RMSE_log**, with κ = `2000` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x4032c97662301a11eb728fee50ab6352f9031854e796853bc3533d2002b8f0c4` - **Chain tx hash:** `0xa78c1cdf96ae810ee096d0a93e8f4d4ee0ea9c94742642b5f2e428fe3ba97876` - **Chain block:** `41555219` --- ## File Mapping This bundle consists of: `L1-408.md`, `L1-408.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-408.md` | Source of truth — edit this | Human or LLM | | `L1-408.json` | Structured metadata for the registry | LLM regenerates from the sections above | **Prompt for your LLM after editing this Markdown:** > Read the attached Markdown. Regenerate the sibling `.json` so every field matches. > Preserve the schema documented in the rows above. > Output each file in its own fenced code block tagged with the filename. > Output only the JSON object. _This Markdown was auto-synthesized from the catalog row for `L1-408`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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📋 JSON metadata

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  "chain_hash": "0x4032c97662301a11eb728fee50ab6352f9031854e796853bc3533d2002b8f0c4",
  "chain_tx_hash": "0xa78c1cdf96ae810ee096d0a93e8f4d4ee0ea9c94742642b5f2e428fe3ba97876",
  "domain": "Computational Biology",
  "hardness_fn": {
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    "kappa": 2000,
    "metric": "Ne_estimation_RMSE_log",
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    "regime": "Existence of the recovered population_genetic_parameter_vector is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 100); population_structure_subdivision dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Multinomial sets the irreducible data-fidelity floor.",
    "secondary": "selection_coefficient_RMSE"
  },
  "physics_fingerprint": {
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    "carrier": "N/A",
    "difficulty_delta": 5,
    "domain": "Computational Biology",
    "integration_axis": "generations",
    "noise_model": "multinomial",
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      "O.likelihood.allele_frequency",
      "S.mcmc.popgen_posterior"
    ],
    "problem_class": "parameter_estimation",
    "sensing_mechanism": "allele_frequency_sequencing",
    "solution_space": "population_genetic_parameter_vector",
    "sub_domain": "Population genetics",
    "title": "Wright-Fisher Population Genetics"
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      "s_selection",
      "N_sampled_alleles"
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    "allowed_problem_classes": [
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    "center_spec": {
      "epsilon_fn_center": "0.3 Ne_estimation_RMSE_log",
      "forward_operator": "allele_frequency_sequencing",
      "input_format": "measurement_only",
      "omega": {
        "N_generations": 20,
        "N_sampled_alleles": 100,
        "Ne_effective": 1000,
        "s_selection": 0.0
      },
      "problem_class": "parameter_estimation"
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    "epsilon_bounds": {
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        1.0
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    },
    "omega_bounds": {
      "N_generations": [
        5,
        100
      ],
      "N_sampled_alleles": [
        10,
        1000
      ],
      "Ne_effective": [
        10,
        100000
      ],
      "s_selection": [
        -0.1,
        0.1
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Population genetics",
  "title": "Wright-Fisher Population Genetics"
}

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