{
  "schemaVersion": 1,
  "modelVersion": "1.0",
  "evidenceType": "analytic worked example",
  "license": "CC0-1.0",
  "identities": 10000,
  "assumptions": [
    "Fixed number of independent draws with replacement; probabilities remain constant.",
    "Each read identifies its sequence without error. No synthesis failure, degradation or filtering.",
    "An identity is unseen if it receives zero reads. No error-correction decoder is simulated.",
    "Uneven probabilities are a deliberately chosen sensitivity case, not fitted laboratory data."
  ],
  "formula": "E[U] = sum_i (1 - p_i)^N",
  "scenarios": [
    {
      "id": "uniform",
      "label": "Uniform",
      "groups": [
        {
          "count": 10000,
          "probability": 0.0001
        }
      ]
    },
    {
      "id": "uneven",
      "label": "10% underrepresented",
      "groups": [
        {
          "count": 1000,
          "probability": 0.00001
        },
        {
          "count": 9000,
          "probability": 0.00011
        }
      ]
    }
  ],
  "rows": [
    {
      "scenario": "uniform",
      "coverage": 1,
      "reads": 10000,
      "expectedUnseen": 3678.6104643292983,
      "expectedUnseenFraction": 0.36786104643292983,
      "probabilityAnyUnseenUpperBound": 1
    },
    {
      "scenario": "uneven",
      "coverage": 1,
      "reads": 10000,
      "expectedUnseen": 3900.4954627828056,
      "expectedUnseenFraction": 0.39004954627828053,
      "probabilityAnyUnseenUpperBound": 1
    },
    {
      "scenario": "uniform",
      "coverage": 2,
      "reads": 20000,
      "expectedUnseen": 1353.2174948273018,
      "expectedUnseenFraction": 0.13532174948273018,
      "probabilityAnyUnseenUpperBound": 1
    },
    {
      "scenario": "uneven",
      "coverage": 2,
      "reads": 20000,
      "expectedUnseen": 1815.8376934152448,
      "expectedUnseenFraction": 0.18158376934152448,
      "probabilityAnyUnseenUpperBound": 1
    },
    {
      "scenario": "uniform",
      "coverage": 5,
      "reads": 50000,
      "expectedUnseen": 67.36262610599526,
      "expectedUnseenFraction": 0.0067362626105995265,
      "probabilityAnyUnseenUpperBound": 1
    },
    {
      "scenario": "uneven",
      "coverage": 5,
      "reads": 50000,
      "expectedUnseen": 643.298960955635,
      "expectedUnseenFraction": 0.0643298960955635,
      "probabilityAnyUnseenUpperBound": 1
    },
    {
      "scenario": "uniform",
      "coverage": 10,
      "reads": 100000,
      "expectedUnseen": 0.45377233958961144,
      "expectedUnseenFraction": 0.00004537723395896114,
      "probabilityAnyUnseenUpperBound": 0.45377233958961144
    },
    {
      "scenario": "uneven",
      "coverage": 10,
      "reads": 100000,
      "expectedUnseen": 368.02782615376213,
      "expectedUnseenFraction": 0.036802782615376214,
      "probabilityAnyUnseenUpperBound": 1
    },
    {
      "scenario": "uniform",
      "coverage": 15,
      "reads": 150000,
      "expectedUnseen": 0.0030567296449017676,
      "expectedUnseenFraction": 3.0567296449017676e-7,
      "probabilityAnyUnseenUpperBound": 0.0030567296449017676
    },
    {
      "scenario": "uneven",
      "coverage": 15,
      "reads": 150000,
      "expectedUnseen": 223.1291004143824,
      "expectedUnseenFraction": 0.02231291004143824,
      "probabilityAnyUnseenUpperBound": 1
    },
    {
      "scenario": "uniform",
      "coverage": 20,
      "reads": 200000,
      "expectedUnseen": 0.00002059093361766296,
      "expectedUnseenFraction": 2.059093361766296e-9,
      "probabilityAnyUnseenUpperBound": 0.00002059093361766296
    },
    {
      "scenario": "uneven",
      "coverage": 20,
      "reads": 200000,
      "expectedUnseen": 135.33393238900985,
      "expectedUnseenFraction": 0.013533393238900985,
      "probabilityAnyUnseenUpperBound": 1
    }
  ],
  "generatedAt": "2026-10-18T18:15:34.678Z",
  "runtime": "v24.21.0",
  "sourceSha256": "d5d830d5bf7a4cbd25d839cf271625d8ff00e68c82a919dd43912fe9a9af812e"
}