{"abstract":"R0 ignores mortality before breeding.","category":"Ecological population dynamics","checks":7,"contract":"l0=1 and l[x+1]=l[x]*px[x]; R0=sum l[x]*mx[x]; generation time T=sum x*l[x]*mx[x]/R0; r=ln(R0)/T (None if T=0); e0 = sum over x of (l[x]+l[x+1])/2; return [R0, T, r, e0] rounded 6 with [0.0, None, None, e0] when R0=0; None for empty or mismatched schedules.","evaluation_group":"w2-ecopop-life-table","failed_approach":"Weighting by next-age survivorship applies a post-breeding census to a birth-pulse table.","family":"w2-ecopop-life-table-net-reproductive-rate","id":"FA-65481","implementations":{"attempt":{"sha256":"4226a999e971a27b9bc05910c23b32e104700da5697f4f29a62adc72546f858c","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(px, mx):\n    n = len(px)\n    if n == 0 or len(mx) != n:\n        return None\n    l = [1.0]\n    for x in range(1, n + 1):\n        l.append(l[-1] * px[x - 1])\n    e0 = round(sum((l[x] + l[x + 1]) / 2 for x in range(n)), 6)\n    r0 = sum(l[x + 1] * mx[x] for x in range(n))\n    if r0 <= 0:\n        return [0.0, None, None, e0]\n    gen = sum(x * l[x] * mx[x] for x in range(n)) / r0\n    rate = math.log(r0) / gen if gen > 0 else None\n    return [round(r0, 6), round(gen, 6), None if rate is None else round(rate, 6), e0]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('regression: songbird', ([0.3, 0.6, 0.6, 0.5], [0.0, 1.5, 2.0, 2.0]), [1.026, 1.77193, 0.014486, 1.115]),\n  ('regression: perennial plant',\n   ([0.1, 0.8, 0.9, 0.9, 0.0], [0.0, 0.0, 5.0, 8.0, 8.0]),\n   [1.4944, 3.079229, 0.130463, 0.8168]),\n  ('regression: replacement cohort', ([0.5, 0.5], [0.0, 4.0]), [2.0, 1.0, 0.693147, 1.125]),\n  ('regression: age zero breeding only', ([0.5, 0.2], [1.5, 0.0]), [1.5, 0.0, None, 1.05]),\n  ('control: sterile cohort', ([0.9, 0.9], [0.0, 0.0]), [0.0, None, None, 1.805]),\n  ('control: mismatched schedules', ([0.5], [0.0, 1.0]), None),\n  ('regression: annual insect', ([0.05, 0.0], [0.0, 30.0]), [1.5, 1.0, 0.405465, 0.55])],\n [('regression: songbird', ([0.3, 0.6, 0.6, 0.5], [0.0, 1.5, 2.0, 2.0]), [1.026, 1.77193, 0.014486, 1.115]),\n  ('regression: perennial plant',\n   ([0.1, 0.8, 0.9, 0.9, 0.0], [0.0, 0.0, 5.0, 8.0, 8.0]),\n   [1.4944, 3.079229, 0.130463, 0.8168]),\n  ('regression: age zero breeding only', ([0.5, 0.2], [1.5, 0.0]), [1.5, 0.0, None, 1.05]),\n  ('control: sterile cohort', ([0.9, 0.9], [0.0, 0.0]), [0.0, None, None, 1.805]),\n  ('control: mismatched schedules', ([0.5], [0.0, 1.0]), None),\n  ('regression: annual insect', ([0.05, 0.0], [0.0, 30.0]), [1.5, 1.0, 0.405465, 0.55]),\n  ('regression: long-lived',\n   ([0.95, 0.95, 0.95, 0.95, 0.95, 0.9], [0.0, 0.0, 0.2, 0.4, 0.4, 0.4]),\n   [1.158765, 3.659605, 0.040265, 5.146364])],\n [('regression: songbird', ([0.3, 0.6, 0.6, 0.5], [0.0, 1.5, 2.0, 2.0]), [1.026, 1.77193, 0.014486, 1.115]),\n  ('regression: perennial plant',\n   ([0.1, 0.8, 0.9, 0.9, 0.0], [0.0, 0.0, 5.0, 8.0, 8.0]),\n   [1.4944, 3.079229, 0.130463, 0.8168]),\n  ('regression: replacement cohort', ([0.5, 0.5], [0.0, 4.0]), [2.0, 1.0, 0.693147, 1.125]),\n  ('control: sterile cohort', ([0.9, 0.9], [0.0, 0.0]), [0.0, None, None, 1.805]),\n  ('control: mismatched schedules', ([0.5], [0.0, 1.0]), None),\n  ('regression: annual insect', ([0.05, 0.0], [0.0, 30.0]), [1.5, 1.0, 0.405465, 0.55]),\n  ('regression: long-lived',\n   ([0.95, 0.95, 0.95, 0.95, 0.95, 0.9], [0.0, 0.0, 0.2, 0.4, 0.4, 0.4]),\n   [1.158765, 3.659605, 0.040265, 5.146364])],\n [('regression: perennial plant',\n   ([0.1, 0.8, 0.9, 0.9, 0.0], [0.0, 0.0, 5.0, 8.0, 8.0]),\n   [1.4944, 3.079229, 0.130463, 0.8168]),\n  ('regression: replacement cohort', ([0.5, 0.5], [0.0, 4.0]), [2.0, 1.0, 0.693147, 1.125]),\n  ('regression: age zero breeding only', ([0.5, 0.2], [1.5, 0.0]), [1.5, 0.0, None, 1.05]),\n  ('control: sterile cohort', ([0.9, 0.9], [0.0, 0.0]), [0.0, None, None, 1.805]),\n  ('control: mismatched schedules', ([0.5], [0.0, 1.0]), None),\n  ('regression: annual insect', ([0.05, 0.0], [0.0, 30.0]), [1.5, 1.0, 0.405465, 0.55]),\n  ('regression: long-lived',\n   ([0.95, 0.95, 0.95, 0.95, 0.95, 0.9], [0.0, 0.0, 0.2, 0.4, 0.4, 0.4]),\n   [1.158765, 3.659605, 0.040265, 5.146364])],\n [('regression: songbird', ([0.3, 0.6, 0.6, 0.5], [0.0, 1.5, 2.0, 2.0]), [1.026, 1.77193, 0.014486, 1.115]),\n  ('regression: perennial plant',\n   ([0.1, 0.8, 0.9, 0.9, 0.0], [0.0, 0.0, 5.0, 8.0, 8.0]),\n   [1.4944, 3.079229, 0.130463, 0.8168]),\n  ('regression: replacement cohort', ([0.5, 0.5], [0.0, 4.0]), [2.0, 1.0, 0.693147, 1.125]),\n  ('control: sterile cohort', ([0.9, 0.9], [0.0, 0.0]), [0.0, None, None, 1.805]),\n  ('control: mismatched schedules', ([0.5], [0.0, 1.0]), None),\n  ('regression: annual insect', ([0.05, 0.0], [0.0, 30.0]), [1.5, 1.0, 0.405465, 0.55]),\n  ('regression: long-lived',\n   ([0.95, 0.95, 0.95, 0.95, 0.95, 0.9], [0.0, 0.0, 0.2, 0.4, 0.4, 0.4]),\n   [1.158765, 3.659605, 0.040265, 5.146364])]]\nfor label, args, expected in fixtures[N - 1]:\n    check(label, solve(*args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"broken":{"sha256":"b945506b1e97a4c51e6efe925487bc670b6a594415ba1a0ef4ed5df090ca98da","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(px, mx):\n    n = len(px)\n    if n == 0 or len(mx) != n:\n        return None\n    l = [1.0]\n    for x in range(1, n + 1):\n        l.append(l[-1] * px[x - 1])\n    e0 = round(sum((l[x] + l[x + 1]) / 2 for x in range(n)), 6)\n    r0 = sum(mx[x] for x in range(n))\n    if r0 <= 0:\n        return [0.0, None, None, e0]\n    gen = sum(x * l[x] * mx[x] for x in range(n)) / r0\n    rate = math.log(r0) / gen if gen > 0 else None\n    return [round(r0, 6), round(gen, 6), None if rate is None else round(rate, 6), e0]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('regression: songbird', ([0.3, 0.6, 0.6, 0.5], [0.0, 1.5, 2.0, 2.0]), [1.026, 1.77193, 0.014486, 1.115]),\n  ('regression: perennial plant',\n   ([0.1, 0.8, 0.9, 0.9, 0.0], [0.0, 0.0, 5.0, 8.0, 8.0]),\n   [1.4944, 3.079229, 0.130463, 0.8168]),\n  ('regression: replacement cohort', ([0.5, 0.5], [0.0, 4.0]), [2.0, 1.0, 0.693147, 1.125]),\n  ('regression: age zero breeding only', ([0.5, 0.2], [1.5, 0.0]), [1.5, 0.0, None, 1.05]),\n  ('control: sterile cohort', ([0.9, 0.9], [0.0, 0.0]), [0.0, None, None, 1.805]),\n  ('control: mismatched schedules', ([0.5], [0.0, 1.0]), None),\n  ('regression: annual insect', ([0.05, 0.0], [0.0, 30.0]), [1.5, 1.0, 0.405465, 0.55])],\n [('regression: songbird', ([0.3, 0.6, 0.6, 0.5], [0.0, 1.5, 2.0, 2.0]), [1.026, 1.77193, 0.014486, 1.115]),\n  ('regression: perennial plant',\n   ([0.1, 0.8, 0.9, 0.9, 0.0], [0.0, 0.0, 5.0, 8.0, 8.0]),\n   [1.4944, 3.079229, 0.130463, 0.8168]),\n  ('regression: age zero breeding only', ([0.5, 0.2], [1.5, 0.0]), [1.5, 0.0, None, 1.05]),\n  ('control: sterile cohort', ([0.9, 0.9], [0.0, 0.0]), [0.0, None, None, 1.805]),\n  ('control: mismatched schedules', ([0.5], [0.0, 1.0]), None),\n  ('regression: annual insect', ([0.05, 0.0], [0.0, 30.0]), [1.5, 1.0, 0.405465, 0.55]),\n  ('regression: long-lived',\n   ([0.95, 0.95, 0.95, 0.95, 0.95, 0.9], [0.0, 0.0, 0.2, 0.4, 0.4, 0.4]),\n   [1.158765, 3.659605, 0.040265, 5.146364])],\n [('regression: songbird', ([0.3, 0.6, 0.6, 0.5], [0.0, 1.5, 2.0, 2.0]), [1.026, 1.77193, 0.014486, 1.115]),\n  ('regression: perennial plant',\n   ([0.1, 0.8, 0.9, 0.9, 0.0], [0.0, 0.0, 5.0, 8.0, 8.0]),\n   [1.4944, 3.079229, 0.130463, 0.8168]),\n  ('regression: replacement cohort', ([0.5, 0.5], [0.0, 4.0]), [2.0, 1.0, 0.693147, 1.125]),\n  ('control: sterile cohort', ([0.9, 0.9], [0.0, 0.0]), [0.0, None, None, 1.805]),\n  ('control: mismatched schedules', ([0.5], [0.0, 1.0]), None),\n  ('regression: annual insect', ([0.05, 0.0], [0.0, 30.0]), [1.5, 1.0, 0.405465, 0.55]),\n  ('regression: long-lived',\n   ([0.95, 0.95, 0.95, 0.95, 0.95, 0.9], [0.0, 0.0, 0.2, 0.4, 0.4, 0.4]),\n   [1.158765, 3.659605, 0.040265, 5.146364])],\n [('regression: perennial plant',\n   ([0.1, 0.8, 0.9, 0.9, 0.0], [0.0, 0.0, 5.0, 8.0, 8.0]),\n   [1.4944, 3.079229, 0.130463, 0.8168]),\n  ('regression: replacement cohort', ([0.5, 0.5], [0.0, 4.0]), [2.0, 1.0, 0.693147, 1.125]),\n  ('regression: age zero breeding only', ([0.5, 0.2], [1.5, 0.0]), [1.5, 0.0, None, 1.05]),\n  ('control: sterile cohort', ([0.9, 0.9], [0.0, 0.0]), [0.0, None, None, 1.805]),\n  ('control: mismatched schedules', ([0.5], [0.0, 1.0]), None),\n  ('regression: annual insect', ([0.05, 0.0], [0.0, 30.0]), [1.5, 1.0, 0.405465, 0.55]),\n  ('regression: long-lived',\n   ([0.95, 0.95, 0.95, 0.95, 0.95, 0.9], [0.0, 0.0, 0.2, 0.4, 0.4, 0.4]),\n   [1.158765, 3.659605, 0.040265, 5.146364])],\n [('regression: songbird', ([0.3, 0.6, 0.6, 0.5], [0.0, 1.5, 2.0, 2.0]), [1.026, 1.77193, 0.014486, 1.115]),\n  ('regression: perennial plant',\n   ([0.1, 0.8, 0.9, 0.9, 0.0], [0.0, 0.0, 5.0, 8.0, 8.0]),\n   [1.4944, 3.079229, 0.130463, 0.8168]),\n  ('regression: replacement cohort', ([0.5, 0.5], [0.0, 4.0]), [2.0, 1.0, 0.693147, 1.125]),\n  ('control: sterile cohort', ([0.9, 0.9], [0.0, 0.0]), [0.0, None, None, 1.805]),\n  ('control: mismatched schedules', ([0.5], [0.0, 1.0]), None),\n  ('regression: annual insect', ([0.05, 0.0], [0.0, 30.0]), [1.5, 1.0, 0.405465, 0.55]),\n  ('regression: long-lived',\n   ([0.95, 0.95, 0.95, 0.95, 0.95, 0.9], [0.0, 0.0, 0.2, 0.4, 0.4, 0.4]),\n   [1.158765, 3.659605, 0.040265, 5.146364])]]\nfor label, args, expected in fixtures[N - 1]:\n    check(label, solve(*args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"fixed":{"sha256":"fcb1ffe1d1b6c83c92eee3b6193450587ec61aa4618acc7d03f54b44b3d6955f","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(px, mx):\n    n = len(px)\n    if n == 0 or len(mx) != n:\n        return None\n    l = [1.0]\n    for x in range(1, n + 1):\n        l.append(l[-1] * px[x - 1])\n    e0 = round(sum((l[x] + l[x + 1]) / 2 for x in range(n)), 6)\n    r0 = sum(l[x] * mx[x] for x in range(n))\n    if r0 <= 0:\n        return [0.0, None, None, e0]\n    gen = sum(x * l[x] * mx[x] for x in range(n)) / r0\n    rate = math.log(r0) / gen if gen > 0 else None\n    return [round(r0, 6), round(gen, 6), None if rate is None else round(rate, 6), e0]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('regression: songbird', ([0.3, 0.6, 0.6, 0.5], [0.0, 1.5, 2.0, 2.0]), [1.026, 1.77193, 0.014486, 1.115]),\n  ('regression: perennial plant',\n   ([0.1, 0.8, 0.9, 0.9, 0.0], [0.0, 0.0, 5.0, 8.0, 8.0]),\n   [1.4944, 3.079229, 0.130463, 0.8168]),\n  ('regression: replacement cohort', ([0.5, 0.5], [0.0, 4.0]), [2.0, 1.0, 0.693147, 1.125]),\n  ('regression: age zero breeding only', ([0.5, 0.2], [1.5, 0.0]), [1.5, 0.0, None, 1.05]),\n  ('control: sterile cohort', ([0.9, 0.9], [0.0, 0.0]), [0.0, None, None, 1.805]),\n  ('control: mismatched schedules', ([0.5], [0.0, 1.0]), None),\n  ('regression: annual insect', ([0.05, 0.0], [0.0, 30.0]), [1.5, 1.0, 0.405465, 0.55])],\n [('regression: songbird', ([0.3, 0.6, 0.6, 0.5], [0.0, 1.5, 2.0, 2.0]), [1.026, 1.77193, 0.014486, 1.115]),\n  ('regression: perennial plant',\n   ([0.1, 0.8, 0.9, 0.9, 0.0], [0.0, 0.0, 5.0, 8.0, 8.0]),\n   [1.4944, 3.079229, 0.130463, 0.8168]),\n  ('regression: age zero breeding only', ([0.5, 0.2], [1.5, 0.0]), [1.5, 0.0, None, 1.05]),\n  ('control: sterile cohort', ([0.9, 0.9], [0.0, 0.0]), [0.0, None, None, 1.805]),\n  ('control: mismatched schedules', ([0.5], [0.0, 1.0]), None),\n  ('regression: annual insect', ([0.05, 0.0], [0.0, 30.0]), [1.5, 1.0, 0.405465, 0.55]),\n  ('regression: long-lived',\n   ([0.95, 0.95, 0.95, 0.95, 0.95, 0.9], [0.0, 0.0, 0.2, 0.4, 0.4, 0.4]),\n   [1.158765, 3.659605, 0.040265, 5.146364])],\n [('regression: songbird', ([0.3, 0.6, 0.6, 0.5], [0.0, 1.5, 2.0, 2.0]), [1.026, 1.77193, 0.014486, 1.115]),\n  ('regression: perennial plant',\n   ([0.1, 0.8, 0.9, 0.9, 0.0], [0.0, 0.0, 5.0, 8.0, 8.0]),\n   [1.4944, 3.079229, 0.130463, 0.8168]),\n  ('regression: replacement cohort', ([0.5, 0.5], [0.0, 4.0]), [2.0, 1.0, 0.693147, 1.125]),\n  ('control: sterile cohort', ([0.9, 0.9], [0.0, 0.0]), [0.0, None, None, 1.805]),\n  ('control: mismatched schedules', ([0.5], [0.0, 1.0]), None),\n  ('regression: annual insect', ([0.05, 0.0], [0.0, 30.0]), [1.5, 1.0, 0.405465, 0.55]),\n  ('regression: long-lived',\n   ([0.95, 0.95, 0.95, 0.95, 0.95, 0.9], [0.0, 0.0, 0.2, 0.4, 0.4, 0.4]),\n   [1.158765, 3.659605, 0.040265, 5.146364])],\n [('regression: perennial plant',\n   ([0.1, 0.8, 0.9, 0.9, 0.0], [0.0, 0.0, 5.0, 8.0, 8.0]),\n   [1.4944, 3.079229, 0.130463, 0.8168]),\n  ('regression: replacement cohort', ([0.5, 0.5], [0.0, 4.0]), [2.0, 1.0, 0.693147, 1.125]),\n  ('regression: age zero breeding only', ([0.5, 0.2], [1.5, 0.0]), [1.5, 0.0, None, 1.05]),\n  ('control: sterile cohort', ([0.9, 0.9], [0.0, 0.0]), [0.0, None, None, 1.805]),\n  ('control: mismatched schedules', ([0.5], [0.0, 1.0]), None),\n  ('regression: annual insect', ([0.05, 0.0], [0.0, 30.0]), [1.5, 1.0, 0.405465, 0.55]),\n  ('regression: long-lived',\n   ([0.95, 0.95, 0.95, 0.95, 0.95, 0.9], [0.0, 0.0, 0.2, 0.4, 0.4, 0.4]),\n   [1.158765, 3.659605, 0.040265, 5.146364])],\n [('regression: songbird', ([0.3, 0.6, 0.6, 0.5], [0.0, 1.5, 2.0, 2.0]), [1.026, 1.77193, 0.014486, 1.115]),\n  ('regression: perennial plant',\n   ([0.1, 0.8, 0.9, 0.9, 0.0], [0.0, 0.0, 5.0, 8.0, 8.0]),\n   [1.4944, 3.079229, 0.130463, 0.8168]),\n  ('regression: replacement cohort', ([0.5, 0.5], [0.0, 4.0]), [2.0, 1.0, 0.693147, 1.125]),\n  ('control: sterile cohort', ([0.9, 0.9], [0.0, 0.0]), [0.0, None, None, 1.805]),\n  ('control: mismatched schedules', ([0.5], [0.0, 1.0]), None),\n  ('regression: annual insect', ([0.05, 0.0], [0.0, 30.0]), [1.5, 1.0, 0.405465, 0.55]),\n  ('regression: long-lived',\n   ([0.95, 0.95, 0.95, 0.95, 0.95, 0.9], [0.0, 0.0, 0.2, 0.4, 0.4, 0.4]),\n   [1.158765, 3.659605, 0.040265, 5.146364])]]\nfor label, args, expected in fixtures[N - 1]:\n    check(label, solve(*args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"}},"limitations":"Deterministic bounded teaching model with a stipulated contract; not a validated scientific or public-health modelling library. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.","method":"Deterministic executable model with adversarial boundary fixtures.","provenance":{"created_by":"Failure Map","dependencies":"Python standard library","family":"w2-ecopop-life-table-net-reproductive-rate","generated_at":"2026-09-29T14:47:34.521463+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Population projections set harvest quotas, conservation status and pest-control timing; a wrong update order, boundary or rate conversion silently changes management advice.","repair":"Restore the net reproductive rate rule: `r0 = sum(l[x] * mx[x] for x in range(n))`.","root_cause":"Fecundity is summed without survivorship weighting.","sha256":"bea6fd336738ef978eb3c2314c796be5e2a46b5f5ae752f62d9eea6b308ec4ca","title":"Cohort life table statistics: net reproductive rate · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":40.118,"exit_code":1,"observations":[{"actual":[0.594,3.060606,-0.170187,1.115],"check":"regression: songbird","expected":[1.026,1.77193,0.014486,1.115],"passed":false},{"actual":[0.8784,5.238616,-0.02475,0.8168],"check":"regression: perennial plant","expected":[1.4944,3.079229,0.130463,0.8168],"passed":false},{"actual":[1.0,2.0,0.0,1.125],"check":"regression: replacement cohort","expected":[2.0,1.0,0.693147,1.125],"passed":false},{"actual":[0.75,0.0,null,1.05],"check":"regression: age zero breeding only","expected":[1.5,0.0,null,1.05],"passed":false},{"actual":[0.0,null,null,1.805],"check":"control: sterile cohort","expected":[0.0,null,null,1.805],"passed":true},{"actual":null,"check":"control: mismatched schedules","expected":null,"passed":true},{"actual":[0.0,null,null,0.55],"check":"regression: annual 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