{"abstract":"Predicted richness can exceed the mainland pool.","category":"Ecological population dynamics","checks":7,"contract":"I0 = imax*exp(-distance/d0); E0 = emax*a0/area; S* = I0*P/(I0+E0); turnover = I0*E0/(I0+E0); return [S*, turnover, I0, E0] rounded 4; None for non-positive parameters or negative distance.","contract_signature":"pool, imax, emax, distance, d0, area, a0","evaluation_group":"w2-ecopop-island-biogeography","failed_approach":"Using E0 in the numerator predicts richness falling with immigration.","family":"w2-ecopop-island-biogeography-equilibrium-richness","id":"FA-65761","implementations":{"attempt":{"sha256":"5ff33e8e2017ce51f439eb70d634b09cad20bc3e67c0554e409ef83d87bfe4c2","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(pool, imax, emax, distance, d0, area, a0):\n    if min(pool, imax, emax, d0, a0, area) <= 0 or distance < 0:\n        return None\n    i0 = imax * math.exp(-distance / d0)\n    e0 = emax * a0 / area\n    s_eq = pool * e0 / (i0 + e0)\n    turnover = i0 * e0 / (i0 + e0)\n    return [round(s_eq, 4), round(turnover, 4), round(i0, 4), round(e0, 4)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('regression: near large island', (200, 5.0, 2.0, 10, 50, 100, 10), [190.6839, 0.1907, 4.0937, 0.2]),\n  ('regression: remote small island', (200, 5.0, 2.0, 300, 50, 2, 10), [0.2476, 0.0124, 0.0124, 10.0]),\n  ('regression: mainland adjacent', (120, 3.0, 1.0, 0, 40, 10, 10), [90.0, 0.75, 3.0, 1.0]),\n  ('regression: reference area', (80, 2.0, 2.0, 40, 40, 10, 10), [21.5153, 0.5379, 0.7358, 2.0]),\n  ('control: invalid area', (80, 2.0, 2.0, 40, 40, 0, 10), None),\n  ('control: negative distance', (80, 2.0, 2.0, -5, 40, 10, 10), None),\n  ('regression: archipelago mid', (150, 4.0, 3.0, 60, 30, 25, 5), [71.1454, 0.2846, 0.5413, 0.6])],\n [('regression: near large island', (200, 5.0, 2.0, 10, 50, 100, 10), [190.6839, 0.1907, 4.0937, 0.2]),\n  ('regression: remote small island', (200, 5.0, 2.0, 300, 50, 2, 10), [0.2476, 0.0124, 0.0124, 10.0]),\n  ('regression: mainland adjacent', (120, 3.0, 1.0, 0, 40, 10, 10), [90.0, 0.75, 3.0, 1.0]),\n  ('regression: reference area', (80, 2.0, 2.0, 40, 40, 10, 10), [21.5153, 0.5379, 0.7358, 2.0]),\n  ('control: invalid area', (80, 2.0, 2.0, 40, 40, 0, 10), None),\n  ('control: negative distance', (80, 2.0, 2.0, -5, 40, 10, 10), None),\n  ('regression: archipelago mid', (150, 4.0, 3.0, 60, 30, 25, 5), [71.1454, 0.2846, 0.5413, 0.6])],\n [('regression: near large island', (200, 5.0, 2.0, 10, 50, 100, 10), [190.6839, 0.1907, 4.0937, 0.2]),\n  ('regression: remote small island', (200, 5.0, 2.0, 300, 50, 2, 10), [0.2476, 0.0124, 0.0124, 10.0]),\n  ('regression: mainland adjacent', (120, 3.0, 1.0, 0, 40, 10, 10), [90.0, 0.75, 3.0, 1.0]),\n  ('regression: reference area', (80, 2.0, 2.0, 40, 40, 10, 10), [21.5153, 0.5379, 0.7358, 2.0]),\n  ('control: invalid area', (80, 2.0, 2.0, 40, 40, 0, 10), None),\n  ('control: negative distance', (80, 2.0, 2.0, -5, 40, 10, 10), None),\n  ('regression: archipelago mid', (150, 4.0, 3.0, 60, 30, 25, 5), [71.1454, 0.2846, 0.5413, 0.6])],\n [('regression: near large island', (200, 5.0, 2.0, 10, 50, 100, 10), [190.6839, 0.1907, 4.0937, 0.2]),\n  ('regression: remote small island', (200, 5.0, 2.0, 300, 50, 2, 10), [0.2476, 0.0124, 0.0124, 10.0]),\n  ('regression: mainland adjacent', (120, 3.0, 1.0, 0, 40, 10, 10), [90.0, 0.75, 3.0, 1.0]),\n  ('regression: reference area', (80, 2.0, 2.0, 40, 40, 10, 10), [21.5153, 0.5379, 0.7358, 2.0]),\n  ('control: invalid area', (80, 2.0, 2.0, 40, 40, 0, 10), None),\n  ('control: negative distance', (80, 2.0, 2.0, -5, 40, 10, 10), None),\n  ('regression: archipelago mid', (150, 4.0, 3.0, 60, 30, 25, 5), [71.1454, 0.2846, 0.5413, 0.6])],\n [('regression: near large island', (200, 5.0, 2.0, 10, 50, 100, 10), [190.6839, 0.1907, 4.0937, 0.2]),\n  ('regression: remote small island', (200, 5.0, 2.0, 300, 50, 2, 10), [0.2476, 0.0124, 0.0124, 10.0]),\n  ('regression: mainland adjacent', (120, 3.0, 1.0, 0, 40, 10, 10), [90.0, 0.75, 3.0, 1.0]),\n  ('regression: reference area', (80, 2.0, 2.0, 40, 40, 10, 10), [21.5153, 0.5379, 0.7358, 2.0]),\n  ('control: invalid area', (80, 2.0, 2.0, 40, 40, 0, 10), None),\n  ('control: negative distance', (80, 2.0, 2.0, -5, 40, 10, 10), None),\n  ('regression: archipelago mid', (150, 4.0, 3.0, 60, 30, 25, 5), [71.1454, 0.2846, 0.5413, 0.6])]]\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":"defda69167dcc6e358bf589eb244620fcd4caf09a5ce8c316df1cfbc52e5c4f5","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(pool, imax, emax, distance, d0, area, a0):\n    if min(pool, imax, emax, d0, a0, area) <= 0 or distance < 0:\n        return None\n    i0 = imax * math.exp(-distance / d0)\n    e0 = emax * a0 / area\n    s_eq = i0 * pool / e0\n    turnover = i0 * e0 / (i0 + e0)\n    return [round(s_eq, 4), round(turnover, 4), round(i0, 4), round(e0, 4)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('regression: near large island', (200, 5.0, 2.0, 10, 50, 100, 10), [190.6839, 0.1907, 4.0937, 0.2]),\n  ('regression: remote small island', (200, 5.0, 2.0, 300, 50, 2, 10), [0.2476, 0.0124, 0.0124, 10.0]),\n  ('regression: mainland adjacent', (120, 3.0, 1.0, 0, 40, 10, 10), [90.0, 0.75, 3.0, 1.0]),\n  ('regression: reference area', (80, 2.0, 2.0, 40, 40, 10, 10), [21.5153, 0.5379, 0.7358, 2.0]),\n  ('control: invalid area', (80, 2.0, 2.0, 40, 40, 0, 10), None),\n  ('control: negative distance', (80, 2.0, 2.0, -5, 40, 10, 10), None),\n  ('regression: archipelago mid', (150, 4.0, 3.0, 60, 30, 25, 5), [71.1454, 0.2846, 0.5413, 0.6])],\n [('regression: near large island', (200, 5.0, 2.0, 10, 50, 100, 10), [190.6839, 0.1907, 4.0937, 0.2]),\n  ('regression: remote small island', (200, 5.0, 2.0, 300, 50, 2, 10), [0.2476, 0.0124, 0.0124, 10.0]),\n  ('regression: mainland adjacent', (120, 3.0, 1.0, 0, 40, 10, 10), [90.0, 0.75, 3.0, 1.0]),\n  ('regression: reference area', (80, 2.0, 2.0, 40, 40, 10, 10), [21.5153, 0.5379, 0.7358, 2.0]),\n  ('control: invalid area', (80, 2.0, 2.0, 40, 40, 0, 10), None),\n  ('control: negative distance', (80, 2.0, 2.0, -5, 40, 10, 10), None),\n  ('regression: archipelago mid', (150, 4.0, 3.0, 60, 30, 25, 5), [71.1454, 0.2846, 0.5413, 0.6])],\n [('regression: near large island', (200, 5.0, 2.0, 10, 50, 100, 10), [190.6839, 0.1907, 4.0937, 0.2]),\n  ('regression: remote small island', (200, 5.0, 2.0, 300, 50, 2, 10), [0.2476, 0.0124, 0.0124, 10.0]),\n  ('regression: mainland adjacent', (120, 3.0, 1.0, 0, 40, 10, 10), [90.0, 0.75, 3.0, 1.0]),\n  ('regression: reference area', (80, 2.0, 2.0, 40, 40, 10, 10), [21.5153, 0.5379, 0.7358, 2.0]),\n  ('control: invalid area', (80, 2.0, 2.0, 40, 40, 0, 10), None),\n  ('control: negative distance', (80, 2.0, 2.0, -5, 40, 10, 10), None),\n  ('regression: archipelago mid', (150, 4.0, 3.0, 60, 30, 25, 5), [71.1454, 0.2846, 0.5413, 0.6])],\n [('regression: near large island', (200, 5.0, 2.0, 10, 50, 100, 10), [190.6839, 0.1907, 4.0937, 0.2]),\n  ('regression: remote small island', (200, 5.0, 2.0, 300, 50, 2, 10), [0.2476, 0.0124, 0.0124, 10.0]),\n  ('regression: mainland adjacent', (120, 3.0, 1.0, 0, 40, 10, 10), [90.0, 0.75, 3.0, 1.0]),\n  ('regression: reference area', (80, 2.0, 2.0, 40, 40, 10, 10), [21.5153, 0.5379, 0.7358, 2.0]),\n  ('control: invalid area', (80, 2.0, 2.0, 40, 40, 0, 10), None),\n  ('control: negative distance', (80, 2.0, 2.0, -5, 40, 10, 10), None),\n  ('regression: archipelago mid', (150, 4.0, 3.0, 60, 30, 25, 5), [71.1454, 0.2846, 0.5413, 0.6])],\n [('regression: near large island', (200, 5.0, 2.0, 10, 50, 100, 10), [190.6839, 0.1907, 4.0937, 0.2]),\n  ('regression: remote small island', (200, 5.0, 2.0, 300, 50, 2, 10), [0.2476, 0.0124, 0.0124, 10.0]),\n  ('regression: mainland adjacent', (120, 3.0, 1.0, 0, 40, 10, 10), [90.0, 0.75, 3.0, 1.0]),\n  ('regression: reference area', (80, 2.0, 2.0, 40, 40, 10, 10), [21.5153, 0.5379, 0.7358, 2.0]),\n  ('control: invalid area', (80, 2.0, 2.0, 40, 40, 0, 10), None),\n  ('control: negative distance', (80, 2.0, 2.0, -5, 40, 10, 10), None),\n  ('regression: archipelago mid', (150, 4.0, 3.0, 60, 30, 25, 5), [71.1454, 0.2846, 0.5413, 0.6])]]\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-island-biogeography-equilibrium-richness","generated_at":"2026-09-29T14:47:37.102668+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.","root_cause":"The equilibrium omits I0 from the denominator.","sha256":"cc543bfc7818bb5199197044a61c22c3d69401d5514026218d11994670060c7f","title":"MacArthur-Wilson island equilibrium: equilibrium richness · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verified":true,"visibility":"public","verification":{"attempt":{"elapsed_ms":39.722,"exit_code":1,"observations":[{"actual":[9.3161,0.1907,4.0937,0.2],"check":"regression: near large island","expected":[190.6839,0.1907,4.0937,0.2],"passed":false},{"actual":[199.7524,0.0124,0.0124,10.0],"check":"regression: remote small island","expected":[0.2476,0.0124,0.0124,10.0],"passed":false},{"actual":[30.0,0.75,3.0,1.0],"check":"regression: mainland adjacent","expected":[90.0,0.75,3.0,1.0],"passed":false},{"actual":[58.4847,0.5379,0.7358,2.0],"check":"regression: reference area","expected":[21.5153,0.5379,0.7358,2.0],"passed":false},{"actual":null,"check":"control: invalid area","expected":null,"passed":true},{"actual":null,"check":"control: negative distance","expected":null,"passed":true},{"actual":[78.8546,0.2846,0.5413,0.6],"check":"regression: archipelago mid","expected":[71.1454,0.2846,0.5413,0.6],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: near large island\", \"actual\": [9.3161, 0.1907, 4.0937, 0.2], \"expected\": [190.6839, 0.1907, 4.0937, 0.2], \"passed\": false}, {\"check\": \"regression: remote small island\", \"actual\": [199.7524, 0.0124, 0.0124, 10.0], \"expected\": [0.2476, 0.0124, 0.0124, 10.0], \"passed\": false}, {\"check\": \"regression: mainland adjacent\", \"actual\": [30.0, 0.75, 3.0, 1.0], \"expected\": [90.0, 0.75, 3.0, 1.0], \"passed\": false}, {\"check\": \"regression: reference area\", \"actual\": [58.4847, 0.5379, 0.7358, 2.0], \"expected\": [21.5153, 0.5379, 0.7358, 2.0], \"passed\": false}, {\"check\": \"control: invalid area\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"control: negative distance\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"regression: archipelago mid\", \"actual\": [78.8546, 0.2846, 0.5413, 0.6], \"expected\": [71.1454, 0.2846, 0.5413, 0.6], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":38.758,"exit_code":1,"observations":[{"actual":[4093.6538,0.1907,4.0937,0.2],"check":"regression: near large island","expected":[190.6839,0.1907,4.0937,0.2],"passed":false},{"actual":[0.2479,0.0124,0.0124,10.0],"check":"regression: remote small island","expected":[0.2476,0.0124,0.0124,10.0],"passed":false},{"actual":[360.0,0.75,3.0,1.0],"check":"regression: mainland adjacent","expected":[90.0,0.75,3.0,1.0],"passed":false},{"actual":[29.4304,0.5379,0.7358,2.0],"check":"regression: reference area","expected":[21.5153,0.5379,0.7358,2.0],"passed":false},{"actual":null,"check":"control: invalid area","expected":null,"passed":true},{"actual":null,"check":"control: negative distance","expected":null,"passed":true},{"actual":[135.3353,0.2846,0.5413,0.6],"check":"regression: archipelago mid","expected":[71.1454,0.2846,0.5413,0.6],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: near large island\", \"actual\": [4093.6538, 0.1907, 4.0937, 0.2], \"expected\": [190.6839, 0.1907, 4.0937, 0.2], \"passed\": false}, {\"check\": \"regression: remote small island\", \"actual\": [0.2479, 0.0124, 0.0124, 10.0], \"expected\": [0.2476, 0.0124, 0.0124, 10.0], \"passed\": false}, {\"check\": \"regression: mainland adjacent\", \"actual\": [360.0, 0.75, 3.0, 1.0], \"expected\": [90.0, 0.75, 3.0, 1.0], \"passed\": false}, {\"check\": \"regression: reference area\", \"actual\": [29.4304, 0.5379, 0.7358, 2.0], \"expected\": [21.5153, 0.5379, 0.7358, 2.0], \"passed\": false}, {\"check\": \"control: invalid area\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"control: negative distance\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"regression: archipelago mid\", \"actual\": [135.3353, 0.2846, 0.5413, 0.6], \"expected\": [71.1454, 0.2846, 0.5413, 0.6], \"passed\": false}], \"passed\": false}\n"}},"member_only":{"stages":["fixed"],"fields":["implementations.fixed","verification.fixed","harness","repair"],"note":"The verified repair, its recorded checks, the repair description, and the scoring harness are available to members."}}