FAILURE MAP
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FA-65756 / Ecological population dynamics / Open access

MacArthur-Wilson island equilibrium: area effect on extinction · case 01

Large islands lose species faster than small ones.

Verified by executionVariant 1 · 7 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The area ratio is inverted.

THE FAILURE

The area ratio is inverted.

Unsuccessful approach: Dropping the reference area makes extinction depend on the area unit.

Case 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.

Why this case matters

Population projections set harvest quotas, conservation status and pest-control timing; a wrong update order, boundary or rate conversion silently changes management advice.

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(pool, imax, emax, distance, d0, area, a0):
    if min(pool, imax, emax, d0, a0, area) <= 0 or distance < 0:
        return None
    i0 = imax * math.exp(-distance / d0)
    e0 = emax * area / a0
    s_eq = i0 * pool / (i0 + e0)
    turnover = i0 * e0 / (i0 + e0)
    return [round(s_eq, 4), round(turnover, 4), round(i0, 4), round(e0, 4)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: near large island', (200, 5.0, 2.0, 10, 50, 100, 10), [190.6839, 0.1907, 4.0937, 0.2]),
  ('regression: remote small island', (200, 5.0, 2.0, 300, 50, 2, 10), [0.2476, 0.0124, 0.0124, 10.0]),
  ('regression: mainland adjacent', (120, 3.0, 1.0, 0, 40, 10, 10), [90.0, 0.75, 3.0, 1.0]),
  ('regression: reference area', (80, 2.0, 2.0, 40, 40, 10, 10), [21.5153, 0.5379, 0.7358, 2.0]),
  ('control: invalid area', (80, 2.0, 2.0, 40, 40, 0, 10), None),
  ('control: negative distance', (80, 2.0, 2.0, -5, 40, 10, 10), None),
  ('regression: archipelago mid', (150, 4.0, 3.0, 60, 30, 25, 5), [71.1454, 0.2846, 0.5413, 0.6])],
 [('regression: near large island', (200, 5.0, 2.0, 10, 50, 100, 10), [190.6839, 0.1907, 4.0937, 0.2]),
  ('regression: remote small island', (200, 5.0, 2.0, 300, 50, 2, 10), [0.2476, 0.0124, 0.0124, 10.0]),
  ('regression: mainland adjacent', (120, 3.0, 1.0, 0, 40, 10, 10), [90.0, 0.75, 3.0, 1.0]),
  ('regression: reference area', (80, 2.0, 2.0, 40, 40, 10, 10), [21.5153, 0.5379, 0.7358, 2.0]),
  ('control: invalid area', (80, 2.0, 2.0, 40, 40, 0, 10), None),
  ('control: negative distance', (80, 2.0, 2.0, -5, 40, 10, 10), None),
  ('regression: archipelago mid', (150, 4.0, 3.0, 60, 30, 25, 5), [71.1454, 0.2846, 0.5413, 0.6])],
 [('regression: near large island', (200, 5.0, 2.0, 10, 50, 100, 10), [190.6839, 0.1907, 4.0937, 0.2]),
  ('regression: remote small island', (200, 5.0, 2.0, 300, 50, 2, 10), [0.2476, 0.0124, 0.0124, 10.0]),
  ('regression: mainland adjacent', (120, 3.0, 1.0, 0, 40, 10, 10), [90.0, 0.75, 3.0, 1.0]),
  ('regression: reference area', (80, 2.0, 2.0, 40, 40, 10, 10), [21.5153, 0.5379, 0.7358, 2.0]),
  ('control: invalid area', (80, 2.0, 2.0, 40, 40, 0, 10), None),
  ('control: negative distance', (80, 2.0, 2.0, -5, 40, 10, 10), None),
  ('regression: archipelago mid', (150, 4.0, 3.0, 60, 30, 25, 5), [71.1454, 0.2846, 0.5413, 0.6])],
 [('regression: near large island', (200, 5.0, 2.0, 10, 50, 100, 10), [190.6839, 0.1907, 4.0937, 0.2]),
  ('regression: remote small island', (200, 5.0, 2.0, 300, 50, 2, 10), [0.2476, 0.0124, 0.0124, 10.0]),
  ('regression: mainland adjacent', (120, 3.0, 1.0, 0, 40, 10, 10), [90.0, 0.75, 3.0, 1.0]),
  ('regression: reference area', (80, 2.0, 2.0, 40, 40, 10, 10), [21.5153, 0.5379, 0.7358, 2.0]),
  ('control: invalid area', (80, 2.0, 2.0, 40, 40, 0, 10), None),
  ('control: negative distance', (80, 2.0, 2.0, -5, 40, 10, 10), None),
  ('regression: archipelago mid', (150, 4.0, 3.0, 60, 30, 25, 5), [71.1454, 0.2846, 0.5413, 0.6])],
 [('regression: near large island', (200, 5.0, 2.0, 10, 50, 100, 10), [190.6839, 0.1907, 4.0937, 0.2]),
  ('regression: remote small island', (200, 5.0, 2.0, 300, 50, 2, 10), [0.2476, 0.0124, 0.0124, 10.0]),
  ('regression: mainland adjacent', (120, 3.0, 1.0, 0, 40, 10, 10), [90.0, 0.75, 3.0, 1.0]),
  ('regression: reference area', (80, 2.0, 2.0, 40, 40, 10, 10), [21.5153, 0.5379, 0.7358, 2.0]),
  ('control: invalid area', (80, 2.0, 2.0, 40, 40, 0, 10), None),
  ('control: negative distance', (80, 2.0, 2.0, -5, 40, 10, 10), None),
  ('regression: archipelago mid', (150, 4.0, 3.0, 60, 30, 25, 5), [71.1454, 0.2846, 0.5413, 0.6])]]
for label, args, expected in fixtures[N - 1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
regression: near large island[33.9812, 3.3981, 4.0937, 20.0][190.6839, 0.1907, 4.0937, 0.2]Failed
regression: remote small island[6.0106, 0.012, 0.0124, 0.4][0.2476, 0.0124, 0.0124, 10.0]Failed
regression: mainland adjacent[90.0, 0.75, 3.0, 1.0][90.0, 0.75, 3.0, 1.0]Passed
regression: reference area[21.5153, 0.5379, 0.7358, 2.0][21.5153, 0.5379, 0.7358, 2.0]Passed
control: invalid areaNoneNonePassed
control: negative distanceNoneNonePassed
regression: archipelago mid[5.2248, 0.5225, 0.5413, 15.0][71.1454, 0.2846, 0.5413, 0.6]Failed

SHA-256 / 2a4e8894ad415f65b736ed711f744a4a9de87a64a5e53f321ad696d7a313af55

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(pool, imax, emax, distance, d0, area, a0):
    if min(pool, imax, emax, d0, a0, area) <= 0 or distance < 0:
        return None
    i0 = imax * math.exp(-distance / d0)
    e0 = emax / area
    s_eq = i0 * pool / (i0 + e0)
    turnover = i0 * e0 / (i0 + e0)
    return [round(s_eq, 4), round(turnover, 4), round(i0, 4), round(e0, 4)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: near large island', (200, 5.0, 2.0, 10, 50, 100, 10), [190.6839, 0.1907, 4.0937, 0.2]),
  ('regression: remote small island', (200, 5.0, 2.0, 300, 50, 2, 10), [0.2476, 0.0124, 0.0124, 10.0]),
  ('regression: mainland adjacent', (120, 3.0, 1.0, 0, 40, 10, 10), [90.0, 0.75, 3.0, 1.0]),
  ('regression: reference area', (80, 2.0, 2.0, 40, 40, 10, 10), [21.5153, 0.5379, 0.7358, 2.0]),
  ('control: invalid area', (80, 2.0, 2.0, 40, 40, 0, 10), None),
  ('control: negative distance', (80, 2.0, 2.0, -5, 40, 10, 10), None),
  ('regression: archipelago mid', (150, 4.0, 3.0, 60, 30, 25, 5), [71.1454, 0.2846, 0.5413, 0.6])],
 [('regression: near large island', (200, 5.0, 2.0, 10, 50, 100, 10), [190.6839, 0.1907, 4.0937, 0.2]),
  ('regression: remote small island', (200, 5.0, 2.0, 300, 50, 2, 10), [0.2476, 0.0124, 0.0124, 10.0]),
  ('regression: mainland adjacent', (120, 3.0, 1.0, 0, 40, 10, 10), [90.0, 0.75, 3.0, 1.0]),
  ('regression: reference area', (80, 2.0, 2.0, 40, 40, 10, 10), [21.5153, 0.5379, 0.7358, 2.0]),
  ('control: invalid area', (80, 2.0, 2.0, 40, 40, 0, 10), None),
  ('control: negative distance', (80, 2.0, 2.0, -5, 40, 10, 10), None),
  ('regression: archipelago mid', (150, 4.0, 3.0, 60, 30, 25, 5), [71.1454, 0.2846, 0.5413, 0.6])],
 [('regression: near large island', (200, 5.0, 2.0, 10, 50, 100, 10), [190.6839, 0.1907, 4.0937, 0.2]),
  ('regression: remote small island', (200, 5.0, 2.0, 300, 50, 2, 10), [0.2476, 0.0124, 0.0124, 10.0]),
  ('regression: mainland adjacent', (120, 3.0, 1.0, 0, 40, 10, 10), [90.0, 0.75, 3.0, 1.0]),
  ('regression: reference area', (80, 2.0, 2.0, 40, 40, 10, 10), [21.5153, 0.5379, 0.7358, 2.0]),
  ('control: invalid area', (80, 2.0, 2.0, 40, 40, 0, 10), None),
  ('control: negative distance', (80, 2.0, 2.0, -5, 40, 10, 10), None),
  ('regression: archipelago mid', (150, 4.0, 3.0, 60, 30, 25, 5), [71.1454, 0.2846, 0.5413, 0.6])],
 [('regression: near large island', (200, 5.0, 2.0, 10, 50, 100, 10), [190.6839, 0.1907, 4.0937, 0.2]),
  ('regression: remote small island', (200, 5.0, 2.0, 300, 50, 2, 10), [0.2476, 0.0124, 0.0124, 10.0]),
  ('regression: mainland adjacent', (120, 3.0, 1.0, 0, 40, 10, 10), [90.0, 0.75, 3.0, 1.0]),
  ('regression: reference area', (80, 2.0, 2.0, 40, 40, 10, 10), [21.5153, 0.5379, 0.7358, 2.0]),
  ('control: invalid area', (80, 2.0, 2.0, 40, 40, 0, 10), None),
  ('control: negative distance', (80, 2.0, 2.0, -5, 40, 10, 10), None),
  ('regression: archipelago mid', (150, 4.0, 3.0, 60, 30, 25, 5), [71.1454, 0.2846, 0.5413, 0.6])],
 [('regression: near large island', (200, 5.0, 2.0, 10, 50, 100, 10), [190.6839, 0.1907, 4.0937, 0.2]),
  ('regression: remote small island', (200, 5.0, 2.0, 300, 50, 2, 10), [0.2476, 0.0124, 0.0124, 10.0]),
  ('regression: mainland adjacent', (120, 3.0, 1.0, 0, 40, 10, 10), [90.0, 0.75, 3.0, 1.0]),
  ('regression: reference area', (80, 2.0, 2.0, 40, 40, 10, 10), [21.5153, 0.5379, 0.7358, 2.0]),
  ('control: invalid area', (80, 2.0, 2.0, 40, 40, 0, 10), None),
  ('control: negative distance', (80, 2.0, 2.0, -5, 40, 10, 10), None),
  ('regression: archipelago mid', (150, 4.0, 3.0, 60, 30, 25, 5), [71.1454, 0.2846, 0.5413, 0.6])]]
for label, args, expected in fixtures[N - 1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
regression: near large island[199.0276, 0.0199, 4.0937, 0.02][190.6839, 0.1907, 4.0937, 0.2]Failed
regression: remote small island[2.4484, 0.0122, 0.0124, 1.0][0.2476, 0.0124, 0.0124, 10.0]Failed
regression: mainland adjacent[116.129, 0.0968, 3.0, 0.1][90.0, 0.75, 3.0, 1.0]Failed
regression: reference area[62.9016, 0.1573, 0.7358, 0.2][21.5153, 0.5379, 0.7358, 2.0]Failed
control: invalid areaNoneNonePassed
control: negative distanceNoneNonePassed
regression: archipelago mid[122.7826, 0.0982, 0.5413, 0.12][71.1454, 0.2846, 0.5413, 0.6]Failed

SHA-256 / a7449adbc334648835a5a2e8519c96c26f24269231a94b0b98ce102b428a241b

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 7 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

Member access is invitation-based. Sign in with your invited account to inspect the repair.

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Verification & scope

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.

Observations recorded using Python 3.12.14 at 2026-09-29T14:47:37.102668+00:00.

Case digest / 07e2d484bcc3a78161daad635693494b1d5dc4b79a06f34648a81f1d97a542b7