FAILURE MAP
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FA-65586 / Ecological population dynamics / Open access

Levins metapopulation with habitat destruction: extinction ratio · case 01

Equilibrium occupancy falls as colonisation improves.

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

ROOT CAUSE

The extinction-to-colonisation ratio is inverted.

THE FAILURE

The extinction-to-colonisation ratio is inverted.

Unsuccessful approach: Multiplying the rates has the wrong dimension.

Case contract

Occupancy p: p += c*p*(1-D-p) - e*p each year, clamped to [0, 1-D]; equilibrium max(0, 1-D-e/c); return [equilibrium rounded 6, trajectory rounded 6]; None for c<=0, e<0 or D outside [0,1).

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(c, e, destroyed, p0, years):
    if c <= 0 or e < 0 or not 0 <= destroyed < 1:
        return None
    eq = max(0.0, 1 - destroyed - c / e)
    p = p0
    traj = []
    for _ in range(years):
        p = p + c * p * (1 - destroyed - p) - e * p
        p = min(max(p, 0.0), 1 - destroyed)
        traj.append(round(p, 6))
    return [round(eq, 6), traj]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: butterfly network',
   (0.5, 0.1, 0.2, 0.1, 6),
   [0.6, [0.125, 0.154687, 0.18913, 0.227984, 0.27039, 0.314952]]),
  ('regression: intact habitat',
   (0.4, 0.1, 0.0, 0.05, 5),
   [0.75, [0.064, 0.081562, 0.103369, 0.130106, 0.162367]]),
  ('regression: heavy destruction extinction',
   (0.3, 0.2, 0.5, 0.3, 6),
   [0.0, [0.258, 0.225131, 0.198669, 0.176895, 0.158663, 0.143177]]),
  ('regression: overshoot clamp', (2.5, 0.05, 0.3, 0.6, 3), [0.68, [0.7, 0.665, 0.689937]]),
  ('control: invalid destruction', (0.5, 0.1, 1.0, 0.1, 3), None),
  ('regression: empty network', (0.5, 0.1, 0.2, 0.0, 3), [0.6, [0.0, 0.0, 0.0]]),
  ('regression: high turnover',
   (1.2, 0.8, 0.25, 0.4, 5),
   [0.083333, [0.248, 0.198995, 0.171376, 0.15327, 0.140407]])],
 [('regression: butterfly network',
   (0.5, 0.1, 0.2, 0.1, 6),
   [0.6, [0.125, 0.154687, 0.18913, 0.227984, 0.27039, 0.314952]]),
  ('regression: intact habitat',
   (0.4, 0.1, 0.0, 0.05, 5),
   [0.75, [0.064, 0.081562, 0.103369, 0.130106, 0.162367]]),
  ('regression: heavy destruction extinction',
   (0.3, 0.2, 0.5, 0.3, 6),
   [0.0, [0.258, 0.225131, 0.198669, 0.176895, 0.158663, 0.143177]]),
  ('regression: overshoot clamp', (2.5, 0.05, 0.3, 0.6, 3), [0.68, [0.7, 0.665, 0.689937]]),
  ('control: invalid destruction', (0.5, 0.1, 1.0, 0.1, 3), None),
  ('regression: empty network', (0.5, 0.1, 0.2, 0.0, 3), [0.6, [0.0, 0.0, 0.0]]),
  ('regression: high turnover',
   (1.2, 0.8, 0.25, 0.4, 5),
   [0.083333, [0.248, 0.198995, 0.171376, 0.15327, 0.140407]])],
 [('regression: butterfly network',
   (0.5, 0.1, 0.2, 0.1, 6),
   [0.6, [0.125, 0.154687, 0.18913, 0.227984, 0.27039, 0.314952]]),
  ('regression: intact habitat',
   (0.4, 0.1, 0.0, 0.05, 5),
   [0.75, [0.064, 0.081562, 0.103369, 0.130106, 0.162367]]),
  ('regression: heavy destruction extinction',
   (0.3, 0.2, 0.5, 0.3, 6),
   [0.0, [0.258, 0.225131, 0.198669, 0.176895, 0.158663, 0.143177]]),
  ('regression: overshoot clamp', (2.5, 0.05, 0.3, 0.6, 3), [0.68, [0.7, 0.665, 0.689937]]),
  ('control: invalid destruction', (0.5, 0.1, 1.0, 0.1, 3), None),
  ('regression: empty network', (0.5, 0.1, 0.2, 0.0, 3), [0.6, [0.0, 0.0, 0.0]]),
  ('regression: high turnover',
   (1.2, 0.8, 0.25, 0.4, 5),
   [0.083333, [0.248, 0.198995, 0.171376, 0.15327, 0.140407]])],
 [('regression: butterfly network',
   (0.5, 0.1, 0.2, 0.1, 6),
   [0.6, [0.125, 0.154687, 0.18913, 0.227984, 0.27039, 0.314952]]),
  ('regression: intact habitat',
   (0.4, 0.1, 0.0, 0.05, 5),
   [0.75, [0.064, 0.081562, 0.103369, 0.130106, 0.162367]]),
  ('regression: heavy destruction extinction',
   (0.3, 0.2, 0.5, 0.3, 6),
   [0.0, [0.258, 0.225131, 0.198669, 0.176895, 0.158663, 0.143177]]),
  ('regression: overshoot clamp', (2.5, 0.05, 0.3, 0.6, 3), [0.68, [0.7, 0.665, 0.689937]]),
  ('control: invalid destruction', (0.5, 0.1, 1.0, 0.1, 3), None),
  ('regression: empty network', (0.5, 0.1, 0.2, 0.0, 3), [0.6, [0.0, 0.0, 0.0]]),
  ('regression: high turnover',
   (1.2, 0.8, 0.25, 0.4, 5),
   [0.083333, [0.248, 0.198995, 0.171376, 0.15327, 0.140407]])],
 [('regression: butterfly network',
   (0.5, 0.1, 0.2, 0.1, 6),
   [0.6, [0.125, 0.154687, 0.18913, 0.227984, 0.27039, 0.314952]]),
  ('regression: intact habitat',
   (0.4, 0.1, 0.0, 0.05, 5),
   [0.75, [0.064, 0.081562, 0.103369, 0.130106, 0.162367]]),
  ('regression: heavy destruction extinction',
   (0.3, 0.2, 0.5, 0.3, 6),
   [0.0, [0.258, 0.225131, 0.198669, 0.176895, 0.158663, 0.143177]]),
  ('regression: overshoot clamp', (2.5, 0.05, 0.3, 0.6, 3), [0.68, [0.7, 0.665, 0.689937]]),
  ('control: invalid destruction', (0.5, 0.1, 1.0, 0.1, 3), None),
  ('regression: empty network', (0.5, 0.1, 0.2, 0.0, 3), [0.6, [0.0, 0.0, 0.0]]),
  ('regression: high turnover',
   (1.2, 0.8, 0.25, 0.4, 5),
   [0.083333, [0.248, 0.198995, 0.171376, 0.15327, 0.140407]])]]
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: butterfly network[0.0, [0.125, 0.154687, 0.18913, 0.227984, 0.27039, 0.314952]][0.6, [0.125, 0.154687, 0.18913, 0.227984, 0.27039, 0.314952]]Failed
regression: intact habitat[0.0, [0.064, 0.081562, 0.103369, 0.130106, 0.162367]][0.75, [0.064, 0.081562, 0.103369, 0.130106, 0.162367]]Failed
regression: heavy destruction extinction[0.0, [0.258, 0.225131, 0.198669, 0.176895, 0.158663, 0.143177]][0.0, [0.258, 0.225131, 0.198669, 0.176895, 0.158663, 0.143177]]Passed
regression: overshoot clamp[0.0, [0.7, 0.665, 0.689937]][0.68, [0.7, 0.665, 0.689937]]Failed
control: invalid destructionNoneNonePassed
regression: empty network[0.0, [0.0, 0.0, 0.0]][0.6, [0.0, 0.0, 0.0]]Failed
regression: high turnover[0.0, [0.248, 0.198995, 0.171376, 0.15327, 0.140407]][0.083333, [0.248, 0.198995, 0.171376, 0.15327, 0.140407]]Failed

SHA-256 / 286a00addb2fdeffc03b878de1a3074c03a9345778c8075fcd3bd03da517434f

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(c, e, destroyed, p0, years):
    if c <= 0 or e < 0 or not 0 <= destroyed < 1:
        return None
    eq = max(0.0, 1 - destroyed - e * c)
    p = p0
    traj = []
    for _ in range(years):
        p = p + c * p * (1 - destroyed - p) - e * p
        p = min(max(p, 0.0), 1 - destroyed)
        traj.append(round(p, 6))
    return [round(eq, 6), traj]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: butterfly network',
   (0.5, 0.1, 0.2, 0.1, 6),
   [0.6, [0.125, 0.154687, 0.18913, 0.227984, 0.27039, 0.314952]]),
  ('regression: intact habitat',
   (0.4, 0.1, 0.0, 0.05, 5),
   [0.75, [0.064, 0.081562, 0.103369, 0.130106, 0.162367]]),
  ('regression: heavy destruction extinction',
   (0.3, 0.2, 0.5, 0.3, 6),
   [0.0, [0.258, 0.225131, 0.198669, 0.176895, 0.158663, 0.143177]]),
  ('regression: overshoot clamp', (2.5, 0.05, 0.3, 0.6, 3), [0.68, [0.7, 0.665, 0.689937]]),
  ('control: invalid destruction', (0.5, 0.1, 1.0, 0.1, 3), None),
  ('regression: empty network', (0.5, 0.1, 0.2, 0.0, 3), [0.6, [0.0, 0.0, 0.0]]),
  ('regression: high turnover',
   (1.2, 0.8, 0.25, 0.4, 5),
   [0.083333, [0.248, 0.198995, 0.171376, 0.15327, 0.140407]])],
 [('regression: butterfly network',
   (0.5, 0.1, 0.2, 0.1, 6),
   [0.6, [0.125, 0.154687, 0.18913, 0.227984, 0.27039, 0.314952]]),
  ('regression: intact habitat',
   (0.4, 0.1, 0.0, 0.05, 5),
   [0.75, [0.064, 0.081562, 0.103369, 0.130106, 0.162367]]),
  ('regression: heavy destruction extinction',
   (0.3, 0.2, 0.5, 0.3, 6),
   [0.0, [0.258, 0.225131, 0.198669, 0.176895, 0.158663, 0.143177]]),
  ('regression: overshoot clamp', (2.5, 0.05, 0.3, 0.6, 3), [0.68, [0.7, 0.665, 0.689937]]),
  ('control: invalid destruction', (0.5, 0.1, 1.0, 0.1, 3), None),
  ('regression: empty network', (0.5, 0.1, 0.2, 0.0, 3), [0.6, [0.0, 0.0, 0.0]]),
  ('regression: high turnover',
   (1.2, 0.8, 0.25, 0.4, 5),
   [0.083333, [0.248, 0.198995, 0.171376, 0.15327, 0.140407]])],
 [('regression: butterfly network',
   (0.5, 0.1, 0.2, 0.1, 6),
   [0.6, [0.125, 0.154687, 0.18913, 0.227984, 0.27039, 0.314952]]),
  ('regression: intact habitat',
   (0.4, 0.1, 0.0, 0.05, 5),
   [0.75, [0.064, 0.081562, 0.103369, 0.130106, 0.162367]]),
  ('regression: heavy destruction extinction',
   (0.3, 0.2, 0.5, 0.3, 6),
   [0.0, [0.258, 0.225131, 0.198669, 0.176895, 0.158663, 0.143177]]),
  ('regression: overshoot clamp', (2.5, 0.05, 0.3, 0.6, 3), [0.68, [0.7, 0.665, 0.689937]]),
  ('control: invalid destruction', (0.5, 0.1, 1.0, 0.1, 3), None),
  ('regression: empty network', (0.5, 0.1, 0.2, 0.0, 3), [0.6, [0.0, 0.0, 0.0]]),
  ('regression: high turnover',
   (1.2, 0.8, 0.25, 0.4, 5),
   [0.083333, [0.248, 0.198995, 0.171376, 0.15327, 0.140407]])],
 [('regression: butterfly network',
   (0.5, 0.1, 0.2, 0.1, 6),
   [0.6, [0.125, 0.154687, 0.18913, 0.227984, 0.27039, 0.314952]]),
  ('regression: intact habitat',
   (0.4, 0.1, 0.0, 0.05, 5),
   [0.75, [0.064, 0.081562, 0.103369, 0.130106, 0.162367]]),
  ('regression: heavy destruction extinction',
   (0.3, 0.2, 0.5, 0.3, 6),
   [0.0, [0.258, 0.225131, 0.198669, 0.176895, 0.158663, 0.143177]]),
  ('regression: overshoot clamp', (2.5, 0.05, 0.3, 0.6, 3), [0.68, [0.7, 0.665, 0.689937]]),
  ('control: invalid destruction', (0.5, 0.1, 1.0, 0.1, 3), None),
  ('regression: empty network', (0.5, 0.1, 0.2, 0.0, 3), [0.6, [0.0, 0.0, 0.0]]),
  ('regression: high turnover',
   (1.2, 0.8, 0.25, 0.4, 5),
   [0.083333, [0.248, 0.198995, 0.171376, 0.15327, 0.140407]])],
 [('regression: butterfly network',
   (0.5, 0.1, 0.2, 0.1, 6),
   [0.6, [0.125, 0.154687, 0.18913, 0.227984, 0.27039, 0.314952]]),
  ('regression: intact habitat',
   (0.4, 0.1, 0.0, 0.05, 5),
   [0.75, [0.064, 0.081562, 0.103369, 0.130106, 0.162367]]),
  ('regression: heavy destruction extinction',
   (0.3, 0.2, 0.5, 0.3, 6),
   [0.0, [0.258, 0.225131, 0.198669, 0.176895, 0.158663, 0.143177]]),
  ('regression: overshoot clamp', (2.5, 0.05, 0.3, 0.6, 3), [0.68, [0.7, 0.665, 0.689937]]),
  ('control: invalid destruction', (0.5, 0.1, 1.0, 0.1, 3), None),
  ('regression: empty network', (0.5, 0.1, 0.2, 0.0, 3), [0.6, [0.0, 0.0, 0.0]]),
  ('regression: high turnover',
   (1.2, 0.8, 0.25, 0.4, 5),
   [0.083333, [0.248, 0.198995, 0.171376, 0.15327, 0.140407]])]]
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: butterfly network[0.75, [0.125, 0.154687, 0.18913, 0.227984, 0.27039, 0.314952]][0.6, [0.125, 0.154687, 0.18913, 0.227984, 0.27039, 0.314952]]Failed
regression: intact habitat[0.96, [0.064, 0.081562, 0.103369, 0.130106, 0.162367]][0.75, [0.064, 0.081562, 0.103369, 0.130106, 0.162367]]Failed
regression: heavy destruction extinction[0.44, [0.258, 0.225131, 0.198669, 0.176895, 0.158663, 0.143177]][0.0, [0.258, 0.225131, 0.198669, 0.176895, 0.158663, 0.143177]]Failed
regression: overshoot clamp[0.575, [0.7, 0.665, 0.689937]][0.68, [0.7, 0.665, 0.689937]]Failed
control: invalid destructionNoneNonePassed
regression: empty network[0.75, [0.0, 0.0, 0.0]][0.6, [0.0, 0.0, 0.0]]Failed
regression: high turnover[0.0, [0.248, 0.198995, 0.171376, 0.15327, 0.140407]][0.083333, [0.248, 0.198995, 0.171376, 0.15327, 0.140407]]Failed

SHA-256 / 283c2861b0c5d5ec246d9339294055571a0d279a034a6bd9e036374141efdd0b

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.

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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 2026-09-29T14:47:35.337185+00:00.

Case digest / 86a6aac6327174b2767a01352f5d63609ce8566eace411699794dd2ae47661fe