FAILURE MAP
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FA-65591 / Ecological population dynamics / Open access

Levins metapopulation with habitat destruction: occupancy ceiling · case 01

Occupancy exceeds the fraction of habitat that still exists.

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

ROOT CAUSE

Occupancy is capped at 1 rather than 1-D.

THE FAILURE

Occupancy is capped at 1 rather than 1-D.

Unsuccessful approach: Removing the ceiling allows occupancy above the available habitat.

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 - e / c)
    p = p0
    traj = []
    for _ in range(years):
        p = p + c * p * (1 - destroyed - p) - e * p
        p = min(max(p, 0.0), 1.0)
        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 = [[('control: 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]]),
  ('control: intact habitat',
   (0.4, 0.1, 0.0, 0.05, 5),
   [0.75, [0.064, 0.081562, 0.103369, 0.130106, 0.162367]]),
  ('control: 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: no extinction', (0.6, 0.0, 0.1, 0.2, 4), [0.9, [0.284, 0.388966, 0.508231, 0.627697]]),
  ('control: invalid destruction', (0.5, 0.1, 1.0, 0.1, 3), None),
  ('control: empty network', (0.5, 0.1, 0.2, 0.0, 3), [0.6, [0.0, 0.0, 0.0]])],
 [('control: 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]]),
  ('control: intact habitat',
   (0.4, 0.1, 0.0, 0.05, 5),
   [0.75, [0.064, 0.081562, 0.103369, 0.130106, 0.162367]]),
  ('regression: overshoot clamp', (2.5, 0.05, 0.3, 0.6, 3), [0.68, [0.7, 0.665, 0.689937]]),
  ('control: no extinction', (0.6, 0.0, 0.1, 0.2, 4), [0.9, [0.284, 0.388966, 0.508231, 0.627697]]),
  ('control: invalid destruction', (0.5, 0.1, 1.0, 0.1, 3), None),
  ('control: empty network', (0.5, 0.1, 0.2, 0.0, 3), [0.6, [0.0, 0.0, 0.0]]),
  ('control: high turnover',
   (1.2, 0.8, 0.25, 0.4, 5),
   [0.083333, [0.248, 0.198995, 0.171376, 0.15327, 0.140407]])],
 [('control: 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]]),
  ('control: intact habitat',
   (0.4, 0.1, 0.0, 0.05, 5),
   [0.75, [0.064, 0.081562, 0.103369, 0.130106, 0.162367]]),
  ('control: 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: no extinction', (0.6, 0.0, 0.1, 0.2, 4), [0.9, [0.284, 0.388966, 0.508231, 0.627697]]),
  ('control: empty network', (0.5, 0.1, 0.2, 0.0, 3), [0.6, [0.0, 0.0, 0.0]]),
  ('control: high turnover',
   (1.2, 0.8, 0.25, 0.4, 5),
   [0.083333, [0.248, 0.198995, 0.171376, 0.15327, 0.140407]])],
 [('control: intact habitat',
   (0.4, 0.1, 0.0, 0.05, 5),
   [0.75, [0.064, 0.081562, 0.103369, 0.130106, 0.162367]]),
  ('control: 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: no extinction', (0.6, 0.0, 0.1, 0.2, 4), [0.9, [0.284, 0.388966, 0.508231, 0.627697]]),
  ('control: invalid destruction', (0.5, 0.1, 1.0, 0.1, 3), None),
  ('control: empty network', (0.5, 0.1, 0.2, 0.0, 3), [0.6, [0.0, 0.0, 0.0]]),
  ('control: high turnover',
   (1.2, 0.8, 0.25, 0.4, 5),
   [0.083333, [0.248, 0.198995, 0.171376, 0.15327, 0.140407]])],
 [('control: 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]]),
  ('control: intact habitat',
   (0.4, 0.1, 0.0, 0.05, 5),
   [0.75, [0.064, 0.081562, 0.103369, 0.130106, 0.162367]]),
  ('regression: overshoot clamp', (2.5, 0.05, 0.3, 0.6, 3), [0.68, [0.7, 0.665, 0.689937]]),
  ('control: no extinction', (0.6, 0.0, 0.1, 0.2, 4), [0.9, [0.284, 0.388966, 0.508231, 0.627697]]),
  ('control: invalid destruction', (0.5, 0.1, 1.0, 0.1, 3), None),
  ('control: empty network', (0.5, 0.1, 0.2, 0.0, 3), [0.6, [0.0, 0.0, 0.0]]),
  ('control: 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
control: butterfly network[0.6, [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]]Passed
control: intact habitat[0.75, [0.064, 0.081562, 0.103369, 0.130106, 0.162367]][0.75, [0.064, 0.081562, 0.103369, 0.130106, 0.162367]]Passed
control: 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[0.68, [0.72, 0.648, 0.69984]][0.68, [0.7, 0.665, 0.689937]]Failed
control: no extinction[0.9, [0.284, 0.388966, 0.508231, 0.627697]][0.9, [0.284, 0.388966, 0.508231, 0.627697]]Passed
control: invalid destructionNoneNonePassed
control: empty network[0.6, [0.0, 0.0, 0.0]][0.6, [0.0, 0.0, 0.0]]Passed

SHA-256 / 12a9cd7b9d7aa4a4ec8354fc00c09847b8c960d4bcf658b6282947cb4d62f547

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 = max(p, 0.0)
        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 = [[('control: 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]]),
  ('control: intact habitat',
   (0.4, 0.1, 0.0, 0.05, 5),
   [0.75, [0.064, 0.081562, 0.103369, 0.130106, 0.162367]]),
  ('control: 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: no extinction', (0.6, 0.0, 0.1, 0.2, 4), [0.9, [0.284, 0.388966, 0.508231, 0.627697]]),
  ('control: invalid destruction', (0.5, 0.1, 1.0, 0.1, 3), None),
  ('control: empty network', (0.5, 0.1, 0.2, 0.0, 3), [0.6, [0.0, 0.0, 0.0]])],
 [('control: 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]]),
  ('control: intact habitat',
   (0.4, 0.1, 0.0, 0.05, 5),
   [0.75, [0.064, 0.081562, 0.103369, 0.130106, 0.162367]]),
  ('regression: overshoot clamp', (2.5, 0.05, 0.3, 0.6, 3), [0.68, [0.7, 0.665, 0.689937]]),
  ('control: no extinction', (0.6, 0.0, 0.1, 0.2, 4), [0.9, [0.284, 0.388966, 0.508231, 0.627697]]),
  ('control: invalid destruction', (0.5, 0.1, 1.0, 0.1, 3), None),
  ('control: empty network', (0.5, 0.1, 0.2, 0.0, 3), [0.6, [0.0, 0.0, 0.0]]),
  ('control: high turnover',
   (1.2, 0.8, 0.25, 0.4, 5),
   [0.083333, [0.248, 0.198995, 0.171376, 0.15327, 0.140407]])],
 [('control: 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]]),
  ('control: intact habitat',
   (0.4, 0.1, 0.0, 0.05, 5),
   [0.75, [0.064, 0.081562, 0.103369, 0.130106, 0.162367]]),
  ('control: 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: no extinction', (0.6, 0.0, 0.1, 0.2, 4), [0.9, [0.284, 0.388966, 0.508231, 0.627697]]),
  ('control: empty network', (0.5, 0.1, 0.2, 0.0, 3), [0.6, [0.0, 0.0, 0.0]]),
  ('control: high turnover',
   (1.2, 0.8, 0.25, 0.4, 5),
   [0.083333, [0.248, 0.198995, 0.171376, 0.15327, 0.140407]])],
 [('control: intact habitat',
   (0.4, 0.1, 0.0, 0.05, 5),
   [0.75, [0.064, 0.081562, 0.103369, 0.130106, 0.162367]]),
  ('control: 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: no extinction', (0.6, 0.0, 0.1, 0.2, 4), [0.9, [0.284, 0.388966, 0.508231, 0.627697]]),
  ('control: invalid destruction', (0.5, 0.1, 1.0, 0.1, 3), None),
  ('control: empty network', (0.5, 0.1, 0.2, 0.0, 3), [0.6, [0.0, 0.0, 0.0]]),
  ('control: high turnover',
   (1.2, 0.8, 0.25, 0.4, 5),
   [0.083333, [0.248, 0.198995, 0.171376, 0.15327, 0.140407]])],
 [('control: 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]]),
  ('control: intact habitat',
   (0.4, 0.1, 0.0, 0.05, 5),
   [0.75, [0.064, 0.081562, 0.103369, 0.130106, 0.162367]]),
  ('regression: overshoot clamp', (2.5, 0.05, 0.3, 0.6, 3), [0.68, [0.7, 0.665, 0.689937]]),
  ('control: no extinction', (0.6, 0.0, 0.1, 0.2, 4), [0.9, [0.284, 0.388966, 0.508231, 0.627697]]),
  ('control: invalid destruction', (0.5, 0.1, 1.0, 0.1, 3), None),
  ('control: empty network', (0.5, 0.1, 0.2, 0.0, 3), [0.6, [0.0, 0.0, 0.0]]),
  ('control: 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
control: butterfly network[0.6, [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]]Passed
control: intact habitat[0.75, [0.064, 0.081562, 0.103369, 0.130106, 0.162367]][0.75, [0.064, 0.081562, 0.103369, 0.130106, 0.162367]]Passed
control: 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[0.68, [0.72, 0.648, 0.69984]][0.68, [0.7, 0.665, 0.689937]]Failed
control: no extinction[0.9, [0.284, 0.388966, 0.508231, 0.627697]][0.9, [0.284, 0.388966, 0.508231, 0.627697]]Passed
control: invalid destructionNoneNonePassed
control: empty network[0.6, [0.0, 0.0, 0.0]][0.6, [0.0, 0.0, 0.0]]Passed

SHA-256 / 86e65deae779fb89745d68a24aa549d468e5519dd8cf37d62e0178b5efd22ed8

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 2026-09-29T14:47:35.336697+00:00.

Case digest / 8f73e0bb22544ef455c9cfdec0b5f5fcf4f954f60b14d719442096967f2c2c67