FA-65446 / Ecological population dynamics / Open access

Holling functional response consumption: prey depletion cap · case 01

More prey are eaten than exist.

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

ROOT CAUSE

Total consumption is not capped by the prey available.

THE FAILURE

Total consumption is not capped by the prey available.

Unsuccessful approach: Capping at prey per predator times predators is not the prey stock.

Case contract

Per-predator intake f: type 1 = a*N capped at 1/h (uncapped when h==0), type 2 = aN/(1+ahN), type 3 = aN^2/(1+ahN^2); eaten = min(f*predators*duration, N); return [f rounded 6, eaten rounded 4]; None for negative parameters or unknown kind.

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(kind, a, h, prey, predators, duration):
    if a < 0 or h < 0 or prey < 0:
        return None
    if kind == 1:
        f = a * prey if h == 0 else min(a * prey, 1 / h)
    elif kind == 2:
        f = a * prey / (1 + a * h * prey)
    elif kind == 3:
        f = a * prey ** 2 / (1 + a * h * prey ** 2)
    else:
        return None
    eaten = f * predators * duration
    return [round(f, 6), round(eaten, 4)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('control: type 1 saturated filter feeder', (1, 0.5, 0.25, 20, 2, 1), [4.0, 8.0]),
  ('control: type 1 unsaturated', (1, 0.1, 0.5, 10, 1, 2), [1.0, 2.0]),
  ('control: type 1 no handling', (1, 0.3, 0.0, 40, 1, 1), [12.0, 12.0]),
  ('control: type 2 wolves on moose', (2, 0.8, 0.5, 30, 3, 2), [1.846154, 11.0769]),
  ('control: type 2 low density', (2, 0.2, 0.1, 3, 1, 1), [0.566038, 0.566]),
  ('regression: type 3 prey switching', (3, 0.05, 0.2, 12, 2, 3), [2.95082, 12]),
  ('regression: depletion cap', (2, 2.0, 0.05, 10, 20, 5), [10.0, 10])],
 [('control: type 2 wolves on moose', (2, 0.8, 0.5, 30, 3, 2), [1.846154, 11.0769]),
  ('control: type 2 low density', (2, 0.2, 0.1, 3, 1, 1), [0.566038, 0.566]),
  ('regression: type 3 prey switching', (3, 0.05, 0.2, 12, 2, 3), [2.95082, 12]),
  ('control: type 3 high density', (3, 0.1, 0.4, 50, 1, 1), [2.475248, 2.4752]),
  ('regression: depletion cap', (2, 2.0, 0.05, 10, 20, 5), [10.0, 10]),
  ('control: unknown kind', (4, 0.1, 0.1, 10, 1, 1), None),
  ('control: no prey', (2, 0.5, 0.5, 0, 2, 1), [0.0, 0.0])],
 [('control: type 1 saturated filter feeder', (1, 0.5, 0.25, 20, 2, 1), [4.0, 8.0]),
  ('regression: type 3 prey switching', (3, 0.05, 0.2, 12, 2, 3), [2.95082, 12]),
  ('control: type 3 high density', (3, 0.1, 0.4, 50, 1, 1), [2.475248, 2.4752]),
  ('regression: depletion cap', (2, 2.0, 0.05, 10, 20, 5), [10.0, 10]),
  ('control: unknown kind', (4, 0.1, 0.1, 10, 1, 1), None),
  ('control: no prey', (2, 0.5, 0.5, 0, 2, 1), [0.0, 0.0]),
  ('control: invalid negative handling', (2, 0.5, -0.1, 10, 1, 1), None)],
 [('control: type 1 saturated filter feeder', (1, 0.5, 0.25, 20, 2, 1), [4.0, 8.0]),
  ('control: type 1 unsaturated', (1, 0.1, 0.5, 10, 1, 2), [1.0, 2.0]),
  ('control: type 1 no handling', (1, 0.3, 0.0, 40, 1, 1), [12.0, 12.0]),
  ('regression: type 3 prey switching', (3, 0.05, 0.2, 12, 2, 3), [2.95082, 12]),
  ('regression: depletion cap', (2, 2.0, 0.05, 10, 20, 5), [10.0, 10]),
  ('control: no prey', (2, 0.5, 0.5, 0, 2, 1), [0.0, 0.0]),
  ('control: invalid negative handling', (2, 0.5, -0.1, 10, 1, 1), None)],
 [('control: type 1 unsaturated', (1, 0.1, 0.5, 10, 1, 2), [1.0, 2.0]),
  ('control: type 1 no handling', (1, 0.3, 0.0, 40, 1, 1), [12.0, 12.0]),
  ('control: type 2 wolves on moose', (2, 0.8, 0.5, 30, 3, 2), [1.846154, 11.0769]),
  ('control: type 2 low density', (2, 0.2, 0.1, 3, 1, 1), [0.566038, 0.566]),
  ('regression: type 3 prey switching', (3, 0.05, 0.2, 12, 2, 3), [2.95082, 12]),
  ('control: type 3 high density', (3, 0.1, 0.4, 50, 1, 1), [2.475248, 2.4752]),
  ('regression: depletion cap', (2, 2.0, 0.05, 10, 20, 5), [10.0, 10])]]
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 fixture	Actual	Expected	Outcome
control: type 1 saturated filter feeder	`[4.0, 8.0]`	`[4.0, 8.0]`	Passed
control: type 1 unsaturated	`[1.0, 2.0]`	`[1.0, 2.0]`	Passed
control: type 1 no handling	`[12.0, 12.0]`	`[12.0, 12.0]`	Passed
control: type 2 wolves on moose	`[1.846154, 11.0769]`	`[1.846154, 11.0769]`	Passed
control: type 2 low density	`[0.566038, 0.566]`	`[0.566038, 0.566]`	Passed
regression: type 3 prey switching	`[2.95082, 17.7049]`	`[2.95082, 12]`	Failed
regression: depletion cap	`[10.0, 1000.0]`	`[10.0, 10]`	Failed

SHA-256 / 2a73cb5adb0e6d0e67b288aa7f8a6912f334cd01a40dbc88b9fb19585c4d36a0

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(kind, a, h, prey, predators, duration):
    if a < 0 or h < 0 or prey < 0:
        return None
    if kind == 1:
        f = a * prey if h == 0 else min(a * prey, 1 / h)
    elif kind == 2:
        f = a * prey / (1 + a * h * prey)
    elif kind == 3:
        f = a * prey ** 2 / (1 + a * h * prey ** 2)
    else:
        return None
    eaten = min(f * predators * duration, prey * predators)
    return [round(f, 6), round(eaten, 4)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('control: type 1 saturated filter feeder', (1, 0.5, 0.25, 20, 2, 1), [4.0, 8.0]),
  ('control: type 1 unsaturated', (1, 0.1, 0.5, 10, 1, 2), [1.0, 2.0]),
  ('control: type 1 no handling', (1, 0.3, 0.0, 40, 1, 1), [12.0, 12.0]),
  ('control: type 2 wolves on moose', (2, 0.8, 0.5, 30, 3, 2), [1.846154, 11.0769]),
  ('control: type 2 low density', (2, 0.2, 0.1, 3, 1, 1), [0.566038, 0.566]),
  ('regression: type 3 prey switching', (3, 0.05, 0.2, 12, 2, 3), [2.95082, 12]),
  ('regression: depletion cap', (2, 2.0, 0.05, 10, 20, 5), [10.0, 10])],
 [('control: type 2 wolves on moose', (2, 0.8, 0.5, 30, 3, 2), [1.846154, 11.0769]),
  ('control: type 2 low density', (2, 0.2, 0.1, 3, 1, 1), [0.566038, 0.566]),
  ('regression: type 3 prey switching', (3, 0.05, 0.2, 12, 2, 3), [2.95082, 12]),
  ('control: type 3 high density', (3, 0.1, 0.4, 50, 1, 1), [2.475248, 2.4752]),
  ('regression: depletion cap', (2, 2.0, 0.05, 10, 20, 5), [10.0, 10]),
  ('control: unknown kind', (4, 0.1, 0.1, 10, 1, 1), None),
  ('control: no prey', (2, 0.5, 0.5, 0, 2, 1), [0.0, 0.0])],
 [('control: type 1 saturated filter feeder', (1, 0.5, 0.25, 20, 2, 1), [4.0, 8.0]),
  ('regression: type 3 prey switching', (3, 0.05, 0.2, 12, 2, 3), [2.95082, 12]),
  ('control: type 3 high density', (3, 0.1, 0.4, 50, 1, 1), [2.475248, 2.4752]),
  ('regression: depletion cap', (2, 2.0, 0.05, 10, 20, 5), [10.0, 10]),
  ('control: unknown kind', (4, 0.1, 0.1, 10, 1, 1), None),
  ('control: no prey', (2, 0.5, 0.5, 0, 2, 1), [0.0, 0.0]),
  ('control: invalid negative handling', (2, 0.5, -0.1, 10, 1, 1), None)],
 [('control: type 1 saturated filter feeder', (1, 0.5, 0.25, 20, 2, 1), [4.0, 8.0]),
  ('control: type 1 unsaturated', (1, 0.1, 0.5, 10, 1, 2), [1.0, 2.0]),
  ('control: type 1 no handling', (1, 0.3, 0.0, 40, 1, 1), [12.0, 12.0]),
  ('regression: type 3 prey switching', (3, 0.05, 0.2, 12, 2, 3), [2.95082, 12]),
  ('regression: depletion cap', (2, 2.0, 0.05, 10, 20, 5), [10.0, 10]),
  ('control: no prey', (2, 0.5, 0.5, 0, 2, 1), [0.0, 0.0]),
  ('control: invalid negative handling', (2, 0.5, -0.1, 10, 1, 1), None)],
 [('control: type 1 unsaturated', (1, 0.1, 0.5, 10, 1, 2), [1.0, 2.0]),
  ('control: type 1 no handling', (1, 0.3, 0.0, 40, 1, 1), [12.0, 12.0]),
  ('control: type 2 wolves on moose', (2, 0.8, 0.5, 30, 3, 2), [1.846154, 11.0769]),
  ('control: type 2 low density', (2, 0.2, 0.1, 3, 1, 1), [0.566038, 0.566]),
  ('regression: type 3 prey switching', (3, 0.05, 0.2, 12, 2, 3), [2.95082, 12]),
  ('control: type 3 high density', (3, 0.1, 0.4, 50, 1, 1), [2.475248, 2.4752]),
  ('regression: depletion cap', (2, 2.0, 0.05, 10, 20, 5), [10.0, 10])]]
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 fixture	Actual	Expected	Outcome
control: type 1 saturated filter feeder	`[4.0, 8.0]`	`[4.0, 8.0]`	Passed
control: type 1 unsaturated	`[1.0, 2.0]`	`[1.0, 2.0]`	Passed
control: type 1 no handling	`[12.0, 12.0]`	`[12.0, 12.0]`	Passed
control: type 2 wolves on moose	`[1.846154, 11.0769]`	`[1.846154, 11.0769]`	Passed
control: type 2 low density	`[0.566038, 0.566]`	`[0.566038, 0.566]`	Passed
regression: type 3 prey switching	`[2.95082, 17.7049]`	`[2.95082, 12]`	Failed
regression: depletion cap	`[10.0, 200]`	`[10.0, 10]`	Failed

SHA-256 / 28a67891b3eec8c2b0d91e837474463c75e7eacbf2bafdb1541957f20a4c6296

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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 2026-09-29T14:47:34.048405+00:00.

Case digest / 305ad030c330e92fcd5ea82167a5c117a603ac810e1cc519926de1fc7a32e859