FA-65706 / Ecological population dynamics / Open access

Two-patch source-sink dispersal with ceilings: dispersal conservation · case 01

Dispersal creates individuals.

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

ROOT CAUSE

Emigrants are added to the destination but not removed from the origin.

THE FAILURE

Emigrants are added to the destination but not removed from the origin.

Unsuccessful approach: Swapping the flows sends emigrants back to their own patch.

Case contract

Each year each patch grows by its lambda and is capped at its own ceiling, then fraction disperse of each post-growth patch moves to the other simultaneously; return yearly [N1, N2] rounded 4.

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(n0s, lambdas, caps, disperse, years):
    n = [float(x) for x in n0s]
    traj = []
    for _ in range(years):
        grown = [min(n[j] * lambdas[j], caps[j]) for j in range(2)]
        out = [grown[j] * disperse for j in range(2)]
        n = [grown[0] + out[1], grown[1] + out[0]]
        traj.append([round(x, 4) for x in n])
    return traj
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: meadow source woodland sink',
   ([100, 20], [1.5, 0.7], [200, 200], 0.2, 5),
   [[122.8, 41.2], [153.128, 59.912], [168.3877, 73.5507], [170.2971, 81.1884], [171.3664, 85.4655]]),
  ('regression: ceiling binding in source',
   ([180, 10], [1.4, 0.8], [200, 50], 0.1, 4),
   [[180.8, 27.2], [182.176, 39.584], [183.1667, 48.5005], [183.88, 54.9203]]),
  ('control: no dispersal',
   ([50, 50], [1.2, 0.9], [100, 100], 0.0, 3),
   [[60.0, 45.0], [72.0, 40.5], [86.4, 36.45]]),
  ('regression: full exchange',
   ([60, 0], [1.1, 0.5], [100, 100], 1.0, 3),
   [[0.0, 66.0], [33.0, 0.0], [0.0, 36.3]]),
  ('regression: both sinks',
   ([100, 100], [0.8, 0.6], [150, 150], 0.3, 4),
   [[74.0, 66.0], [53.32, 45.48], [38.0456, 31.8984], [27.0472, 22.5283]]),
  ('regression: sink ceiling binding',
   ([10, 120], [1.3, 1.2], [300, 100], 0.25, 4),
   [[34.75, 78.25], [57.3563, 81.7188], [80.438, 92.1877], [103.427, 101.1423]]),
  ('regression: unequal ceilings',
   ([90, 40], [2.0, 1.5], [120, 60], 0.05, 5),
   [[117.0, 63.0], [117.0, 63.0], [117.0, 63.0], [117.0, 63.0], [117.0, 63.0]])],
 [('regression: meadow source woodland sink',
   ([100, 20], [1.5, 0.7], [200, 200], 0.2, 5),
   [[122.8, 41.2], [153.128, 59.912], [168.3877, 73.5507], [170.2971, 81.1884], [171.3664, 85.4655]]),
  ('regression: ceiling binding in source',
   ([180, 10], [1.4, 0.8], [200, 50], 0.1, 4),
   [[180.8, 27.2], [182.176, 39.584], [183.1667, 48.5005], [183.88, 54.9203]]),
  ('control: no dispersal',
   ([50, 50], [1.2, 0.9], [100, 100], 0.0, 3),
   [[60.0, 45.0], [72.0, 40.5], [86.4, 36.45]]),
  ('regression: full exchange',
   ([60, 0], [1.1, 0.5], [100, 100], 1.0, 3),
   [[0.0, 66.0], [33.0, 0.0], [0.0, 36.3]]),
  ('regression: both sinks',
   ([100, 100], [0.8, 0.6], [150, 150], 0.3, 4),
   [[74.0, 66.0], [53.32, 45.48], [38.0456, 31.8984], [27.0472, 22.5283]]),
  ('regression: sink ceiling binding',
   ([10, 120], [1.3, 1.2], [300, 100], 0.25, 4),
   [[34.75, 78.25], [57.3563, 81.7188], [80.438, 92.1877], [103.427, 101.1423]]),
  ('regression: unequal ceilings',
   ([90, 40], [2.0, 1.5], [120, 60], 0.05, 5),
   [[117.0, 63.0], [117.0, 63.0], [117.0, 63.0], [117.0, 63.0], [117.0, 63.0]])],
 [('regression: meadow source woodland sink',
   ([100, 20], [1.5, 0.7], [200, 200], 0.2, 5),
   [[122.8, 41.2], [153.128, 59.912], [168.3877, 73.5507], [170.2971, 81.1884], [171.3664, 85.4655]]),
  ('regression: ceiling binding in source',
   ([180, 10], [1.4, 0.8], [200, 50], 0.1, 4),
   [[180.8, 27.2], [182.176, 39.584], [183.1667, 48.5005], [183.88, 54.9203]]),
  ('control: no dispersal',
   ([50, 50], [1.2, 0.9], [100, 100], 0.0, 3),
   [[60.0, 45.0], [72.0, 40.5], [86.4, 36.45]]),
  ('regression: full exchange',
   ([60, 0], [1.1, 0.5], [100, 100], 1.0, 3),
   [[0.0, 66.0], [33.0, 0.0], [0.0, 36.3]]),
  ('regression: both sinks',
   ([100, 100], [0.8, 0.6], [150, 150], 0.3, 4),
   [[74.0, 66.0], [53.32, 45.48], [38.0456, 31.8984], [27.0472, 22.5283]]),
  ('regression: sink ceiling binding',
   ([10, 120], [1.3, 1.2], [300, 100], 0.25, 4),
   [[34.75, 78.25], [57.3563, 81.7188], [80.438, 92.1877], [103.427, 101.1423]]),
  ('regression: unequal ceilings',
   ([90, 40], [2.0, 1.5], [120, 60], 0.05, 5),
   [[117.0, 63.0], [117.0, 63.0], [117.0, 63.0], [117.0, 63.0], [117.0, 63.0]])],
 [('regression: meadow source woodland sink',
   ([100, 20], [1.5, 0.7], [200, 200], 0.2, 5),
   [[122.8, 41.2], [153.128, 59.912], [168.3877, 73.5507], [170.2971, 81.1884], [171.3664, 85.4655]]),
  ('regression: ceiling binding in source',
   ([180, 10], [1.4, 0.8], [200, 50], 0.1, 4),
   [[180.8, 27.2], [182.176, 39.584], [183.1667, 48.5005], [183.88, 54.9203]]),
  ('control: no dispersal',
   ([50, 50], [1.2, 0.9], [100, 100], 0.0, 3),
   [[60.0, 45.0], [72.0, 40.5], [86.4, 36.45]]),
  ('regression: full exchange',
   ([60, 0], [1.1, 0.5], [100, 100], 1.0, 3),
   [[0.0, 66.0], [33.0, 0.0], [0.0, 36.3]]),
  ('regression: both sinks',
   ([100, 100], [0.8, 0.6], [150, 150], 0.3, 4),
   [[74.0, 66.0], [53.32, 45.48], [38.0456, 31.8984], [27.0472, 22.5283]]),
  ('regression: sink ceiling binding',
   ([10, 120], [1.3, 1.2], [300, 100], 0.25, 4),
   [[34.75, 78.25], [57.3563, 81.7188], [80.438, 92.1877], [103.427, 101.1423]]),
  ('regression: unequal ceilings',
   ([90, 40], [2.0, 1.5], [120, 60], 0.05, 5),
   [[117.0, 63.0], [117.0, 63.0], [117.0, 63.0], [117.0, 63.0], [117.0, 63.0]])],
 [('regression: meadow source woodland sink',
   ([100, 20], [1.5, 0.7], [200, 200], 0.2, 5),
   [[122.8, 41.2], [153.128, 59.912], [168.3877, 73.5507], [170.2971, 81.1884], [171.3664, 85.4655]]),
  ('regression: ceiling binding in source',
   ([180, 10], [1.4, 0.8], [200, 50], 0.1, 4),
   [[180.8, 27.2], [182.176, 39.584], [183.1667, 48.5005], [183.88, 54.9203]]),
  ('control: no dispersal',
   ([50, 50], [1.2, 0.9], [100, 100], 0.0, 3),
   [[60.0, 45.0], [72.0, 40.5], [86.4, 36.45]]),
  ('regression: full exchange',
   ([60, 0], [1.1, 0.5], [100, 100], 1.0, 3),
   [[0.0, 66.0], [33.0, 0.0], [0.0, 36.3]]),
  ('regression: both sinks',
   ([100, 100], [0.8, 0.6], [150, 150], 0.3, 4),
   [[74.0, 66.0], [53.32, 45.48], [38.0456, 31.8984], [27.0472, 22.5283]]),
  ('regression: sink ceiling binding',
   ([10, 120], [1.3, 1.2], [300, 100], 0.25, 4),
   [[34.75, 78.25], [57.3563, 81.7188], [80.438, 92.1877], [103.427, 101.1423]]),
  ('regression: unequal ceilings',
   ([90, 40], [2.0, 1.5], [120, 60], 0.05, 5),
   [[117.0, 63.0], [117.0, 63.0], [117.0, 63.0], [117.0, 63.0], [117.0, 63.0]])]]
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
regression: meadow source woodland sink	`[[152.8, 44.0], [206.16, 70.8], [209.912, 89.56], [212.5384, 102.692], [214.3769, 111.8844]]`	`[[122.8, 41.2], [153.128, 59.912], [168.3877, 73.5507], [170.2971, 81.1884], [171.3664, 85.4655]]`	Failed
regression: ceiling binding in source	`[[200.8, 28.0], [202.24, 42.4], [203.392, 53.92], [204.3136, 63.136]]`	`[[180.8, 27.2], [182.176, 39.584], [183.1667, 48.5005], [183.88, 54.9203]]`	Failed
control: no dispersal	`[[60.0, 45.0], [72.0, 40.5], [86.4, 36.45]]`	`[[60.0, 45.0], [72.0, 40.5], [86.4, 36.45]]`	Passed
regression: full exchange	`[[66.0, 66.0], [105.6, 105.6], [152.8, 152.8]]`	`[[0.0, 66.0], [33.0, 0.0], [0.0, 36.3]]`	Failed
regression: both sinks	`[[98.0, 84.0], [93.52, 73.92], [88.1216, 66.7968], [82.5207, 61.2273]]`	`[[74.0, 66.0], [53.32, 45.48], [38.0456, 31.8984], [27.0472, 22.5283]]`	Failed
regression: sink ceiling binding	`[[38.0, 103.25], [74.4, 112.35], [121.72, 124.18], [183.236, 139.559]]`	`[[34.75, 78.25], [57.3563, 81.7188], [80.438, 92.1877], [103.427, 101.1423]]`	Failed
regression: unequal ceilings	`[[123.0, 66.0], [123.0, 66.0], [123.0, 66.0], [123.0, 66.0], [123.0, 66.0]]`	`[[117.0, 63.0], [117.0, 63.0], [117.0, 63.0], [117.0, 63.0], [117.0, 63.0]]`	Failed

SHA-256 / 7f11cebdff53e88612bde8d3690bcfd9cba82cf73ead39908c8481d683164f60

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(n0s, lambdas, caps, disperse, years):
    n = [float(x) for x in n0s]
    traj = []
    for _ in range(years):
        grown = [min(n[j] * lambdas[j], caps[j]) for j in range(2)]
        out = [grown[j] * disperse for j in range(2)]
        n = [grown[0] - out[1] + out[0], grown[1] - out[0] + out[1]]
        traj.append([round(x, 4) for x in n])
    return traj
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: meadow source woodland sink',
   ([100, 20], [1.5, 0.7], [200, 200], 0.2, 5),
   [[122.8, 41.2], [153.128, 59.912], [168.3877, 73.5507], [170.2971, 81.1884], [171.3664, 85.4655]]),
  ('regression: ceiling binding in source',
   ([180, 10], [1.4, 0.8], [200, 50], 0.1, 4),
   [[180.8, 27.2], [182.176, 39.584], [183.1667, 48.5005], [183.88, 54.9203]]),
  ('control: no dispersal',
   ([50, 50], [1.2, 0.9], [100, 100], 0.0, 3),
   [[60.0, 45.0], [72.0, 40.5], [86.4, 36.45]]),
  ('regression: full exchange',
   ([60, 0], [1.1, 0.5], [100, 100], 1.0, 3),
   [[0.0, 66.0], [33.0, 0.0], [0.0, 36.3]]),
  ('regression: both sinks',
   ([100, 100], [0.8, 0.6], [150, 150], 0.3, 4),
   [[74.0, 66.0], [53.32, 45.48], [38.0456, 31.8984], [27.0472, 22.5283]]),
  ('regression: sink ceiling binding',
   ([10, 120], [1.3, 1.2], [300, 100], 0.25, 4),
   [[34.75, 78.25], [57.3563, 81.7188], [80.438, 92.1877], [103.427, 101.1423]]),
  ('regression: unequal ceilings',
   ([90, 40], [2.0, 1.5], [120, 60], 0.05, 5),
   [[117.0, 63.0], [117.0, 63.0], [117.0, 63.0], [117.0, 63.0], [117.0, 63.0]])],
 [('regression: meadow source woodland sink',
   ([100, 20], [1.5, 0.7], [200, 200], 0.2, 5),
   [[122.8, 41.2], [153.128, 59.912], [168.3877, 73.5507], [170.2971, 81.1884], [171.3664, 85.4655]]),
  ('regression: ceiling binding in source',
   ([180, 10], [1.4, 0.8], [200, 50], 0.1, 4),
   [[180.8, 27.2], [182.176, 39.584], [183.1667, 48.5005], [183.88, 54.9203]]),
  ('control: no dispersal',
   ([50, 50], [1.2, 0.9], [100, 100], 0.0, 3),
   [[60.0, 45.0], [72.0, 40.5], [86.4, 36.45]]),
  ('regression: full exchange',
   ([60, 0], [1.1, 0.5], [100, 100], 1.0, 3),
   [[0.0, 66.0], [33.0, 0.0], [0.0, 36.3]]),
  ('regression: both sinks',
   ([100, 100], [0.8, 0.6], [150, 150], 0.3, 4),
   [[74.0, 66.0], [53.32, 45.48], [38.0456, 31.8984], [27.0472, 22.5283]]),
  ('regression: sink ceiling binding',
   ([10, 120], [1.3, 1.2], [300, 100], 0.25, 4),
   [[34.75, 78.25], [57.3563, 81.7188], [80.438, 92.1877], [103.427, 101.1423]]),
  ('regression: unequal ceilings',
   ([90, 40], [2.0, 1.5], [120, 60], 0.05, 5),
   [[117.0, 63.0], [117.0, 63.0], [117.0, 63.0], [117.0, 63.0], [117.0, 63.0]])],
 [('regression: meadow source woodland sink',
   ([100, 20], [1.5, 0.7], [200, 200], 0.2, 5),
   [[122.8, 41.2], [153.128, 59.912], [168.3877, 73.5507], [170.2971, 81.1884], [171.3664, 85.4655]]),
  ('regression: ceiling binding in source',
   ([180, 10], [1.4, 0.8], [200, 50], 0.1, 4),
   [[180.8, 27.2], [182.176, 39.584], [183.1667, 48.5005], [183.88, 54.9203]]),
  ('control: no dispersal',
   ([50, 50], [1.2, 0.9], [100, 100], 0.0, 3),
   [[60.0, 45.0], [72.0, 40.5], [86.4, 36.45]]),
  ('regression: full exchange',
   ([60, 0], [1.1, 0.5], [100, 100], 1.0, 3),
   [[0.0, 66.0], [33.0, 0.0], [0.0, 36.3]]),
  ('regression: both sinks',
   ([100, 100], [0.8, 0.6], [150, 150], 0.3, 4),
   [[74.0, 66.0], [53.32, 45.48], [38.0456, 31.8984], [27.0472, 22.5283]]),
  ('regression: sink ceiling binding',
   ([10, 120], [1.3, 1.2], [300, 100], 0.25, 4),
   [[34.75, 78.25], [57.3563, 81.7188], [80.438, 92.1877], [103.427, 101.1423]]),
  ('regression: unequal ceilings',
   ([90, 40], [2.0, 1.5], [120, 60], 0.05, 5),
   [[117.0, 63.0], [117.0, 63.0], [117.0, 63.0], [117.0, 63.0], [117.0, 63.0]])],
 [('regression: meadow source woodland sink',
   ([100, 20], [1.5, 0.7], [200, 200], 0.2, 5),
   [[122.8, 41.2], [153.128, 59.912], [168.3877, 73.5507], [170.2971, 81.1884], [171.3664, 85.4655]]),
  ('regression: ceiling binding in source',
   ([180, 10], [1.4, 0.8], [200, 50], 0.1, 4),
   [[180.8, 27.2], [182.176, 39.584], [183.1667, 48.5005], [183.88, 54.9203]]),
  ('control: no dispersal',
   ([50, 50], [1.2, 0.9], [100, 100], 0.0, 3),
   [[60.0, 45.0], [72.0, 40.5], [86.4, 36.45]]),
  ('regression: full exchange',
   ([60, 0], [1.1, 0.5], [100, 100], 1.0, 3),
   [[0.0, 66.0], [33.0, 0.0], [0.0, 36.3]]),
  ('regression: both sinks',
   ([100, 100], [0.8, 0.6], [150, 150], 0.3, 4),
   [[74.0, 66.0], [53.32, 45.48], [38.0456, 31.8984], [27.0472, 22.5283]]),
  ('regression: sink ceiling binding',
   ([10, 120], [1.3, 1.2], [300, 100], 0.25, 4),
   [[34.75, 78.25], [57.3563, 81.7188], [80.438, 92.1877], [103.427, 101.1423]]),
  ('regression: unequal ceilings',
   ([90, 40], [2.0, 1.5], [120, 60], 0.05, 5),
   [[117.0, 63.0], [117.0, 63.0], [117.0, 63.0], [117.0, 63.0], [117.0, 63.0]])],
 [('regression: meadow source woodland sink',
   ([100, 20], [1.5, 0.7], [200, 200], 0.2, 5),
   [[122.8, 41.2], [153.128, 59.912], [168.3877, 73.5507], [170.2971, 81.1884], [171.3664, 85.4655]]),
  ('regression: ceiling binding in source',
   ([180, 10], [1.4, 0.8], [200, 50], 0.1, 4),
   [[180.8, 27.2], [182.176, 39.584], [183.1667, 48.5005], [183.88, 54.9203]]),
  ('control: no dispersal',
   ([50, 50], [1.2, 0.9], [100, 100], 0.0, 3),
   [[60.0, 45.0], [72.0, 40.5], [86.4, 36.45]]),
  ('regression: full exchange',
   ([60, 0], [1.1, 0.5], [100, 100], 1.0, 3),
   [[0.0, 66.0], [33.0, 0.0], [0.0, 36.3]]),
  ('regression: both sinks',
   ([100, 100], [0.8, 0.6], [150, 150], 0.3, 4),
   [[74.0, 66.0], [53.32, 45.48], [38.0456, 31.8984], [27.0472, 22.5283]]),
  ('regression: sink ceiling binding',
   ([10, 120], [1.3, 1.2], [300, 100], 0.25, 4),
   [[34.75, 78.25], [57.3563, 81.7188], [80.438, 92.1877], [103.427, 101.1423]]),
  ('regression: unequal ceilings',
   ([90, 40], [2.0, 1.5], [120, 60], 0.05, 5),
   [[117.0, 63.0], [117.0, 63.0], [117.0, 63.0], [117.0, 63.0], [117.0, 63.0]])]]
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
regression: meadow source woodland sink	`[[177.2, -13.2], [241.848, -51.088], [247.1523, -82.9139], [251.6079, -109.6477], [255.3507, -132.1041]]`	`[[122.8, 41.2], [153.128, 59.912], [168.3877, 73.5507], [170.2971, 81.1884], [171.3664, 85.4655]]`	Failed
regression: ceiling binding in source	`[[219.2, -11.2], [220.896, -29.856], [222.3885, -46.2733], [223.7019, -60.7205]]`	`[[180.8, 27.2], [182.176, 39.584], [183.1667, 48.5005], [183.88, 54.9203]]`	Failed
control: no dispersal	`[[60.0, 45.0], [72.0, 40.5], [86.4, 36.45]]`	`[[60.0, 45.0], [72.0, 40.5], [86.4, 36.45]]`	Passed
regression: full exchange	`[[132.0, -66.0], [233.0, -166.0], [283.0, -266.0]]`	`[[0.0, 66.0], [33.0, 0.0], [0.0, 36.3]]`	Failed
regression: both sinks	`[[86.0, 54.0], [79.72, 21.48], [79.0424, -2.3784], [82.6322, -20.8253]]`	`[[74.0, 66.0], [53.32, 45.48], [38.0456, 31.8984], [27.0472, 22.5283]]`	Failed
regression: sink ceiling binding	`[[-8.75, 121.75], [-39.2188, 127.8438], [-88.7305, 137.7461], [-169.187, 153.8374]]`	`[[34.75, 78.25], [57.3563, 81.7188], [80.438, 92.1877], [103.427, 101.1423]]`	Failed
regression: unequal ceilings	`[[123.0, 57.0], [123.0, 57.0], [123.0, 57.0], [123.0, 57.0], [123.0, 57.0]]`	`[[117.0, 63.0], [117.0, 63.0], [117.0, 63.0], [117.0, 63.0], [117.0, 63.0]]`	Failed

SHA-256 / 1215e592f79a3c8774527a16e5cdb3b96ad87f28b7af0b07cf033c43734088b4

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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.

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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 2026-09-29T14:47:36.598542+00:00.

Case digest / e65ba51e311ace3b1f5b5a999c259d58b0ded5fa5c675dca620664fc511bc966