FA-65451 / Ecological population dynamics / Open access
Leslie matrix projection with optional plus group: fecundity row · case 01
Births stay fixed at the initial level every year.
ROOT CAUSE
Reproduction uses the initial age vector instead of the current one.
THE FAILURE
Reproduction uses the initial age vector instead of the current one.
Unsuccessful approach: Excluding class 0 from reproduction drops juvenile fecundity.
Case contract
Births new[0] = sum f_i*n_i; survivors new[i+1] = s_i*n_i; with plus_group the last class also retains s_last*n_last; ratio is total(t)/total(t-1) of the final year (None if the previous total was 0 or no years); return [final vector rounded 4, total rounded 4, ratio rounded 6].
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(fecundity, survival, n0, years, plus_group):
m = len(n0)
n = [float(x) for x in n0]
ratio = None
prev_total = sum(n)
for _ in range(years):
new = [0.0] * m
new[0] = sum(fecundity[i] * n0[i] for i in range(m))
for i in range(m - 1):
new[i + 1] = survival[i] * n[i]
if plus_group:
new[m - 1] += survival[m - 1] * n[m - 1]
prev_total = sum(n)
n = new
ratio = sum(n) / prev_total if prev_total > 0 else None
return [[round(x, 4) for x in n], round(sum(n), 4), None if ratio is None else round(ratio, 6)]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: three-class bird',
([0.0, 1.2, 1.8], [0.4, 0.7], [100, 50, 20], 3, False),
[[96.48, 44.4, 26.88], 167.76, 0.94566]),
('regression: plus group fish',
([0.0, 0.5, 2.0], [0.5, 0.6, 0.8], [200, 80, 40], 4, True),
[[322.9, 139.0, 171.16], 633.06, 1.221652]),
('control: extinct population', ([0.0, 1.0], [0.5], [0, 0], 2, False), [[0.0, 0.0], 0.0, None]),
('control: zero years', ([0.0, 1.0], [0.5], [10, 10], 0, False), [[10.0, 10.0], 20.0, None]),
('regression: juvenile breeders',
([0.3, 0.9, 1.1], [0.6, 0.5, 0.2], [50, 30, 10], 3, True),
[[67.34, 36.96, 19.58], 123.88, 1.10805]),
('regression: single step',
([0.2, 1.5, 0.0], [0.8, 0.3], [10, 20, 30], 1, False),
[[32.0, 8.0, 6.0], 46.0, 0.766667]),
('regression: senescent plus group',
([0.0, 0.0, 3.0], [0.9, 0.9, 0.5], [0, 0, 10], 3, True),
[[7.5, 13.5, 25.55], 46.55, 1.046067])],
[('regression: three-class bird',
([0.0, 1.2, 1.8], [0.4, 0.7], [100, 50, 20], 3, False),
[[96.48, 44.4, 26.88], 167.76, 0.94566]),
('control: extinct population', ([0.0, 1.0], [0.5], [0, 0], 2, False), [[0.0, 0.0], 0.0, None]),
('control: zero years', ([0.0, 1.0], [0.5], [10, 10], 0, False), [[10.0, 10.0], 20.0, None]),
('regression: juvenile breeders',
([0.3, 0.9, 1.1], [0.6, 0.5, 0.2], [50, 30, 10], 3, True),
[[67.34, 36.96, 19.58], 123.88, 1.10805]),
('regression: single step',
([0.2, 1.5, 0.0], [0.8, 0.3], [10, 20, 30], 1, False),
[[32.0, 8.0, 6.0], 46.0, 0.766667]),
('regression: senescent plus group',
([0.0, 0.0, 3.0], [0.9, 0.9, 0.5], [0, 0, 10], 3, True),
[[7.5, 13.5, 25.55], 46.55, 1.046067]),
('regression: four classes',
([0.0, 0.0, 1.0, 2.0], [0.5, 0.6, 0.7], [40, 30, 20, 10], 5, False),
[[30.6, 14.4, 11.16, 9.66], 65.82, 0.94569])],
[('regression: three-class bird',
([0.0, 1.2, 1.8], [0.4, 0.7], [100, 50, 20], 3, False),
[[96.48, 44.4, 26.88], 167.76, 0.94566]),
('regression: plus group fish',
([0.0, 0.5, 2.0], [0.5, 0.6, 0.8], [200, 80, 40], 4, True),
[[322.9, 139.0, 171.16], 633.06, 1.221652]),
('control: extinct population', ([0.0, 1.0], [0.5], [0, 0], 2, False), [[0.0, 0.0], 0.0, None]),
('control: zero years', ([0.0, 1.0], [0.5], [10, 10], 0, False), [[10.0, 10.0], 20.0, None]),
('regression: juvenile breeders',
([0.3, 0.9, 1.1], [0.6, 0.5, 0.2], [50, 30, 10], 3, True),
[[67.34, 36.96, 19.58], 123.88, 1.10805]),
('regression: senescent plus group',
([0.0, 0.0, 3.0], [0.9, 0.9, 0.5], [0, 0, 10], 3, True),
[[7.5, 13.5, 25.55], 46.55, 1.046067]),
('regression: four classes',
([0.0, 0.0, 1.0, 2.0], [0.5, 0.6, 0.7], [40, 30, 20, 10], 5, False),
[[30.6, 14.4, 11.16, 9.66], 65.82, 0.94569])],
[('regression: plus group fish',
([0.0, 0.5, 2.0], [0.5, 0.6, 0.8], [200, 80, 40], 4, True),
[[322.9, 139.0, 171.16], 633.06, 1.221652]),
('control: extinct population', ([0.0, 1.0], [0.5], [0, 0], 2, False), [[0.0, 0.0], 0.0, None]),
('control: zero years', ([0.0, 1.0], [0.5], [10, 10], 0, False), [[10.0, 10.0], 20.0, None]),
('regression: juvenile breeders',
([0.3, 0.9, 1.1], [0.6, 0.5, 0.2], [50, 30, 10], 3, True),
[[67.34, 36.96, 19.58], 123.88, 1.10805]),
('regression: single step',
([0.2, 1.5, 0.0], [0.8, 0.3], [10, 20, 30], 1, False),
[[32.0, 8.0, 6.0], 46.0, 0.766667]),
('regression: senescent plus group',
([0.0, 0.0, 3.0], [0.9, 0.9, 0.5], [0, 0, 10], 3, True),
[[7.5, 13.5, 25.55], 46.55, 1.046067]),
('regression: four classes',
([0.0, 0.0, 1.0, 2.0], [0.5, 0.6, 0.7], [40, 30, 20, 10], 5, False),
[[30.6, 14.4, 11.16, 9.66], 65.82, 0.94569])],
[('regression: three-class bird',
([0.0, 1.2, 1.8], [0.4, 0.7], [100, 50, 20], 3, False),
[[96.48, 44.4, 26.88], 167.76, 0.94566]),
('control: extinct population', ([0.0, 1.0], [0.5], [0, 0], 2, False), [[0.0, 0.0], 0.0, None]),
('control: zero years', ([0.0, 1.0], [0.5], [10, 10], 0, False), [[10.0, 10.0], 20.0, None]),
('regression: juvenile breeders',
([0.3, 0.9, 1.1], [0.6, 0.5, 0.2], [50, 30, 10], 3, True),
[[67.34, 36.96, 19.58], 123.88, 1.10805]),
('regression: single step',
([0.2, 1.5, 0.0], [0.8, 0.3], [10, 20, 30], 1, False),
[[32.0, 8.0, 6.0], 46.0, 0.766667]),
('regression: senescent plus group',
([0.0, 0.0, 3.0], [0.9, 0.9, 0.5], [0, 0, 10], 3, True),
[[7.5, 13.5, 25.55], 46.55, 1.046067]),
('regression: four classes',
([0.0, 0.0, 1.0, 2.0], [0.5, 0.6, 0.7], [40, 30, 20, 10], 5, False),
[[30.6, 14.4, 11.16, 9.66], 65.82, 0.94569])]]
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: three-class bird | [[96.0, 38.4, 26.88], 161.28, 0.993103] | [[96.48, 44.4, 26.88], 167.76, 0.94566] | Failed |
| regression: plus group fish | [[120.0, 60.0, 144.16], 324.16, 1.028426] | [[322.9, 139.0, 171.16], 633.06, 1.221652] | Failed |
| control: extinct population | [[0.0, 0.0], 0.0, None] | [[0.0, 0.0], 0.0, None] | Passed |
| control: zero years | [[10.0, 10.0], 20.0, None] | [[10.0, 10.0], 20.0, None] | Passed |
| regression: juvenile breeders | [[53.0, 31.8, 19.58], 104.38, 1.011434] | [[67.34, 36.96, 19.58], 123.88, 1.10805] | Failed |
| regression: single step | [[32.0, 8.0, 6.0], 46.0, 0.766667] | [[32.0, 8.0, 6.0], 46.0, 0.766667] | Passed |
| regression: senescent plus group | [[30.0, 27.0, 25.55], 82.55, 1.387395] | [[7.5, 13.5, 25.55], 46.55, 1.046067] | Failed |
SHA-256 / 8f6502a82a3588f7212b6bb6eb82b7459d18159d2518f3717e56db876db13a4e
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(fecundity, survival, n0, years, plus_group):
m = len(n0)
n = [float(x) for x in n0]
ratio = None
prev_total = sum(n)
for _ in range(years):
new = [0.0] * m
new[0] = sum(fecundity[i] * n[i] for i in range(1, m))
for i in range(m - 1):
new[i + 1] = survival[i] * n[i]
if plus_group:
new[m - 1] += survival[m - 1] * n[m - 1]
prev_total = sum(n)
n = new
ratio = sum(n) / prev_total if prev_total > 0 else None
return [[round(x, 4) for x in n], round(sum(n), 4), None if ratio is None else round(ratio, 6)]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: three-class bird',
([0.0, 1.2, 1.8], [0.4, 0.7], [100, 50, 20], 3, False),
[[96.48, 44.4, 26.88], 167.76, 0.94566]),
('regression: plus group fish',
([0.0, 0.5, 2.0], [0.5, 0.6, 0.8], [200, 80, 40], 4, True),
[[322.9, 139.0, 171.16], 633.06, 1.221652]),
('control: extinct population', ([0.0, 1.0], [0.5], [0, 0], 2, False), [[0.0, 0.0], 0.0, None]),
('control: zero years', ([0.0, 1.0], [0.5], [10, 10], 0, False), [[10.0, 10.0], 20.0, None]),
('regression: juvenile breeders',
([0.3, 0.9, 1.1], [0.6, 0.5, 0.2], [50, 30, 10], 3, True),
[[67.34, 36.96, 19.58], 123.88, 1.10805]),
('regression: single step',
([0.2, 1.5, 0.0], [0.8, 0.3], [10, 20, 30], 1, False),
[[32.0, 8.0, 6.0], 46.0, 0.766667]),
('regression: senescent plus group',
([0.0, 0.0, 3.0], [0.9, 0.9, 0.5], [0, 0, 10], 3, True),
[[7.5, 13.5, 25.55], 46.55, 1.046067])],
[('regression: three-class bird',
([0.0, 1.2, 1.8], [0.4, 0.7], [100, 50, 20], 3, False),
[[96.48, 44.4, 26.88], 167.76, 0.94566]),
('control: extinct population', ([0.0, 1.0], [0.5], [0, 0], 2, False), [[0.0, 0.0], 0.0, None]),
('control: zero years', ([0.0, 1.0], [0.5], [10, 10], 0, False), [[10.0, 10.0], 20.0, None]),
('regression: juvenile breeders',
([0.3, 0.9, 1.1], [0.6, 0.5, 0.2], [50, 30, 10], 3, True),
[[67.34, 36.96, 19.58], 123.88, 1.10805]),
('regression: single step',
([0.2, 1.5, 0.0], [0.8, 0.3], [10, 20, 30], 1, False),
[[32.0, 8.0, 6.0], 46.0, 0.766667]),
('regression: senescent plus group',
([0.0, 0.0, 3.0], [0.9, 0.9, 0.5], [0, 0, 10], 3, True),
[[7.5, 13.5, 25.55], 46.55, 1.046067]),
('regression: four classes',
([0.0, 0.0, 1.0, 2.0], [0.5, 0.6, 0.7], [40, 30, 20, 10], 5, False),
[[30.6, 14.4, 11.16, 9.66], 65.82, 0.94569])],
[('regression: three-class bird',
([0.0, 1.2, 1.8], [0.4, 0.7], [100, 50, 20], 3, False),
[[96.48, 44.4, 26.88], 167.76, 0.94566]),
('regression: plus group fish',
([0.0, 0.5, 2.0], [0.5, 0.6, 0.8], [200, 80, 40], 4, True),
[[322.9, 139.0, 171.16], 633.06, 1.221652]),
('control: extinct population', ([0.0, 1.0], [0.5], [0, 0], 2, False), [[0.0, 0.0], 0.0, None]),
('control: zero years', ([0.0, 1.0], [0.5], [10, 10], 0, False), [[10.0, 10.0], 20.0, None]),
('regression: juvenile breeders',
([0.3, 0.9, 1.1], [0.6, 0.5, 0.2], [50, 30, 10], 3, True),
[[67.34, 36.96, 19.58], 123.88, 1.10805]),
('regression: senescent plus group',
([0.0, 0.0, 3.0], [0.9, 0.9, 0.5], [0, 0, 10], 3, True),
[[7.5, 13.5, 25.55], 46.55, 1.046067]),
('regression: four classes',
([0.0, 0.0, 1.0, 2.0], [0.5, 0.6, 0.7], [40, 30, 20, 10], 5, False),
[[30.6, 14.4, 11.16, 9.66], 65.82, 0.94569])],
[('regression: plus group fish',
([0.0, 0.5, 2.0], [0.5, 0.6, 0.8], [200, 80, 40], 4, True),
[[322.9, 139.0, 171.16], 633.06, 1.221652]),
('control: extinct population', ([0.0, 1.0], [0.5], [0, 0], 2, False), [[0.0, 0.0], 0.0, None]),
('control: zero years', ([0.0, 1.0], [0.5], [10, 10], 0, False), [[10.0, 10.0], 20.0, None]),
('regression: juvenile breeders',
([0.3, 0.9, 1.1], [0.6, 0.5, 0.2], [50, 30, 10], 3, True),
[[67.34, 36.96, 19.58], 123.88, 1.10805]),
('regression: single step',
([0.2, 1.5, 0.0], [0.8, 0.3], [10, 20, 30], 1, False),
[[32.0, 8.0, 6.0], 46.0, 0.766667]),
('regression: senescent plus group',
([0.0, 0.0, 3.0], [0.9, 0.9, 0.5], [0, 0, 10], 3, True),
[[7.5, 13.5, 25.55], 46.55, 1.046067]),
('regression: four classes',
([0.0, 0.0, 1.0, 2.0], [0.5, 0.6, 0.7], [40, 30, 20, 10], 5, False),
[[30.6, 14.4, 11.16, 9.66], 65.82, 0.94569])],
[('regression: three-class bird',
([0.0, 1.2, 1.8], [0.4, 0.7], [100, 50, 20], 3, False),
[[96.48, 44.4, 26.88], 167.76, 0.94566]),
('control: extinct population', ([0.0, 1.0], [0.5], [0, 0], 2, False), [[0.0, 0.0], 0.0, None]),
('control: zero years', ([0.0, 1.0], [0.5], [10, 10], 0, False), [[10.0, 10.0], 20.0, None]),
('regression: juvenile breeders',
([0.3, 0.9, 1.1], [0.6, 0.5, 0.2], [50, 30, 10], 3, True),
[[67.34, 36.96, 19.58], 123.88, 1.10805]),
('regression: single step',
([0.2, 1.5, 0.0], [0.8, 0.3], [10, 20, 30], 1, False),
[[32.0, 8.0, 6.0], 46.0, 0.766667]),
('regression: senescent plus group',
([0.0, 0.0, 3.0], [0.9, 0.9, 0.5], [0, 0, 10], 3, True),
[[7.5, 13.5, 25.55], 46.55, 1.046067]),
('regression: four classes',
([0.0, 0.0, 1.0, 2.0], [0.5, 0.6, 0.7], [40, 30, 20, 10], 5, False),
[[30.6, 14.4, 11.16, 9.66], 65.82, 0.94569])]]
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: three-class bird | [[96.48, 44.4, 26.88], 167.76, 0.94566] | [[96.48, 44.4, 26.88], 167.76, 0.94566] | Passed |
| regression: plus group fish | [[322.9, 139.0, 171.16], 633.06, 1.221652] | [[322.9, 139.0, 171.16], 633.06, 1.221652] | Passed |
| control: extinct population | [[0.0, 0.0], 0.0, None] | [[0.0, 0.0], 0.0, None] | Passed |
| control: zero years | [[10.0, 10.0], 20.0, None] | [[10.0, 10.0], 20.0, None] | Passed |
| regression: juvenile breeders | [[40.76, 27.42, 15.08], 83.26, 0.958113] | [[67.34, 36.96, 19.58], 123.88, 1.10805] | Failed |
| regression: single step | [[30.0, 8.0, 6.0], 44.0, 0.733333] | [[32.0, 8.0, 6.0], 46.0, 0.766667] | Failed |
| regression: senescent plus group | [[7.5, 13.5, 25.55], 46.55, 1.046067] | [[7.5, 13.5, 25.55], 46.55, 1.046067] | Passed |
SHA-256 / ec92db166f2c07a1cba1ddbcd92b454951d41004a227f40eea498bd0159a7154
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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Sign in to the archive ↗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 2026-09-29T14:47:34.135621+00:00.
Case digest / ee71c9ef3e59ec6be8c4d4a7b88c059ea7640510d0b0df7a251e8d2ecba44598