Source: https://guthlabs.ai/docs/instruments/allele-genotype-frequency-from-pedigree-counts/mechanism/

instrument mechanism / verified-clean

# Allele/Genotype Frequency from Pedigree Counts mechanism

The inspectable method record for Allele/Genotype Frequency from Pedigree Counts, kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Model scope

The allele-frequency formulas are conditionally correct, but the specification is incomplete and ambiguous because it omits the HWE expected-count formulas and does not define the required constraints on N and genotype counts. Retain the educational/not-medical-advice label, and explicitly state that this is not a clinical, diagnostic, or population-inference result.

- The allele-frequency formula p=(2×AA+Aa)/(2N) is standard only when N is the total number of individuals and AA, Aa, and aa are mutually exclusive, exhaustive genotype counts at a biallelic locus.

- q=1−p is standard under the same biallelic-locus assumption; otherwise q should be computed from the allele count for the alternate allele.

- The specification claims to output expected HWE genotype counts but does not provide formulas. The required standard formulas are expected_AA=Np², expected_Aa=2Npq, and expected_aa=Nq².

- The phrase 'codominant/recessive' is ambiguous: raw genotype counts support this calculation, but recessive phenotype counts alone do not identify AA versus Aa without additional assumptions or data.

- Pedigree-derived counts are not automatically population-genetic random-sample counts, so HWE expected counts require an explicit idealized random-mating/population-sampling assumption.

## Units and conventions

- AA, Aa, and aa are nonnegative integer counts of individuals, not percentages or frequencies.

- N is the total individual count and must equal AA+Aa+aa.

- The locus is biallelic, with no missing, ambiguous, or additional alleles/genotypes.

- p denotes the frequency of the A allele and q denotes the frequency of the a allele.

- Expected HWE outputs are counts of individuals; p and q are dimensionless proportions.

- HWE expected counts assume random mating and the stated idealized population assumptions.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "AA": 36,
    "Aa": 48,
    "aa": 16,
    "N": 100
  },
  "expected_outputs": {
    "p": 0.6,
    "q": 0.4,
    "expected_AA": 36,
    "expected_Aa": 48,
    "expected_aa": 16
  },
  "working": "Check N: 36+48+16=100. A-allele count = 2×36+48=72+48=120. Total allele count = 2×100=200. p=120/200=0.6. q=1−0.6=0.4. HWE expected_AA=100×0.6²=100×0.36=36. expected_Aa=2×100×0.6×0.4=200×0.24=48. expected_aa=100×0.4²=100×0.16=16."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The N=0 vector produces a 0/0 division and all downstream outputs are undefined; the instrument must reject it. The convention probe also exposes an unvalidated mismatch between supplied N and the sum of genotype counts.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/allele-genotype-frequency-from-pedigree-counts/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/allele-genotype-frequency-from-pedigree-counts/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/allele-genotype-frequency-from-pedigree-counts/qualification/>)

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json`

- `evidence-tranche5/tranche5-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`