Marker-level pedigree meiosis qualification

Historical evidence: these measurements retain their recorded revisions, fixtures and limitations; website rendering does not rerun scientific qualification.

Scope

This is the bounded qualification for the byte-matrix Mendelian inheritance oracle frozen in docs/design/pedigree_marker_meiosis.md. It uses no external data, runtime, package dependency, broad benchmark, or large pedigree.

Exact fixtures cover founder-ID alignment, later founders, a grandchild, paternal and maternal phase meanings, one-marker and zero-length chromosomes, fixed zero/one/multiple crossovers, crossover/marker equality, multiple chromosomes, canonical traversal, invalid inputs, output options, operational batches, external pedigree permutations, chromosome subsets, unrelated-animal addition, and R global-RNG isolation. Mendelian checking compares every child allele independently with the corresponding two parental alleles; the observed inconsistency count is zero.

Focused relationship experiment

The relationship fixture contains four unrelated founders and four families of eight offspring: (S1,D1), (S1,D2), (S2,D1), and (S2,D2). Thus it has parent-offspring, full-sib, paternal-half-sib, and maternal-half-sib groups. There are 256 independent, single-marker chromosomes. Founder alleles are fixed Bernoulli-0.5 fixture values. With z = genotype - 1, relationships are calculated independently of meiosis as 2 * tcrossprod(z) / 256.

Markers are divided into sixteen fixed blocks of sixteen. For each relationship group, the Monte Carlo standard error is the standard deviation of its sixteen block means divided by four. The predeclared acceptance interval is the realized mean plus or minus four standard errors and must contain the pedigree expectation.

Group	Mean	Monte Carlo SE	Four-SE interval	Pair SD	Expected
Parent-offspring	0.481323	0.029466	[0.363461, 0.599186]	0.053108	0.50
Full siblings	0.479422	0.029319	[0.362145, 0.596700]	0.051567	0.50
Paternal half siblings	0.236389	0.030953	[0.112578, 0.360201]	0.046949	0.25
Maternal half siblings	0.253479	0.029711	[0.134636, 0.372322]	0.053130	0.25
Unrelated founders	0.001302	0.028430	[-0.112418, 0.115022]	0.065442	0.00

All expectations lie inside their uncertainty-based intervals. Nonzero full-sib and half-sib pair standard deviations demonstrate realized segregation variation rather than fixed pedigree coefficients.

Authoritative source