Paternity badge: "father is not 19058m" (OSU family 2022005)

Status: TENTATIVE · 2026-10-08 · observations, not conclusions · GBS (ApeKI) on the 21110M male_ref frame, Akagi chromosome numbering · no new alignment or variant calls were made for this page.

What the badge says

OSU family 2022005 is recorded as Cascade (mother) × USDA 19058m (father), 369 GBS-sequenced seedlings (PRJNA1424574). The badge marks a seedling whose paternal alleles are not consistent with 19058m being its father. It does not say who the father is. It carries a grade: strong (Y) for 20 seedlings, strong (autosomal) for 47, moderate for 5 and possible for 1 (2022005-164, which the original flag missed). Nothing is graded weak. The 72 badged seedlings are 19.5 % of the family; the grades are a description of how far each seedling sits from the 290 reference seedlings, not a probability that 19058m is excluded.

Loading seedling card…

Table: the clicked seedling's values. OH and flip are given with their 95 % 5-Mb block-bootstrap intervals, the number of sites or site pairs they rest on, the reference 99th percentile they are compared with, the number of 5-Mb blocks and autosomes carrying excess evidence, the Y lineage, and the grade with its criterion.

How a seedling is tested

Three measurements enter the grade. The first two are autosomal and use the same site classes and depth filters for every seedling; the third uses the Y chromosome and applies only to sons.

Opposite homozygotes versus 19058m (OH). Where 19058m is homozygous (depth ≥ 10, no reads of the other allele in his GBS library), a true child must carry his allele. OH is the fraction of such sites, at seedling depth ≥ 8, where the seedling has zero reads of that allele; sites where Cascade is homozygous for the other allele and sites where Cascade is heterozygous both count. The rate is pooled over the nine autosomes (median 9,903 sites per flagged seedling, minimum 2,161). It is not zero in true children, because GBS restriction-site null alleles drop one parental allele at some tags: the reference median is 0.038.

Paternal flip rate. Where 19058m is heterozygous and Cascade homozygous, his two homologs were phased by chaining across 224 reference progeny. A true child follows one homolog along a chromosome and switches only at crossovers; a child of another male has no homolog to follow and switches at random. The flip rate is the fraction of consecutive informative observations at which the inherited homolog switches, pooled over chromosomes (Chr02 and Chr07, with 16 and 21 phased sites, contribute almost nothing). Flip tests homolog identity rather than allele frequency, which is what gives the badge its specificity.

Y lineage. Male-specific 31-mers from four assembled hop Y chromosomes, counted over all reads with Cascade's own k-mers removed (sex verification, 2026-10-04). 19058m carries an American-type (Am) Y of the MN586 type; a son with a lupulus-type (L) Y, or an MN1421-type Am-Y (2022005-320), cannot have received it from him. This line is independent of the autosomal statistics and decisive when it applies. Daughters, and the 4 sons carrying a 19058m-type Am-Y, are graded on the autosomal line only.

Figure: all 369 seedlings ranked by OH versus 19058m, each with its 95 % 5-Mb block-bootstrap interval. The dotted line is the leave-one-out 99th percentile of the 290 reference seedlings (0.062). Grey = reference, green = the 7 sex/ploidy anomalies excluded from the reference, orange = moderate, blue = strong; the clicked seedling is highlighted.

Figure: the same 369 seedlings ranked by paternal flip rate with block-bootstrap intervals; the reference 99th percentile is 0.107. The two triploid-like seedlings 2022005-308 and -374 sit high on flip because they carry both 19058m homologs, which is why they were removed from the paternity rule by hand.

The reference set and how uncertainty is measured

The original flag (2026-10-04) was a hard cut on two point estimates, flip > 0.12 and OH > 0.06, read off a bimodal histogram; it carried no interval and no null. The audit of 2026-10-08 added both.

The reference set was declared before grading: the 297 unflagged seedlings minus 7 sex-chromosome or ploidy anomalies (2022005-004, -011, -076, -180, -328, -308, -374), 290 seedlings. Among them OH has median 0.038 (robust s.d. 0.0099, 99th percentile 0.062) and flip median 0.049 (robust s.d. 0.021, 99th percentile 0.107); for a reference seedling the percentile leaves that seedling out. The reference is defined by the flag it audits, so a child of a close 19058m relative with a mild signal could sit inside it and widen its tail (2022005-164 is such a case); the thresholds are, if anything, conservative.

Uncertainty is a 5-Mb block bootstrap: the 440 autosomal blocks of the atlas grid are resampled with replacement 2,000 times and OH and flip recomputed. A binomial (Wilson) interval on pooled sites is too narrow because all sites in a block share one inherited haplotype and one dropout history; the block intervals are a median 2.2× (OH) and 1.5× (flip) wider over the 369 seedlings. Neighbouring blocks are still treated as independent, so linkage makes even these somewhat narrow. Distance from the reference is also given as a robust z and an empirical percentile.

Figure: distribution of OH versus 19058m in the 290 reference seedlings against the 72 flagged seedlings. Every flagged seedling is at or above the reference 99.3rd percentile (robust z ≥ 3.4).

Figure: the same comparison for the paternal flip rate; every flagged seedling is at or above the reference 99.7th percentile (robust z ≥ 3.6).

The grades and their criteria

Thresholds were fixed before the results were seen.

The 5 moderate seedlings are all daughters. For 2022005-243, -362 and -364 the OH lower bound (0.061, 0.061, 0.059) touches the reference tail while flip is far outside it (0.19, 0.21, 0.16); for 2022005-086 and -230 the flip lower bound (0.106, 0.105) is just under 0.107 while OH is clearly outside (0.084, 0.100). All 5 have 23–41 excess blocks on 7–8 autosomes and KING kinship to 19058m of 0.10–0.27; the record notes they look like children of a relative of 19058m rather than 19058m children with noisy data, which is a reading, not a result.

Grading was run twice, with the declared and the replacement block test described below; both give 67 strong / 5 moderate / 0 weak for the 72.

Controls

False positives on the reference set. The 290 reference seedlings were graded by the same rules. The declared rule grades 2/290 (0.7 %) moderate and 0 strong; the replacement rule 1/290 (0.3 %). 2022005-200 is a genuine false positive: its flip lower bound is 0.112 against 0.107, but OH is 0.036, KING to 19058m is 0.32 and the independent paternity check calls 19058m its father with confidence. 2022005-164 is better read as a missed case: OH 0.080 (0.064–0.098) with 33 excess blocks on 6 autosomes, KING −0.22, 26 atlas mismatch bins, independent check "not father, probable"; it escaped the flag only because its flip, 0.092, is under the 0.12 cut.

Wrong-father control (sensitivity of OH alone). The OH arm was re-run in the OSU panel call set with five other males as putative fathers, threshold 0.063 from the 19058m baseline in that call set. Against three relatives of 19058m (KING 0.31–0.36) the 290 reference seedlings are called "not father" in 34–80 % of cases (w1007-220 98/290, 21429m 162/290, 21018m 233/290); against an unrelated Am-Y male (21375m, KING 0.04) in 37 %; against a 19058m child (19105×19058m, 4,391 sites) in 18 %. OH alone is therefore a low-sensitivity test, and the flag's specificity rests on also requiring flip. The control implies that false negatives are more likely than false positives: 72 is probably a minimum.

A per-block test that failed. The declared test for evidence being spread over the genome was a per-block binomial test against the pooled reference rate (p < 0.001, ≥ 2 events). It failed its must-fail control: reference seedlings had a median of 8 "excess" blocks on 4 autosomes, because OH events cluster by inherited 19058m homolog (likely paternal null alleles) and are over-dispersed. It was replaced post hoc by an empirical test: a block counts only if the seedling's rate exceeds every reference seedling's rate in that block (leave-one-out; ≥ 10 sites, ≥ 3 events); reference seedlings then have a median of 1 block (99th percentile 11.2). Both versions are kept in the table.

Independent paternity check (calibrated simulation nulls, 2026-10-06): of the 72 flagged, 55 "not father, confident", 13 "not father, probable", 4 unresolved; of the 290 reference, 173 "father, confident", 111 "father, probable", 4 unresolved, 2 "not father, probable" (2022005-164 and -277, the latter a low-data library with 1,403 OH sites). That check used the 72 as its truth set, so this is consistency, not validation.

Figure: the clicked seedling's OH (top) and flip (bottom) per 5-Mb block along the nine autosomes. The grey band is the range of the 290 reference seedlings in that block, the line their median; a coloured dot marks a block where the seedling exceeds every reference seedling with ≥ 3 events. For flagged seedlings the excess blocks number 14–164 (median 39.5) on 5–9 autosomes (median 9); the single most-affected chromosome holds a median 36 % of them (maximum 80 %, 2022005-230) and chromosome-end blocks 14 %.

Why the 5-Mb ancestry tiles often show nothing

The atlas paints EU (A) / NAm (B) clade ancestry per 5-Mb bin. It does not paint which 19058m homolog a seedling carries. Over the autosomes 19058m is AA in 189 bins and AB in 250, never BB; Cascade is AA in 94 and AB in 345. A child of a different father can show a tile that Cascade × 19058m cannot produce in one situation only: a B allele in one of the 93 bins (21 % of the autosomal grid) where both parents are AA, and only if the other father carries NAm ancestry exactly there. Everywhere else a different father of similar, mostly European, ancestry paints the same tiles.

Accordingly 22 of the 72 flagged seedlings have 0 mismatch bins, 22 have exactly 1 (14 of them L-Y sons), and 45 have no chromosome in the atlas's mismatch class, while their SNP-level evidence is 14–164 excess blocks. The single bins sit mostly in the first or last bin of a chromosome.

Figure: per seedling, the number of atlas 5-Mb ancestry bins that fit neither parental combination (x, log-scaled above 10) against the number of SNP-level 5-Mb blocks above every reference seedling (y). The dotted line is the reference 99th percentile of excess blocks (11.2). Flagged seedlings with 0–1 atlas bins still carry 14–82 excess blocks; the atlas tile is a rare side effect of the paternity evidence, not the evidence.

Limits, and what would change a call

Provenance

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