Consistency Auditing of Reported Plant Breeding Statistics

Audits published or draft plant breeding tables for internal arithmetic consistency. Analysis of variance tables, precision statistics and genetic variability parameters are jointly over-determined by exact algebraic identities; 'BKVerify' recomputes every derivable quantity using rounding-interval arithmetic and reports a value as inconsistent only when no combination of values inside the reported rounding intervals can satisfy the identity. The package deliberately restricts itself to relationships that hold irrespective of which variance-component definition an author adopted, so that flagged results reflect arithmetic inconsistency rather than methodological disagreement. Implemented checks cover analysis of variance internal structure, coefficient of variation, standard error of mean and critical difference, the genetic advance identity of Johnson, Robinson and Comstock (1955) , the relation between genotypic and phenotypic coefficients of variation and broad-sense heritability, and admissibility of reported correlation matrices.

BKVerify

Consistency auditing of reported plant breeding statistics.

Psychology has statcheck, which recomputes p-values from reported test statistics; when journals began running it during peer review, reporting inconsistencies fell sharply (Nuijten & Wicherts 2024). Quantitative genetics has no equivalent, despite our tables being more auditable: the numbers printed in a variability table are not independent, they are linked by exact algebraic identities.

BKVerify recomputes every derivable quantity and reports whether the printed values can be reconciled.

The identities

The four columns printed in almost every variability table carry only two degrees of freedom:

And the ANOVA table is over-determined by three more:

Plus admissibility of any reported correlation matrix (symmetry, unit diagonal, |r| ≤ 1, positive semi-definiteness).

Every identity above is independent of which phenotypic variance definition the author adopted. That is deliberate, and it is the whole design constraint of the package — see What this does not do.

Quick start

library(BKVerify)

v <- bk_example("variability")   # 7 traits; 2 rows deliberately corrupted
bk_check_variability(v)

BKVerify audit <variability>
--------------------------------------------------------------
  28 checks: 25 consistent, 3 INCONSISTENT, 0 indeterminate, 0 n/a

  [INCONSISTENT] Grains per spike  h2 = (GCV/PCV)^2
        reported [89.045, 89.055]   implied [84.81, 85.11]
        note: definition-free: sigma^2_p cancels
  [INCONSISTENT] Grains per spike  GAM = K * h2 * PCV
        reported [26.615, 26.625]   implied [27.87, 27.90]
        note: no standard selection differential reconciles this row
  [INCONSISTENT] Grain yield per plant (g)  GAM = K * h2 * PCV
        reported [34.385, 34.395]   implied [29.88, 29.91]
        note: no standard selection differential reconciles this row
--------------------------------------------------------------

Audit a whole paper at once:

bk_audit(
  bk_check_variability(bk_example("variability")),
  bk_check_anova(bk_example("anova")),
  bk_check_corr(bk_example("corr"))
)

The failure pattern localises the error

Because the identities overlap, which tests fail tells you which printed number is wrong — not merely that something is:

gam_from_cv never touches h². h2_from_cv never touches GAM. The row that passes tells you where the fault is not.

Rounding is handled rigorously, not tolerantly

A value printed as 88.14 is not the number 88.14; it asserts the interval [88.135, 88.145). Every check is an interval comparison, and a value is flagged only when no combination of values inside the reported intervals can satisfy the identity.

Validated on 20,000 simulated RCBD trials (24 genotypes, 3 replications):

For the correlation matrix, non-definiteness is declared only when it is provable at the reported precision, via Weyl's inequality: λ_min(R) + δ√(n²−n) < 0 ⟹ no matrix inside the rounding box is positive semi-definite. Otherwise the verdict is indeterminate, and the package says so rather than guessing.

Selection intensity

A paper that omits its selection intensity is indistinguishable from one that used a different intensity. With k = "auto" (the default), BKVerify tests the whole family (K = 2.64, 2.06, 1.76, 1.40) and reports which member reconciles each trait:

k_used = "1.76 (10%)"
note   = "reconciles only at 10% selection intensity; confirm against the text"

That is a reporting observation, not an arithmetic accusation, and it is labelled as such.

What this does not do

This is the most important section.

• It does not recompute heritability from mean squares. σ²p is defined at least three defensible ways in the literature (σ²g + σ²e; σ²g + σ²e/r; forms carrying a genotype × environment term), and authors seldom state which they used. Flagging on that basis would confuse methodological disagreement with arithmetic error. Every identity implemented here survives that ambiguity.
• It does not flag |path coefficient| > 1 as impossible. Direct effects exceeding unity are a legitimate consequence of multicollinearity. They belong under diagnostics, not under impossibility. (Planned for Tier 3.)
• It does not read PDFs. Input is a clean data frame. Table extraction is a separate, much messier problem and mixing it in would import its error rate.
• It does not judge the analysis. A consistent verdict means the printed numbers can be reconciled. It says nothing about whether the design was sound, the model appropriate, or any discrepancy deliberate.

Roadmap

• Tier 1 — implemented. Zero-ambiguity identities: ANOVA structure, precision statistics, the variability identities, matrix admissibility.
• Tier 2 — formula-family reconciliation. Given mean squares, report which σ²p definition reproduces the reported h², rather than asserting one. Output is "consistent under σ²g + σ²e/r", never "error".
• Tier 3 — model validity. Detect algebraically dependent traits in path and correlation input (grain yield = biological yield × harvest index makes the system singular and the direct effects meaningless), plus VIF and condition number diagnostics.

Development

The package has no dependencies beyond stats. After editing roxygen comments:

devtools::document()   # regenerate man/ and NAMESPACE
devtools::test()
devtools::check()      # must be clean before submission

References

Burton, G. W. & DeVane, E. H. (1953). Estimating heritability in tall fescue from replicated clonal material. Agronomy Journal 45, 478–481.

Johnson, H. W., Robinson, H. F. & Comstock, R. E. (1955). Estimates of genetic and environmental variability in soybeans. Agronomy Journal 47, 314–318.

Nuijten, M. B. & Wicherts, J. M. (2024). Implementing statcheck during peer review is related to a steep decline in statistical-reporting inconsistencies. Advances in Methods and Practices in Psychological Science 7.

Licence

GPL-3