BKQualit

Analysis of Qualitative Traits, Segregation and Genetic Linkage

Qualitative traits are usually analysed with a hand-typed chi-square and left there. BKQualit does the rest of the job: it names the gene action, says why a hypothesis failed, estimates linkage properly, and draws the figure.

Written for teaching and research in genetics and plant breeding by Dr. Praveen Kumar B. K., Department of Genetics and Plant Breeding, Agriculture University, Jodhpur.

Install

install.packages("BKQualit")            # once on CRAN
# development version
remotes::install_github("bkpraveenars-del/BKQualit")

Five functions, one plotting verb

Every result prints a plain-English verdict and plots with bq_plot().

Sixty seconds with the package

library(BKQualit)

## 1. Which ratio fits? Do not guess - fit them all.
res <- bq_segregate(bq_data("f2"), phenotype = "phenotype",
                    count = "count", trait = "trait")
res
bq_plot(res)

It fits every classical ratio with the right number of classes, ranks them by goodness of fit, and tells you what each one means (output abridged; the full printout also carries the Monte Carlo p value, the observed-versus-expected table, and every candidate ratio that was tried):

BEST-FITTING RATIO for each trait:

        Trait   n  Ratio  ChiSq df      p Verdict
 flower_colour 478    3:1 0.0251  1 0.8741    fits
     seed_coat 405    9:7 0.0004  1 0.9850    fits
    grain_type 462  9:6:1 0.0067  2 0.9966    fits
      awn_type 592   13:3 0.7096  1 0.3996    fits

Implied gene action:
   seed_coat : 9:7 - duplicate recessive epistasis (complementary genes)
   grain_type : 9:6:1 - duplicate genes with cumulative effect
   awn_type : 13:3 - dominant suppression epistasis

## 2. The ratio failed. Is the hypothesis wrong, or are the families unalike?
het <- bq_heterogeneity(bq_data("families"), family = "family",
                        classes = c("dominant", "recessive"),
                        trait = "trait", ratio = c(3, 1))
het

Trait: disease_reaction
        Source   ChiSq df      p Sig
        Pooled 25.5670  1 0.0000 ***
 Heterogeneity 58.8975 11 0.0000 ***
         Total 84.4645 12 0.0000 ***
  Interpretation: families are HETEROGENEOUS (p = 0.0000).
  Do not pool them; examine the families separately.

That distinction is the whole point. A single pooled chi-square would have called the 3:1 hypothesis wrong; the partition shows the real problem is that the families disagree, so pooling them was never valid.

## 3. Linkage by maximum likelihood, not by the old product-ratio table
lk <- bq_linkage(bq_data("linkage"), pair = "pair",
                 classes = c("AB", "Ab", "aB", "ab"),
                 design = "design", phase = "phase")
lk
bq_plot(lk)                    # likelihood profiles with the LOD = 3 line
bq_plot(lk, type = "estimates")

## 4. Which descriptors earn their place on the DUS form?
dv <- bq_diversity(bq_data("dus"),
        descriptors = c("growth_habit", "leaf_pubescence", "flower_colour",
                        "seed_colour", "seed_shape"))
dv
bq_plot(dv)

## 5. Group the accessions, and see what drives the grouping
mc <- bq_mca(bq_data("dus"),
        descriptors = c("growth_habit", "leaf_pubescence", "flower_colour",
                        "seed_colour", "seed_shape", "pod_curvature"),
        accession = "accession", numeric_vars = "plant_height_cm", k = 3)
mc
bq_plot(mc)                     # accessions and descriptor states together
bq_plot(mc, type = "dendrogram")

What is done differently here

The chi-square is partitioned, not just reported. Pooled plus heterogeneity equals total, exactly. A poor fit is attributed either to the wrong hypothesis or to variation between families. Most software gives you one number and leaves the diagnosis to you.

Yates’ correction is applied only at one degree of freedom. That is where it is defined. Applying it to a 9:3:3:1 table, which is common in practice, makes the test conservative for no reason.

Sparse tables get a Monte Carlo exact test. The chi-square approximation is unreliable when an expected count falls below five, which happens routinely in the rarest class of a 15:1 or 63:1 table.

Linkage is estimated by maximising the likelihood. The recombination fraction comes from the multinomial likelihood, not the product-ratio approximation, and the confidence interval comes from likelihood-ratio inversion rather than a symmetric standard error - which matters, because the likelihood is skewed as r approaches its boundary at 0.5. Coupling and repulsion phase, F2 and backcross, are all handled.

MCA inertias are Benzecri-adjusted. Raw indicator inertias badly understate the structure because splitting a descriptor into several columns injects inertia that carries no information. On the bundled data the first two axes carry 30% of the raw inertia but 86% of the adjusted inertia. The adjusted figure is the honest one.

Gower distance handles mixed data. Nominal and numeric descriptors enter the same distance, so plant height can sit alongside flower colour.

Companion packages

A note on the bundled data

The four example datasets are simulated from known parameters, so the correct answer is known in advance and the package can be tested against arithmetic rather than against itself. They are not field observations and should not be cited as such.

f2_segregation.csv was generated on these expectations, which bq_segregate() recovers when no ratio is stated:

family_segregation.csv holds two traits of twelve families each. flower_colour was drawn entirely from 3:1, so both the pooled and the heterogeneity chi-square should be non-significant. disease_reaction was drawn from a mixture of different underlying proportions, so the heterogeneity chi-square should be significant and pooling is not justified. That contrast is the teaching point of bq_heterogeneity().

linkage_data.csv covers all four design-by-phase combinations plus an independent pair:

Every generating value below 0.5 falls inside its own confidence interval. The F-G pair was generated under independent assortment, and its LOD of 0.17 is far below the threshold of 3.

dus_descriptors.csv holds forty accessions scored for six nominal descriptors, two ordered descriptors and one numeric variable, with deliberately unequal state frequencies so that the ranking by discriminating power is meaningful.

Citation

citation("BKQualit")

B. K., Praveen Kumar (2026). BKQualit: Analysis of Qualitative Traits, Segregation and Genetic Linkage. R package version 0.1.0. https://github.com/bkpraveenars-del/BKQualit

References

Mather K (1951). The Measurement of Linkage in Heredity, 2nd ed. Methuen, London.

Allard RW (1956). Formulas and tables to facilitate the calculation of recombination values in heredity. Hilgardia 24, 235-278. doi:10.3733/hilg.v24n10p235

Gower JC (1971). A general coefficient of similarity and some of its properties. Biometrics 27, 857-871. doi:10.2307/2528823

License

GPL-3