Package {BKQualit}

BKQualit: Analysis of Qualitative Traits in Plant Breeding

Description

Tools for the genetic analysis of qualitative (discretely inherited) characters: testing observed segregation against Mendelian expectations, partitioning chi-square across families into pooled and heterogeneity components, estimating linkage by maximum likelihood, and summarising and clustering qualitative descriptors of the kind recorded on a distinctness, uniformity and stability (DUS) form.

Analysis functions

bq_segregate

Fit observed counts to Mendelian ratios; ranks a library of classical ratios and names the gene action implied.

bq_heterogeneity

Partition the total chi-square over families into pooled and heterogeneity components.

bq_linkage

Estimate the recombination fraction by maximum likelihood with a logarithm of odds (LOD) score and a likelihood-ratio confidence interval.

bq_diversity

Shannon, Simpson and evenness indices for qualitative descriptors, with discriminating power.

bq_mca

Multiple correspondence analysis with the Benzecri adjustment, plus Gower-distance clustering of accessions.

Support

bq_data loads the bundled example datasets, bq_plot draws every result, bq_save writes all figures for a result to disk, and bq_palette, theme_bq, scale_colour_bq and scale_fill_bq provide the shared visual style.

Design

Every analysis function returns a classed list with a print method that states the conclusion in words as well as numbers, and a bq_plot method. Nothing is written to the user's file space unless bq_save is called explicitly.

Author(s)

Praveen Kumar B. K. bkpraveenars@gmail.com

References

Mather K (1951). The Measurement of Linkage in Heredity, 2nd edition. 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

Load a bundled example dataset

Description

Reads one of the demonstration datasets shipped with the package. The datasets are simulated from known parameters and exist for documentation, teaching and regression testing.

Usage

bq_data(name = c("f2", "families", "linkage", "dus"))

Arguments

Value

A data frame.

Examples

str(bq_data("f2"))
head(bq_data("dus"))

Diversity of qualitative descriptors

Description

Summarises a set of categorical descriptors, of the kind recorded on a distinctness, uniformity and stability (DUS) form, into per-descriptor diversity indices, and identifies which descriptors actually discriminate among accessions.

Usage

bq_diversity(data, descriptors, accession = NULL, group = NULL)

Arguments

Details

Three complementary indices are reported for each descriptor. The Shannon-Weaver index H' = -\sum p_i \log p_i is sensitive to rare states; the Simpson index 1 - \sum p_i^2 is dominated by common states; and evenness J' = H'/\log s rescales Shannon by the number of observed states s so that descriptors with different numbers of states can be compared directly. A descriptor with a single observed state is monomorphic, contributes nothing to discrimination, and is flagged.

A descriptor is useful only if it separates accessions. The discriminating power reported here is the probability that two randomly chosen accessions differ in that descriptor, which equals the Simpson index; descriptors are ranked on it so that the least informative can be dropped from a characterisation form.

Value

An object of class bq_diversity containing per-descriptor diversity indices, the frequency of every state, and, if group is supplied, the same indices within each group.

See Also

bq_mca

Examples

d <- bq_data("dus")
res <- bq_diversity(d,
  descriptors = c("growth_habit", "leaf_pubescence", "flower_colour",
                  "seed_colour", "seed_shape"),
  accession = "accession")
res
bq_plot(res)
bq_plot(res, type = "frequencies")

Pooled and heterogeneity chi-square across families

Description

Partitions the total chi-square computed over several segregating families into a pooled component and a heterogeneity component. This is the standard way to decide why a segregation hypothesis fails.

Usage

bq_heterogeneity(data, family, classes, trait = NULL, ratio = c(3, 1))

Arguments

Details

Writing \chi^2_i for the goodness-of-fit statistic of family i, the total is \sum_i \chi^2_i on k(c-1) degrees of freedom, the pooled statistic is computed from the summed counts on c-1 degrees of freedom, and the heterogeneity statistic is the difference on (k-1)(c-1) degrees of freedom, where k is the number of families and c the number of phenotype classes. The partition is exact.

The two components answer different questions. A significant pooled chi-square with a non-significant heterogeneity means the families behave alike but the hypothesised ratio is wrong. A significant heterogeneity means the families do not behave alike, so pooling them is not justified and the pooled test should not be interpreted.

Value

An object of class bq_heterogeneity containing the per-family goodness of fit and the pooled, heterogeneity and total chi-square components.

See Also

bq_segregate

Examples

d <- bq_data("families")
res <- bq_heterogeneity(d, family = "family",
                        classes = c("dominant", "recessive"),
                        trait = "trait", ratio = c(3, 1))
res
bq_plot(res)

Estimate genetic linkage by maximum likelihood

Description

Estimates the recombination fraction between two loci from two-locus second filial generation (F2) or backcross counts, and tests it against independent assortment.

Usage

bq_linkage(data, pair, classes, design = NULL, phase = NULL, conf = 0.95)

Arguments

Details

For a backcross the recombination fraction is the proportion of recombinant progeny, a binomial parameter. For an F2 in coupling phase the four phenotype classes occur in the proportions (2+\theta)/4, (1-\theta)/4, (1-\theta)/4 and \theta/4 with \theta=(1-r)^2; in repulsion phase the outer and inner proportions are exchanged. The recombination fraction is obtained by maximising the multinomial likelihood numerically rather than from the older product-ratio approximation.

The LOD score compares the fitted model with independent assortment, and a value above 3 is the conventional threshold for declaring linkage. The confidence interval is obtained by likelihood-ratio inversion, retaining every value of the recombination fraction whose log-likelihood lies within 1.921 of the maximum; this is preferred to a symmetric standard-error interval because the likelihood is skewed near the boundary. Map distance is reported as 100 times the recombination fraction and is not corrected for double crossovers.

Value

An object of class bq_linkage containing the estimated recombination fraction, its confidence interval, the logarithm of odds (LOD) score, the map distance and a test against independent assortment, together with the likelihood profile for plotting.

References

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

Examples

d <- bq_data("linkage")
res <- bq_linkage(d, pair = "pair",
                  classes = c("AB", "Ab", "aB", "ab"),
                  design = "design", phase = "phase")
res
bq_plot(res)
bq_plot(res, type = "estimates")

Multiple correspondence analysis and Gower clustering of accessions

Description

Places accessions and descriptor states in a common low-dimensional space by multiple correspondence analysis (MCA), and groups the accessions by hierarchical clustering of the Gower distance.

Usage

bq_mca(data, descriptors, accession = NULL, numeric_vars = NULL,
       k = 3, ndim = 2)

Arguments

Details

MCA is computed from the singular value decomposition of the standardised indicator matrix. Writing Z for the n \times J indicator of Q descriptors, P = Z/(nQ), and r, c for its row and column margins, the decomposition is applied to D_r^{-1/2}(P - rc^{\top})D_c^{-1/2}. Row and column principal coordinates then satisfy the transition relation F = (Z/Q)G_{std}, so an accession sits at the centroid of the descriptor states it carries, which is what makes an MCA biplot directly readable.

The raw principal inertias of an indicator MCA understate the structure badly, because coding a descriptor into several columns injects inertia that carries no information. The Benzecri adjustment is therefore also reported: axes with inertia above 1/Q are rescaled to ((Q/(Q-1))(\lambda - 1/Q))^2. Interpret the adjusted percentages, not the raw ones.

The Gower distance handles nominal and numeric descriptors together: nominal descriptors contribute 0 when two accessions match and 1 when they differ, numeric descriptors contribute the absolute difference divided by the range, and the contributions are averaged. Clustering uses Ward's minimum-variance criterion on that distance.

Value

An object of class bq_mca containing the principal inertias with the Benzecri adjustment, row and column coordinates, the Gower distance matrix, the clustering, and a modal profile of each cluster.

References

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

See Also

bq_diversity

Examples

d <- bq_data("dus")
res <- bq_mca(d,
  descriptors = c("growth_habit", "leaf_pubescence", "flower_colour",
                  "seed_colour", "seed_shape", "pod_curvature"),
  accession = "accession", numeric_vars = "plant_height_cm", k = 3)
res
bq_plot(res)
bq_plot(res, type = "dendrogram")
bq_plot(res, type = "scree")

Colour palettes for qualitative-trait figures

Description

Returns the colours used throughout the package. Categorical palettes are returned unchanged when enough colours are available and interpolated otherwise; sequential palettes are always interpolated.

Usage

bq_palette(name = c("phenotype", "fit", "linkage", "descriptor", "contrast"),
           n = NULL, reverse = FALSE)

Arguments

Value

A character vector of hexadecimal colours.

Examples

bq_palette("phenotype")
bq_palette("linkage", 6)

Plot a BKQualit result

Description

A single plotting verb for every analysis in the package. The method chosen depends on the class of x.

Usage

bq_plot(x, ...)

Arguments

Details

Several results accept a type argument selecting among alternative views: bq_linkage offers "profile" and "estimates"; bq_diversity offers "indices" and "frequencies"; bq_mca offers "biplot", "dendrogram" and "scree".

Value

A ggplot object.

See Also

bq_save

Examples

res <- bq_segregate(bq_data("f2"), phenotype = "phenotype",
                    count = "count", trait = "trait")
bq_plot(res)

Save every figure from a BKQualit result

Description

Convenience wrapper that writes all available views of a result to disk as PNG files. Nothing is written unless this function is called.

Usage

bq_save(x, path = tempdir(), prefix = NULL, width = 8, height = 5.5,
        dpi = 300)

Arguments

Value

Character vector of the files written, invisibly.

Examples

res <- bq_segregate(bq_data("f2"), phenotype = "phenotype",
                    count = "count", trait = "trait")
bq_save(res, path = tempdir())

Test observed segregation against Mendelian ratios

Description

Fits observed phenotype counts to the classical Mendelian expectations. When no ratio is stated, a library of standard mono-, di- and trihybrid ratios with the matching number of classes is fitted and ranked, and the gene action implied by the best fit is named.

Usage

bq_segregate(data = NULL, phenotype = NULL, count = NULL,
             trait = NULL, ratio = NULL, counts = NULL,
             simulate = TRUE, B = 10000, seed = 1L)

Arguments

Details

The Pearson chi-square is reported with the Yates continuity correction applied only when there is a single degree of freedom, which is where the correction is defined; applying it more widely is a common error that makes tests conservative. A Monte Carlo exact test is also run, because the chi-square approximation is unreliable when an expected count falls below five, as it often does in the rarest class of a 63:1 or 9:3:3:1 table.

A high p value does not prove the hypothesis. It means the data are compatible with it. Where two ratios fit almost equally well, the printed output says so rather than declaring a winner.

Value

An object of class bq_segregate holding the fitted ratios ranked by goodness of fit, the observed and expected counts, and the gene action implied by the best-fitting ratio.

References

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

See Also

bq_heterogeneity, bq_plot

Examples

d <- bq_data("f2")
res <- bq_segregate(d, phenotype = "phenotype", count = "count",
                    trait = "trait")
res
bq_plot(res)

## a single trait against a stated hypothesis
bq_segregate(counts = c(purple = 312, white = 104), ratio = c(3, 1))

Discrete colour and fill scales for BKQualit palettes

Description

Discrete scales built on the package palettes. scale_color_bq is an alias of scale_colour_bq.

Usage

scale_colour_bq(pal_name = "phenotype", reverse = FALSE, ...)

scale_fill_bq(pal_name = "phenotype", reverse = FALSE, ...)

Arguments

Value

A ggplot2 scale object.

See Also

bq_palette, theme_bq

Examples

library(ggplot2)
ggplot(bq_data("dus"), aes(growth_habit, fill = seed_shape)) +
  geom_bar() +
  scale_fill_bq("descriptor", name = "Seed shape") +
  theme_bq()

The BKQualit ggplot2 theme

Description

A clean theme with a soft background, muted grid and a coloured title, applied by every plotting method in the package. It can be added to any ggplot of your own.

Usage

theme_bq(base_size = 12, base_family = "", grid = TRUE)

Arguments

Value

A ggplot2 theme object.

Examples

library(ggplot2)
ggplot(bq_data("dus"), aes(growth_habit)) +
  geom_bar(fill = bq_palette("phenotype", 1)) +
  theme_bq()