A starting point {qtl}R Documentation

Introductory comments on R/qtl

Description

A brief introduction to the R/qtl package, with a walk-through of an analysis.

New to R and/or R/qtl?

Walk-through of an analysis

Here we briefly describe the use of R/qtl to analyze an experimental cross. A more extensive tutorial on its use is distributed with the package and is also available at https://rqtl.org/rqtltour.pdf.

A difficult first step in the use of most data analysis software is the import of data. With R/qtl, one may import data in several different formats by use of the function read.cross. The internal data structure used by R/qtl is rather complicated, and is described in the help file for read.cross. We won't discuss data import any further here, except to say that the comma-delimited format ("csv") is recommended. If you have trouble importing data, send an email to Karl Broman, broman@wisc.edu, perhaps attaching examples of your data files. (Such data will be kept confidential.) Also see the sample data files and code at https://rqtl.org/sampledata/.

We consider the example data hyper, an experiment on hypertension in the mouse, kindly provided by Bev Paigen and Gary Churchill. Use the data function to load the data.

data(hyper)

The hyper data set has class "cross". The function summary.cross gives summary information on the data, and checks the data for internal consistency. A number of other utility functions are available; hopefully these are self-explanatory.

summary(hyper)
nind(hyper)
nphe(hyper)
nchr(hyper)
nmar(hyper)
totmar(hyper)

The function plot.cross gives a graphical summary of the data; it calls plotMissing (to plot a matrix displaying missing genotypes) and plotMap (to plot the genetic maps), and also displays histograms or barplots of the phenotypes. The plotMissing function can plot individuals ordered by their phenotypes; you can see that for most markers, only individuals with extreme phenotypes were genotyped.

plot(hyper)
plotMissing(hyper)
plotMissing(hyper, reorder=TRUE)
plotMap(hyper)

Note that one marker (on chromosome 14) has no genotype data. The function drop.nullmarkers removes such markers from the data.

hyper <- drop.nullmarkers(hyper)
totmar(hyper)

The function est.rf estimates the recombination fraction between each pair of markers, and calculates a LOD score for the test of r = 1/2. This is useful for identifying markers that are placed on the wrong chromosome. Note that since, for these data, many markers were typed only on recombinant individuals, the pairwise recombination fractions show rather odd patterns.

hyper <- est.rf(hyper)
plotRF(hyper)
plotRF(hyper, chr=c(1,4))

To re-estimate the genetic map for an experimental cross, use the function est.map. The function plotMap, in addition to plotting a single map, can plot the comparison of two genetic maps (as long as they are composed of the same numbers of chromosomes and markers per chromosome). The function replace.map map be used to replace the genetic map in a cross with a new one.

newmap <- est.map(hyper, error.prob=0.01, verbose=TRUE)
plotMap(hyper, newmap)
hyper <- replace.map(hyper, newmap)

The function calc.errorlod may be used to assist in identifying possible genotyping errors; it calculates the error LOD scores described by Lincoln and Lander (1992). The calc.errorlod function return a modified version of the input cross, with error LOD scores included. The function top.errorlod prints the genotypes with values above a cutoff (by default, the cutoff is 4.0).

hyper <- calc.errorlod(hyper, error.prob=0.01)
top.errorlod(hyper)

The function plotGeno may be used to inspect the observed genotypes for a chromosome, with likely genotyping errors flagged.

plotGeno(hyper, chr=16, ind=c(24:34, 71:81))

Before doing QTL analyses, some intermediate calculations need to be performed. The function calc.genoprob calculates conditional genotype probabilities given the multipoint marker data. sim.geno simulates sequences of genotypes from their joint distribution, given the observed marker data.

As with calc.errorlod, these functions return a modified version of the input cross, with the intermediate calculations included. The step argument indicates the density of the grid on which the calculations will be performed, and determines the density at which LOD scores will be calculated.

hyper <- calc.genoprob(hyper, step=2.5, error.prob=0.01)
hyper <- sim.geno(hyper, step=2.5, n.draws=64, error.prob=0.01)

The function scanone performs a genome scan with a single QTL model. By default, it performs standard interval mapping (Lander and Botstein 1989): use of a normal model and the EM algorithm. If one specifies method="hk", Haley-Knott regression is performed (Haley and Knott 1992). These two methods require the results from calc.genoprob.

out.em <- scanone(hyper)
out.hk <- scanone(hyper, method="hk")

If one specifies method="imp", a genome scan is performed by the multiple imputation method of Sen and Churchill (2001). This method requires the results from sim.geno.

out.imp <- scanone(hyper, method="imp")

The output of scanone is a data.frame with class "scanone". The function plot.scanone may be used to plot the results, and may plot up to three sets of results against each other, as long as they conform appropriately.

plot(out.em)
plot(out.hk, col="blue", add=TRUE)
plot(out.imp, col="red", add=TRUE)
plot(out.hk, out.imp, out.em, chr=c(1,4), lty=1,
col=c("blue","red","black"))

The function summary.scanone may be used to list information on the peak LOD for each chromosome for which the LOD exceeds a specified threshold.

summary(out.em)
summary(out.em, threshold=3)
summary(out.hk, threshold=3)
summary(out.imp, threshold=3)

The function max.scanone returns the maximum LOD score, genome-wide.

max(out.em)
max(out.hk)
max(out.imp)

One may also use scanone to perform a permutation test to get a genome-wide LOD significance threshold.

operm.hk <- scanone(hyper, method="hk", n.perm=1000)

The result has class "scanoneperm". The summary.scanoneperm function may be used to calculate LOD thresholds.

summary(operm.hk, alpha=0.05)

The permutation results may also be used in the summary.scanone function to calculate LOD thresholds and genome-scan-adjusted p-values.

summary(out.hk, perms=operm.hk, alpha=0.05, pvalues=TRUE)

We should say at this point that the function save.image will save your workspace to disk. You'll wish you had used this if R crashes.

save.image()

The function scantwo performs a two-dimensional genome scan with a two-QTL model. Methods "em", "hk" and "imp" are all available. scantwo is considerably slower than scanone, and can require a great deal of memory. Thus, you may wish to re-run calc.genoprob and/or sim.geno with a more coarse grid.

hyper <- calc.genoprob(hyper, step=10, err=0.01)
hyper <- sim.geno(hyper, step=10, n.draws=64, err=0.01)

out2.hk <- scantwo(hyper, method="hk")
out2.em <- scantwo(hyper)
out2.imp <- scantwo(hyper, method="imp")

The output is an object with class scantwo. The function plot.scantwo may be used to plot the results. The upper triangle contains LOD scores for tests of epistasis, while the lower triangle contains LOD scores for the full model.

plot(out2.hk)
plot(out2.em)
plot(out2.imp)

The function summary.scantwo lists the interesting aspects of the output. For each pair of chromosomes (k,l), it calculates the maximum LOD score for the full model, M_f(k,l); a LOD score indicating evidence for a second QTL, allowing for epistasis), M_{fv1}(k,l); a LOD score indicating evidence for epistasis, M_i(k,l); the LOD score for the additive QTL model, M_a(k,l); and a LOD score indicating evidence for a second QTL, assuming no epistasis, M_{av1}(k,l).

You must provide five LOD thresholds, corresponding to the above five LOD scores, and in that order. A chromosome pair is printed if either (a) M_f(k,l) \ge T_f and (M_{fv1}(k,l) \ge T_{fv1} or M_i(k,l) \ge T_i), or (b) M_a(k,l) \ge T_a and M_{av1}(k,l) \ge T_{av1}.

summary(out2.em, thresholds=c(6.2, 5.0, 4.6, 4.5, 2.3))
summary(out2.em, thresholds=c(6.2, 5.0, Inf, 4.5, 2.3))

In the latter case, the interaction LOD score will be ignored.

The function max.scantwo returns the maximum joint and additive LODs for a two-dimensional genome scan.

max(out2.em)

Permutation tests may also performed with scantwo; it may take a few days of CPU time. The output is a list containing the maxima of the above five LOD scores for each of the imputations.

operm2 <- scantwo(hyper, method="hk", n.perm=100)
summary(operm2, alpha=0.05)

Citing R/qtl

To cite R/qtl in publications, use the Broman et al. (2003) reference listed below.

Author(s)

Karl W Broman, broman@wisc.edu

References

Broman, K. W. and Sen, Ś. (2009) A guide to QTL mapping with R/qtl. Springer. https://rqtl.org/book/

Broman, K. W., Wu, H., Sen, Ś. and Churchill, G. A. (2003) R/qtl: QTL mapping in experimental crosses. Bioinformatics 19, 889–890.

Haley, C. S. and Knott, S. A. (1992) A simple regression method for mapping quantitative trait loci in line crosses using flanking markers. Heredity 69, 315–324.

Lander, E. S. and Botstein, D. (1989) Mapping Mendelian factors underlying quantitative traits using RFLP linkage maps. Genetics 121, 185–199.

Lincoln, S. E. and Lander, E. S. (1992) Systematic detection of errors in genetic linkage data. Genomics 14, 604–610.

Sen, Ś. and Churchill, G. A. (2001) A statistical framework for quantitative trait mapping. Genetics 159, 371–387.

[Package qtl version 1.66 Index]