Performing polyploid QTL analysis using polyqtlR
Peter M. Bourke
2023-12-10
Introduction
It is nowadays increasingly feasible to conduct genetic analyses in
polyploid populations thanks to developments in genotyping technologies
as well as tools designed to deal with these genotypes.
polyqtlR is one such tool that provides a number of
functions to perform quantitative trait locus (QTL) mapping in F1
populations of outcrossing, heterozygous polyploid species. For more
details on the methodology, please see the 2021 Bioinformatics
publication of Bourke et
al..
polyqtlR assumes that a number of prior steps have
already been performed - in particular, that an integrated linkage map
for the mapping population has been generated. The package has been
developed to utilise the output of the mapping software
polymapR, although any alternative mapping software that
produces phased and integrated linkage maps could also be used. However,
the input files may have to be altered in such cases. Currently,
bi-allelic SNP markers are the expected raw genotypic data, which is
also the data format used by polymapR in map construction.
However, some functions can also accept probabilistic genotypic data,
for example in the estimation of IBD probabilities. Full functionality
of probabilistic genotypes in the package has yet to be implemented but
is planned for future releases. The assignment of marker dosages in
polyploid species can be achieved using a number of R packages such as
fitPoly (Voorrips, Gort, and Vosman
2011). More background on the steps of dosage-calling and
polyploid linkage mapping can be found in a review of the topic by (Peter M. Bourke, Voorrips, et al. 2018).
The QTL analysis functions primarily rely on identity-by-descent
(IBD) probabilities, which are the probabilities of inheritance of
particular combinations of parental haplotypes. Single-marker QTL
detection methods are also available. The package was originally
developed with the IBD output of TetraOrigin (Zheng et al. 2016) in mind. However, the
TetraOrigin package was implemented in the proprietary software
Mathematica, which many users may not have access to without
buying a licence. Since 2021 an updated method called PolyOrigin
(extended for multi-parental populations) has been released in the
OpenSource julia software (Zheng et al.
2021). Alternative options to estimate IBD probabilities for
multiple ploidy levels (2x, 3x, 4x and 6x) are also provided directly
polyqtlR.
Genotyping errors are a regular feature of modern marker datasets.
Although linkage mapping software such as polymapR has been
shown to be relatively robust against genotyping errors (Peter M. Bourke, Geest, et al. 2018), if
present in sufficiently large proportions (~10 % errors or more) issues
may arise with map accuracy and QTL detection. Therefore, a number of
functions have been included in polyqtlR to check map
accuracy using the estimated IBD probabilities, and to re-impute marker
genotypes if required. These imputed genotypes may then be used in an
iterative process to re-estimate the linkage map and re-run a QTL
analysis.
This tutorial goes through each of the steps in a typical QTL
analysis using the example datasets provided with the package, outlining
the different options that are available. However, it is certainly
recommended to consult the documentation that accompanies each of the
functions by running the ? command before the function name
(e.g. ?QTLscan).
Installing polyqtlR
polyqtlR can be installed using the following call from
within R:
install.packages("polyqtlR")There are a number of package dependencies which should be installed,
e.g. Rcpp, foreach, or
doParallel. Usually these will be automatically installed
as well but if not, you can always install them yourself one by one,
e.g.
install.packages("Rcpp")
install.packages("foreach")
install.packages("doParallel")before re-trying the installation of polyqtlR.
Eventually when all dependencies are on your computer, you should be
able to successfully run the following command (i.e. without
any error message):
library(polyqtlR)It is also a good time to load the datasets that you will need to perform a typical analysis, namely a phased maplist, a set of SNP marker genotypes (discrete dosage scores) and a set of trait data (phenotypes):
data("phased_maplist.4x", "SNP_dosages.4x", "Phenotypes_4x")In the example that follows we are using a simulated tetraploid dataset with 2 chromosomes for simplicity.
IBD probabilities
Currently two options to estimate IBD probabilities in an F1
population exist within polyqtlR. The first uses a
heuristic approach originally developed for tetraploids but later
applied to hexaploid populations (Peter M. Bourke
2014; Geest et al. 2017) and implemented here in the
polyqtlR::estimate_IBD function. This can be very
computationally efficient at higher ploidy levels (and has been
generalised to all ploidy levels), but the algorithm ignores
partially-informative marker information. In datasets with large numbers
of haplotype-specific markers this is not such an issue, but in datasets
with fewer such markers the accuracy of the resulting IBD probabilities
is compromised. The method behind TetraOrigin (Zheng et al. 2016) for offspring IBD
probability estimation given a known parental marker phasing has also
been implemented in the polyqtlR::estimate_IBD function
(this is the default method used). Note that unlike the original
TetraOrigin software, parental marker phasing is not re-estimated.
However, this is usually a direct output of the linkage mapping
procedure (e.g. using polymapR).
Data structures
As the IBD data are the most central objects in this package it is
worth spending a moment describing them. In polyqtlR, IBD
probabilities are organised in nested list form. The first level of
structure are the linkage groups. In our example dataset, the list has
two elements corresponding to the two linkage groups, each of which is
itself a list containing the following elements:
IBDtype The type of IBD probability, either “genotypeIBD” or “haplotypeIBD”
IBDarray A 3d array of IBD probabilities, with dimensions “locus”,“genotype class”, “individual”
map The integrated linkage map (marker names and cM positions, in order)
parental_phase The phasing of the markers in the parental map
marginal.likelihoods A list of marginal likelihoods of different valencies if method “hmm” was used, otherwise
NULLvalency The predicted valency that maximised the marginal likelihood, per offspring. For method “heur”,
NULLoffspring The offspring names
biv_dec Whether bivalents only (
TRUE) or also multivalents were allowed (FALSE) in the proceduregap Here
NULL, but later this can hold a numeric value (e.g. 1 cM) if IBDs are ‘splined’ or interpolated.genocodes Ordered list of genotype codes used to represent the different genotype classes
pairing Log likelihoods of each of the different pairing scenarios considered
ploidy The ploidy of parent 1
ploidy2 The ploidy of parent 2
method The method used, either “hmm” (Hidden Markov Model), “heur” (heuristic) or “hmm_TO” (Hidden Markov Model TetraOrigin)
error The offspring error prior (eps) used in the calculation.
All functions within polyqtlR for estimating or
importing IBD probabilities will automatically return them in this
form.
HMM for IBD estimation
The estimate_IBD function of polyqtlR with
the default setting method = "hmm" estimates offspring IBD
probabilities using a Hidden Markov Model (HMM) developed by Zheng et al
(Zheng et al. 2016) in the TetraOrigin
package but generalised in polyqtlR to multiple ploidy
levels. Currently, diploid (2x), triploid (3x = 4x \(\times\) 2x), tetraploid (4x) and hexaploid
(6x) populations are handled. genotypes can either be
discrete (i.e. integer marker dosage scores), or probabilistic
(i.e. the probabilities of each of the ploidy + 1 possible
scores). For triploids, tetraploids and hexaploids, the possibility of
incorporating double reduction (Peter M. Bourke
et al. 2015) (i.e. allowing for the phenomenon of
multivalent pairing) is available, although this can have serious
performance implications for hexaploids (and in hexaploids, the option
of allowing multivalent pairing in both parents for the same
chromosome is by default disabled as it requires very high RAM
requirements (> 32 Gb). Use argument
full_multivalent_hexa = TRUE to allow multivalents
simultaneously at the same position from both hexaploid parents).
Some of the code used to estimate these IBD probabilities has been
programmed in C++ to improve performance, and relies on both the
Rcpp and RcppArmadillo packages to provide the
interface between R, C++ and the Armadillo C++ library.
The expected format of input files is that used by the mapping
software polymapR (Peter M. Bourke,
Geest, et al. 2018). If you have used other software for map
construction and/or genotype calling, you will need to convert your
input files to the correct format. There are already some tools
available to do this (although it should be quite straightforward if you
look at the expected format using the example data files provided here).
For example, if you generated the phased linkage map using
mappoly (Mollinari and Garcia
2019), you can convert your map to the required format using the
convert_mappoly_to_phased.maplist function (check out the
help using ?convert_mappoly_to_phased.maplist for
details).
The genotypes can be either discrete or probabilistic. If the
genotypes are discrete, they must be provided as a matrix of marker
dosage scores (for example as provided in this tutorial in
SNP_dosages.4x) with marker names as row-names, and
individual names (including the two parents) as column-names. Checks are
performed and non-numeric data is converted to numeric data if needed.
Alternatively, probabilistic genotypes can be provided which can either
be the direct output of the fitpoly (Voorrips, Gort, and Vosman 2011) function
saveMarkerModels, or from some other polyploid-appropriate
genotype-calling software. For example, if polyRAD (Clark, Lipka, and Sacks 2019) or
updog (Gerard et al. 2018)
were used for genotype calling, a conversion step is needed. Functions
for doing this are provided by polymapR. Check out
?polymapR::convert_polyRAD or
?polymapR::convert_updog for details.
We run the function estimate_IBD using the phased
linkage map phased_maplist.4x as generated by
polymapR, in this case allowing for multivalents
(bivalent_decoding = FALSE), as follows:
IBD_4x <- estimate_IBD(phased_maplist = phased_maplist.4x,
genotypes = SNP_dosages.4x,
ploidy = 4,
bivalent_decoding = FALSE,
ncores = 4)Note that the default setting of bivalent_decoding is
TRUE, as the function evaluates faster if only bivalents
are considered (the difference in run-time becomes more pronounced for
hexaploids). However, allowing multivalents in the model gives a more
complete and correct picture.
Here we chose to enable parallel processing to speed up the
calculations. Note that jobs are split across linkage groups, so with 5
linkage groups it would have made more sense to use 5 cores if they were
available. Use parallel::detectCores() to display how many
CPU cores are available, and use 1 or 2 less than this at the very most.
In this dataset there are only 2 linkage groups, so no more than 2 cores
are needed.
nc <- parallel::detectCores() - 1Optional: Importing IBDs from TetraOrigin or PolyOrigin
If so desired, the TetraOrigin package (Mathematica software) or the
PolyOrigin package (julia software) can be used to estimate IBD
probabilities rather than using the estimate_IBD function.
The results should be quite similar for diploids or tetraploids. If
mapping in triploid or hexaploid populations,
polyqtlR::estimate_IBD should be used.
TetraOrigin
TetraOrigin produces by default a large .txt output file after running the function “inferTetraOrigin”. However, it is convenient to produce a summary of this output using the “saveAsSummaryITO” function, which produces a .csv file summarising the results. Information on how to use TetraOrigin is provided with the package itself, downloadable from GitHub.
The function import_IBD imports the .csv output of
TetraOrigin::saveAsSummaryITO. It takes a number of arguments, such as
folder, which is the folder containing the output of
TetraOrigin. For example, if we wanted to import IBDs from the subfolder
“TetraOrigin” for a species with 5 linkage groups, we would run the
following:
IBD_4x <- import_IBD(method = "TO", #TO for TetraOrigin
folder = "TetraOrigin",
filename = paste0("TetraOrigin_Output_bivs_LinkageGroup",1:5,"_Summary"),
bivalent_decoding = TRUE)Here it is assumed that the TetraOrigin summary filenames are “TetraOrigin_Output_bivs_LinkageGroup1_Summary.csv” etc. If all goes well, the following messages will be printed per linkage group:
Importing map data under description inferTetraOrigin-Summary,Genetic map of biallelic markers
Importing parental phasing under description inferTetraOrigin-Summary,MAP of parental haplotypes
Importing IBD data under description inferTetraOrigin-Summary,Conditonal genotype probabilityPolyOrigin
A more recent version of the TetraOrigin software has been released in julia, extended for multi-parental populations of either diploid or tetraploid species. Details of the method can be found in Zheng et al. (2021) (Zheng et al. 2021). The software, as well as vignettes detailing how to use it can also be found on GitHub.
Assuming the output files are in a folder called “PolyOrigin” with filestem “PolyOrigin_Output”, a similar call to import the IBDs would be:
IBD_4x <- import_IBD(method = "PO", #PO for PolyOrigin
folder = "PolyOrigin",
filename = "PolyOrigin_Output")Note that bivalent_decoding or error do not
need to be specified when method = "PO", as these
parameters are looked up from the PolyOrigin log file. Note also that
previously the summary output of TetraOrigin was split up per linkage
group. In PolyOrigin, the output from all linkage groups is kept
together.
“Heuristic” method for IBD estimation
In cases where the results are needed quickly, or where there are
very large numbers of markers, or for ploidy levels above 6, it is
convenient to use the heuristic approach to IBD estimation. We do this
using the estimate_IBD function as follows:
IBD_4x <- estimate_IBD(phased_maplist = phased_maplist.4x,
genotypes = SNP_dosages.4x,
method = "heur",
ploidy = 4)Note that the attribute IBDtype is now
haplotypeIBD, referring to the fact that these IBDs are the
probabilities of inheriting each parental haplotype at a locus, as
opposed to the probabilities of inheriting particular combinations of
parental alleles at a locus (genotypeIBD). Although
similar, certain downstream functions such as exploreQTL
can only work with the former (although you will still be able to
visualise QTL allele effects with the visualiseQTL
function). The accuracy of these IBDs is generally lower than
if method = "hmm" had been used (and therefore the power of
subsequent QTL analyses will be somewhat reduced).
High marker densities
Particularly at higher ploidy levels (6x), it becomes computationally
expensive to estimate IBDs using the hmm method. Our
experience has shown that for hexaploids with a mapping population size
of 400 or more individuals running on 4 cores, about 200 - 300 markers
per chromosome can be accommodated on an “above-average” desktop
computer (16 GB RAM). Running on a single core will reduce the committed
memory, but the evaluation time will therefore be much longer. 250
markers per chromosome should be already enough to estimate IBDs with
high accuracy - including extra markers over this amount will add
incrementally less information (following the law of diminishing
returns).
The function thinmap can be used to make a selection of
markers that tries to maximise their distribution across the genome and
across parental homologues. The argument bin_size is used
to specify the size of the bins in which markers are selected -
increasing this results in fewer markers being used. The ideal
bin_size is 1 cM, although at higher ploidies and with
higher marker densities, wider bins may be needed. The function is
called as follows:
thinned_maplist.4x <- thinmap(maplist = phased_maplist.4x,
dosage_matrix = SNP_dosages.4x)## 87 markers from a possible 93 on LG1 were included.
##
## 89 markers from a possible 93 on LG2 were included.
The object thinned_maplist.4x can then be used in place
of phased_maplist.4x in a call to
estimate_IBD.
Interpolating IBDs
Regardless of how they were generated, IBD probabilities are estimated at all marker positions provided. When we perform an initial scan for QTL, it is often more efficient to look for QTL at a grid of evenly-spaced positions (such as at every 1 cM). This is because the genotype data has been replaced with multi-point IBD estimates at the marker positions. Information at e.g. ten different markers within a 0.5 cM window is virtually identical and therefore just one representative for this locus should approximate the full information, while reducing the number of statistical tests. This becomes particularly relevant when we generate significance thresholds using permutation tests later, which are computationally quite demanding.
It is therefore recommended to interpolate the probabilities using
the spline_IBD function as follows:
IBD_4x.spl <- spline_IBD(IBD_list = IBD_4x,
gap = 1) #grid at 1 cM spacingVisualising IBD haplotypes
Before performing a QTL analysis, it is a good idea to visualise the
IBD probabilities as these can give indications about the quality of the
genotypes, the linkage maps and the parental marker phasing. The
function visualiseHaplo was developed originally to examine
the inherited haplotypes of offspring with extreme (usually favourable)
trait scores to see whether their inherited alleles are consistent with
a predicted QTL model (we return to this later). But as a first look at
the data quality, the function is also useful.
Haplotypes of linkage group 1 of the first nine F1 offspring can be visualised as follows:
visualiseHaplo(IBD_list = IBD_4x,
display_by = "name",
linkage_group = 1,
select_offspring = colnames(SNP_dosages.4x)[3:11], #cols 1+2 are parents
multiplot = c(3,3)) #plot layout in 3x3 grid
Here the quality of the predicted haplotypes appears to be high -
dark colours signifying high confidence (probabilities close to 1) and
small numbers of recombinations predicted. Regions of dark red signify
double reduction, which were permitted during the estimation of IBDs
using estimate_IBD. In poorer-quality datasets,
considerably more “noise” may be present, with less certainty about the
correct configuration per offspring.
The function returns a list of 2 elements (recombinants
and allele_fish) which do not concern us here but which we
will return to later. Note that we selected the
offspring to display using the select_offspring argument -
using the option select_offspring = all will return the
whole population. We have also opted to
display_by = "name", as opposed to
display_by = "phenotype", in which case further arguments
are required. For convenience the plots were combined into a 3 x 3 grid
using the multiplot argument. For more options, including
how to overlay recombination events, see
?visualiseHaplo.
An example of IBD probabilities that show much higher levels of uncertainty might look something like the following:
Here, there are unrealistically-high numbers of recombinations predicted, suggesting that the algorithm had difficulty correctly assigning genotype classes. In such cases it may be worthwhile to re-examine the steps prior to IBD estimation, in particular genotype calling. We will return to this issue again later.
Genotypic Information
Another approach to assessing the quality of the IBD probabilities, as well as understanding the “QTL detection landscape” to some degree is to estimate the Genotypic Information Coefficient (GIC). The GIC is calculated per homologue across the whole population, and ranges from 0 (no information) to 1 (full information). To maximise QTL detection power and precision, we would like the GIC to be uniform and as high as possible (Peter M. Bourke et al. 2019). Note that the GIC is only defined for bivalent pairing, and therefore estimates of GIC from a multivalent-aware HMM are based on offspring predicted to have come from a bivalent-based meiosis for that linkage group (this tends to be most of the population anyway).
We calculate the GIC as follows:
GIC_4x <- estimate_GIC(IBD_list = IBD_4x)We can also visualise the output of this function as follows:
visualiseGIC(GIC_list = GIC_4x)
At the telomeres there is usually a tapering off of information, a result of having shared marker information from one side only in these regions. It is often possible to discern the relationship between marker coverage and GIC directly from this visualisation, although it should be noted that non-simplex marker alleles provide incomplete information about inheritance. So for example in an autotetraploid, a marker in duplex condition in parent 1, phased to homologues 1 and 3, does not provide much information about the inheritance of homologues 1 and 3. This is because on average, \(\frac{2}{3}\) of the population will inherit only one copy of the marker allele, which may have come from either homologue 1 or homologue 3. Without neighbouring marker information to support a decision, we remain unsure, as both possibilities are equally likely.
Performing a QTL scan
In order to perform a QTL scan, we also need phenotypes. There is
already an example set of phenotypes included with the package which we
previously loaded with the call data(Phenotypes_4x). We
first look at the required structure of this (data-frame):
dim(Phenotypes_4x)## [1] 150 3head(Phenotypes_4x)## year geno pheno
## 1 2014 F1_01 53.63065
## 2 2014 F1_02 59.02528
## 3 2014 F1_03 52.96245
## 4 2014 F1_04 48.23597
## 5 2014 F1_05 52.02645
## 6 2014 F1_06 44.62646Here we see that there are 3 columns in this data-frame, namely “year”, “geno” and “pheno”. There can be as many extra columns as you like for different traits, but at a minumum there must always be two columns, one corresponding to the genotype identifiers (the names of the F1 individuals in the mapping population) and one corresponding to trait scores of some kind (numeric). If a trait was qualitatively scored, for example as “resistant” or “susceptible”, then you first need to re-code this as (e.g.) 1 and 0.
Including experimental blocks
Note also that there is a separate column for “year” in this dataset.
In general, only 1 level of experimental blocking is allowed. If there
were replicated observations within blocks, then a more complicated
nested block analysis would be needed. In such instances, it would
probably be best to first derive best linear unbiased estimates (BLUEs)
for the trait, with the full nested block structure provided. See the
section on BLUEs below for more details. However,
the QTL functions provided within polyqtlR are unable to
inherit variance components from such an approach, and can only deal
with the means in this case.
Running an initial QTL scan
Assuming we have a simple blocking structure as is the case here (single measurements per genotype repeated over 3 years) we can proceed with a preliminary QTL scan as follows:
qtl_LODs.4x <- QTLscan(IBD_list = IBD_4x,
Phenotype.df = Phenotypes_4x,
genotype.ID = "geno",
trait.ID = "pheno",
block = "year")QTLscan by default uses an additive-effects model (Peter M. Bourke et al. 2021). Since package
v.0.1.0 it is also possible to run a QTL scan using the full model as
described in (Hackett, Bradshaw, and Bryan
2014), which uses the genotypic IBD probabilties rather than the
haplotype IBD probabilities as regressors in the detection model.
Although this risks over-fitting (as the model is over-parametrised,
particularly if genotype probabilities were estimated allowing for
double reduction which adds many extra genotype classes), it may be
useful to also check and compare the results after significance
thresholds have been calculated (see below). The full model can be
accessed in the QTLscan function by setting argument
allelic_interaction = TRUE.
The function gives a summary table of the trait over the different
blocks, which can be useful for identifying possibly outlying
observations. Because the function calls on the lm function
from base R, missing values are not allowed in the trait scores.
QTLscan performs some imputation if blocks are present, by
estimating block effects and using them and the observed values to
predict a missing phenotype. If this behaviour is not desired, then
manually removing these datapoints beforehand is necessary.
QTLscan can only work if the genotype identifiers (the
offspring names) match completely between the trait data and the IBD
data. If this is not the case, an error will result. The function
reports the number of offspring with matching genotype and phenotype
identifiers, so the user can record the population size that was used in
the analysis.
Visualising QTL results
The object returned by QTLscan is a list with a number
of items, including:
QTL.res A matrix of QTL results
Perm.res The results of a permutation test, if run (see below). In our example here, this field is
NULL, i.e empty.Residuals Vector of residual phenotypes after blocks or co-factors have been fitted.
Map The linkage map upon which the IBD probabilities were based.
More details on the output can be found by running
?QTLscan. There are a number of functions in the package
for visualising the results. One option is to plot per linkage group,
which can be achieved using the plotQTL function and grid
layout (layout = 'g'). An example call would be as
follows:
plotQTL(LOD_data = qtl_LODs.4x,
layout = "g",
colour = "darkgreen")
As before, details of the options available for this function can be
accessed using ?plotQTL.
An alternative is to plot the results of the whole-genome scan on a
single track, which since package v.0.1.0 is the default plotting
behaviour of the plotQTL function:
plotQTL(LOD_data = qtl_LODs.4x,
colour = "dodgerblue")
plotQTL can also visualise the results of a number of
analysis together. By default, the superimposed plots are re-scaled so
that threshold lines overlap (argument rescale = TRUE).
This is covered in more detail in the section on co-factors.
Significance thresholds
Although it already appears like we have an interesting peak on LG 1,
we are not sure whether this region is truly associated with our trait
or not. One method of establishing whether the association is
significant is to run a permutation test. Currently the package has two
options. The first uses the full structure of your data as provided.
However, it is much faster to run a permutation test when your data has
a simple structure, with no experimental blocks or no genetic
co-factors. To deal with experimental blocks, you should estimate BLUEs first before running the permutation test. For
genetic co-factors, you can first run an analysis with the co-factor(s)
included, and then use the residuals as your phenotype. However, it is
also possible (but not recommended) to simply run a permutation test
without these steps, using the QTLscan function as
follows:
qtl_LODs.4x <- QTLscan(IBD_list = IBD_4x,
Phenotype.df = Phenotypes_4x,
genotype.ID = "geno",
trait.ID = "pheno",
block = "year",
perm_test = TRUE,
ncores = nc)If we now plot the results, the threshold line is automatically included:
plotQTL(LOD_data = qtl_LODs.4x,
colour = "dodgerblue")## LG_names not detected in LOD_data. Re-creating LG names for plot...
However, if you ran this step you will have noticed that it is quite
slow. Therefore, it is recommended to first estimate a mean phenotypic
value per individual over years before running the permutation test,
which we do here using best linear unbiased estimates in the
nlme package which fits a linear mixed model with genotype
as fixed effect.
BLUEs
We can estimate the best linear unbiased estimates using the
BLUE function as follows:
blues <- BLUE(data = Phenotypes_4x,
model = pheno~geno,
random = ~1|year,
genotype.ID = "geno")The resulting object is a data-frame with columns “geno” and “blue”,
which we need in our revised call to QTLscan:
qtl_LODs.4x <- QTLscan(IBD_list = IBD_4x,
Phenotype.df = blues,
genotype.ID = "geno",
trait.ID = "blue",
perm_test = TRUE,
ncores = nc)If we now plot the results, the threshold line is automatically included:
plotQTL(LOD_data = qtl_LODs.4x,
colour = "dodgerblue")
Note that the LOD scores have now increased, but the significance threshold has also increased. This has to do with how the LOD score is estimated, using a ratio of the RSS from your fitted model at a putative QTL position with that of the NULL model with no QTL. In the case of blocks, the NULL model already contains your blocking term, and so a portion of the phenotypic variance is already accounted for when calculating the LOD score. When using BLUEs as your phenotype, you first correct your phenotypes for block effects, but the NULL model now has no explanatory variables, which artificially inflates your LODs. However, a permutation test will account for these sorts of discrepancies, and the region of the genome that lies above the threshold should be the same.
Adding genetic co-factors
In many situations we may wish to include already-identified QTL
positions as fixed genetic effects in a QTL search. This can help to
reduce the amount of unwanted background variance in the phenotypic data
which can lead to greater power to detect QTL at other positions.
Another possible reason could be to test whether multiple peaks on a
single linkage group are independent. There are two options for
including co-factors in the package. We could use the automated function
check_cofactors which performs all steps automatically, or
we can run a manual co-factor analysis using QTLscan by
specifying the cofactor_df argument.
Manual co-factor analysis
We first describe the manual approach using QTLscan
directly, as this clearly demonstrates how co-factors can be included,
and offers the most flexibility. To this we supply a data-frame with at
least two columns: the first one giving the linkage group identifier and
the second column giving the cM position (note that column identifiers
are not mandatory, the function looks for LG in column 1 and cM in
column 2 by itself). Since package v.0.1.0 it is possible to add a third
column, to specify whether the co-factor should be added as an
additive-effects-only QTL, or whether allelic interactions are also to
be modelled whemn fitting the co-factor.
Before we add the QTL peak as a co-factor, we need to know where it is. We search for the peak as follows:
findPeak(qtl_LODs.4x, linkage_group = 1)## chromosome marker position LOD thresh
## 9 1 LG1_12.3_0x1_h5 12.3 12.29909 5.27213## [1] 12.3The peak position is therefore at 12.3 cM. We include this as a co-factor as follows:
qtl_LODs.4x_cofactor <- QTLscan(IBD_list = IBD_4x,
Phenotype.df = Phenotypes_4x,
genotype.ID = "geno",
trait.ID = "pheno",
block = "year",
cofactor_df = data.frame("LG" = 1,
"cM" = 12.3),
perm_test = FALSE,
ncores = nc)#nc is the number of cores, defined earlierNote that we have not performed a permutation test here. This is
possible, but again the running time is somewhat longer than one would
like. Therefore, we can use the residuals of the fitted NULL model
(including blocks and the co-factor) as a new set of phenotypes as a way
to again access the optimised permutation test of
QTLscan:
new_pheno <- qtl_LODs.4x_cofactor$Residuals
head(new_pheno)## geno Pheno Block
## 1 F1_01 3.06894507 2014
## 2 F1_02 4.80132691 2014
## 3 F1_03 0.09938343 2014
## 4 F1_04 -1.65306259 2014
## 5 F1_05 0.96184614 2014
## 6 F1_06 -5.48341785 2014colnames(new_pheno)## [1] "geno" "Pheno" "Block"Note the colnames of the new_pheno, we will need these.
We now estimate BLUEs using these as our phenotypes (to account for
block effects) and re-run the analysis as follows:
blues <- BLUE(data = new_pheno,
model = Pheno~geno,
random = ~1|Block,
genotype.ID = "geno")qtl_LODs.4x_cofactor <- QTLscan(IBD_list = IBD_4x,
Phenotype.df = blues,
genotype.ID = "geno",
trait.ID = "blue",
perm_test = TRUE,
ncores = nc)plotQTL(LOD_data = qtl_LODs.4x_cofactor,
colour = "red")
Note that if we wanted to include multiple co-factors, we could do
this by supplying a data-frame with multiple rows in
cofactor_df. As before, check out ?QTLscan for
full details.
Automatic co-factor analysis
A useful alternative to a manual co-factor analysis is to use an
automatic co-factor analysis which attempts to build a multi-QTL model
by maximising the signficance at all detected QTL peaks. To use this
function, we first estimate BLUEs over blocks, and then run the
check_cofactors function as follows:
blues <- BLUE(data = Phenotypes_4x,
model = pheno~geno,
random = ~1|year,
genotype.ID = "geno")
QTLmodel <- check_cofactors(IBD_list = IBD_4x,
Phenotype.df = blues,
genotype.ID = "geno",
trait.ID = "blue",
LOD_data = qtl_LODs.4x,
ncores = nc)
QTLmodel## LG cM deltaLOD CofactorID
## 1 1 12.3 7.026958 NAThe output gives 4 columns: the LG of the QTL, its cM position, the
difference between the LOD at the peak and the significance threshold
(ie. a threshold-adjusted LOD score) and the CofactorID. Note that the
last one is NA in our case, as this QTL peak was detected
without including any other genetic co-factor in the model. For more
details refer as usual to the help documentation
?check_cofactors.
It can be useful to directly run the PVE function after
this to look at the percentage variance explained of the QTL model and
all sub-models (note that this function is also presented in its own
separate section later. The output of
check_cofactors can be passed directly to
PVE:
PVE(IBD_list = IBD_4x,
Phenotype.df = blues,
genotype.ID = "geno",
trait.ID = "blue",
QTL_df = QTLmodel)## Warning in PVE(IBD_list = IBD_4x, Phenotype.df = blues, genotype.ID = "geno", : Maximal QTL model has a single QTL!
## A single QTL scan using function QTLscan provides comparable results!## $`1 QTL model`
## Q1
## 67.79Comparing multiple analyses
It is often convenient to plot the results of different analyses
together. For example comparing the results of a single marker analysis
with an IBD-based approach, or plotting an initial QTL scan versus the
results when a set of genetic co-factors were also included. In cases
where significance thresholds were determined in separate analyses, this
will soon lead to cluttered-looking plots with multiple significance
thresholds on top of each other. One possibility is to disable the
visualisation of significance thresholds when rendering each plot.
However, it is often of interest to compare the results in terms of the
presence (or absence) of significant QTL peaks. For this reason the
default behaviour of plotQTL when multiple results are
passed to LOD_data is to re-scale the overlaid plots so
that the significance thresholds for each set of results overlaps
perfectly. In this case, LOD_data should be a list
of separate QTL results, each of which is the output of a separate call
to the function QTLscan or
singleMarkerRegression. Re-scaling can be disabled by
setting rescale = FALSE.
We can compare the results obtained earlier from the original and co-factor analyses as follows:
plotQTL(LOD_data = list(qtl_LODs.4x,
qtl_LODs.4x_cofactor))
Exploring the QTL peak
Once we have detected a QTL, we may also wish to determine what the
most likely QTL segregation type is. In other words, we would like to
know the source of favourable QTL alleles, or find out which particular
alleles lead to an improvement (or reduction) in a trait of interest.
However, in order to be able to do this using the
exploreQTL function, we again need to have calculated the
best linear unbiased estimates, but without
co-factors (where the variation associated with our discovered QTL has
essentially been removed from the data!). Therefore, first go back and
re-estimate the BLUEs using the original phenotypes:
blues <- BLUE(data = Phenotypes_4x,
model = pheno~geno,
random = ~1|year,
genotype.ID = "geno")We then use these adjusted means in our call to the
exploreQTL function as follows:
qtl_explored <- exploreQTL(IBD_list = IBD_4x,
Phenotype.df = blues,
genotype.ID = "geno",
trait.ID = "blue",
linkage_group = 1,
LOD_data = qtl_LODs.4x)## Fitting specified QTL models at position 12.3 cM on linkage group 1
##
## There are 50 individuals with matching identifiers between phenotypic and genotypic datasets.
##
## The QTL configuration for trait blue at 12.3 cM on linkage group 1 with seg type:
## Qooo x oooo and additive gene action had BIC 8.0435Note that we need only specify the linkage_group - the
peak LOD position on that linkage group is taken by default.
Alternatively, a specific position can be supplied using argument
cM (check out ?exploreQTL for extra
details).
The function by default plots the BIC (Bayesian Information
Criterion) for each of the models supplied. The BIC gives a measure of
the likelihood of the different QTL models tested. Note that we did not
actually supply a list of different models to test to the function - a
pre-defined list was looked up by the function instead. Different models
can be supplied using the QTLconfig argument. To see the
default list that was supplied in the case of a tetraploid, use the
following code:
default_QTLconfig <- get("segList_4x",envir = getNamespace("polyqtlR"))
default_QTLconfig[1:2]## [[1]]
## [[1]]$homs
## [1] 1
##
## [[1]]$mode
## [1] "a"
##
##
## [[2]]
## [[2]]$homs
## [1] 2
##
## [[2]]$mode
## [1] "a"length(default_QTLconfig)## [1] 224For a triploid population we would get “segList_3x” etc. Here we see the first 2 models out of a total of 224 models tested, the first being “Qooo x oooo” (“$homs” = 1) and additive (“$mode” = “a”), the second being “oQoo x oooo” and additive, etc.
From the plot we see that model 1 was actually the most likely. The
function also reports what this model was, but we can also check out the
first element of the previously-defined default_QTLconfig
as follows:
default_QTLconfig[[1]] #replace 1 with 27 to see the second most-likely model## $homs
## [1] 1
##
## $mode
## [1] "a"The green dashed line is the default cut-off for competing QTL
models, which is any model within 6 BIC units of the minimum BIC. This
can be adjusted using the deltaBIC argument. Currently, the
function only considers simple additive and dominant bi-allelic QTL
models, although testing multi-allelic QTL models is also possible and
has already been implemented previously (Peter M.
Bourke et al. 2019). Please contact the author if you would
require more model flexibility (however for many purposes it is arguably
better to stick to a range of simpler models to prevent
over-fitting).
It can also be helpful to visualise the QTL effects for comparison purposes. This can be achieved as follows:
visualiseQTLeffects(IBD_list = IBD_4x,
Phenotype.df = blues,
genotype.ID = "geno",
trait.ID = "blue",
linkage_group = 1,
LOD_data = qtl_LODs.4x)
The visualisation appears to be consistent with the predicted model, i.e. that the allele originating from homologue 1 of parent 1 contributes positively to the trait. Note that there is a limitation to predicting the effects of specific alleles within a mapping population, as there is no reference against which to compare. We have opted here to display the differences between the overall (fixed) population mean and the mean trait value of individuals carrying each of homologues in turn. As such, we are using the whole population as a reference, even though it is a mix of individuals with different allelic compositions. This is not ideal, but is probably the best we can do. An alternative would be to choose one of the parental alleles as a reference level and determine the contrasts between that allele and each of the others in turn. Here again there would be a mixing of signals, as polyploid individuals carry multiple alleles. In short, the results presented here from the exploration of the QTL peak should be interpreted with caution. Larger population sizes may help clarify the resolution of allele effects, but the best situation would be to compare the effects of specific alleles across multiple populations.
Compare QTL results with offspring
We might also like to see whether the QTL results tally with the
allelic conformation of the population if sorted by phenotype. For this,
we use the display_by = "phenotype" argument in the
visualiseHaplo function. First, we look at the distribution
of (BLUE) phenotypes of the population:
hist(x = blues$blue)
Suppose we are only interested in offspring with a trait value higher than 44. We can choose to only display the haplotypes of these offspring as follows:
visualiseHaplo(IBD_list = IBD_4x,
display_by = "phenotype",
Phenotype.df = blues,
genotype.ID = "geno",
trait.ID = "blue",
pheno_range = c(44,max(blues$blue)),
linkage_group = 1,
multiplot = c(3,3))
All these offspring seem to carry homologue 1 as anticipated, although certain individuals (like F1_24) possess recombinations in the region of the QTL, which might be of interest for further fine-mapping work. However, the main point here is that the results seem to be consistent with the predictions from the BIC analysis.
Single Marker Analysis
The usual method of QTL detection in polyploid mapping populations is
to use single-marker approaches, looking for associations between marker
allele dosages and the trait of interest. The function
singleMarkerRegresion does this, again using a permutation
test to determine significance thresholds. While IBD-based analyses
require markers to be present on a linkage map, single-marker analyses
have no such constraints and therefore all markers can be included in
the analysis, even if they did not map. By also providing a linkage map,
visualisations will be more informative - since any unmapped markers
will be assigned to chromosome 0 for plotting, with no meaningful
order.
A single marker analysis can be performed as follows:
qtl_SMR.4x <- singleMarkerRegression(dosage_matrix = SNP_dosages.4x,
Phenotype.df = blues,
genotype.ID = "geno",
trait.ID = "blue",
return_R2 = TRUE,
perm_test = TRUE,
ncores = nc,
maplist = phased_maplist.4x)The results can be plotted alongside the IBD-based results:
plotQTL(LOD_data = list(qtl_LODs.4x,
qtl_SMR.4x),
plot_type = c("lines","points"), #IBD results as lines, SMR results as points..
pch = 19,
colour = c("darkgreen","navyblue"))
PVE
It is often useful to estimate the percentage of variance explained
(PVE) by your maximal QTL model. The function PVE computes
this, as well as looking at all possible sub-models. In this example it
is pretty trivial, as there was only a single QTL detected which
explains about 31% of the phenotypic variation:
PVE(IBD_list = IBD_4x,
Phenotype.df = Phenotypes_4x,
genotype.ID = "geno",
trait.ID = "pheno",
block = "year",
QTL_df = data.frame("LG" = 1,"cM" = 12.3))## Warning in PVE(IBD_list = IBD_4x, Phenotype.df = Phenotypes_4x, genotype.ID = "geno", : Maximal QTL model has a single QTL!
## A single QTL scan using function QTLscan provides comparable results!## Summary of trait: pheno over blocks
##
## | | Min.| 1st Qu.| Median| Mean| 3rd Qu.| Max.| NA's|
## |:----|--------:|--------:|--------:|--------:|--------:|--------:|----:|
## |2014 | 43.05715| 49.12318| 52.85265| 51.83483| 54.36611| 60.27919| 0|
## |2015 | 25.78358| 28.65918| 31.90446| 31.94833| 34.36686| 41.13060| 0|
## |2016 | 33.28601| 36.58176| 40.40502| 39.72945| 42.19982| 46.08645| 0|## $`1 QTL model`
## Q1
## 31.52Meiosis & Recombinations
We have by now identified the major QTL affecting our trait, and both explored and visualised the allelic effects at the QTL peak positions. However there are a number of remaining topics that could lead to a more complete understanding, leveraging the information contained in the IBD probabilities.
Meiosis report
It is interesting to look at what went on in parental meiosis in the population, as it may give an indication on e.g. the pairing behaviour of chromosomes during meiosis. For many polyploid crops this is not necessarily a well-understood process, so we provide some tools to help give insights into whether your species of interest is autopolyploid, allopolyploid or something in between (“segmental allopolyploid”).
To this end, we run the function meiosis_report as
follows:
mr <- meiosis_report(IBD_list = IBD_4x)
Preferential pairing
Apart from visualising the deviations (in counts) from a purely
random bivalent pairing model, the function meiosis_report
also analyses all predicted bivalent pairings and performs an
uncorrected \(\chi^2\) test to detect
deviations from a polyomic model. If multivalents were also included
during IBD estimation these are also counted and recorded, but do not
contribute to the \(\chi^2\) test or
output plots. Note that the colour of the output plot conveys
information about the results of the \(\chi^2\) test: green signifying no strong
deviation from a polysomic model, while red colours indicating a more
severe deviation from a polysomic model. In this example, there is no
suggestion of anything but polysomic inheritance, associated with
autopolyploidy.
An alternative approach to visualise the pairing behaviour of
parental homologues is provided by the function
visualisePairing. This function displays deviations from
random expectations as before, but using line thickness to represent the
magnitude of the deviation (by default, an excess of pairing counts is
coloured red and a lack of counts coloured blue). One argument needed in
order for the function to work is datawidemax, which is the
data-wide maximum deviation. This is then given the line width as
specified by max.lwd, and all other deviations are scaled
accordingly. See ?visualisePairing for more details.
The function can be run using the output of
meiosis_report as follows:
par(mfrow = c(1,2))
visualisePairing(meiosis_report.ls = mr,
parent = "P1",
datawidemax = 5)
Recombination landscape
It can be very informative to perform an analysis of all the predicted recombinations (from cross-over events), as these can indicate issues such as poor map order, problematic individuals (carrying too many predicted recombinations) or errors in marker phase. The position of these can also be biologically relevant, indicating recombination hot-spots or cold-spots. They also provide a means to correct genotyping errors, if we take the view that genotyping errors are a more likely cause of multiple recombination events in an individual rather than cross-overs (which they usually are). In short, an analysis of the recombination landscape offers a lot of scope for improved understanding on many levels.
Within polyqtlR a number of tools are provided for this.
We start by looking at the function count_recombinations,
which generates a summary of the recombination events per linkage group
and per individual:
recom.ls <- count_recombinations(IBD_4x)Note that this function has only been implemented in the context of bivalent pairing - a likely future update is to also consider and count recombination events from multivalents.
The output is a rather long list giving, per linkage group and per
individual the probability of the most likely pairing configuration and
the most likely positions of the recombination break-point (taken as the
midpoint of the two bounding positions which define the interval).
Although we do not know the precise break-point around cross-over
events, this value can be taken as indicative of the likely location. To
then make sense of this list we call on the visualisation function
plotRecLS (plot the
Recombination
LandScape) to plot the results and
return some summary information from the plots:
layout(matrix(c(1,3,2,3),nrow=2)) #make tidy layout
RLS_summary <- plotRecLS(recom.ls) #capture the function output as well
The green lines show a fitted spline to the recombination count data
- which are also returned by the function. Indeed, if you explore the
output saved in RLS_summary you should see that there are
two items: $per_LG and per_individual. In the
per-linkage group item, recombination rates that have been interpolated
using the splines (rec.rates) are given (per linkage
group). In the per-individual item, a named vector of the genome-wide
counts of recombinations is given, which can be useful in identifying
offspring that perhaps should not have been included in the mapping.
It is also of interest to overlay the predicted recombinations with
the visualised haplotypes. This can be done with the
visualiseHaplo function, similar to what we did earlier but
now adding the argument recombination_data to the call:
visualiseHaplo(IBD_list = IBD_4x,
display_by = "name",
linkage_group = 1,
select_offspring = colnames(SNP_dosages.4x)[3:11], #cols 1+2 are parents
multiplot = c(3,3), #plot layout in 3x3 grid
recombination_data = recom.ls) 
It is interesting to note the problems with reconstructing the inheritance probabilities of individual F1_01 - compare this to the reconstruction earlier when we also allowed for multivalents and double reduction. F1_04 has also been reconstructed differently, but here the bivalent-only based prediction does not seem to have caused serious conflicts.
Searching for recombinant individuals
We have analysed the recombination landscape, but suppose for the
sake of argument we were interested in all offspring that had inherited
homologues 1 and 3 from linkage group 1 in the region of our detected
QTL. Although we only found evidence for a positive effect of homologue
1, we could imagine a different dataset where there was a second QTL on
homologue 3 some distance away. If we wanted to stack these QTL, then
recombinant offspring could offer the possibility of stacking these QTL
in coupling linkage. We can search for these individuals using the
visualiseHaplo function.
We display the offspring by “name” as before.
However, we now also provide details of the
recombinant_scan homologues that we are interested in. The
output of this initial function call will be used in the subsequent
step, so we save the output as “visHap1”. We will also use
multi-plotting for convenience. Note that the plots have been suppressed
here (as there are too many of them to begin with):
visHap1 <- visualiseHaplo(IBD_list = IBD_4x,
display_by = "name",
select_offspring = "all",
linkage_group = 1,
cM_range = c(1.56,50),
recombinant_scan = c(1,3),
multiplot = c(4,2))We now look at the output of the function:
visHap1## $recombinants
## [1] "F1_02" "F1_03" "F1_16" "F1_22" "F1_26" "F1_41"
##
## $allele_fish
## NULLSix offspring have been identified as having a recombination in this
region. There may be others, as this function is only searching among
the IBD results for potential recombinants and may miss some with less
clear features. However, six is already enough to continue with. We pass
the names of these individuals to the function again (in place of “all”
offspring) using the select_offspring argument, and
specifying the individuals mentioned in
visHap1$recombinants, and specifying the desired region of
linkage_group 1 using cM_range as follows:
visualiseHaplo(IBD_list = IBD_4x,
display_by = "name",
select_offspring = visHap1$recombinants,
linkage_group = 1,
cM_range = c(1.56,50),#note: start position = first marker @1.56 cM
recombinant_scan = c(1,3),
multiplot = c(3,2),
recombination_data = recom.ls) # we can add this track for clarity
In each of these individuals we can see evidence for a recombination between homologues 1 and 3 in the specified region.
Note - currently this process takes two steps, which could
be confusing. A planned update will allow this to be done in a single
step, using the recombination_data instead.
Fishing for specific alleles
The other output associated with the function is
$allele_fish, which allows us to fish out individuals that
carry a particular allele or combinations of alleles around a particular
locus. Suppose we were just interested in the offspring that carried
homologue 1 of chromosome 1 around the QTL, so in the region up to 15 cM
say. We can “fish out” these individuals as follows:
visHap2 <- visualiseHaplo(IBD_list = IBD_4x,
display_by = "name",
select_offspring = "all",
linkage_group = 1,
cM_range = c(1.56,15),
allele_fish = 1,
multiplot = c(4,2)) Note that these individuals must carry homologue 1 for almost all of the specified segment - therefore specifying a longer segment could also result in fewer individuals (as they are more likely to carry recombined chromosomes). As before, we can inspect the output of this function call as follows:
visHap2## $recombinants
## NULL
##
## $allele_fish
## $allele_fish$h1
## [1] "F1_02" "F1_08" "F1_10" "F1_15" "F1_17" "F1_19" "F1_23" "F1_31" "F1_32"
## [10] "F1_34" "F1_35" "F1_40" "F1_43" "F1_44" "F1_46" "F1_49"Here there are 16 offspring carrying that particular segment of
homologue 1. We can visualise them using a call to the
visualiseHaplo function as before:
visualiseHaplo(IBD_list = IBD_4x,
display_by = "name",
select_offspring = visHap2$allele_fish$h1,
linkage_group = 1,
cM_range = c(1.56,15),
multiplot = c(4,4))
If all went well, these offspring should all possess the homologue 1 allele in this particular region. Examining the plots shows this to be the case.
Correcting genotyping errors
One final topic that is useful to include here is that of error correction in our marker genotypes. Particularly when using some next-generation sequencing based methods for genotyping, errors in the data can become quite a problem. One of the many applications of IBD probabilities (and their method of estimation) is to try to determine what the offspring in a population actually inherited in terms of their parental alleles. In the Hidden Markov Model introduced earlier, we did not discuss choice of prior for genotyping errors. The function uses a default prior of 0.01. What this means in practice is that we put a very high weight on our genotype observations: with such a prior in a tetraploid, the probability that an offspring score of ‘1’ is in fact a true ‘1’ is 0.99, while the probability of it being 0, 2, 3 or 4 is 0.01 (and therefore the probability of its true state being 0 is only 0.01/4 i.e. only 0.25 %). This is clearly a very strong prior on our observed genotype values and can lead to many erroneous recombinations being predicted.
A very simple solution to this issue when there seems to be evidence of many genotyping errors (see previous haplotype plot for an example) is to increase the error prior when estimating the IBD probabilities, to effectively suppress incorrect prediction of double recombination events. In general, a prior of 0.1 or even 0.2 will suppress spurious recombinations from being predicted. Note that an error prior of 0.8 in a tetraploid means we actually consider all possible dosage scores as equally likely (with a probability of 0.2). However, setting an error prior at this level means that you consider your data to be random noise.
To facilitate this procedure, the function maxL_IBD is
provided which runs the step of IBD estimation over the range of
errors provided, merging the results by selecting those
that maximise the marginal likelihood of the data, per individual (and
per linkage group). A default set of error priors (0.01, 0.05, 0.1, 0.2)
are checked which should adequetly cover the range of possible error
rates commonly encountered. To run this function, use the following call
(basically takes the same arguments as estimate_IBD but
with errors instead of error to signify
multiple error priors being applied):
IBD_multiError <- maxL_IBD(phased_maplist = phased_maplist.4x,
genotypes = SNP_dosages.4x,
ploidy = 4,
bivalent_decoding = FALSE,
errors = c(0.01,0.02,0.05,0.1,0.2),
ncores = 4)The output is now a list, but to access the IBD object we have been
using here throughout, simply extract the maxL_IBD element
of the output, i.e.
IBD_4x <- IBD_multiError$maxL_IBDOnce you are happy with the results (again, using the visualisation
tools described earlier) you have one further possibility open to you:
to re-impute your marker genotypes given these “smoothed” IBD
probabilities. This can be achieved using the function
impute_dosages. To demonstrate this here, we will
artificially introduce some genotyping errors (something you normally
would not do), and then re-estimate the IBDs using a higher
error prior:
# Copy our dosage matrix to a new matrix:
error_dosages <- SNP_dosages.4x
# Only work with offspring errors for now:
F1cols <- 3:ncol(error_dosages)
# Count number of (offspring) dosage scores:
ndose <- length(error_dosages[,F1cols])
# Generate a vector of random positions (10% of total nr):
set.seed(42)
error.pos <- sample(1:ndose,round(ndose*0.1))
# Replace real values with these random scores (simple error simulation):
error_dosages[,F1cols][error.pos] <- sapply(error_dosages[,F1cols][error.pos], function(x) sample(setdiff(0:4,x),1))
# Re-estimate IBD probabilities, using the maxL_IBD function:
IBD_multiError <- maxL_IBD(phased_maplist = phased_maplist.4x,
genotypes = error_dosages,
ploidy = 4,
errors = c(0.01, 0.02, 0.05, 0.1, 0.3),
ncores = nc)
IBD_4x.err <- IBD_multiError$maxL_IBD
# Re-impute marker dosages
new_dosages <- impute_dosages(IBD_list=IBD_4x.err,dosage_matrix=error_dosages,
min_error_prior = 0.01,
rounding_error = 0.2)## ____________________________________________________________________________
##
## 186 out of a total possible 186 markers were imputed
## In the original dataset there were 0 % missing values among the 186 markers
## In the imputed dataset there are now 1.4 % missing values among these, using a rounding threshold of 0.2
##
## ____________________________________________________________________________
## The % of markers with changed dosage scores is as follows (0 = no change):
## error.matrix
## 0 1 2 3 4
## 89.44 4.18 2.88 1.72 0.35# Check the results:
round(length(which(error_dosages[,F1cols] != SNP_dosages.4x[,F1cols])) / ndose,2)## [1] 0.1round(length(which(new_dosages[,F1cols] != SNP_dosages.4x[,F1cols])) / ndose,2)## [1] 0.01So having had 10 % genotyping errors to begin with, we have reduced the error rate in the data to 1 %, but also introduced 1.4 % missing values (these are often around true recombination break-points where we cannot easily decide which parental homologue was inherited). A missing value is an error of sorts, but has a much smaller impact on linkage map quality than a true genotyping error. These corrected genotypes may then be used in an iterative process to improve the underlying linkage map, although usually a single or at most 2 iterations should be used. Previous experience has shown that this approach can also lead to significant improvements in subsequent QTL mapping.
Concluding remarks
We hope you have been able to successfully run a QTL analysis and explore polyploid meiotic dynamics using your data and the methods described here. The package may still be further improved and developed, and feedback on performance, suggestions for improvements / extensions and bug reporting is most welcome; please contact the developer Peter Bourke (peter.bourke at wur.nl).