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Genome polarisation (Baird et al. 2023) uses the diem algorithm to estimate which allele of a single nucleotide polymorphic marker belongs to which side of a barrier to gene flow based on whole-genome associations. The key result is then the marker polarity (whether to read the marker as in the diem input file or whether to flip the homozygous state labels 0↔︎2), marker diagnostic index (how relevant the marker is with respect to the barrier to gene flow), and marker polarity support (how certain we are regarding whether to flip the state labels or not).
This information is stored in a file
MarkerDiagnosticsWithOptimalPolarities.txt with columns Marker,
newPolarity, DI, and Support. However, the diem
function
generates other outputs, which help to control the genome polarisation
analyses and to interpret the results. Some of this information is
identical to the function return value. The documentation for the return
values can be found by running ?diem
. This vignette
explains the outputs saved to files.
Three output files will be saved to the working directory or to the
path specified in the verbose
argument. Those are:
The MarkerDiagnosticsWithOptimalPolarities.txt is a
tab-delimited table with four columns and the number of rows equal to
the number of markers across all compartments used to run genome
polarisation with diem
. This is the key results file
identifying the marker relevance with respect to the detected barrier to
gene flow.
The first column Marker is an index of the marker
that is successive in the files as they are ordered in the
files
argument in the diem
call. The value in
the Marker column will correspond to the respective index in the file
ending with includedSites.txt if the input files were generated
by the vcf2diem
function.
The second column newPolarity contains TRUE/FALSE
values, specifying which allele in the specific marker belongs to which
side of the barrier. When the value is FALSE
, encoded as 0
in Eq. 22 (Baird et al. 2023), the allele
encoded as 0 in its homozygous state in the input file belongs to the
barrier side associated with low values of hybrid index of the
individuals. When the newPolarity value for a marker is
TRUE
, the homozygous states need to be flipped 0↔︎2 to
correctly associate with the barrier sides. In terms of interpretation,
this means that the allele encoded as 2 in its homozygous state is
associated with low values of the hybrid index [sic!]. Which specific
alleles these are for any marker can be found in the
includedSites.txt file from the vcf2diem
.
The third column DI is numeric with values of the diagnostic index of the markers as specified in Eq. 20 (Baird et al. 2023). The diagnostic index is a log likelihood, so its values are always negative. Polarised markers with high diagnostic index characterize the barrier to gene flow. Such markers will tend to be fixed for one allele on either side of the barrier. Conversely, markers with low diagnostic index will have signal orthogonal to the detected barrier to gene flow. They could reflect ancestral genetic variation, standing variation not contributing to the barrier to gene flow, or artifacts such as overmerging of repeated motifs onto the reference.
The fourth column Support is numeric and the values represent polarity support for the markers as given in Eq. 21 (Baird et al. 2023). The support is the gain in likelihood when the correct marker 0↔︎2 ‘flipping’ is compared to its reverse. High marker support gives confidence that the marker polarity reflects the detected barrier to gene flow. In general, markers with high diagnostic index tend to also have high support.
The HIwithOptimalPolarities.txt is a tab-delimited
one-column matrix of individual hybrid indices with row names
corresponding to the individual indices. Note that the hybrid indices
are calculated from the polarised genotypes for all individuals found in
the input files, not only those specified in the ChosenInds
argument of the diem
function. The hybrid indices are
calculated as genome admixture from summaries of polarised genotypes as
in Eq. 7 (Baird et al. 2023).
CAUTION:These hybrid indices are calculated without taking into account the diagnosticity of markers! As such they may not show barrier signal well at all. Hybrid indices and genome polarisation diagrams should be calculated and plotted after the user decides on a diagnostic index threshold. The ideal threshold will be specific to your dataset. Check
vignette("diemr-diagnostic-index-expecation-maximisation-in-r")
for guidelines how to calculate it.
If you choose to ignore this warning and include all markers when
calculating hybrid indices you will find the range of hybrid indices is
small, and centred on 0.5. This is because most genome sites are close
to invariant, and so diem
will flip homozygous state labels
0↔︎2 at random. A purely random answer will give hybrid index equal to
0.5. You can rescale hybrid indices with a large random influence using
Eq. 11 (Baird et al. 2023), so they lie on
the interval \([0,1]\).
The I4withOptimalPolarities.txt file contains genome-wide summaries of genomic states for all input genomes (Eq. 4 in (Baird et al. 2023)). It is a tab-delimited table with four columns representing the unknown state (column name “_“) that cannot be encoded as a genotype in terms of the two most frequent alleles, the second column representing homozygote encoding 0, the third column heterozygote encoding 1 and the fourth column homozygote encoding 2. The rows are all individuals in the input files, with row names corresponding to indices.
The 4-genomic state counts can be used to calculate the hybrid index,
observed heterozygosity and error rate for all individuals. The
equations 7, 9, and 10 (Baird et al. 2023)
are implemented in the function pHetErrOnStateCount
that
can be applied to the rows of the I4withOptimalPolarities.
However, note that the \({}^4\mathbf{I}\) in the output was
calculated from all markers (see CAUTION in the
previous section). We advice the users to preferentially filter their
markers based on their diagnosticity after the diem
analysis and recalculate the hybrid indices and the \({}^4\mathbf{I}\) from
the filtered, polarised genotypes.
The diem
function can output additional files useful for
tracking algorithm convergence during iterations and ensuring repeatable
initialisation of genome polarisation. The flowchart in Figure 1 specifies what processes generate the files
and how the user controls what files will be stored and where.
The verbose
argument in the diem
function
controls the stored output files. The default value
verbose = FALSE
writes three key output
files in the current working directory (Figure
1). To locate the files, the current working directory can be found
with:
Additionally, the verbose
argument can trigger a verbose
output in two ways.
verbose
contains a character string with a path to
a specific folder, the verbose output will be stored in that
location.verbose = TRUE
, the verbose output will be stored
in the current working directory.The optimal approach to genome polarisation with diem
is
to strip all possible data cues before the analysis. In this way, if
diem
finds a barrier you can be certain it is an intrinsic
property of the data. Using random initial marker polarities is central
to this approach. We recommend setting the diem
argument
markerPolarity = FALSE
. The function then generates random
polarities for the initiation of the algorithm iterations.
This initial state for diem
is saved in file
NullMarkerPolarities.txt. It is a text file the first line
describing the contents of the file. The following lines show
space-separated TRUE or FALSE values, where each row corresponds to a
compartment as they were specified in the files
argument in
diem
. Because diem
is a deterministic
algorithm, if you start it from the same initial state, you will get
precisely the same answer. You can test this by setting
markerPolarity
to be the list from
NullMarkerPolarities.
nullPolarities <- readLines("folder/NullMarkerPolarities.txt")[-1]
nullPolarities <- lapply(
strsplit(nullPolarities, split = " "),
as.logical
)
diem(..., markerPolarities = nullPolarities)
You can also test the convergence of the algorithm from different
initial states by running the same analysis, but each time generating a
new random null by setting markerPolarities = FALSE
.
The file MarkersWithChangedPolarities.txt is a tab-delimited file with three columns and a variable number of rows. The column changedMarkers shows indices of markers across all compartments for which the polarity was changed in the given iteration compared to the marker polarity in the previous iteration. The column time gives a time stamp of when the changes were recorded. The column iteration specifies the iteration of the algorithm.
Note that here, markers are pooled across all compartments. The information is useful in tracking convergence in postprocessing, and so is not of interest to the casual user. During the analysis run, keeping the information about polarity changes separate for each compartment is computationally more tractable, especially in parallel processing. A set of files specifying the information for each compartment is stored in a likelihood folder (Figure 1).
The contents of the files is analogical as in the MarkersWithChangedPolarities.txt. The difference being that the marker indices are sequential for each compartment.
The contents of the files correspond to the contents of the MarkerDiagnosticsWithOptimalPolarities.txt. Here, the polarities, diagnostic indices and their supports are reported separately for each iteration and for each compartment.
Both sets of compartment-specific temporary files are initially
stored regardless of the value in the verbose
argument, as
they are used internally during the analysis. When
verbose = FALSE
, diem
attempts to delete the
likelihood folder on exit.
The internal ModelOfDiagnostic
function implements Eq.
19 (Baird et al. 2023) that is the
powerful tool to detect the most prominent barrier to gene flow in the
data. Seeing how individuals become separated on either side of the
barrier provides insights into the algorithm convergence.
The WarpSwitch.pdf files plot differences in sorted rescaled hybrid indices (Eq. 12) used to identify the barrier to gene flow (Baird et al. 2023). The WarpSwitch.txt files then describe what genomic states the ideal diagnostic marker would have for all included individuals (Eq. 13), and how the ideal 4-genomic state count matrix (Eq. 14) would look like for the first ten individuals.
The SortedRescaledHybridIndex.pdf shows how the differences in hybrid indices between individuals belonging to either side of the barrier become more pronounced with progressing iterations. Note that in order to identify which individuals are placed where, one needs to replicate the figure from hybrid index values in files HI.txt.
The files RescaledHItobetaOfRescaledHI.pdf show the weight
for the hybrid index (Eq. 15) that together with the parameter value in
the diem
argument epsilon
will inform on how
much emphasis the analysis puts on the ideal state with the center of
the barrier identified in the WarpSwich files.
The visualisation in the iteration-specific graphics provide a tangible track record of how the theoretical ideals of pure individuals and perfectly diagnostic markers contribute to informing on a barrier to gene flow in a realistic scenario, where there are no pure individuals and no perfectly diagnostic markers.
The log.txt file provides a human-readable overview of the
diem
iterations. During initialisation stage, the log file
will list the number of (chosen) markers and (chosen) individuals in the
analysis run, followed by the top seven rows of the 4-genomic state count matrix \({}^4\mathbf{I}\) with null
polarisation, correction for small data (Eq. 5), top seven rows of the
\({}^4\mathbf{A}\), which is the \({}^4\mathbf{I}\) matrix corrected for
compartment- and individual-specific ploidies and is used to calculate
the hybrid index, the top seven rows of the weighted \({}^4\mathbf{V}\) matrix (Eq. 16), and the
respective log-likelihood values (Eq. 19).
For subsequent iterations, the log file also quantifies how many markers switch polarities between iterations, and shows the corresponding change to the \({}^4\mathbf{I}\).
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.