MAPpoly is an R package to construct genetic maps in autopolyploids with even ploidy levels. This quick start guide will present some essential functions to construct a tetraploid potato map. Please refer to MAPpolyâ€™s Reference Manual and the Extended Tutorial for a comprehensive description of all functions.

There are several functions to read discrete and probabilistic dosage-based genotype data sets in MAPpoly. You can read a data set from TXT, CSV, VCF, fitPoly-generated or import it from the R packages polyRAD, polymapR, and updog. The data set distributed along with MAPpoly is a subset of markers from (Pereira et al., 2021) in CSV format. Let us read it into MAPpoly

```
library(mappoly)
file.name <- system.file("extdata/potato_example.csv", package = "mappoly")
dat <- read_geno_csv(file.in = file.name, ploidy = 4)
print(dat, detailed = T)
plot(dat)
```

The output figure shows a bar plot on the left-hand side with the number of markers in each allele dosage combination in \(P_1\) and \(P_2\), respectively. The upper-right plot contains the \(\log_{10}(p-value)\) from \(\chi^2\) tests for all markers, considering the expected segregation patterns under Mendelian inheritance.

Quality control (QC) procedures are fundamental to identify:

- Individuals from crosses other than \(P_1 \times P_2\)
- Individuals and markers that exceeds a defined threshold of missing data points
- Markers with distorted segregation
- Markers with the same genotypic information (redundant markers). Removed markers are positioned into the final map.

Depending on the data set, these procedures can be conducted in any order. Let us first remove individuals from crosses other than \(P_1 \times P_2\). When using the interactive function, the user needs to select a polygon around the individuals to be removed by clicking its vertices and pressing Esc.

Now, let us filter out markers and individuals with more than 5% of missing data. You can update the threshold interactively

```
dat <- filter_missing(dat, type = "marker", filter.thres = .05)
dat <- filter_missing(dat, type = "individual", filter.thres = .05)
```

Finally, we can filter out markers with distorted segregation and redundant information. At this point, we do not consider preferential pairing and double reduction.

```
seq.filt <- filter_segregation(dat, chisq.pval.thres = 0.05/dat$n.mrk)
seq.filt <- make_seq_mappoly(seq.filt)
seq.red <- elim_redundant(seq.filt)
```

After filtering, 1990 markers were left to be mapped. Now, let us create a sequence of ordered markers to proceed with the analysis. You can also plot the data set for a specific sequence of markers

and check the distribution of the markers in the reference genome, if the information is available

The two-point analysis calculates the pairwise recombination fraction
in a sequence of markers. At this point of the analysis, where we have
many markers, we use the function `est_pairwise_rf2`

, which
has a less detailed output than the original
`est_pairwise_rf`

(which will be used later) but can handle
tens of thousands of markers, even when using a personal computer.
Nevertheless, the analysis can take a while depending on the number of
markers if few cores are available.

```
ncores <- parallel::detectCores() - 1
tpt <- est_pairwise_rf2(seq.init, ncpus = ncores)
m <- rf_list_to_matrix(tpt) ## converts rec. frac. list into a matrix
sgo <- make_seq_mappoly(go) ## creates a sequence of markers in the genome order
plot(m, ord = sgo, fact = 5) ## plots a rec. frac. matrix using the genome order, averaging neighbor cells in a 5 x 5 grid
```

We can cluster the markers in linkage groups by using function
`group_mappoly`

. The function uses the recombination fraction
matrix and UPGMA method to group markers. Use the option
`comp.mat = TRUE`

to compare the linkage-based clustering
results with the chromosome information. If your data set does not
contain chromosome information, use the option
`comp.mat = FALSE`

. You also can use the interactive version
to change the number of expected groups

In the table above, the rows indicate linkage groups obtained using linkage information and, the columns are the chromosomes in the reference genome. Notice the diagonal indicating the concordance between the two sources of information.

Markers are ordered within linkage groups. In this tutorial, we will show the step-by-step procedure using Linkage Group 1 (LG1). You can do the same for the remaining linkage groups.

Since we had a good concordance between genome and linkage
information, we will use only markers assigned to a particular linkage
group using both sources of information. We will do that using
`genomic.info = 1`

, so the function uses the intersection of
the markers assigned using linkage and the chromosome with the highest
number of allocated markers. To use only the linkage information, do not
use the argument `genomic.info`

. You also need the
recombination fraction matrix for that group.

Let us order the markers in the sequence using the MDS algorithm.

Usually, at this point, the user can use diagnostic plots to remove
markers that disturb the ordering procedure. We didnâ€™t use that
procedure in this tutorial, but we encourage the user to check the
example in `?mds_mappoly`

. Now, let us use the reference
genome to order the markers.

You also can order the markers the reference genome

For the sake of this short tutorial, let us use the MDS order
(`s1.mds`

) to phase the markers. Still, you can also try the
genome order (`s1.gen`

) and compare the resulting maps using
function `compare_maps`

, and you will notice that the genomic
order yields a better map since its likelihood is higher.

Estimating the genetic map for a given order involves the computation
of recombination fraction between adjacent markers and inferring the
linkage phase configuration of those markers in both parents. The core
function to perform these tasks in `MAPpoly`

is
`est_rf_hmm_sequential`

. This function uses the pairwise recombination fraction as the first source of
information to sequentially position allelic variants in specific
parental homologs. The algorithm relies on the likelihood obtained
through a hidden Markov model (HMM) for situations where pairwise
analysis has limited power. Once all markers are positioned, the final
map is reconstructed using the HMM multipoint algorithm. For a detailed
description of the `est_rf_hmm_sequential`

arguments, please
refer to MAPpolyâ€™s Reference Manual
and the Extended
Tutorial.

First we need to calculate the pairwise recombination fraction for
markers in sequence `s1.mds`

using
`est_pairwise_rf`

, which contains the information necessary
to the proper working of the phasing algorithm.

```
tpt1 <- est_pairwise_rf(s1.mds, ncpus = ncores)
lg1.map <- est_rf_hmm_sequential(input.seq = s1.mds,
start.set = 3,
thres.twopt = 10,
thres.hmm = 20,
extend.tail = 50,
info.tail = TRUE,
twopt = tpt1,
sub.map.size.diff.limit = 5,
phase.number.limit = 20,
reestimate.single.ph.configuration = TRUE,
tol = 10e-3,
tol.final = 10e-4)
```

Now, use the functions `print`

and `plot`

to
view the map results:

Now let us update the recombination fractions by allowing a global
error in the HMM recombination fraction re-estimation. Using this
approach, the genetic mapâ€™s length will be updated by removing spurious
recombination events. This procedure can be applied using either the
probability distribution provided by the genotype calling software using
function `est_full_hmm_with_prior_prob`

or assuming a global
genotype error like the following example

```
lg1.map.up <- est_full_hmm_with_global_error(input.map = lg1.map, error = 0.05,
verbose = TRUE)
plot(lg1.map.up, mrk.names = TRUE, cex = 0.7)
```

We can also use the ordinary least squares (OLS) method and the weighted MDS followed by fitting a one dimensional principal curve (wMDS_to_1D_pc)

```
lg1.map.ols <- reest_rf(lg1.map, m1, method = "ols")
lg1.map.mds <- reest_rf(lg1.map, m1, method = "wMDS_to_1D_pc", input.mds = mds.o1)
```

Now let us create a list with the maps and plot the results

To use the genetic map in conjunction with QTL analysis software, we need to obtain the homolog probability for all linkage groups for all individuals in the full-sib population. In this short guide, we will proceed only with one linkage group, but this procedure should be applied to all chromosomes in real situations. Let us use the updated map

```
g1 <- calc_genoprob_error(lg1.map.up, step = 1, error = 0.05)
to.qtlpoly <- export_qtlpoly(g1) #export to QTLpoly
h1 <- calc_homologprob(g1)
plot(h1, lg = 1, ind = 10)
```

Now let us compute the preferential pairing profile for linkage group 1

It is possible to export a phased map to an external CSV file using

For a script with a complete analysis of the data set presented here, please refer to the Complete script