Outcrossing Populations

The following example is intended to show the usage of OneMap functions for linkage mapping in outcrossing (non-inbred) populations. With basic knowledge of R syntax, one should have no problems using it. If you are not familiar with R, we recommend reading the vignette Introduction to R.

Hopefully these examples will be clear enough to help any user to understand its functionality and start using it. You do not need to be an expert in R to build your linkage map, but some concepts are necessary and will help you through the process.

There is a github OneMap version which is constantly improved, we strong recommend all users to try this version. In augusto-garcia/onemap github page you can find instructions to install the package from github and also more fancy tutorials.

Creating the data file

This step may be quite difficult, because the data file is not very simple and some errors can occur while reading it. The input file format is similar to that used by MAPMAKER/EXP (Lander et al., 1987), so experienced users of genetic analysis software should be already familiar with this scenario.

Basically, the input file is a text file, where the first line indicates the cross type and the second line provides information about the number of individuals, the number of markers, the presence of physical marker locations and the presence of phenotypic data. The third line contains sample IDs. Then, the genotype information is included separately for each marker. The character * indicates the beginning of information input for a new marker, followed by the marker name. Next, there is a code indicating the marker type, according to Wu’s et al. (2002a) notation. Actually, it is recommended to check Wu’s et al. (2002a) paper before using OneMap.

Marker types must be one of the following: A.1, A.2, A.3, A.4, B1.5, B2.6, B3.7, C.8, D1.9, D1.10, D1.11, D1.12, D1.13, D2.14, D2.15, D2.16, D2.17 or D2.18, each one corresponding to a row of the following table:

Parent Offspring
Crosstype Cross Observed bands Observed bands Segregation
\(A\) 1 \(ab \times cd\) \(ab \times cd\) \(ac, ad, bc, bd\) \(1:1:1:1\)
2 \(ab \times ac\) \(ab \times ac\) \(a, ac, ba, bc\) \(1:1:1:1\)
3 \(ab \times co\) \(ab \times c\) \(ac, a, bc,b\) \(1:1:1:1\)
4 \(ao \times bo\) \(a \times b\) \(ab, a, b, o\) \(1:1:1:1\)
\(B\) \(B_1\) 5 \(ab \times ao\) \(ab \times a\) \(ab, 2a,b\) \(1:2:1\)
\(B_2\) 6 \(ao \times ab\) \(a \times ab\) \(ab,2a,b\) \(1:2:1\)
\(B_3\) 7 \(ab \times ab\) \(ab \times ab\) \(a, 2ab,b\) \(1:2:1\)
\(C\) 8 \(ao \times ao\) \(a \times a\) \(3a, o\) \(3:1\)
\(D\) \(D_1\) 9 \(ab \times cc\) \(ab \times c\) \(ac, bc\) \(1:1\)
10 \(ab \times aa\) \(ab \times a\) \(a, ab\) \(1:1\)
11 \(ab \times oo\) \(ab \times o\) \(a, b\) \(1:1\)
12 \(bo \times aa\) \(b \times a\) \(ab, a\) \(1:1\)
13 \(ao \times oo\) \(a \times o\) \(a, o\) \(1:1\)
\(D_2\) 14 \(cc \times ab\) \(c \times ab\) \(ac, bc\) \(1:1\)
15 \(aa \times ab\) \(a \times ab\) \(a, ab\) \(1:1\)
16 \(oo \times ab\) \(o \times ab\) \(a, b\) \(1:1\)
17 \(aa \times bo\) \(a \times b\) \(ab, a\) \(1:1\)
18 \(oo \times ao\) \(o \times a\) \(a, o\) \(1:1\)

Letters A, B, C and D indicate the segregation type (i.e., 1:1:1:1, 1:2:1, 3:1 or 1:1, respectively), while the number after the dot (e.g., A.1) indicates the observed bands in the offspring. The paper cited above gives details with respect to marker types; we will not discuss them here, but it is easy to see that each marker is classified based on the band patterns of parents and progeny.

Finally, after each marker name, comes the genotype data for the segregating population. The coding for marker genotypes used by OneMap is also the same one proposed by Wu et al. (2002a) and the possible values vary according to the specific marker type. Missing data are indicated with the character - (minus sign) and an empty space separates the information for each individual. Phenotype information, if present, follows genotypic data with a similar structure. Details are found in the help of function read_onemap.

Here is an example of such file for 10 individuals and 5 markers (the three zeros in the second line indicate that there is no chromosome information, physical position information or phenotypic data, respectively). It is very similar to a MAPMAKER/EXP file, but has additional information about the cross type.

data type outcross
10 5 0 0 0
I1 I2 I3 I4 I5 I6 I7 I8 I9 I10
*M1 B3.7 ab ab - ab b ab ab - ab b
*M2 D2.18 o - a a - o a - o o
*M3 D1.13 o a a o o - a o a o
*M4 A.4 ab b - ab a b ab b - a
*M5 D2.18 a a o - o o a o o o

Notice that once the marker type is identified, no variations of symbols presented on the table for the observed bands is allowed. For example, for A.1, only ac, ad, bc and bd genotypes are expected (plus missing values). We notice in FAQs that this is a common mistake made by users, so please be careful.

The input file must be saved in text format, with extensions like .raw. It is a good idea to open the text file called onemap_example_out.raw (available with OneMap and saved in the directory you installed it) to see how this file should be. You can see where OneMap is installed using the command

Simulating the data file (new!)

OneMap offers wrapper functions for PedigreeSim (Voorrips and Maliepaard, 2012) software to simulate mapping populations.

Run PedigreeSim (new!)

First, download PedigreeSim java file. It will require java installed. You can run PedigreeSim directly and use its output files in OneMap or you can use the wrapper function named run_pedsim that facilitates this procedure.

The function do not provide every possibilities offered by PedigreeSim software. If you want to change any parameter that is not available in the function, please use directly the PedigreeSim software. Here is the software documentation for more information.

The function allows to create outcrossing, f2 intercross and backcross populations from bi-parental. You can define it in pop argument. You must change the path.pedsim to the path where the PedigreeSim.jar is stored in your system. You can also define the number of chromosomes (argument chromosome), the number of markers in each chromosome (n.marker), the total size of the groups in cM (tot.size.cm), the position of centromere (centromere), number of individuals in the population (n.ind), the marker types (mk.types, see the table in session Creating the data file) and the number of markers of each type (n.types).

We suggest you to open the output files founderfile, chromfile, mapfile and parfile to check if they agree with your intentions before proceed to other analysis.

Convert PedigreeSim output to OneMap raw data (new!)

Once you run PedigreeSim (directly or using our run_pedsim function), you should have the output file genotypes.dat (see an example file called sim_cod_out_genotypes.dat in OneMap extdata directory). To convert this to OneMap raw file, you just need to specify the cross type (cross), which ones are the parents (parent1 and parent2) and if you want to include missing genotypes (miss.perc). Only cross types outcross and f2 intercross are supported by now.

Convert PedigreeSim output to VCF file (new!)

The same output file from PedigreeSim, the genotypes.dat can be used to simulate a VCF file together with the PedigreeSim mapfile and chrom. The advantages to simulate a VCF instead of OneMap raw file is that VCF is a standard file format and can store a lot of other information included the allele counts (usually in the field AD or DPR). The pedsim2vcf function can simulate the allele counts using negative binomial or updog distributions (argument method). The main arguments for the distributions are defined with arguments mean.depth, that defines the mean allele depth in the progeny, p.mean.depth that defines the mean allele depth in the parents, argument disper.par defines the dispersion parameter, mean.phred defines the mean phred score of the sequencing technology used. The function can also simulate missing data (miss.perc). Through arguments pos and chr you can define vectors with physical position and chromosome of each marker. With argument haplo.ref you define which one of the haplotypes in genotypes.dat will be considered the reference. Establishing phase as TRUE, the VCF will have phased genotypes. After allele counts are simulated, the genotypes are re-estimated using a binomial distribution. The VCF generated by this function only have one or two FORMAT fields, the GT and AD (if counts = TRUE). Dominant markers are not supported by this function.

## Counts simulation changed 0.3064592 % of the given genotypes

The function prints on screen the percentage of genotypes changed between simulated by PedigreeSim and re-estimated using a binomial distribution and simulated allele counts. Notice that this percentage increase if you reduce the mean depth or increase bias or dispersion parameter.

In the session Importing data from VCF file below you will see how to import VCF files as OneMap objects.

Importing data

Once the input file is created, the data can be loaded and saved into an R onemap object. The function used to import data is named read_onemap. Its usage is quite simple:

The first argument is the directory where the input file is located, so modify it accordingly. The second one is the data file name. In this example, an object named onemap_example_out was created. If you leave the argument dir blank, the file will be loaded from your working directory.

You can change the working directory in R using function setwd() or in the toolbar clicking File -> Change dir. If you set your working directory to the one containing the input file, you can just type:

If no error has occurred, a message will display some basic information about the data, such as number of individuals and number of markers:

##  Working...
## 
##  --Read the following data:
##  Type of cross:           outcross 
##  Number of individuals:   100 
##  Number of markers:       30 
##  Chromosome information:  no 
##  Position information:    no 
##  Number of traits:        3 
##  Missing trait values:       
##   Pheno1: 0 
##   Pheno2: 3 
##   Pheno3: 0

Because this particular dataset is distributed along with the package, as an alternative you can load it typing

Loading the data creates an object of class onemap, which will further be used in the analysis. R command print recognizes objects of this class. Thus, if you type:

you will see some information about the object:

##   This is an object of class 'onemap'
##     Type of cross:      outcross 
##     No. individuals:    100 
##     No. markers:        30 
##     CHROM information:  no 
##     POS information:    no 
##     Percent genotyped:  100 
## 
##     Segregation types:
##                 A.1 -->  3
##                 A.2 -->  1
##                 A.4 -->  4
##                B1.5 -->  1
##                B2.6 -->  2
##                B3.7 -->  5
##                 C.8 -->  2
##               D1.10 -->  2
##               D1.12 -->  1
##               D1.13 -->  2
##               D2.15 -->  1
##               D2.16 -->  2
##               D2.17 -->  2
##               D2.18 -->  2
## 
##     No. traits:         3 
##     Missing trait values: 
##   Pheno1: 0 
##   Pheno2: 3 
##   Pheno3: 0

Also, you can use the plot.onemap function to see graphically markers genotypes:

Changing the argument all to FALSE, the markers will be separated by their type. In this case, you can note that the graphic cells size will adapt to the number of markers of the same type. In other words, the greater is the number of markers with the same type, smaller are the cells for this type.

This function can take quite some time, depending on the number of markers involved. More informations about this plot function can be found using ?plot.onemap.

Also, you can see graphically the number of markers by segregation pattern with the plot_by_segreg_type function:

(new!)

Using the same functions to import the dataset, we can evaluate the simulated data by run_pedsim and pedsim2raw:

##  Working...
## 
##  --Read the following data:
##  Type of cross:           outcross 
##  Number of individuals:   200 
##  Number of markers:       54 
##  Chromosome information:  no 
##  Position information:    no 
##  Number of traits:        0

Importing data from VCF file

You can import information from VCF to OneMap using onemap_read_vcfR function.

With the onemap_read_vcfR you can convert the object from vcfR package directly to onemap. The onemap_read_vcfR function keeps chromosome and position information for each marker in the onemap object generated.

We will use the example file vcf_example_out.vcf to show how it works, which contains markers from the same population of onemap_example_out.raw.

First, we convert the VCF file to vcfR object:

## 
##    *****       ***   vcfR   ***       *****
##    This is vcfR 1.8.0 
##      browseVignettes('vcfR') # Documentation
##      citation('vcfR') # Citation
##    *****       *****      *****       *****
## Scanning file to determine attributes.
## File attributes:
##   meta lines: 8
##   header_line: 9
##   variant count: 25
##   column count: 103
## 
Meta line 8 read in.
## All meta lines processed.
## gt matrix initialized.
## Character matrix gt created.
##   Character matrix gt rows: 25
##   Character matrix gt cols: 103
##   skip: 0
##   nrows: 25
##   row_num: 0
## 
Processed variant: 25
## All variants processed

As described in the vcfR package vignette, memory use is a important consideration when using vcfR. Depending of your dataset, the object created can be very large and occupy a lot of memory.

After, you can use onemap_read_vcfR function to convert this object to onemap object. The parameters used are the vcfR.object (which was just created), the identification of each parent (here you must define only one sample for each parent) and the cross type.

Depending of your dataset, this function can take some time to run.

Note that the conversion filter out markers which are not informative for the informed cross type. For example, in outcrossing species, markers that have both parents homozygous (aa x bb) do not inform recombinations and are removed of the data set. Only markers types contained the table at Creating the data file are kept in the onemap object. Function onemap_read_vcfR print at the screen the reason why markers were filtered.

You can also have more missing data in the returned object compared with the VCF. This is because the onemap_read_vcfR replace by missing data the genotypes that are not expected for that marker type. For example, for a marker type D1.10 (ab x aa), we only expect aa and ab genotypes, if there are bb genotypes they will be replaced by missing data. You can see the percentage of missing data at the resulted onemap object with:

##   This is an object of class 'onemap'
##     Type of cross:      outcross 
##     No. individuals:    92 
##     No. markers:        24 
##     CHROM information:  yes 
##     POS information:    yes 
##     Percent genotyped:  99 
## 
##     Segregation types:
##                B3.7 -->  18
##               D1.10 -->  6
## 
##     No. traits:         0

After the conversion, we can save the vcfR.object as a .RData and remove it from the workspace, once it can occupy a lot of memory and turn the other process too slow.

NOTE:From version 2.0.6 to 2.1.1005, OneMap had the vcf2raw function to convert vcf to .raw. Now, this function is defunct, but it can be replaced by a combination of onemap_read_vcfR and write_onemap_raw functions. See Exporting .raw file from onemap object session to further information about write_onemap_raw.

Filter onemap object by missing data

If your onemap object have too much missing genotypes you can face problems during the analysis. Check the percentage of missing genotypes in our data set printing the onemap object:

##   This is an object of class 'onemap'
##     Type of cross:      outcross 
##     No. individuals:    92 
##     No. markers:        24 
##     CHROM information:  yes 
##     POS information:    yes 
##     Percent genotyped:  99 
## 
##     Segregation types:
##                B3.7 -->  18
##               D1.10 -->  6
## 
##     No. traits:         0

Our example has 1% of missing genotypes (99% are genotyped). If you want to filter markers according with its percentage of missing data, you can use the function filter_missing:

## Number of markers removed from the onemap object:  0

Any of our markers were filtered, because, in this example, we do not have many missing data.

Graphical view of genotypes and allele depths (new!)

Function create_depth_profile generates dispersion graphics with x and y axis representing, respectively, the reference and alternative allele depths. The function is only available for biallelic markers in VCF files with allele counts information. Each dot represent a genotype for mks markers and inds individuals. If both arguments receives NULL, all markers and individuals are considered. Dots are colored according with the genotypes present in onemap object (GTfrom = onemap) or in VCF file (GTfrom = vcf). A rds file is generated with the data in the graphic (rds.file). The alpha argument control the transparency of color of each dot. Control this parameter is a good idea when having big amount of markers and individuals. The x_lim and y_lim control the axis scale limits, by default, it uses the maximum value of the counts.

Here is an example for the vcf_example_out dataset.

## Summary of reference counts: 
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   1.000   4.000   6.000   5.431   7.000   8.000 
## Summary of alternative counts: 
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   1.000   4.000   5.000   5.349   7.000   8.000

Because the genotypes are from VCF file, the legend points the VCF codification? ./. represent missing data; 0/0 homozygotes for reference alleles; 0/1 heterozygotes; 1/1 homozygotes for alternative allele. You can also have phased genotypes represented which have pipe | instead of bar /.

Using the same functions we can import and check the simulated dataset generated by run_pedsim and pedsim2vcf above:

## Scanning file to determine attributes.
## File attributes:
##   meta lines: 4
##   header_line: 5
##   variant count: 42
##   column count: 211
## 
Meta line 4 read in.
## All meta lines processed.
## gt matrix initialized.
## Character matrix gt created.
##   Character matrix gt rows: 42
##   Character matrix gt cols: 211
##   skip: 0
##   nrows: 42
##   row_num: 0
## 
Processed variant: 42
## All variants processed

## Warning in create_depths_profile(onemap.obj = simu_cod_out, vcfR.object = vcfR.object, : Only biallelic codominant markers are supported. The multiallelic markers present in onemap object will not be plotted.
## Summary of reference counts: 
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    1.00   28.00   51.00   65.95   88.00  511.00 
## Summary of alternative counts: 
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    1.00   12.00   34.00   43.38   64.25  308.00
## Warning: Removed 6 rows containing missing values (geom_point).

See that we had one warning message about the multiallelic markers in our dataset, they were not plotted.

Combining OneMap datasets

If you have more than one dataset of markers, all from the same mapping population, you can use the function combine_onemap to merge them into only one onemap object.

In our example, we have two datasets:

  • first: onemap_example_out with 30 markers and 100 individuals
  • second: vcf_example_out with 24 biallelic markers and 92 individuals.

The combine_function recognizes the correspondent individuals by the ID, thus, it is important define exactly same IDs to respective individuals in both raw files. Compared with the first file, the second file do not have markers informations for 8 individuals. The combine_onemap will complete those informations with NA.

In our examples, we have only genotypic information, but the function can also merge the phenotypic information if it exists.

##   This is an object of class 'onemap'
##     Type of cross:      outcross 
##     No. individuals:    100 
##     No. markers:        54 
##     CHROM information:  yes 
##     POS information:    yes 
##     Percent genotyped:  96 
## 
##     Segregation types:
##                 A.1 -->  3
##                 A.2 -->  1
##                 A.4 -->  4
##                B1.5 -->  1
##                B2.6 -->  2
##                B3.7 -->  23
##                 C.8 -->  2
##               D1.10 -->  8
##               D1.12 -->  1
##               D1.13 -->  2
##               D2.15 -->  1
##               D2.16 -->  2
##               D2.17 -->  2
##               D2.18 -->  2
## 
##     No. traits:         3 
##     Missing trait values: 
##   Pheno1: 0 
##   Pheno2: 3 
##   Pheno3: 0

The function arguments are the names of the onemap objects you want to combine.

Plotting markers genotypes from the outputted onemap object, we can see that there are more missing data - (black vertical lines) for some individuals, because they were missing in the second file.

Find redundant markers

It is possible that there are redundant markers in your dataset, specially when dealing with too many markers. Redundant markers have the same genotypic informations that others markers, usually because didn’t happen recombination events between each other. They will not increase informations to the map, but will increase computational effort during the map building. Therefore, it is a good practice to remove them to build the map and, once the map is already builded, they can be added again.

First, we use the function find_bins to group the markers into bins according with their genotypic informations. In other words, markers with the same genotypic informations will be at the same bin.

## This is an object of class 'onemap_bin'
##     No. individuals:                         100 
##     No. markers in original dataset:         54 
##     No. of bins found:                       52 
##     Average of markers per bin:              1.038462 
##     Type of search performed:                non exact

The first argument is the onemap object and the exact argument specify if only markers with exact same informations will be at the same bin. Using FALSE at this second argument, missing data will not be considered and the marker with the lowest amount of missing data will be the representative marker on the bin.

Our example dataset have only two redundant marker. We can create a new onemap object without them, using the create_data_bins function. This function keeps only the most representative marker of each bin from bins object.

##   This is an object of class 'onemap'
##     Type of cross:      outcross 
##     No. individuals:    100 
##     No. markers:        52 
##     CHROM information:  yes 
##     POS information:    yes 
##     Percent genotyped:  96 
## 
##     Segregation types:
##                 A.1 -->  3
##                 A.2 -->  1
##                 A.4 -->  4
##                B1.5 -->  1
##                B2.6 -->  2
##                B3.7 -->  22
##                 C.8 -->  2
##               D1.10 -->  7
##               D1.12 -->  1
##               D1.13 -->  2
##               D2.15 -->  1
##               D2.16 -->  2
##               D2.17 -->  2
##               D2.18 -->  2
## 
##     No. traits:         3 
##     Missing trait values: 
##   Pheno1: 0 
##   Pheno2: 3 
##   Pheno3: 0

The arguments for create_data_bins function are the onemap object and the object created by find_bins function.

Exporting .raw file from onemap object

The functions onemap_read_vcfR generates new onemap objects without use a input .raw file. Also, the functions combine_onemap and create_data_bins manipulates the information of the original .raw file and creates a new dataset. In both cases, you do not have a input file .raw that contains the same informations of the analysed data. If you want to create a new input file with the dataset you are working after using this functions, you can use the function write_onemap_raw.

The file new_dataset.raw will be generated in your working directory. In our example, it contains only non-redundant markers from onemap_example_out and vcf_example_out datasets.

Testing segregation pattern

For the map building process it is also important to know which markers have deviations in the expected segregation pattern. It can be a good practice to remove them from the map building process, because they can adversely affect the map building, and, once the map is builded, they can be inserted.

The function test_segregation_of_a_marker performs chi-square test according with mendelian segregation to check if a specific marker is following the expected segregation pattern.

## $Hypothesis
## [1] "1:1:1:1"
## 
## $qui.quad
## X-squared 
##      2.64 
## 
## $p.val
## [1] 0.4505201
## 
## $perc.genot
## [1] 100

The arguments are the onemap object and the number of the marker you want to test.

You can also test all the markers in your onemap object using the test_segregation function. The results can be viewed printing the output object of class onemap_segreg_test.

##    Marker      H0 Chi-square   p-value % genot.
## 1      M1   1:2:1       1.76 0.4147829      100
## 2      M2     1:1       0.04 0.8414806      100
## 3      M3     1:1       0.36 0.5485062      100
## 4      M4 1:1:1:1       2.64 0.4505201      100
## 5      M5     1:1       1.96 0.1615133      100
## 6      M6   1:2:1       1.52 0.4676664      100
## 7      M7     1:1       0.16 0.6891565      100
## 8      M8   1:2:1       0.86 0.6505091      100
## 9      M9     1:1       0.04 0.8414806      100
## 10    M10     1:1       0.36 0.5485062      100
## 11    M11     1:1       0.16 0.6891565      100
## 12    M12 1:1:1:1       6.48 0.0904546      100
## 13    M13     3:1       0.00 1.0000000      100
## 14    M14 1:1:1:1       0.40 0.9402425      100
## 15    M15 1:1:1:1       2.24 0.5241127      100
##  [ reached 'max' / getOption("max.print") -- omitted 37 rows ]

The only argument of the function is a onemap object.

Once we have the onemap_segreg_testobject, the function select_segreg can be used to show only the markers considered with/without segregation distortion. By default, it uses as threshold for the test a global \(\alpha=0.05\), corrected for multiple test with Bonferroni correction.

## [1] "M17" "M19" "M25"
##  [1] "M1"    "M2"    "M3"    "M4"    "M5"    "M6"    "M7"    "M8"    "M9"   
## [10] "M10"   "M11"   "M12"   "M13"   "M14"   "M15"   "M16"   "M18"   "M20"  
## [19] "M21"   "M22"   "M23"   "M24"   "M26"   "M27"   "M28"   "M29"   "M30"  
## [28] "SNP1"  "SNP2"  "SNP3"  "SNP5"  "SNP6"  "SNP7"  "SNP8"  "SNP9"  "SNP10"
## [37] "SNP11" "SNP12" "SNP13" "SNP14" "SNP16" "SNP17" "SNP18" "SNP20" "SNP21"
## [46] "SNP22" "SNP23" "SNP24" "SNP25"

It is not recommended, but you can define a different threshold value changing the threshold argument of the function select_segreg.

For the next steps will be useful to know the numbers of each markers with segregation distortion, so then you can keep those out of your map building analysis. These numbers refer to the lines where markers are located on the data file.

To access the corresponding number for of this markers you can change the numbers argument:

## [1] 17 19 25
##  [1]  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 18 20 21 22 23 24 26 27 28
## [26] 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52

You can also see the results graphically by:

Strategies for this tutorial example

Now, we start the map building analysis. In this example we follow two different strategies:

  • Using only recombinations informations.

  • Using the recombinations and also the reference genome informations, once our example have CHROM and POS informations for some of the markers.

First, we will apply the strategy using only recombinations informations. In a second part of this tutorial we show a way to use also reference genome informations. At the and of our analysis we will be able to compare this two strategies drawing the resulted genetic maps.

Using only recombinations informations

Estimating two-point recombination fractions

To start the map building analysis, the first step is estimating the recombination fraction between all pairs of markers, using two-point tests.

Although two-point tests were implemented in C language, which is usually much faster than R, this step can take quite some time, depending on the number of markers involved and their segregation type, because all combinations will be estimated and tested. Besides, the results use a lot of memory and a rather powerful computer is needed.

When the two-point analysis is finished, an object of class rf_2pts is created. Typing

will show a message with the criteria used in the analysis and some other information:

##   This is an object of class 'rf_2pts'
## 
##   Criteria: LOD = 3 , Maximum recombination fraction = 0.5 
## 
##   This object is too complex to print
##   Type 'print(object, c(mrk1=marker, mrk2=marker))' to see
##     the analysis for two markers
##     mrk1 and mrk2 can be the names or numbers of both markers

If you want to see the results for given markers, say M1 and M3, the command is:

##   Results of the 2-point analysis for markers: M1 and M3 
##   Criteria: LOD =  3 , Maximum recombination fraction =  0.5 
## 
##           rf      LOD
## CC 0.2954514 1.646878
## CR 0.2954514 1.646878
## RC 0.7045486 1.646878
## RR 0.7045486 1.646878

Each line corresponds to a possible linkage phase. CC denotes coupling phase in both parents, CR and RC denote coupling phase in parent 1 and 2, respectively, and repulsion in the other, and RR denotes repulsion phase in both parents. Value rf is the maximum likelihood estimate of the recombination fraction, with its corresponding LOD Score.

Assigning markers to linkage groups

Once the recombination fractions and linkage phases for all pairs of markers have been estimated and tested, markers can be assigned to linkage groups. To do this, first use the function make_seq to create a sequence with the markers you want to assign.

The function make_seq is used to create sequences from objects of several kinds, as will be seen along this tutorial.

Here, the object is of class rf_2pts and the second argument specifies which markers one wants to use. If one wants to use only a subset of markers, say M1 and M2, the option will be a vector with the corresponding numbers of the markers, as c(1,2), you can also use a string "all" to specify that you want to analyze all markers. In our example, we will use the vector with the numbers of the markers with no segregation distortion.

Because the identification of the markers can be cumbersome, one should use the function marker type to see their numbers, names and types:

##   Marker 1 ( M1 ) is of type B3.7 
##   Marker 2 ( M2 ) is of type D2.18 
##   Marker 3 ( M3 ) is of type D1.13 
##   Marker 4 ( M4 ) is of type A.4 
##   Marker 5 ( M5 ) is of type D2.18 
##   Marker 6 ( M6 ) is of type B3.7 
##   Marker 7 ( M7 ) is of type D2.15 
##   Marker 8 ( M8 ) is of type B3.7 
##   Marker 9 ( M9 ) is of type D1.10 
##   Marker 10 ( M10 ) is of type D2.17 
##   Marker 11 ( M11 ) is of type D2.16 
##   Marker 12 ( M12 ) is of type A.2 
##   Marker 13 ( M13 ) is of type C.8 
##   Marker 14 ( M14 ) is of type A.4 
##   Marker 15 ( M15 ) is of type A.4 
##   Marker 16 ( M16 ) is of type D2.17 
##   Marker 18 ( M18 ) is of type A.1 
##   Marker 20 ( M20 ) is of type A.1 
##   Marker 21 ( M21 ) is of type D2.16 
##   Marker 22 ( M22 ) is of type D1.10 
##   Marker 23 ( M23 ) is of type C.8 
##   Marker 24 ( M24 ) is of type B3.7 
##   Marker 26 ( M26 ) is of type A.1 
##   Marker 27 ( M27 ) is of type D1.12 
##   Marker 28 ( M28 ) is of type A.4 
##   Marker 29 ( M29 ) is of type D1.13 
##   Marker 30 ( M30 ) is of type B3.7 
##   Marker 31 ( SNP1 ) is of type B3.7 
##   Marker 32 ( SNP2 ) is of type B3.7 
##   Marker 33 ( SNP3 ) is of type B3.7 
##   Marker 34 ( SNP5 ) is of type B3.7 
##   Marker 35 ( SNP6 ) is of type B3.7 
##   Marker 36 ( SNP7 ) is of type B3.7 
##   Marker 37 ( SNP8 ) is of type B3.7 
##   Marker 38 ( SNP9 ) is of type B3.7 
##   Marker 39 ( SNP10 ) is of type B3.7 
##   Marker 40 ( SNP11 ) is of type B3.7 
##   Marker 41 ( SNP12 ) is of type B3.7 
##   Marker 42 ( SNP13 ) is of type B3.7 
##   Marker 43 ( SNP14 ) is of type D1.10 
##   Marker 44 ( SNP16 ) is of type B3.7 
##   Marker 45 ( SNP17 ) is of type D1.10 
##   Marker 46 ( SNP18 ) is of type D1.10 
##   Marker 47 ( SNP20 ) is of type D1.10 
##   Marker 48 ( SNP21 ) is of type D1.10 
##   Marker 49 ( SNP22 ) is of type B3.7 
##   Marker 50 ( SNP23 ) is of type B3.7 
##   Marker 51 ( SNP24 ) is of type B3.7 
##   Marker 52 ( SNP25 ) is of type B3.7

The grouping step is very simple and can be done by using the function group:

##    Selecting markers: 
##    group    1 
##     ........................
##    group    2 
##     ................
##    group    3 
##     ......

For this function, optional arguments are LOD and max.rf, which define thresholds to be used when assigning markers to linkage groups. If none provided (default), it uses as default values of LOD Score 3 and maximum recombination fraction 0.50.

Also, you can use the function suggest_lod to calculate a suggested LOD score considering that multiple tests are being performed.

## [1] 3.639312

And apply this suggested value to the two-point tests:

##    Selecting markers: 
##    group    1 
##     ........................
##    group    2 
##     ................
##    group    3 
##     ......

The previous command generates an object of class group and the command print for such object has two options. If you type:

you will get detailed information about the groups, that is, all linkage groups will be printed, displaying the names of markers in each one of them.

##   This is an object of class 'group'
##   It was generated from the object "mark_no_dist"
## 
##   Criteria used to assign markers to groups:
##     LOD = 3.639312 , Maximum recombination fraction = 0.5 
## 
##   No. markers:            49 
##   No. groups:             3 
##   No. linked markers:     49 
##   No. unlinked markers:   0 
## 
##   Printing groups:
##   Group 1 : 25 markers
##     M1 M2 M3 M5 M6 M10 M11 M12 M14 M15 M26 M28 M30 SNP1 SNP2 SNP3 SNP5 SNP6 SNP7 SNP8 SNP9 SNP10 SNP11 SNP12 SNP13 
## 
##   Group 2 : 17 markers
##     M4 M9 M16 M20 M21 M23 M24 M27 M29 SNP17 SNP18 SNP20 SNP21 SNP22 SNP23 SNP24 SNP25 
## 
##   Group 3 : 7 markers
##     M7 M8 M13 M18 M22 SNP14 SNP16

However, in case you just want to see some basic information (such as the number of groups, number of linked markers, etc), use

##   This is an object of class 'group'
##   It was generated from the object "mark_no_dist"
## 
##   Criteria used to assign markers to groups:
##     LOD = 3.639312 , Maximum recombination fraction = 0.5 
## 
##   No. markers:            49 
##   No. groups:             3 
##   No. linked markers:     49 
##   No. unlinked markers:   0

You can notice that all markers are linked to some linkage group. If the LOD Score threshold is changed to a higher value, some markers are kept unassigned:

##    Selecting markers: 
##    group    1 
##     ........................
##    group    2 
##     ..........
##    group    3 
##     .....
##    group    4 
##     ....
##   This is an object of class 'group'
##   It was generated from the object "mark_no_dist"
## 
##   Criteria used to assign markers to groups:
##     LOD = 6 , Maximum recombination fraction = 0.5 
## 
##   No. markers:            49 
##   No. groups:             4 
##   No. linked markers:     47 
##   No. unlinked markers:   2 
## 
##   Printing groups:
##   Group 1 : 25 markers
##     M1 M2 M3 M5 M6 M10 M11 M12 M14 M15 M26 M28 M30 SNP1 SNP2 SNP3 SNP5 SNP6 SNP7 SNP8 SNP9 SNP10 SNP11 SNP12 SNP13 
## 
##   Group 2 : 11 markers
##     M4 M9 M16 M20 M21 M23 M27 SNP17 SNP18 SNP20 SNP21 
## 
##   Group 3 : 6 markers
##     M8 M13 M18 M22 SNP14 SNP16 
## 
##   Group 4 : 5 markers
##     M24 SNP22 SNP23 SNP24 SNP25 
## 
##   Unlinked markers: 2  markers
##     M7 M29

Changing back to the previous criteria, now setting the maximum recombination fraction to 0.40:

##    Selecting markers: 
##    group    1 
##     ........................
##    group    2 
##     ................
##    group    3 
##     ......
##   This is an object of class 'group'
##   It was generated from the object "mark_no_dist"
## 
##   Criteria used to assign markers to groups:
##     LOD = 3.639312 , Maximum recombination fraction = 0.4 
## 
##   No. markers:            49 
##   No. groups:             3 
##   No. linked markers:     49 
##   No. unlinked markers:   0 
## 
##   Printing groups:
##   Group 1 : 25 markers
##     M1 M2 M3 M5 M6 M10 M11 M12 M14 M15 M26 M28 M30 SNP1 SNP2 SNP3 SNP5 SNP6 SNP7 SNP8 SNP9 SNP10 SNP11 SNP12 SNP13 
## 
##   Group 2 : 17 markers
##     M4 M9 M16 M20 M21 M23 M24 M27 M29 SNP17 SNP18 SNP20 SNP21 SNP22 SNP23 SNP24 SNP25 
## 
##   Group 3 : 7 markers
##     M7 M8 M13 M18 M22 SNP14 SNP16

Genetic mapping of linkage group 3

Once marker assignment to linkage groups is finished, the mapping step can take place. First of all, you must set the mapping function that should be used to display the genetic map throughout the analysis. You can choose between Kosambi or Haldane mapping functions. To use Haldane, type

To use Kosambi

If you do not set one of these functions, the kosambi is used as default.

Now, you must define which linkage group will be mapped. In another words, a linkage group must be extracted from the object of class group, in order to be mapped. For simplicity, we will start here with the smallest one, which is linkage group 3. This can be easily done using the following code:

The first argument (LGs) is an object of class group and the second is a number indicating which linkage group will be extracted, according to the results stored in object LGs. The object LG3, generated by function make_seq, is of class sequence, showing that this function can be used with several types of objects.

If you type

you will see which markers are comprised in the sequence, and also that no parameters have been estimated so far.

## 
## Number of markers: 7
## Markers in the sequence:
## M7 M8 M13 M18 M22 SNP14 SNP16
## 
## Parameters not estimated.

To order these markers, one can use a two-point based algorithm such as Seriation (Buetow and Chakravarti, 1987), Rapid Chain Delineation (Doerge, 1996), Recombination Counting and Ordering (Van Os et al., 2005) and Unidirectional Growth (Tan and Fu, 2006):

In this case, there are some differences between algorithms results (results not shown).

Alternatively, you can also use mds_onemap function to obtain a first draft for the markers order. The mds_onemap is a wrapper function that makes interface between OneMap and MDSMap package. The ordering approach presented in MDSMap provides a faster and efficient way of ordering markers using multi-dimensional scaling. The method also provides diagnostics graphics and parameters to find outliers to help users to filter the dataset. You can find more informations in MDSMap vignette. Here we will show a simple example of how it can be used for ordering our example markers from an outcrossing population.

## Stress: 0.225277102704001
## Mean Nearest Neighbour Fit: 22.0492750538469
## Markers omitted:

If you only specify the input sequence, mds_onemap will use the default parameters. It will generate MDSMap input file in out.file file and the NULL.pdf file with the diagnostic graphics in your work directory. You can use out.file in MDSMap package to try other parameters too. The default method used is the principal curves, know more about using ?mds_onemap and reading the MDSMap vignette.

Besides this algorithms use two-point approach to order the markers, multipoint approach is applied to estimate the genetic distances after the order is estimated. Thus, it can happen that some markers are not considered linked when evaluated by multipoint information, and the function will return an error like this:

ERROR: The linkage between markers 1 and 2 did not reached the OneMap default criteria. They are probably segregating independently

You can automatically remove these markers setting argument rm_unlinked = TRUE. Doing this, the marker will be removed and the ordering algorithms will be restarted. Warning messages will inform which markers were removed. If you don’t get warning messages it means that any marker needed to be removed. This is our case in this example, but if you obtain an error or warning running your dataset, you already know what happened.

NOTE: (new!) If your sequence has many markers (more than 60), we suggest to speed up mds, seriation, rcd, record and ug using BatchMap parallelization approach. See section Speed up analysis with parallelization for more information.

To order by comparing all possible orders (exhaustive search), the function compare can be used:

WARNING: This algorithm can take some time to run, depending on marker types in the linkage group. If you are working in a personal computer, without high capacity, we recommend using maximum of ten markers.

If you have more markers in your group, we suggest to use the following explained approaches order_seq.

In the example, LG3 contains only seven markers. Two of them are of type D1 and one are segregating in 3:1 fashion (type C). Thus, although the number of possible orders is relatively small (360), for each order there are various possible combinations of linkage phases. Also, the convergence of the EM algorithm takes considerably more time, because markers of type C and D are not very informative.

The first argument to the compare function is an object of class sequence (the extracted group LG3), and the object generated by this function is of class compare.

To see the results of the previous step, type

## 
## Number of orders: 50 
## Best 45 unique orders                         LOD    Nested LOD
## -------------------------------------------------------------- 
## order  1:    43  22   7  18   8  13  44
##         CC  CC  CC  RR  RR  RR         0.00       0.00
##         CC  CC  RC  RR  RR  RR        -1.48      -1.48
## --------------------------------------------------------------
## order  2:    43   7  22  18   8  13  44
##         CC  CC  CC  RR  RR  RR        -0.05       0.00
## --------------------------------------------------------------
## order  3:    22  43   7  18   8  13  44
##         CC  CC  CC  RR  RR  RR        -0.15       0.00
##         CC  CC  RC  RR  RR  RR        -1.48      -1.33
## --------------------------------------------------------------
## order  4:    22   7  43  18   8  13  44
##         CC  CC  CC  RR  RR  RR        -0.22       0.00
## --------------------------------------------------------------
## order  5:     7  43  22  18   8  13  44
##         CC  CC  CC  RR  RR  RR        -0.25       0.00
##         CC  CC  CR  RR  RR  RR        -2.26      -2.01
## --------------------------------------------------------------
## order  6:     7  22  43  18   8  13  44
##         CC  CC  CC  RR  RR  RR        -0.42       0.00
## --------------------------------------------------------------
## order  7:     7  18   8  13  44  22  43
##         CC  RR  RR  RR  RC  CC        -0.54       0.00
## --------------------------------------------------------------
## order  8:     7  44  13   8  18  22  43
##         CR  RR  RR  RR  CC  CC        -0.65       0.00
## --------------------------------------------------------------
## order  9:     7  44  13   8  18  43  22
##         CR  RR  RR  RR  CC  CC        -0.80       0.00
## --------------------------------------------------------------
## order 10:     7  18   8  13  44  43  22
##         CC  RR  RR  RR  RC  CC        -0.87       0.00
## --------------------------------------------------------------
## order 11:    43  22   7  13  18   8  44
##         CC  CC  CC  CC  RR  CC        -0.99       0.00
## --------------------------------------------------------------
## order 12:    43   7  22  13  18   8  44
##         CC  CC  CC  CC  RR  CC        -1.03       0.00
## --------------------------------------------------------------
## order 13:    43  22   7  13  44   8  18
##         CC  CC  CC  RR  CC  RR        -1.06       0.00
## --------------------------------------------------------------
## order 14:    43   7  22  13  44   8  18
##         CC  CC  CC  RR  CC  RR        -1.12       0.00
## --------------------------------------------------------------
## order 15:    43  22   7  44  13   8  18
##         CC  CC  RR  RR  RR  RR        -1.13       0.00
##         CC  CC  CR  RR  RR  RR        -2.13      -1.00
## --------------------------------------------------------------
## order 16:    43   7  22  44  13   8  18
##         CC  CC  RR  RR  RR  RR        -1.19       0.00
## --------------------------------------------------------------
## order 17:    43  22   7  18  13   8  44
##         CC  CC  CC  CC  RR  CC        -1.25       0.00
## --------------------------------------------------------------
## order 18:     7  43  22  13  18   8  44
##         CC  CC  CC  CC  RR  CC        -1.26       0.00
## --------------------------------------------------------------
## order 19:    43   7  22  18  13   8  44
##         CC  CC  CC  CC  RR  CC        -1.30       0.00
## --------------------------------------------------------------
## order 20:     7  43  22  44  13   8  18
##         CC  CC  RR  RR  RR  RR        -1.35       0.00
## --------------------------------------------------------------
## order 21:    22  43   7  18  13   8  44
##         CC  CC  CC  CC  RR  CC        -1.40       0.00
## --------------------------------------------------------------
## order 22:     7  43  22  13  44   8  18
##         CC  CC  CC  RR  CC  RR        -1.41       0.00
## --------------------------------------------------------------
## order 23:    22   7  43  18  13   8  44
##         CC  CC  CC  CC  RR  CC        -1.47       0.00
## --------------------------------------------------------------
## order 24:     7  43  22  18  13   8  44
##         CC  CC  CC  CC  RR  CC        -1.50       0.00
## --------------------------------------------------------------
## order 25:    22  43   7  44  13   8  18
##         CC  CC  RR  RR  RR  RR        -1.54       0.00
##         CC  CC  CR  RR  RR  RR        -2.13      -0.60
## --------------------------------------------------------------
## order 26:    22   7  43  44  13   8  18
##         CC  CC  RR  RR  RR  RR        -1.66       0.00
## --------------------------------------------------------------
## order 27:     7  22  43  18  13   8  44
##         CC  CC  CC  CC  RR  CC        -1.67       0.00
## --------------------------------------------------------------
## order 28:     7  13  44   8  18  22  43
##         CC  RR  CC  RR  CC  CC        -1.73       0.00
## --------------------------------------------------------------
## order 29:     7  18  13   8  44  22  43
##         CC  CC  RR  CC  RC  CC        -1.76       0.00
## --------------------------------------------------------------
## order 30:    22  43   7  13  18   8  44
##         CC  CC  CC  CC  RR  CC        -1.77       0.00
## --------------------------------------------------------------
## order 31:    22  43   7  13  44   8  18
##         CC  CC  CC  RR  CC  RR        -1.82       0.00
## --------------------------------------------------------------
## order 32:     7  22  43  44  13   8  18
##         CC  CC  RR  RR  RR  RR        -1.84       0.00
## --------------------------------------------------------------
## order 33:     7  44   8  13  18  22  43
##         CR  CC  RR  CC  CC  CC        -1.87       0.00
## --------------------------------------------------------------
## order 34:     7  13  44   8  18  43  22
##         CC  RR  CC  RR  CC  CC        -1.88       0.00
## --------------------------------------------------------------
## order 35:    22   7  43  13  18   8  44
##         CC  CC  CC  CC  RR  CC        -1.90       0.00
## --------------------------------------------------------------
## order 36:    22   7  43  13  44   8  18
##         CC  CC  CC  RR  CC  RR        -1.98       0.00
## --------------------------------------------------------------
## order 37:     7  18   8  44  13  22  43
##         CC  RR  CC  RR  CC  CC        -2.00       0.00
## --------------------------------------------------------------
## order 38:     7  44   8  13  18  43  22
##         CR  CC  RR  CC  CC  CC        -2.02       0.00
## --------------------------------------------------------------
## order 39:     7  18  13   8  44  43  22
##         CC  CC  RR  CC  RC  CC        -2.11       0.00
## --------------------------------------------------------------
## order 40:     7  22  43  13  18   8  44
##         CC  CC  CC  CC  RR  CC        -2.20       0.00
## --------------------------------------------------------------
## order 41:     7  13  18   8  44  22  43
##         CC  CC  RR  CC  RC  CC        -2.21       0.00
## --------------------------------------------------------------
## order 42:     7  22  43  13  44   8  18
##         CC  CC  CC  RR  CC  RR        -2.29       0.00
## --------------------------------------------------------------
## order 43:     7  44   8  18  13  22  43
##         CR  CC  RR  CC  CC  CC        -2.32       0.00
## --------------------------------------------------------------
## order 44:    43  22   7  44   8  13  18
##         CC  CC  RR  CC  RR  CC        -2.32       0.00
## --------------------------------------------------------------
## order 45:    43   7  22  44   8  13  18
##         CC  CC  RR  CC  RR  CC        -2.37       0.00
## --------------------------------------------------------------

Remember that for outcrossing populations, one needs to estimate marker order and also linkage phases between markers for a given order. However, because two point analysis provides information about linkage phases, this information is taken into consideration in the compare function, reducing the number of combinations to be evaluated. If a given linkage phase has LOD greater than 0.005 in the two point analysis, we assume that this phase is very unlikely and so does not need to be evaluated in the multipoint procedure used by compare. We did extensive simulations which showed that this is a good procedure.

By default, OneMap stores 50 orders, which may or may not be unique. The value of LOD refers to the overall LOD Score, considering all orders tested. Nested LOD refers to LOD Scores within a given order, that is, scores for different combinations of linkage phases for the same marker order.

For example, order 1 has the largest value of log-likelihood and, therefore, its LOD Score is zero for a given combination of linkage phases (CC, CC, RR, RR). For this same order and other linkage phases, LOD Score is -5.20. Analyzing the results for order 2, notice that its highest LOD Score is very close to zero, indicating that this order is also quite plausible. Notice also that Nested LOD will always contain at least one zero value, corresponding to the best combination of phases for markers in a given order. Due to the information provided by two-point analysis, not all combinations are tested and that is the reason why the number of Nested LOD values is different for each order.

Unless one has some biological information, it is a good idea to choose the order with the highest likelihood. The final map can then be obtained with the command

The first argument is the object of class compare. The second argument indicates which order is chosen: 1 is for the order with highest likelihood, 2 is for the second best, and so on. The third argument indicates which combination of phases is chosen for a given order: 1 also means the combination with highest likelihood among all combinations of phases (based on Nested LOD).

For simplicity, these values are defaults, so typing

have the same effect.

To see the final map, type

## 
## Printing map:
## 
## Markers           Position           Parent 1       Parent 2
## 
## 43 SNP14              0.00           a |  | b       a |  | a 
## 22 M22               13.51           a |  | b       a |  | a 
##  7 M7                24.56           a |  | a       a |  | b 
## 18 M18               65.59           a |  | b       c |  | d 
##  8 M8                71.28           b |  | a       b |  | a 
## 13 M13               73.94           a |  | o       a |  | o 
## 44 SNP16             79.82           b |  | a       b |  | a 
## 
## 7 markers            log-likelihood: -398.6863

At the leftmost position, marker names are displayed. Position shows the cumulative distance using the Kosambi mapping function. Finally, Parent 1 and Parent 2 show the diplotypes of both parents, that is, the combination in which alleles are arranged in the chromosomes, given the estimated linkage phase. Notation is the same as that used by Wu et al. (2002a). Details about how ordering algorithms can be chosen and used are presented by Mollinari et al. (2009).

A careful examination of the results can be done using the function rf_graph_table to provide graphical view:

With the default arguments, this functions plots the recombination fractions between the markers pointed in the axes. You can change the number of colors from rainbow palette with the argument n.colors. Hot colors (more close to red) represents lower values of recombination fractions, as shown in the scale at right side of the graphic. White cells indicate combinations of markers for which the recombination fractions cannot be estimated (D1 and D2). If you want to analyze the LOD values between the markers, use graph.LOD = TRUE.

If you change the inter argument to TRUE, you should also specify a output html file name in html.file. This html contains a iterative plotly graphic. If you hover the mouse cursor over the cells it shows some extra information about cells, as percentage of missing data, marker name and type. The output html file is generated in your work directory and opens automatically in your internet browser.

For example, passing on the cell corresponding to markers 8 and 13, you can see their names (M8 and M13 ), types (B3.7 and C.8), recombination fraction (rf = 0.03) and LOD Scores for each possible linkage phase. This is quite useful in helping to interpret the results.

If you want to see corresponding marker numbers (not the names) in the axis just change the argument mrk.axis to numbers. It can make the next steps easier.

The rf_graph_table can also be used to check the order of markers based on the monotonicity of the matrix: as we get away from the secondary diagonal, the recombination fraction values should increase.

Looking at the matrix, it is possible to see a gap between markers M7 and M18 (numbers 7 and 18). In some cases, gaps could indicate that the group must be divided at this position, but here SNP18 (number 43) also show linkage with M8, which points that probably it is only a gap. Adding more markers to this groups could fill this gap.

Changing other arguments of the function you can add/remove labels of the axes (‘lab.xy’) and add a title to the graph (‘main’).

Genetic mapping of linkage group 2

Now, let us map the markers in linkage group number 2.

Again, extract that group from the object LGs:

## 
## Number of markers: 17
## Markers in the sequence:
## M4 M9 M16 M20 M21 M23 M24 M27 M29 SNP17 SNP18 SNP20 SNP21 SNP22 SNP23 SNP24 
## SNP25
## 
## Parameters not estimated.

Note that there are more than 10 markers in this group, so it is infeasible to use the compare function with all of them because it will take a very long time to proceed.

First, use rcd to get a preliminary order estimate:

## 
## order obtained using RCD algorithm:
## 
##  27 47 16 20 4 21 23 45 46 9 48 51 50 24 49 52 29 
## 
## calculating multipoint map using tol =  1e-04 .
## 
## Printing map:
## 
## Markers           Position           Parent 1       Parent 2
## 
## 27 M27                0.00           b |  | o       a |  | a 
## 47 SNP20             98.48           a |  | b       a |  | a 
## 16 M16              149.21           a |  | a       b |  | o 
## 20 M20              160.39           a |  | b       c |  | d 
##  4 M4               173.16           a |  | o       o |  | b 
## 21 M21              187.19           o |  | o       a |  | b 
## 23 M23              192.89           a |  | o       a |  | o 
## 45 SNP17            211.80           a |  | b       a |  | a 
## 46 SNP18            225.91           a |  | b       a |  | a 
##  9 M9               232.12           a |  | b       a |  | a 
## 48 SNP21            239.01           a |  | b       a |  | a 
## 51 SNP24            261.01           a |  | b       b |  | a 
## 50 SNP23            271.95           a |  | b       b |  | a 
## 24 M24              276.90           a |  | b       b |  | a 
## 49 SNP22            280.29           a |  | b       b |  | a 
## 52 SNP25            285.42           a |  | b       b |  | a 
## 29 M29              314.87           o |  | a       o |  | o 
## 
## 17 markers            log-likelihood: -902.103

Use the marker_type function to check the segregation types of all markers in this group:

##   Marker 4 ( M4 ) is of type A.4 
##   Marker 9 ( M9 ) is of type D1.10 
##   Marker 16 ( M16 ) is of type D2.17 
##   Marker 20 ( M20 ) is of type A.1 
##   Marker 21 ( M21 ) is of type D2.16 
##   Marker 23 ( M23 ) is of type C.8 
##   Marker 24 ( M24 ) is of type B3.7 
##   Marker 27 ( M27 ) is of type D1.12 
##   Marker 29 ( M29 ) is of type D1.13 
##   Marker 45 ( SNP17 ) is of type D1.10 
##   Marker 46 ( SNP18 ) is of type D1.10 
##   Marker 47 ( SNP20 ) is of type D1.10 
##   Marker 48 ( SNP21 ) is of type D1.10 
##   Marker 49 ( SNP22 ) is of type B3.7 
##   Marker 50 ( SNP23 ) is of type B3.7 
##   Marker 51 ( SNP24 ) is of type B3.7 
##   Marker 52 ( SNP25 ) is of type B3.7

Based on their segregation types and distribution on the preliminary map, markers M4, M20, M24, SNP22, SNP23, SNP24 and SNP25 are the most informative ones (type A is better, followed by type B). So, let us create a framework of ordered markers using compare for the most informative ones:

Here there is a automatic way of obtain a new sequence only with markers selected by type: (new!)

##   Marker 4 ( M4 ) is of type A.4 
##   Marker 20 ( M20 ) is of type A.1 
##   Marker 24 ( M24 ) is of type B3.7 
##   Marker 49 ( SNP22 ) is of type B3.7 
##   Marker 50 ( SNP23 ) is of type B3.7 
##   Marker 51 ( SNP24 ) is of type B3.7 
##   Marker 52 ( SNP25 ) is of type B3.7
##   Marker 4 ( M4 ) is of type A.4 
##   Marker 20 ( M20 ) is of type A.1 
##   Marker 24 ( M24 ) is of type B3.7 
##   Marker 49 ( SNP22 ) is of type B3.7 
##   Marker 50 ( SNP23 ) is of type B3.7 
##   Marker 51 ( SNP24 ) is of type B3.7

Now, the first argument to make_seq is an object of class rf_2pts, and the second argument is a vector of integers, specifying which molecular markers comprise the sequence.

Select the best order:

Also, we can obtain a useful diagnostic graphic using the function rf_graph_table.

The graphic shows that there are two groups of markers, once M20 and M4 are far from the other markers. These markers could be in different linkage groups or they are distant in the same group. Adding more markers will give more informations to solve this issue.

Next, let us try to map the remaining markers, one at a time. Fist, we will try to add the remaining most informative markers. Starting with SNP25:

## 
## LOD scores correspond to the best linkage phase combination
## for each position
## 
## The symbol "*" outside the box indicates that more than one
## linkage phase is possible for the corresponding position
## 
## 
##        Marker tested: 52
## 
##        Markers     LOD
##      =====================
##      |                   |
##      |           -26.44  |  1  
##      |  20               | 
##      |           -50.47  |  2  
##      |   4               | 
##      |            -8.34  |  3  
##      |  51               | 
##      |            -8.79  |  4  
##      |  50               | 
##      |            -8.43  |  5  
##      |  24               | 
##      |            -2.46  |  6  
##      |  49               | 
##      |             0.00  |  7  
##      |                   |
##      =====================

Based on the LOD Scores, marker SNP25 is probably better located after SNP22 (number 49). Detailed results can be seen with

## 
## LOD is the overall LOD score (among all orders)
## 
## NEST.LOD is the LOD score within the order
## 
## Marker tested: 52
## -------------- 
## |     |      |
## | 20  |      |
## |     |  CR  |  
## |  4  |      |
## |     |  CC  |  
## | 51  |      |
## |     |  CC  |  
## | 50  |      |
## |     |  CC  |  
## | 24  |      |
## |     |  CC  |  
## | 49  |      |
## |     |  CC  |  
## | 52  |      |
## |     |      |
## |------------|
## | LOD |   0.0|
## |------------|
## |NEST.|      |
## | LOD |   0.0|
## --------------

The second argument indicates the position where to place the marker. Note that the first allele arrangement is the most likely one.

It should be pointed out that the framework created by the function compare (with M20, M4, SNP24, SNP23, M24 and SNP22, or numbers 20, 4, 51,50, 24 and 49) could be in reverse order (SNP22, M24, SNP23, SNP24, M4 and M20, or numbers 49, 24, 50, 51, 4, 20) and still represent the same map. Thus, positioning of markers with the try_seq command can be different in your computer. For example, here marker SNP25 (number 52) was better placed at position 7; however if you obtain a reversed order, marker SNP25 would be better placed in position 1. In both cases the best position for this marker is after SNP22.

We can better evaluate the order with rf_graph_table. It requires a object of sequence class with mapping informations.

When using make_seq with an object of class try, the second argument is the position on the map (according to the scale on the right of the output) and the last argument indicates linkage phases (defaults to 1, higher nested LOD).

We can see that SNP25 (or marker 52) was positioned at the end of the sequence and the color pattern shows that it is strongly linked with its neighbors, indicating that it is well positioned, then we will maintain this marker at this position:

Adding other markers, one by one (output not shown):

Checking graphically:

The process of adding markers sequentially can be automated with the use of function order_seq.

## 
## Cross type: outcross 
## Using segregation types of the markers to choose initial subset
## 
## Comparing 60 orders:     
## 
## 
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## 
## 
## 
## Running try algorithm
## 51 --> SNP24 : ......
## 52 --> SNP25 : ......
## 23 --> M23   : ......
##  9 --> M9    : .......
## 27 --> M27   : .......
## 29 --> M29   : ........
## 45 --> SNP17 : ........
## 46 --> SNP18 : .........
## 47 --> SNP20 : .........
## 48 --> SNP21 : .........
## 16 --> M16   : .........
## 21 --> M21   : ..........
## 
## LOD threshold = 3 
## 
## Positioned markers: 27 16 20 4 23 45 50 24 49 
## 
## Markers not placed on the map: 9 21 29 46 47 48 51 52 
## 
## 
## Calculating LOD-Scores
##  9 --> M9    : ..........
## 21 --> M21   : ..........
## 29 --> M29   : ..........
## 46 --> SNP18 : ..........
## 47 --> SNP20 : ..........
## 48 --> SNP21 : ..........
## 51 --> SNP24 : ..........
## 52 --> SNP25 : ..........
## 
## 
## Placing remaining marker(s) at most likely position
## 52 --> SNP25 : ..........
## 48 --> SNP21 : ...........
## 47 --> SNP20 : ............
## 46 --> SNP18 : .............
## 21 --> M21   : ..............
##  9 --> M9    : ...............
## 29 --> M29   : ................
## 51 --> SNP24 : .................
## 
## Estimating final genetic map using tol = 10E-5.

Basically, this function automates what the try_seq function does, using some predefined rules. In the function, n.init = 5 means that five markers (the most informative ones) will be used in the compare step; THRES = 3 indicates that the try_seq step will only add markers to the sequence which can be mapped with LOD Score greater than 3.

NOTE: Although very useful, this function can be misleading, specially if there are not many fully informative markers, so use it carefully. Results can vary between multiple runs on the same markers, of course.

Check the final order:

## 
## Best sequence found.
## Printing map:
## 
## Markers           Position           Parent 1       Parent 2
## 
## 27 M27                0.00           b |  | o       a |  | a 
## 16 M16               11.76           a |  | a       b |  | o 
## 20 M20               22.94           a |  | b       c |  | d 
##  4 M4                35.71           a |  | o       o |  | b 
## 23 M23               53.69           a |  | o       a |  | o 
## 45 SNP17             72.86           a |  | b       a |  | a 
## 50 SNP23            103.35           a |  | b       b |  | a 
## 24 M24              108.37           a |  | b       b |  | a 
## 49 SNP22            112.25           a |  | b       b |  | a 
## 
## 9 markers            log-likelihood: -551.4083 
## 
## 
## 
## The following markers could not be uniquely positioned.
## Printing most likely positions for each unpositioned marker:
## 
## ------------------------------------------------------ 
## |    |   9 |  21 |  29 |  46 |  47 |  48 |  51 |  52 |
## |----|-----|-----|-----|-----|-----|-----|-----|-----| 
## |    |     |     |     |     |     |     |     |     |
## | 27 |     |     |     |     |     |     |     |     | 
## |    |     |     |     |     |     |     |     |     |
## | 16 |     |     |     |     |     |     |     |     | 
## |    |     |     |     |     |     |     |     |     |
## | 20 |     |     |     |     |     |     |     |     | 
## |    |     |     |     |     |     |     |     |     |
## |  4 |     |     |     |     |     |     |     |     | 
## |    |     | *** |     |     |     |     |     |     |
## | 23 |     |     |     |     |     |     |     |     | 
## |    | *** | *   |     | *   |     | *** |     |     |
## | 45 |     |     |     |     |     |     |     |     | 
## |    | *   |     | **  | *** | *** |     | *** |     |
## | 50 |     |     |     |     |     |     |     |     | 
## |    |     |     |     |     |     |     |     |     |
## | 24 |     |     |     |     |     |     |     |     | 
## |    |     |     |     |     |     |     |     |     |
## | 49 |     |     |     |     |     |     |     |     | 
## |    |     |     | *** |     |     |     | **  | *** |
## ------------------------------------------------------ 
## 
## '***' indicates the most likely position(s) (LOD = 0.0)
## 
## '**' indicates very likely positions (LOD > -1.0)
## 
## '*' indicates likely positions (LOD > -2.0)

Note that markers 9, 21, 29, 46, 47, 48, 51 and 52 could not be safely mapped to a single position (LOD Score > THRES in absolute value). The output displays the safe order and the most likely positions for markers not mapped, where *** indicates the most likely position and * corresponds to other plausible positions.

To get the safe order (i.e., without markers 9, 21, 29, 46, 47, 48, 51 and 52), use

and to get the order with all markers, use

## 
## Printing map:
## 
## Markers           Position           Parent 1       Parent 2
## 
## 27 M27                0.00           b |  | o       a |  | a 
## 16 M16               11.76           a |  | a       b |  | o 
## 20 M20               22.94           a |  | b       c |  | d 
##  4 M4                35.71           a |  | o       o |  | b 
## 21 M21               49.40           o |  | o       a |  | b 
## 23 M23               55.18           a |  | o       a |  | o 
## 48 SNP21             67.73           a |  | b       a |  | a 
##  9 M9                74.32           a |  | b       a |  | a 
## 46 SNP18             80.85           a |  | b       a |  | a 
## 45 SNP17             96.14           a |  | b       a |  | a 
## 47 SNP20            121.33           a |  | b       a |  | a 
## 29 M29              170.70           o |  | a       o |  | o 
## 50 SNP23            192.38           a |  | b       b |  | a 
## 24 M24              197.52           a |  | b       b |  | a 
## 49 SNP22            200.80           a |  | b       b |  | a 
## 52 SNP25            205.70           a |  | b       b |  | a 
## 51 SNP24            216.64           a |  | b       b |  | a 
## 
## 17 markers            log-likelihood: -871.9124

Notice that, for this linkage group, the forced map obtained with order_seq is different from that obtained with compare plus try_seq. It depends of which markers we choose to try add first when doing manually.

The order_seq function can also perform two rounds of the try_seq algorithms, first using THRES and then THRES - 1 as threshold. This generally results in safe orders with more markers mapped, but may take longer to run. To do this use the touchdown option:

## 
## Best sequence found.
## Printing map:
## 
## Markers           Position           Parent 1       Parent 2
## 
## 27 M27                0.00           b |  | o       a |  | a 
## 16 M16               11.76           a |  | a       b |  | o 
## 20 M20               22.94           a |  | b       c |  | d 
##  4 M4                35.71           a |  | o       o |  | b 
## 23 M23               52.88           a |  | o       a |  | o 
## 48 SNP21             65.21           a |  | b       a |  | a 
## 45 SNP17             79.22           a |  | b       a |  | a 
## 47 SNP20            103.39           a |  | b       a |  | a 
## 50 SNP23            143.48           a |  | b       b |  | a 
## 24 M24              148.50           a |  | b       b |  | a 
## 49 SNP22            151.80           a |  | b       b |  | a 
## 52 SNP25            156.80           a |  | b       b |  | a 
## 
## 12 markers            log-likelihood: -670.5 
## 
## 
## 
## The following markers could not be uniquely positioned.
## Printing most likely positions for each unpositioned marker:
## 
## ------------------------------------ 
## |    |   9 |  21 |  29 |  46 |  51 |
## |----|-----|-----|-----|-----|-----| 
## |    |     |     |     |     |     |
## | 27 |     |     |     |     |     | 
## |    |     |     |     |     |     |
## | 16 |     |     |     |     |     | 
## |    |     |     |     |     |     |
## | 20 |     |     |     |     |     | 
## |    |     |     |     |     |     |
## |  4 |     |     |     |     |     | 
## |    |     | *** |     |     |     |
## | 23 |     |     |     |     |     | 
## |    |     |     |     |     |     |
## | 48 |     |     |     |     |     | 
## |    | *** |     |     | *** |     |
## | 45 |     |     |     |     |     | 
## |    |     |     |     | *   |     |
## | 47 |     |     |     |     |     | 
## |    |     |     | *** |     | **  |
## | 50 |     |     |     |     |     | 
## |    |     |     |     |     |     |
## | 24 |     |     |     |     |     | 
## |    |     |     |     |     |     |
## | 49 |     |     |     |     |     | 
## |    |     |     |     |     |     |
## | 52 |     |     |     |     |     | 
## |    |     |     | **  |     | *** |
## ------------------------------------ 
## 
## '***' indicates the most likely position(s) (LOD = 0.0)
## 
## '**' indicates very likely positions (LOD > -1.0)
## 
## '*' indicates likely positions (LOD > -2.0)

For this particular sequence, the touchdown step could map safely markers 46 and 52, but this depends on the specific dataset.

Finally, to check for alternative orders (because we did not use exhaustive search), use the ripple_seq function:

## 27-16-20-4-|-21-... OK
## 
## ...-27-|-16-20-4-21-|-23-... OK
## 
## ...-16-|-20-4-21-23-|-48-...
##   Alternative orders:
##   ... 16 20 4 21 23 48 ... :    0.00 ( linkage phases: ... 1 2 2 1 1 ... )
##   ... 16 20 4 23 21 48 ... :   -2.21 ( linkage phases: ... 1 2 2 1 1 ... )
## 
## ...-20-|-4-21-23-48-|-9-...
##   Alternative orders:
##   ... 20 4 21 23 48 9 ... :    0.00 ( linkage phases: ... 2 2 1 1 1 ... )
##   ... 20 4 23 21 48 9 ... :   -2.21 ( linkage phases: ... 2 2 1 1 1 ... )
## 
## ...-4-|-21-23-48-9-|-46-...
##   Alternative orders:
##   ... 4 21 23 48 9 46 ... :    0.00 ( linkage phases: ... 2 1 1 1 1 ... )
##   ... 4 23 21 48 9 46 ... :   -2.21 ( linkage phases: ... 2 1 1 1 1 ... )
## 
## ...-21-|-23-48-9-46-|-45-...
##   Alternative orders:
##   ... 21 23 48 9 46 45 ... :    0.00 ( linkage phases: ... 1 1 1 1 1 ... )
##   ... 21 23 48 46 9 45 ... :   -1.05 ( linkage phases: ... 1 1 1 1 1 ... )
## 
## ...-23-|-48-9-46-45-|-47-...
##   Alternative orders:
##   ... 23 48 9 46 45 47 ... :    0.00 ( linkage phases: ... 1 1 1 1 1 ... )
##   ... 23 48 46 9 45 47 ... :   -1.05 ( linkage phases: ... 1 1 1 1 1 ... )
##   ... 23 48 45 9 46 47 ... :   -1.80 ( linkage phases: ... 1 1 1 1 1 ... )
##   ... 23 48 9 45 46 47 ... :   -3.21 ( linkage phases: ... 1 1 1 1 1 ... )
##   ... 23 45 48 9 46 47 ... :   -3.58 ( linkage phases: ... 1 1 1 1 1 ... )
## 
## ...-48-|-9-46-45-47-|-29-...
##   Alternative orders:
##   ... 48 9 46 45 47 29 ... :    0.00 ( linkage phases: ... 1 1 1 1 3 ... )
##   ... 48 46 9 45 47 29 ... :   -1.05 ( linkage phases: ... 1 1 1 1 3 ... )
##   ... 48 45 9 46 47 29 ... :   -1.80 ( linkage phases: ... 1 1 1 1 3 ... )
##   ... 48 9 45 46 47 29 ... :   -3.21 ( linkage phases: ... 1 1 1 1 3 ... )
## 
## ...-9-|-46-45-47-29-|-50-...
##   Alternative orders:
##   ... 9 46 45 47 29 50 ... :    0.00 ( linkage phases: ... 1 1 1 3 4 ... )
##   ... 9 45 46 47 29 50 ... :   -3.21 ( linkage phases: ... 1 1 1 3 4 ... )
## 
## ...-46-|-45-47-29-50-|-24-... OK
## 
## ...-45-|-47-29-50-24-|-49-... OK
## 
## ...-47-|-29-50-24-49-|-52-... OK
## 
## ...-29-|-50-24-49-52-|-51-...
##   Alternative orders:
##   ... 29 50 24 49 52 51 :    0.00 ( linkage phases: ... 4 1 1 1 1 )
##   ... 29 52 49 24 50 51 :   -0.90 ( linkage phases: ... 4 1 1 1 1 )
##   ... 29 50 24 52 49 51 :   -2.76 ( linkage phases: ... 4 1 1 1 1 )
##   ... 29 50 52 49 24 51 :   -2.79 ( linkage phases: ... 4 1 1 1 1 )
##   ... 29 50 49 52 24 51 :   -3.31 ( linkage phases: ... 4 1 1 1 1 )
##   ... 29 49 52 24 50 51 :   -3.31 ( linkage phases: ... 4 1 1 1 1 )
## 
## 50-|-24-49-52-51
##   Alternative orders:
##   ... 50 24 49 52 51 :    0.00 ( linkage phases: ... 1 1 1 1 )
##   ... 50 24 52 49 51 :   -2.76 ( linkage phases: ... 1 1 1 1 )
##   ... 50 52 49 24 51 :   -2.79 ( linkage phases: ... 1 1 1 1 )
##   ... 50 51 24 49 52 :   -2.85 ( linkage phases: ... 1 1 1 1 )
##   ... 50 49 52 24 51 :   -3.31 ( linkage phases: ... 1 1 1 1 )

We should do this to any of the orders we found, either using try_seq or order_seq. Here, we choose LG2_all for didactic purposes only. The second argument, ws = 4, means that subsets (windows) of four markers will be permuted sequentially (4! orders for each window), to search for other plausible orders. The LOD argument means that only orders with LOD Score smaller than 3.68 will be printed.

The output shows sequences of four numbers, because ws = 4. They are followed by an OK if there is no alternative order with LOD Score smaller than LOD = LOD_sug in absolute value, or by a list of alternative orders. In the example, some sequences showed alternative orders with LOD smaller than LOD = LOD_sug. However, the best order was the original one (LOD = 0.00).

If there were an alternative order more likely than the original, one should check the difference between these orders (and linkage phases).

In some cases, even if there are no better alternative order suggested by ripple_seq, the graphic showed color pattern different of the expected. Then, we can remove doubtful markers (for this groups markers 23 and 29) and try to positioned them again. First, we use the function drop_marker to remove selected marker of our sequence.

The function will provide a sequence with the same order of the estimated map (LG2_all). After, we should estimate the map again using this predefined order (see section Map estimation for an arbitrary order for further information). For this we use the map function:

Warning: If you find an error message like:

Error in as_mapper(.f, ...) : argument ".f" is missing, with no default

It’s because the map function has a very common name and you can have in your environment other function with the same name. In the case of the pointed error, R is using map function from purrr package instead of OneMap, to solve this, simple specify that you want OneMap function with :: command from stringr package:

## 
## Printing map:
## 
## Markers           Position           Parent 1       Parent 2
## 
## 27 M27                0.00           b |  | o       a |  | a 
## 16 M16               11.75           a |  | a       o |  | b 
## 20 M20               22.93           a |  | b       d |  | c 
##  4 M4                35.70           a |  | o       b |  | o 
## 21 M21               52.67           o |  | o       b |  | a 
## 48 SNP21             53.59           a |  | b       a |  | a 
##  9 M9                60.40           a |  | b       a |  | a 
## 46 SNP18             66.83           a |  | b       a |  | a 
## 45 SNP17             81.83           a |  | b       a |  | a 
## 47 SNP20            106.46           a |  | b       a |  | a 
## 50 SNP23            145.68           a |  | b       a |  | b 
## 24 M24              150.69           a |  | b       a |  | b 
## 49 SNP22            153.97           a |  | b       a |  | b 
## 52 SNP25            158.87           a |  | b       a |  | b 
## 51 SNP24            169.81           a |  | b       a |  | b 
## 
## 15 markers            log-likelihood: -780.5746

NOTE: (new!) If your sequence has many markers (more than 60), we suggest to speed up map using BatchMap parallelization approach. See section Speed up analysis with parallelization for more information.

Now, we have the map without markers 23 and 51.

We use try_seq function to positioned them again:

## 23 --> M23   : ................
## 29 --> M29   : .................

Marker 23 kept its previous position, but marker 29 was re-positioned, configuring now a gap between markers 47 and 50. We removed marker 29 of our map, because it color pattern are too different of expected. Then, our final map is:

## 
## Printing map:
## 
## Markers           Position           Parent 1       Parent 2
## 
## 27 M27                0.00           b |  | o       a |  | a 
## 16 M16               11.75           a |  | a       o |  | b 
## 20 M20               22.93           a |  | b       d |  | c 
##  4 M4                35.70           a |  | o       b |  | o 
## 21 M21               50.34           o |  | o       b |  | a 
## 23 M23               54.87           a |  | o       o |  | a 
## 48 SNP21             70.11           a |  | b       a |  | a 
##  9 M9                76.77           a |  | b       a |  | a 
## 46 SNP18             83.19           a |  | b       a |  | a 
## 45 SNP17             98.20           a |  | b       a |  | a 
## 47 SNP20            122.83           a |  | b       a |  | a 
## 50 SNP23            161.89           a |  | b       a |  | b 
## 24 M24              166.89           a |  | b       a |  | b 
## 49 SNP22            170.18           a |  | b       a |  | b 
## 52 SNP25            175.08           a |  | b       a |  | b 
## 51 SNP24            186.02           a |  | b       a |  | b 
## 
## 16 markers            log-likelihood: -811.7886

Genetic mapping of linkage group 1

Finally, linkage group 1 (the largest one) will be analyzed. Extract markers:

Construct the linkage map, by automatically using try algorithm:

Notice that the second round of try_seq added markers 10, 31, 32, 35, 36 and 40.

## 
## Best sequence found.
## Printing map:
## 
## Markers           Position           Parent 1       Parent 2
## 
## 34 SNP5               0.00           a |  | b       a |  | b 
## 32 SNP2              13.48           a |  | b       a |  | b 
## 12 M12               17.26           b |  | a       c |  | a 
## 31 SNP1              22.81           a |  | b       a |  | b 
##  3 M3                46.09           o |  | a       o |  | o 
## 14 M14               59.22           a |  | o       b |  | o 
##  2 M2                66.93           o |  | o       o |  | a 
## 36 SNP7              92.49           b |  | a       b |  | a 
## 35 SNP6             105.45           b |  | a       b |  | a 
##  1 M1               109.86           b |  | a       b |  | a 
## 10 M10              115.37           a |  | a       o |  | b 
## 28 M28              132.05           a |  | o       b |  | o 
## 26 M26              164.42           a |  | b       d |  | c 
## 42 SNP13            179.54           b |  | a       b |  | a 
##  6 M6               185.89           b |  | a       b |  | a 
## 39 SNP10            192.06           b |  | a       b |  | a 
## 41 SNP12            208.53           b |  | a       b |  | a 
## 40 SNP11            225.65           b |  | a       b |  | a 
## 15 M15              267.89           o |  | a       o |  | b 
## 
## 19 markers            log-likelihood: -1313.595 
## 
## 
## 
## The following markers could not be uniquely positioned.
## Printing most likely positions for each unpositioned marker:
## 
## ------------------------------------------ 
## |    |   5 |  11 |  30 |  33 |  37 |  38 |
## |----|-----|-----|-----|-----|-----|-----| 
## |    |     |     |     |     |     |     |
## | 34 |     |     |     |     |     |     | 
## |    |     |     |     | *** |     |     |
## | 32 |     |     |     |     |     |     | 
## |    |     |     | *** | *   |     |     |
## | 12 |     |     |     |     |     |     | 
## |    |     |     |     |     |     |     |
## | 31 |     |     |     |     |     |     | 
## |    |     |     |     |     |     |     |
## |  3 |     |     |     |     |     |     | 
## |    |     |     |     |     |     |     |
## | 14 |     |     |     |     |     |     | 
## |    |     |     |     |     |     |     |
## |  2 |     |     |     |     |     |     | 
## |    |     |     |     |     | *   |     |
## | 36 |     |     |     |     |     |     | 
## |    |     |     |     |     | **  | *   |
## | 35 |     |     |     |     |     |     | 
## |    |     |     |     |     |     |     |
## |  1 |     |     |     |     |     |     | 
## |    |     |     |     |     | *** | *** |
## | 10 |     |     |     |     |     |     | 
## |    |     |     |     |     |     |     |
## | 28 |     |     |     |     |     |     | 
## |    |     |     |     |     |     |     |
## | 26 |     |     |     |     |     |     | 
## |    |     |     |     |     |     |     |
## | 42 |     |     |     |     |     |     | 
## |    |     |     |     |     |     |     |
## |  6 |     |     |     |     |     |     | 
## |    |     |     |     |     |     |     |
## | 39 |     |     |     |     |     |     | 
## |    |     |     |     |     |     |     |
## | 41 |     |     |     |     |     |     | 
## |    |     |     |     |     |     |     |
## | 40 |     |     |     |     |     |     | 
## |    | **  | **  |     |     |     |     |
## | 15 |     |     |     |     |     |     | 
## |    | *** | *** |     |     |     |     |
## ------------------------------------------ 
## 
## '***' indicates the most likely position(s) (LOD = 0.0)
## 
## '**' indicates very likely positions (LOD > -1.0)
## 
## '*' indicates likely positions (LOD > -2.0)

Now, get the order with all markers:

## 
## Printing map:
## 
## Markers           Position           Parent 1       Parent 2
## 
## 34 SNP5               0.00           a |  | b       a |  | b 
## 33 SNP3              12.27           a |  | b       a |  | b 
## 32 SNP2              18.45           a |  | b       a |  | b 
## 30 M30               21.21           a |  | b       a |  | b 
## 12 M12               22.22           b |  | a       c |  | a 
## 31 SNP1              27.77           a |  | b       a |  | b 
##  3 M3                51.05           o |  | a       o |  | o 
## 14 M14               64.18           a |  | o       b |  | o 
##  2 M2                72.05           o |  | o       o |  | a 
## 36 SNP7              95.86           b |  | a       b |  | a 
## 37 SNP8             112.04           b |  | a       b |  | a 
## 35 SNP6             126.75           b |  | a       b |  | a 
##  1 M1               131.15           b |  | a       b |  | a 
## 38 SNP9             137.28           b |  | a       b |  | a 
## 10 M10              148.79           a |  | a       o |  | b 
## 28 M28              165.35           a |  | o       b |  | o 
## 26 M26              197.72           a |  | b       d |  | c 
## 42 SNP13            212.84           b |  | a       b |  | a 
##  6 M6               219.19           b |  | a       b |  | a 
## 39 SNP10            225.36           b |  | a       b |  | a 
## 41 SNP12            241.82           b |  | a       b |  | a 
## 40 SNP11            258.95           b |  | a       b |  | a 
## 15 M15              301.19           o |  | a       o |  | b 
##  5 M5               306.20           o |  | o       o |  | a 
## 11 M11              326.21           o |  | o       b |  | a 
## 
## 25 markers            log-likelihood: -1554.628

Check the map graphically:

Check for alternative orders:

## 34-33-32-30-|-12-...
##   Alternative orders:
##    34 33 32 30 12 ... :    0.00 ( linkage phases: 1 1 1 4 ... )
##    34 32 33 30 12 ... :   -1.29 ( linkage phases: 1 1 1 4 ... )
##    34 33 30 32 12 ... :   -1.55 ( linkage phases: 1 1 1 4 ... )
## 
## ...-34-|-33-32-30-12-|-31-...
##   Alternative orders:
##    34 33 12 30 32 31 ... :    0.00 ( linkage phases:  1 4 4 1 1 ... )
##    34 33 30 12 32 31 ... :   -0.25 ( linkage phases:  1 1 4 4 1 ... )
##    34 33 32 30 12 31 ... :   -0.59 ( linkage phases:  1 1 1 4 4 ... )
##    34 32 33 30 12 31 ... :   -1.88 ( linkage phases:  1 1 1 4 4 ... )
##    34 33 30 32 12 31 ... :   -2.14 ( linkage phases:  1 1 1 4 4 ... )
##    34 33 32 12 30 31 ... :   -2.74 ( linkage phases:  1 1 4 4 1 ... )
## 
## ...-33-|-32-30-12-31-|-3-...
##   Alternative orders:
##   ... 33 12 30 32 31 3 ... :    0.00 ( linkage phases: ... 4 4 1 1 4 ... )
##   ... 33 30 12 32 31 3 ... :   -0.25 ( linkage phases: ... 1 4 4 1 4 ... )
##   ... 33 32 30 12 31 3 ... :   -0.59 ( linkage phases: ... 1 1 4 4 4 ... )
##   ... 33 30 32 12 31 3 ... :   -2.14 ( linkage phases: ... 1 1 4 4 4 ... )
##   ... 33 32 12 30 31 3 ... :   -2.74 ( linkage phases: ... 1 4 4 1 4 ... )
## 
## ...-32-|-30-12-31-3-|-14-...
##   Alternative orders:
##   ... 32 30 12 31 3 14 ... :    0.00 ( linkage phases: ... 1 4 4 4 4 ... )
##   ... 32 12 30 31 3 14 ... :   -2.15 ( linkage phases: ... 4 4 1 4 4 ... )
## 
## ...-30-|-12-31-3-14-|-2-... OK
## 
## ...-12-|-31-3-14-2-|-36-... OK
## 
## ...-31-|-3-14-2-36-|-37-... OK
## 
## ...-3-|-14-2-36-37-|-35-...
##   Alternative orders:
##   ... 3 14 2 36 37 35 ... :    0.00 ( linkage phases: ... 4 2 3 1 1 ... )
##   ... 3 14 2 37 36 35 ... :   -0.89 ( linkage phases: ... 4 2 3 1 1 ... )
## 
## ...-14-|-2-36-37-35-|-1-...
##   Alternative orders:
##   ... 14 2 36 37 35 1 ... :    0.00 ( linkage phases: ... 2 3 1 1 1 ... )
##   ... 14 2 37 36 35 1 ... :   -0.89 ( linkage phases: ... 2 3 1 1 1 ... )
## 
## ...-2-|-36-37-35-1-|-38-...
##   Alternative orders:
##   ... 2 36 37 1 35 38 ... :    0.00 ( linkage phases: ... 3 1 1 1 1 ... )
##   ... 2 36 37 35 1 38 ... :   -0.25 ( linkage phases: ... 3 1 1 1 1 ... )
##   ... 2 37 36 35 1 38 ... :   -1.14 ( linkage phases: ... 3 1 1 1 1 ... )
##   ... 2 37 36 1 35 38 ... :   -2.34 ( linkage phases: ... 3 1 1 1 1 ... )
## 
## ...-36-|-37-35-1-38-|-10-...
##   Alternative orders:
##   ... 36 37 1 35 38 10 ... :   0.00 ( linkage phases: ... 1 1 1 1 1 ... )
##   ... 36 37 35 1 38 10 ... :  -0.25 ( linkage phases: ... 1 1 1 1 1 ... )
##   ... 36 35 1 38 37 10 ... :  -1.23 ( linkage phases: ... 1 1 1 1 1 ... )
##   ... 36 37 38 35 1 10 ... :  -1.35 ( linkage phases: ... 1 1 1 1 1 ... )
##   ... 36 38 35 1 37 10 ... :  -1.42 ( linkage phases: ... 1 1 1 1 1 ... )
##   ... 36 37 38 1 35 10 ... :  -1.54 ( linkage phases: ... 1 1 1 1 1 ... )
##   ... 36 38 1 35 37 10 ... :  -1.69 ( linkage phases: ... 1 1 1 1 1 ... )
##   ... 36 35 38 1 37 10 ... :  -2.45 ( linkage phases: ... 1 1 1 1 1 ... )
##   ... 36 1 35 38 37 10 ... :  -2.50 ( linkage phases: ... 1 1 1 1 1 ... )
##   ... 36 37 1 38 35 10 ... :  -2.78 ( linkage phases: ... 1 1 1 1 1 ... )
##   ... 36 37 35 38 1 10 ... :  -2.85 ( linkage phases: ... 1 1 1 1 1 ... )
## 
## ...-37-|-35-1-38-10-|-28-...
##   Alternative orders:
##   ... 37 1 35 38 10 28 ... :    0.00 ( linkage phases: ... 1 1 1 1 4 ... )
##   ... 37 35 1 38 10 28 ... :   -0.25 ( linkage phases: ... 1 1 1 1 4 ... )
##   ... 37 38 35 1 10 28 ... :   -1.35 ( linkage phases: ... 1 1 1 1 4 ... )
##   ... 37 38 1 35 10 28 ... :   -1.54 ( linkage phases: ... 1 1 1 1 4 ... )
##   ... 37 1 38 35 10 28 ... :   -2.78 ( linkage phases: ... 1 1 1 1 4 ... )
##   ... 37 35 38 1 10 28 ... :   -2.85 ( linkage phases: ... 1 1 1 1 4 ... )
## 
## ...-35-|-1-38-10-28-|-26-...
##   Alternative orders:
##   ... 35 1 38 10 28 26 ... :    0.00 ( linkage phases: ... 1 1 1 4 2 ... )
##   ... 35 38 1 10 28 26 ... :   -2.60 ( linkage phases: ... 1 1 1 4 2 ... )
## 
## ...-1-|-38-10-28-26-|-42-... OK
## 
## ...-38-|-10-28-26-42-|-6-... OK
## 
## ...-10-|-28-26-42-6-|-39-...
##   Alternative orders:
##   ... 10 28 26 42 6 39 ... :    0.00 ( linkage phases: ... 4 2 3 1 1 ... )
##   ... 10 28 26 6 42 39 ... :   -2.30 ( linkage phases: ... 4 2 3 1 1 ... )
## 
## ...-28-|-26-42-6-39-|-41-...
##   Alternative orders:
##   ... 28 26 42 6 39 41 ... :    0.00 ( linkage phases: ... 2 3 1 1 1 ... )
##   ... 28 26 6 42 39 41 ... :   -2.30 ( linkage phases: ... 2 3 1 1 1 ... )
## 
## ...-26-|-42-6-39-41-|-40-...
##   Alternative orders:
##   ... 26 42 6 39 41 40 ... :    0.00 ( linkage phases: ... 3 1 1 1 1 ... )
##   ... 26 6 42 39 41 40 ... :   -2.30 ( linkage phases: ... 3 1 1 1 1 ... )
## 
## ...-42-|-6-39-41-40-|-15-... OK
## 
## ...-6-|-39-41-40-15-|-5-... OK
## 
## ...-39-|-41-40-15-5-|-11-...
##   Alternative orders:
##   ... 39 41 40 15 5 11 :    0.00 ( linkage phases: ... 1 1 1 1 1 )
##   ... 39 41 40 5 15 11 :   -2.57 ( linkage phases: ... 1 1 1 1 1 )
## 
## 41-|-40-15-5-11
##   Alternative orders:
##   ... 41 40 15 5 11 :    0.00 ( linkage phases: ... 1 1 1 1 )
##   ... 41 40 11 5 15 :   -0.82 ( linkage phases: ... 1 1 1 1 )
##   ... 41 40 5 15 11 :   -2.57 ( linkage phases: ... 1 1 1 1 )
##   ... 41 40 11 15 5 :   -2.58 ( linkage phases: ... 1 1 1 1 )

No better order was observed.

Let’s check how it behaves with MDS approach:

## Stress: 0.303935806009325
## Mean Nearest Neighbour Fit: 30.2669402204895
## Markers omitted:

NOTE: (new!) If your sequence has many markers (more than 60), we suggest to speed up mds_onemap using BatchMap parallelization approach. See section Speed up analysis with parallelization for more information.

Based on the drafts from order_seq or/and mds_onemap, we can remove some doubtful markers accordingly with the graphic, try to positioned them again and decide if and where we will maintain them.

Print it:

## 
## Printing map:
## 
## Markers           Position           Parent 1       Parent 2
## 
## 34 SNP5               0.00           a |  | b       a |  | b 
## 33 SNP3              12.27           a |  | b       a |  | b 
## 32 SNP2              18.45           a |  | b       a |  | b 
## 30 M30               21.21           a |  | b       a |  | b 
## 12 M12               22.22           b |  | a       c |  | a 
## 31 SNP1              27.77           a |  | b       a |  | b 
##  3 M3                51.05           o |  | a       o |  | o 
## 14 M14               64.18           a |  | o       b |  | o 
##  2 M2                72.10           o |  | o       o |  | a 
## 36 SNP7              95.93           b |  | a       b |  | a 
## 37 SNP8             112.12           b |  | a       b |  | a 
## 35 SNP6             126.83           b |  | a       b |  | a 
##  1 M1               131.23           b |  | a       b |  | a 
## 38 SNP9             137.34           b |  | a       b |  | a 
## 10 M10              150.29           a |  | a       o |  | b 
## 28 M28              166.58           a |  | o       b |  | o 
## 42 SNP13            203.65           b |  | a       b |  | a 
## 26 M26              219.73           a |  | b       d |  | c 
##  6 M6               228.71           b |  | a       b |  | a 
## 39 SNP10            234.88           b |  | a       b |  | a 
## 41 SNP12            251.25           b |  | a       b |  | a 
## 40 SNP11            268.27           b |  | a       b |  | a 
## 15 M15              309.06           o |  | a       o |  | b 
##  5 M5               314.07           o |  | o       o |  | a 
## 
## 24 markers            log-likelihood: -1518.748

As an option, different algorithms to order markers could be applied:

There are some differences between the results. Seriation did not provide good results in this case. See Mollinari et al. (2009) for an evaluation of these methods.

NOTE: (new!) If your sequence has many markers (more than 60), we suggest to speed up seriation, rcd, record and ug using BatchMap parallelization approach. See section Speed up analysis with parallelization for more information.

Using the recombinations and the reference genome informations

In our example, we have reference genome chromosome and position informations for some of the markers, here we will exemplify one method of using this informations to help build the genetic map.

With the CHROM informations in the input file, you can identify markers belonging to some chromosome using the function make_seq with the rf_2pts object. For example, assign the string "1" for the second argument to get chromosome 1 makers. The output sequence will be automatically ordered by POS informations.

## 
## Number of markers: 12
## Markers in the sequence:
## SNP1 SNP2 SNP3 SNP5 SNP6 SNP7 SNP8 SNP9 SNP10 SNP11 SNP12 SNP13
## 
## Parameters not estimated.

Here we use string "1" because it is our chromosome ID, you can have different string as ID, check this with:

## [1] NA  "1" "2" "3"

We can see that we have markers without chromosome information (NA) and markers with chromosome ID "1", "2" and "3".

Adding markers with no reference genome informations

According to CHROM informations we have three defined linkage groups, now we can try to group the markers without chromosome informations to them using recombination informations. For this, we can use the function group_seq:

##    Selecting markers: 
##    group    1 
##     ........................
##    group    2 
##     ........
##    group    3 
##     ....
##    Selecting markers: 
##    group    1 
##     ......
##    group    2 
##     ............
##    group    3 
##     ........
##    Selecting markers: 
##    group    1 
##     ................
##    group    2 
##     ............
##    group    3 
##     ....

The function works as the function group, but considering pre existing sequences. Setting seqs argument with the string "CHROM", it will considered the pre existing sequences according to CHROM information. You can also indicate others pre existing sequences if it make sense for your study. For that, you should inform a list with objects of class sequences, as the example:

In this case, the command had the same effect of the previous, because we indicate chromosome sequences, but others sequences can be used.

The unlink.mks argument receive a object of class sequence, this define which markers will be tested to group with the sequences in seqs. In our example, we will indicate only the markers with no segregation distortion, using the sequence mark_no_dist. It is also possible to use the string "all" to test all the remaining markers at the rf_2pts object.

In some cases, the same marker can group to more than one sequence, those markers will be considered repeated. We can choose if we want to remove or not (FALSE/TRUE) them of the output sequences, with the argument repeated. Anyway, their numbers will be informed at the list repeated in the output object. In the example case, there are no repeated markers. However, if they exists, it could indicate that their groups actually constitute the same group. Also, genotyping errors can generate repeated markers. Anyway, they deserves better investigations.

We can access detailed information about the results just printing:

##   This is an object of class 'group_seq'
##   Criteria used to assign markers to groups:
##     LOD = 3 , Maximum recombination fraction = 0.5 
## 
##   No. markers in input sequences:
##                        CHR1 :   12 markers
##                        CHR2 :   2 markers
##                        CHR3 :   8 markers
## 
##   No. unlinked input markers:   27 markers
## 
##   No. markers in output sequences:
##                        CHR1 :   25 markers
##                        CHR2 :   7 markers
##                        CHR3 :   17 markers
##   No. unlinked:                 0 markers
##   No. repeated:                 0 markers
## 
##   Printing output sequences:
##   Group CHR1 : 25 markers
##     SNP1 SNP2 SNP3 SNP5 SNP6 SNP7 SNP8 SNP9 SNP10 SNP11 SNP12 SNP13 M1 M2 M3 M5 M6 M10 M11 M12 M14 M15 M26 M28 M30 
## 
##   Group CHR2 : 7 markers
##     SNP14 SNP16 M7 M8 M13 M18 M22 
## 
##   Group CHR3 : 17 markers
##     SNP17 SNP18 SNP20 SNP21 SNP22 SNP23 SNP24 SNP25 M4 M9 M16 M20 M21 M23 M24 M27 M29 
## 
##   Unlinked markers: 0 markers
##     
## 
##   Repeated markers: 0  markers
##

Also, we can access the numbers of repeated markers with:

## [1] NA

We have no repeated markers.

The same way, we can access the output sequences:

## 
## Number of markers: 25
## Markers in the sequence:
## SNP1 SNP2 SNP3 SNP5 SNP6 SNP7 SNP8 SNP9 SNP10 SNP11 SNP12 SNP13 M1 M2 M3 M5 M6 
## M10 M11 M12 M14 M15 M26 M28 M30
## 
## Parameters not estimated.
## 
## Number of markers: 25
## Markers in the sequence:
## SNP1 SNP2 SNP3 SNP5 SNP6 SNP7 SNP8 SNP9 SNP10 SNP11 SNP12 SNP13 M1 M2 M3 M5 M6 
## M10 M11 M12 M14 M15 M26 M28 M30
## 
## Parameters not estimated.

For this function, optional arguments are LOD and max.rf, which define thresholds to be used when assigning markers to linkage groups. If none provided (default), criteria previously defined for the object rf_2pts are used.

Now we can order the markers in each group as we made before in (Genetic mapping of linkage group 1,2 and 3). As showed, we can choose different approaches to order the markers.

To order those groups, first we will use order_seq function to access a preliminary order and after, we will edit some markers position or remove some of them according with they color pattern in rf_graph_table graphic, and other parameters as likelihood and map size.

Genetic mapping of linkage group 1 (with reference genome informations)

NOTE: (new!) If your sequence has many markers (more than 60), we suggest to speed up mds_onemap using BatchMap parallelization approach. See section Speed up analysis with parallelization for more information.

The group is similar to that builded before with only recombinations informations. We will better explore differences in a latter step. Only marker 11 do not follow exactly the expected color pattern, then we will try to repositioned it.

## 11 --> M11   : .........................

Based in those results, we decide to not include marker 11 in our map.

## 
## Printing map:
## 
## Markers           Position           Parent 1       Parent 2
## 
## 34 SNP5               0.00           a |  | b       a |  | b 
## 33 SNP3              12.27           a |  | b       a |  | b 
## 30 M30               15.58           a |  | b       a |  | b 
## 12 M12               16.59           b |  | a       c |  | a 
## 32 SNP2              20.15           a |  | b       a |  | b 
## 31 SNP1              28.31           a |  | b       a |  | b 
##  3 M3                51.17           o |  | a       o |  | o 
## 14 M14               64.54           a |  | o       b |  | o 
##  2 M2                72.44           o |  | o       o |  | a 
## 36 SNP7              96.32           b |  | a       b |  | a 
## 35 SNP6             109.13           b |  | a       b |  | a 
##  1 M1               113.53           b |  | a       b |  | a 
## 38 SNP9             119.59           b |  | a       b |  | a 
## 37 SNP8             136.22           b |  | a       b |  | a 
## 10 M10              149.87           a |  | a       o |  | b 
## 28 M28              167.09           a |  | o       b |  | o 
## 26 M26              199.46           a |  | b       d |  | c 
## 42 SNP13            214.58           b |  | a       b |  | a 
##  6 M6               220.93           b |  | a       b |  | a 
## 39 SNP10            227.10           b |  | a       b |  | a 
## 41 SNP12            243.56           b |  | a       b |  | a 
## 40 SNP11            260.69           b |  | a       b |  | a 
## 15 M15              302.93           o |  | a       o |  | b 
##  5 M5               307.95           o |  | o       o |  | a 
## 
## 24 markers            log-likelihood: -1507.316

Checking for better orders:

## 34-33-30-12-|-32-...
##   Alternative orders:
##    34 33 12 30 32 ... :    0.00 ( linkage phases: 1 4 4 1 ... )
##    34 33 30 12 32 ... :   -0.25 ( linkage phases: 1 1 4 4 ... )
## 
## ...-34-|-33-30-12-32-|-31-...
##   Alternative orders:
##    34 33 12 30 32 31 ... :    0.00 ( linkage phases:  1 4 4 1 1 ... )
##    34 33 30 12 32 31 ... :   -0.25 ( linkage phases:  1 1 4 4 1 ... )
##    34 33 32 30 12 31 ... :   -0.59 ( linkage phases:  1 1 1 4 4 ... )
##    34 32 33 30 12 31 ... :   -1.88 ( linkage phases:  1 1 1 4 4 ... )
##    34 33 30 32 12 31 ... :   -2.14 ( linkage phases:  1 1 1 4 4 ... )
##    34 33 32 12 30 31 ... :   -2.74 ( linkage phases:  1 1 4 4 1 ... )
## 
## ...-33-|-30-12-32-31-|-3-...
##   Alternative orders:
##   ... 33 12 30 32 31 3 ... :    0.00 ( linkage phases: ... 4 4 1 1 3 ... )
##   ... 33 30 12 32 31 3 ... :   -0.25 ( linkage phases: ... 1 4 4 1 3 ... )
##   ... 33 32 30 12 31 3 ... :   -0.59 ( linkage phases: ... 1 1 4 4 3 ... )
##   ... 33 30 32 12 31 3 ... :   -2.14 ( linkage phases: ... 1 1 4 4 3 ... )
##   ... 33 32 12 30 31 3 ... :   -2.74 ( linkage phases: ... 1 4 4 1 3 ... )
## 
## ...-30-|-12-32-31-3-|-14-...
##   Alternative orders:
##   ... 30 12 32 31 3 14 ... :    0.00 ( linkage phases: ... 4 4 1 3 3 ... )
##   ... 30 32 12 31 3 14 ... :   -1.89 ( linkage phases: ... 1 4 4 3 3 ... )
## 
## ...-12-|-32-31-3-14-|-2-... OK
## 
## ...-32-|-31-3-14-2-|-36-... OK
## 
## ...-31-|-3-14-2-36-|-35-... OK
## 
## ...-3-|-14-2-36-35-|-1-... OK
## 
## ...-14-|-2-36-35-1-|-38-...
##   Alternative orders:
##   ... 14 2 36 35 1 38 ... :    0.00 ( linkage phases: ... 2 3 1 1 1 ... )
##   ... 14 2 36 1 35 38 ... :   -1.27 ( linkage phases: ... 2 3 1 1 1 ... )
## 
## ...-2-|-36-35-1-38-|-37-...
##   Alternative orders:
##   ... 2 38 1 35 36 37 ... :    0.00 ( linkage phases: ... 3 1 1 1 1 ... )
##   ... 2 36 35 1 38 37 ... :   -0.99 ( linkage phases: ... 3 1 1 1 1 ... )
##   ... 2 38 35 1 36 37 ... :   -1.15 ( linkage phases: ... 3 1 1 1 1 ... )
##   ... 2 35 1 38 36 37 ... :   -1.16 ( linkage phases: ... 3 1 1 1 1 ... )
##   ... 2 36 38 35 1 37 ... :   -1.18 ( linkage phases: ... 3 1 1 1 1 ... )
##   ... 2 36 38 1 35 37 ... :   -1.45 ( linkage phases: ... 3 1 1 1 1 ... )
##   ... 2 36 35 38 1 37 ... :   -2.21 ( linkage phases: ... 3 1 1 1 1 ... )
##   ... 2 36 1 35 38 37 ... :   -2.25 ( linkage phases: ... 3 1 1 1 1 ... )
## 
## ...-36-|-35-1-38-37-|-10-...
##   Alternative orders:
##   ... 36 37 1 35 38 10 ... :   0.00 ( linkage phases: ... 1 1 1 1 1 ... )
##   ... 36 37 35 1 38 10 ... :  -0.25 ( linkage phases: ... 1 1 1 1 1 ... )
##   ... 36 35 1 38 37 10 ... :  -1.23 ( linkage phases: ... 1 1 1 1 1 ... )
##   ... 36 37 38 35 1 10 ... :  -1.35 ( linkage phases: ... 1 1 1 1 1 ... )
##   ... 36 38 35 1 37 10 ... :  -1.42 ( linkage phases: ... 1 1 1 1 1 ... )
##   ... 36 37 38 1 35 10 ... :  -1.54 ( linkage phases: ... 1 1 1 1 1 ... )
##   ... 36 38 1 35 37 10 ... :  -1.69 ( linkage phases: ... 1 1 1 1 1 ... )
##   ... 36 35 38 1 37 10 ... :  -2.45 ( linkage phases: ... 1 1 1 1 1 ... )
##   ... 36 1 35 38 37 10 ... :  -2.50 ( linkage phases: ... 1 1 1 1 1 ... )
##   ... 36 37 1 38 35 10 ... :  -2.78 ( linkage phases: ... 1 1 1 1 1 ... )
##   ... 36 37 35 38 1 10 ... :  -2.85 ( linkage phases: ... 1 1 1 1 1 ... )
## 
## ...-35-|-1-38-37-10-|-28-...
##   Alternative orders:
##   ... 35 1 38 37 10 28 ... :    0.00 ( linkage phases: ... 1 1 1 1 4 ... )
##   ... 35 38 1 37 10 28 ... :   -1.22 ( linkage phases: ... 1 1 1 1 4 ... )
## 
## ...-1-|-38-37-10-28-|-26-... OK
## 
## ...-38-|-37-10-28-26-|-42-... OK
## 
## ...-37-|-10-28-26-42-|-6-... OK
## 
## ...-10-|-28-26-42-6-|-39-...
##   Alternative orders:
##   ... 10 28 26 42 6 39 ... :    0.00 ( linkage phases: ... 4 2 3 1 1 ... )
##   ... 10 28 26 6 42 39 ... :   -2.30 ( linkage phases: ... 4 2 3 1 1 ... )
## 
## ...-28-|-26-42-6-39-|-41-...
##   Alternative orders:
##   ... 28 26 42 6 39 41 ... :    0.00 ( linkage phases: ... 2 3 1 1 1 ... )
##   ... 28 26 6 42 39 41 ... :   -2.30 ( linkage phases: ... 2 3 1 1 1 ... )
## 
## ...-26-|-42-6-39-41-|-40-...
##   Alternative orders:
##   ... 26 42 6 39 41 40 ... :    0.00 ( linkage phases: ... 3 1 1 1 1 ... )
##   ... 26 6 42 39 41 40 ... :   -2.30 ( linkage phases: ... 3 1 1 1 1 ... )
## 
## ...-42-|-6-39-41-40-|-15-... OK
## 
## ...-6-|-39-41-40-15-|-5-... OK
## 
## 39-|-41-40-15-5
##   Alternative orders:
##   ... 39 41 40 15 5 :    0.00 ( linkage phases: ... 1 1 1 1 )
##   ... 39 41 40 5 15 :   -0.81 ( linkage phases: ... 1 1 1 1 )

Genetic mapping of linkage group 2 (with reference genome informations)

As did before, we will not change markers positions of this group.

Genetic mapping of linkage group 3 (with reference genome informations)

Here, marker 29 have color pattern too different of the expected, removing it could influentiate in other markers ordering. Then we will remove them and search for a new order.

Trying to add marker 29 again.

Checking for better orders:

## 27-16-20-4-|-21-... OK
## 
## ...-27-|-16-20-4-21-|-23-... OK
## 
## ...-16-|-20-4-21-23-|-48-...
##   Alternative orders:
##   ... 16 20 4 21 23 48 ... :    0.00 ( linkage phases: ... 1 2 2 1 1 ... )
##   ... 16 20 4 23 21 48 ... :   -2.27 ( linkage phases: ... 1 2 2 1 1 ... )
## 
## ...-20-|-4-21-23-48-|-9-...
##   Alternative orders:
##   ... 20 4 21 23 48 9 ... :    0.00 ( linkage phases: ... 2 2 1 1 1 ... )
##   ... 20 4 23 21 48 9 ... :   -2.27 ( linkage phases: ... 2 2 1 1 1 ... )
## 
## ...-4-|-21-23-48-9-|-46-...
##   Alternative orders:
##   ... 4 21 23 48 9 46 ... :    0.00 ( linkage phases: ... 2 1 1 1 1 ... )
##   ... 4 23 21 48 9 46 ... :   -2.27 ( linkage phases: ... 2 1 1 1 1 ... )
## 
## ...-21-|-23-48-9-46-|-45-...
##   Alternative orders:
##   ... 21 23 48 9 46 45 ... :    0.00 ( linkage phases: ... 1 1 1 1 1 ... )
##   ... 21 23 48 46 9 45 ... :   -1.00 ( linkage phases: ... 1 1 1 1 1 ... )
## 
## ...-23-|-48-9-46-45-|-47-...
##   Alternative orders:
##   ... 23 48 9 46 45 47 ... :    0.00 ( linkage phases: ... 1 1 1 1 1 ... )
##   ... 23 48 46 9 45 47 ... :   -1.00 ( linkage phases: ... 1 1 1 1 1 ... )
##   ... 23 48 45 9 46 47 ... :   -1.67 ( linkage phases: ... 1 1 1 1 1 ... )
## 
## ...-48-|-9-46-45-47-|-50-...
##   Alternative orders:
##   ... 48 9 46 45 47 50 ... :    0.00 ( linkage phases: ... 1 1 1 1 2 ... )
##   ... 48 46 9 45 47 50 ... :   -1.00 ( linkage phases: ... 1 1 1 1 2 ... )
##   ... 48 45 9 46 47 50 ... :   -1.67 ( linkage phases: ... 1 1 1 1 2 ... )
## 
## ...-9-|-46-45-47-50-|-24-... OK
## 
## ...-46-|-45-47-50-24-|-49-... OK
## 
## ...-45-|-47-50-24-49-|-52-... OK
## 
## ...-47-|-50-24-49-52-|-51-...
##   Alternative orders:
##   ... 47 52 49 24 50 51 :    0.00 ( linkage phases: ... 2 1 1 1 1 )
##   ... 47 50 24 49 52 51 :   -0.34 ( linkage phases: ... 2 1 1 1 1 )
##   ... 47 49 52 24 50 51 :   -2.59 ( linkage phases: ... 2 1 1 1 1 )
## 
## 50-|-24-49-52-51
##   Alternative orders:
##   ... 50 24 49 52 51 :    0.00 ( linkage phases: ... 1 1 1 1 )
##   ... 50 24 52 49 51 :   -2.76 ( linkage phases: ... 1 1 1 1 )

Drawing the genetic maps

Once all linkage groups were obtained using both strategies, we can draw a map for each strategy using the function draw_map. Since version 2.1.1007, OneMap has a new version of draw_map, called draw_map2. The new function draws elegant linkage groups, and presents new arguments to personalize your draw.

If you prefer the old function, we also keep it. Follow examples how to use both of them.

Draw_map

Drawing map builded with only recombinations informations

Drawing map builded with reference genome and recombinations informations

We also can draw a maps comparing corresponding linkage groups in each strategy:

Both strategies produced the same result for CHR2 (the map are only inverted).

Or groups alone:

Function draw_map draws a very simple graphic representation of the genetic map. More recently, we developed a new version called draw_map2 that draws a more sophisticated figure. Furthermore, once the distances and the linkage phases are estimated, other map figures can be drawn by the user with any appropriate software. There are several free software that can be used, such as MapChart (Voorrips, 2002).

Draw_map2

The same figures did with draw_map can be done with draw_map2 function. But it has different capacities and arguments. Here are some examples, but you can find more options in the help page ?write_map2.

Drawing map builded with only recombinations informations

The figure will be saved in your work directory with the default name map.eps. You can change the file name and extension specifying them in the argument output.

Drawing map builded with reference genome and recombinations informations

With the argument tag, we can highlight some markers with other color. The arguments col.group, col.mark and col.tag can be changed to personalize the color of the groups, the markers, and the highlighted markers, respectively.

We also can draw a maps comparing corresponding linkage groups in each strategy:

When defining marker names in tag argument, all markers with these name will be highlighted no matter in which group it/they is/are.

Map estimation for an arbitrary order

If, for any reason, one wants to estimate parameters for a given linkage map (e.g., for other orders on published papers), it is possible to define a sequence and use the map function. For example, for markers M30, M12, M3, M14 and M2, in this order, use

## 
## Printing map:
## 
## Markers           Position           Parent 1       Parent 2
## 
## 30 M30                0.00           a |  | b       a |  | b 
## 12 M12                1.00           b |  | a       c |  | a 
##  3 M3                20.57           o |  | a       o |  | o 
## 14 M14               33.63           a |  | o       b |  | o 
##  2 M2                41.70           o |  | o       o |  | a 
## 
## 5 markers            log-likelihood: -320.9012

NOTE: (new!) If your sequence has many markers (more than 60), we suggest to speed up map using BatchMap parallelization approach. See section Speed up analysis with parallelization for more information.

Warning: If you find an error message like:

Error in as_mapper(.f, ...) : argument ".f" is missing, with no default

It’s because the map function has a very common name and you can have in your environment other function with the same name. In the case of the pointed error, R is using map function from purrr package instead of OneMap, to solve this, simple specify that you want OneMap function with :: command from stringr package::

This is a subset of the first linkage group. When used this way, the map function searches for the best combination of phases between markers and prints the results.

(new!)

Warning: It is not our case in this example, but, sometimes, it can happen that some markers in your sequence doesn’t reach the OneMap linkage criteria when linkage are estimated by HMM multipoint approach using map, it will produce an error like this:

ERROR: The linkage between markers 1 and 2 did not reach the OneMap default criteria. They are probably segregating independently

You can evaluate the marker manually, or you can remove them automatically using map argument rm_unlinked = TRUE. Doing this, the map function will return a vector with marker numbers excluding the problematic marker, then, you can repeat the process without the marker, using make_seq to create a new sequence and repeat the map. You can also do it automatically using the map_avoid_unlinked function:

Using this, if map finds a problematic marker, it will print a warning pointing the marker number which was removed and will automatically repeat the analysis without it.

Furthermore, a sequence can also have user-defined linkage phases. The next example shows (incorrect) phases used for the same order of markers:

If one needs to add or drop markers from a predefined sequence, functions add_marker and drop_marker can be used. For example, to add markers 4 to 8 to any_seq.

## 
## Number of markers: 10
## Markers in the sequence:
## M30 M12 M3 M14 M2 M4 M5 M6 M7 M8
## 
## Parameters not estimated.

Removing markers 3, 4, 5, 12 and 30 from any_seq:

## 
## Number of markers: 5
## Markers in the sequence:
## M14 M2 M6 M7 M8
## 
## Parameters not estimated.

After that, the map needs to be re-estimated.

Speed up analysis with parallelization (new!)

Warning: By now, only available for Unix-like operating systems and for outcrossing and f2 intercross populations.

As already mentioned, OneMap uses HMM multipoint approach to estimate genetic distances, a very robust method, but it can take time to run if you have many markers. In 2017, Schiffthaler et. al release an OneMap fork with modifications in CRAN and in github with the possibility of parallelize the HMM chain dividing markers in batches and use different cores for each phase. Their approach speed up our HMM and keeps the genetic distances estimation quality. It allows to divide the job in maximum four cores according with the four possible phases for outcrossing mapping populations. We add this parallelized approach to the functions: map, mds_onemap, seriation, rcd, record and ug. For better efficiency it is important that batches are composed by 50 markers or more, therefore, this approach is only recommended for linkage groups with many markers.

Here we will show an example how to use the BatchMap approach in some functions that requires HMM. For this, we will simulate a group with 294 markers (we don’t want this vignette takes too much time to run, but usually maps with markers from high-throughput technologies result larger groups). Before start, you can see the time spent for each approach in this example:

Without parallelization (h) With parallelization (h)
rcd 0.6700558 0.1612458
record_map 1.4368436 0.2907308
ug_map 0.7145778 0.1884214
mds_onemap 1.0643083 0.2827314
map 2.0994486 0.6107456

Now, let’s simulate the mapping population and markers.

To prepare the data with defined bach size we use function pick_batch_sizes. It selects a batch size that splits the data into even groups. Argument size defines the batch size next to which an optimum size will be searched. overlap defines the number of markers that overlap between present batch and next. This is used because pre-defined phases at these overlap markers in present batch are used to start the HMM in the next batch. The around argument defines how much the function can vary around the defined number in size to search for the optimum batch size.

Some aspects should be considered to define these arguments, because if the batch size were set too high, there would be less gain in execution time. If the overlap size would be too small, phases would be incorrectly estimated and large gaps would appear in the map, inflating its size. In practise, these values will depend on many factors such as population size, marker quality and species. BatchMap authors recommended to try several configurations on a subset of data and select the best performing one.

Speed up map estimation for an arbitrary order (map function)

Because we simulate this dataset we know the correct order. We can use map_overlapping_batches to estimate genetic distance in this case. This is equivalent to map, but with parallelized process.

Similarly with map, using argument rm_unlinked = TRUE the function will return a vector with marker numbers without the problematic marker. To repeat the analysis removing automatically all problematic markers use map_avoid_unlinked:

As you can see in above maps, heuristic ordering algorithm do not return an optimal order result, mostly if you don’t have many individuals in your population. Because of the erroneous order, generated map size are not close to the simulated size (100 cM) and their heapmaps don’t present the expected color pattern. Two of them get close to the color pattern, they are the ug and the MDS method. They present good global ordering but not local. If you have a reference genome, you can use its position information to rearrange local ordering.

Export estimated parents haplotypes (new!)

In older version, users could only access the estimated linkage phase observing the print in the console:

## 
## Printing map:
## 
## Markers           Position           Parent 1       Parent 2
## 
## 27 M27                0.00           b |  | o       a |  | a 
## 16 M16               11.76           a |  | a       b |  | o 
## 20 M20               22.94           a |  | b       c |  | d 
##  4 M4                35.71           a |  | o       o |  | b 
## 21 M21               49.41           o |  | o       a |  | b 
## 23 M23               55.24           a |  | o       a |  | o 
## 48 SNP21             67.50           a |  | b       a |  | a 
##  9 M9                74.02           a |  | b       a |  | a 
## 46 SNP18             80.43           a |  | b       a |  | a 
## 45 SNP17             95.40           a |  | b       a |  | a 
## 47 SNP20            119.95           a |  | b       a |  | a 
## 50 SNP23            158.43           a |  | b       b |  | a 
## 24 M24              163.43           a |  | b       b |  | a 
## 49 SNP22            166.72           a |  | b       b |  | a 
## 52 SNP25            171.62           a |  | b       b |  | a 
## 51 SNP24            182.56           a |  | b       b |  | a 
## 
## 16 markers            log-likelihood: -811.5279

Now, you can export this information into a data.frame using:

##       group mk.number mk.names     dist P1_1 P1_2 P2_1 P2_2
## 1 Group - 1        27      M27  0.00000    b    o    a    a
## 2 Group - 1        16      M16 11.75801    a    a    b    o
## 3 Group - 1        20      M20 22.93778    a    b    c    d
## 4 Group - 1         4       M4 35.70756    a    o    o    b
## 5 Group - 1        21      M21 49.40658    o    o    a    b
## 6 Group - 1        23      M23 55.24441    a    o    a    o
## 7 Group - 1        48    SNP21 67.49802    a    b    a    a
## 8 Group - 1         9       M9 74.02260    a    b    a    a
## 9 Group - 1        46    SNP18 80.43325    a    b    a    a
##  [ reached 'max' / getOption("max.print") -- omitted 7 rows ]

The data.frame contains: group ID (group), marker number (mk.number) and names (mk.names), position in centimorgan (dist) and parents haplotypes (P1_1, P1_2, P2_1, P2_2).

You can also obtain a data.frame with a list of sequences and personalize the group names:

##   group mk.number mk.names     dist P1_1 P1_2 P2_1 P2_2
## 1  CHR2        43    SNP14  0.00000    a    b    a    a
## 2  CHR2        22      M22 13.50513    a    b    a    a
## 3  CHR2         7       M7 23.08429    a    a    a    b
## 4  CHR2        18      M18 64.51343    a    b    c    d
## 5  CHR2         8       M8 70.19895    b    a    b    a
## 6  CHR2        13      M13 72.86392    a    o    a    o
## 7  CHR2        44    SNP16 78.74250    b    a    b    a
## 8  CHR3        27      M27  0.00000    b    o    a    a
## 9  CHR3        16      M16 11.75801    a    a    b    o
##  [ reached 'max' / getOption("max.print") -- omitted 14 rows ]

Export estimated progeny haplotypes (new!)

Function progeny_haplotypes generates a data.frame with progeny phased haplotypes estimated by OneMap HMM. For progeny, the HMM results in probabilities for each possible genotypes, than the generated data.frame contains all possible genotypes. If most_likely = TRUE the most likely genotype receveis 1 and the rest 0 (if there are two most likely both receive 0.5), if most_likely = FALSE genotypes probabilities will be according with the HMM results. You can choose which individual to be evaluated in ind. The data.frame is composed by the information: individual (ind) and group (grp) ID, position in centimorgan (pos), progeny homologs (homologs) and from each parent the allele came (parents).

##    ind        grp      pos prob homologs parents
## 1    1 CHR2_final  0.00000  0.0       H1      P1
## 2    1 CHR2_final 13.50513  0.0       H1      P1
## 3    1 CHR2_final 23.08429  0.0       H1      P1
## 4    1 CHR2_final 64.51343  1.0       H1      P1
## 5    1 CHR2_final 70.19895  1.0       H1      P1
## 6    1 CHR2_final 72.86392  1.0       H1      P1
## 7    1 CHR2_final 78.74250  0.5       H1      P1
## 8    2 CHR2_final  0.00000  1.0       H1      P1
## 9    2 CHR2_final 13.50513  1.0       H1      P1
## 10   2 CHR2_final 23.08429  1.0       H1      P1
## 11   2 CHR2_final 64.51343  1.0       H1      P1
## 12   2 CHR2_final 70.19895  1.0       H1      P1
##  [ reached 'max' / getOption("max.print") -- omitted 44 rows ]

You can also have a view of progeny estimated haplotypes using plot. It shows which markers came from each parents homologues. position argument defines if haplotypes will be plotted by homologs (stack) or alleles (split). split option is a good way to better view the likelihoods of each alleles.

Comparing estimated and simulated haplotypes

The simulations here included are very useful to test our algorithms efficiency, we made them available in case to be useful for other purposes. Using functions run_pedsim, pedsim2vcf with argument phased TRUE we can convert the phased VCF using vcf2progeny_haplotypes, which keeps the original haplotype. With that we can compare the haplotypes simulated and the ones estimated by the onemap approach.

Here we will use the file sim_out_cod_genotypes.dat to get one phased VCF. See that now we don’t want to simulate read counts or genotype errors, we just want the original haplotypes in VCF format, then we set counts = FALSE and don’t need to define the related arguments.

Now, we can convert the phased VCF to onemap_progeny_haplotypes object using function vcf2progeny_haplotypes. The position, the group names and individuals id will be according with the ones contained in VCF file. This function can take some time to run if you select too many individuals or groups.

## Scanning file to determine attributes.
## File attributes:
##   meta lines: 4
##   header_line: 5
##   variant count: 42
##   column count: 211
## 
Meta line 4 read in.
## All meta lines processed.
## gt matrix initialized.
## Character matrix gt created.
##   Character matrix gt rows: 42
##   Character matrix gt cols: 211
##   skip: 0
##   nrows: 42
##   row_num: 0
## 
Processed variant: 42
## All variants processed

This is the simulated dataset. If OneMap algorithm could get all information needed, it could reproduce this haplotypes exactly how they were in simulated data. Let’s see how OneMap estimate these haplotypes:

##   This is an object of class 'onemap'
##     Type of cross:      outcross 
##     No. individuals:    200 
##     No. markers:        42 
##     CHROM information:  yes 
##     POS information:    yes 
##     Percent genotyped:  100 
## 
##     Segregation types:
##                 A.1 -->  6
##                 A.2 -->  6
##                B3.7 -->  6
##               D1.10 -->  6
##                D1.9 -->  6
##               D2.14 -->  6
##               D2.15 -->  6
## 
##     No. traits:         0
## Computing 861 recombination fractions ...

See that, besides markers are not in their exactly position, the recombination break points are the same as the ones simulated. The marker position could only be exactly the same as the ones simulated if we have a very big (or maybe infinite) population size, but here we have only 200 individuals, but this is not a problem once we could reproduce the haplotypes.

Session Info

## R version 3.6.1 (2019-07-05)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 16.04.6 LTS
## 
## Matrix products: default
## BLAS:   /usr/lib/openblas-base/libblas.so.3
## LAPACK: /usr/lib/libopenblasp-r0.2.18.so
## 
## locale:
##  [1] LC_CTYPE=pt_BR.UTF-8       LC_NUMERIC=C              
##  [3] LC_TIME=pt_BR.UTF-8        LC_COLLATE=en_US.UTF-8    
##  [5] LC_MONETARY=pt_BR.UTF-8    LC_MESSAGES=en_US.UTF-8   
##  [7] LC_PAPER=pt_BR.UTF-8       LC_NAME=C                 
##  [9] LC_ADDRESS=C               LC_TELEPHONE=C            
## [11] LC_MEASUREMENT=pt_BR.UTF-8 LC_IDENTIFICATION=C       
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
## [1] stringr_1.4.0    vcfR_1.8.0       onemap_2.2.0     rmdformats_0.3.5
## [5] knitr_1.29      
## 
## loaded via a namespace (and not attached):
##  [1] colorspace_1.4-1          ellipsis_0.3.1           
##  [3] class_7.3-15              rio_0.5.16               
##  [5] htmlTable_2.0.1           RcppArmadillo_0.9.900.2.0
##  [7] base64enc_0.1-3           rstudioapi_0.11          
##  [9] mice_3.10.0               farver_2.0.3             
## [11] codetools_0.2-16          splines_3.6.1            
## [13] doParallel_1.0.15         memuse_4.0-0             
## [15] Formula_1.2-3             polynom_1.4-0            
## [17] jsonlite_1.7.0            MDSMap_1.1               
## [19] broom_0.7.0               cluster_2.1.0            
## [21] png_0.1-7                 shiny_1.5.0              
## [23] httr_1.4.1                compiler_3.6.1           
## [25] backports_1.1.8           assertthat_0.2.1         
## [27] lazyeval_0.2.2            Matrix_1.2-17            
## [29] fastmap_1.0.1             later_1.1.0.1            
## [31] acepack_1.4.1             htmltools_0.5.0          
## [33] tools_3.6.1               gtable_0.3.0             
## [35] glue_1.4.1.9000           reshape2_1.4.4           
## [37] dplyr_1.0.0               ggthemes_4.2.0           
## [39] Rcpp_1.0.5                carData_3.0-4            
## [41] cellranger_1.1.0          vctrs_0.3.2              
## [43] nlme_3.1-141              ape_5.3                  
## [45] gdata_2.18.0              iterators_1.0.12         
## [47] crosstalk_1.1.0.1         pinfsc50_1.1.0           
## [49] xfun_0.15                 openxlsx_4.1.5           
## [51] mime_0.9                  miniUI_0.1.1.1           
## [53] lifecycle_0.2.0           weights_1.0.1            
## [55] gtools_3.8.2              princurve_2.1.4          
## [57] candisc_0.8-3             MASS_7.3-51.4            
## [59] scales_1.1.1              heplots_1.3-5            
## [61] hms_0.5.3                 promises_1.1.1           
## [63] parallel_3.6.1            smacof_2.1-1             
## [65] RColorBrewer_1.1-2        yaml_2.2.1               
## [67] curl_4.3                  gridExtra_2.3            
## [69] ggplot2_3.3.2             updog_1.2.0              
## [71] rpart_4.1-15              reshape_0.8.8            
## [73] latticeExtra_0.6-29       stringi_1.4.6            
## [75] highr_0.8                
##  [ reached getOption("max.print") -- omitted 51 entries ]

References

Buetow, K. H., Chakravarti, A. Multipoint gene mapping using seriation. I. General methods. American Journal of Human Genetics 41, 180-188, 1987.

Doerge, R.W. Constructing genetic maps by rapid chain delineation. Journal of Agricultural Genomics 2, 1996.

Mollinari, M., Margarido, G. R. A., Vencovsky, R. and Garcia, A. A. F. Evaluation of algorithms used to order markers on genetics maps. Heredity 103, 494-502, 2009.

Schiffthaler, B., Bernhardsson, C., Ingvarsson, P. K., & Street, N. R. BatchMap: A parallel implementation of the OneMap R package for fast computation of F1 linkage maps in outcrossing species. PLoS ONE, 12(12), 1–12, 2017.

Tan, Y., Fu, Y. A novel method for estimating linkage maps. Genetics 173, 2383-2390, 2006.

Van Os H, Stam P, Visser R.G.F., Van Eck H.J. RECORD: a novel method for ordering loci on a genetic linkage map. Theor Appl Genet 112, 30-40, 2005.

Voorrips, R.E. MapChart: software for the graphical presentation of linkage maps and QTLs. Journal of Heredity 93, 77-78, 2002.

Voorrips, R. E., Maliepaard, C. A. The simulation of meiosis in diploid and tetraploid organisms using various genetic models. BMC Bioinformatics, 13(1), 248, 2012.

Wu, R., Ma, C.X., Painter, I. and Zeng, Z.-B. Simultaneous maximum likelihood estimation of linkage and linkage phases in outcrossing species. Theoretical Population Biology 61, 349-363, 2002a.

Wu, R., Ma, C.-X., Wu, S. S. and Zeng, Z.-B. Linkage mapping of sex-specific differences. Genetical Research 79, 85-96, 2002b.

Statistical Genetics Lab
Department of Genetics
Luiz de Queiroz College of Agriculture
University of São Paulo

2020-07-19