# Outcrossing Populations

#### 2020-02-15

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 crosstype.

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

system.file(package = "onemap")

# 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:

onemap_example_out <- read_onemap(dir = "C:/workingdirectory", inputfile = "onemap_example_out.raw")

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:

onemap_example_out <- read_onemap(inputfile = "onemap_example_out.raw")

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

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

data("onemap_example_out")

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:

onemap_example_out

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:

plot(onemap_example_out)

Changing the argument all to FALSE, the markers will be separed 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.

plot(onemap_example_out, all = FALSE)

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 segregattion pattern with the plot_by_segreg_type function:

plot_by_segreg_type(onemap_example_out)

## Importing data from VCF file

If you are working with biallelic markers, as SNPs and indels (marker types B3.7, D1.10 or D2.15), in VCF (Variant Call Format) files, 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 at the end of raw file.

We will use the same example file vcf_example_out.vcf to show how it works.

First, we convert the VCF file to vcfR object:

library(vcfR)
vcfR.object <- read.vcfR(system.file("extdata/vcf_example_out.vcf", package = "onemap"))

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 is the vcfR.object we just created, the identification of each parent (here you must define only one sample for each parent) and the cross type.

vcf_example_out <- onemap_read_vcfR(vcfR.object = vcfR.object,
parent1 = "P1",
parent2 = "P2",
cross = "outcross")

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

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

save(vcfR.object, file = "vcfR.object.RData")
rm(vcfR.object)

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.

# Combining OneMap datasets

If you have more than one dataset of markers, all from the same cross type, 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 phenotipic information if it exists.

comb_example <- combine_onemap(onemap_example_out, vcf_example_out)
comb_example
#>   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.

plot(comb_example)

# 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 pratice 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.

bins <- find_bins(comb_example, exact = FALSE)
bins
#> 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.

bins_example <- create_data_bins(comb_example, bins)
bins_example
#>   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:  97
#>
#>     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 data set. 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 data set you are working after using this functions, you can use the function write_onemap_raw.

write_onemap_raw(comb_example, file.name = "new_dataset.raw", cross="outcross")

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 data sets.

# Testing segregation pattern

For the map building process it is also important to know which markers have deviations in the expecteded segregation pattern. It can be a good pratice 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.

test_segregation_of_a_marker(bins_example, 4)
#> $Hypothesis #> [1] "1:1:1:1" #> #>$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.

segreg_test <- test_segregation(bins_example)
print(segreg_test)
#>    Marker      H0  Chi-square      p-value % genot.
#> 1      M1   1:2:1  1.76000000 4.147829e-01      100
#> 2      M2     1:1  0.04000000 8.414806e-01      100
#> 3      M3     1:1  0.36000000 5.485062e-01      100
#> 4      M4 1:1:1:1  2.64000000 4.505201e-01      100
#> 5      M5     1:1  1.96000000 1.615133e-01      100
#> 6      M6   1:2:1  1.52000000 4.676664e-01      100
#> 7      M7     1:1  0.16000000 6.891565e-01      100
#> 8      M8   1:2:1  0.86000000 6.505091e-01      100
#> 9      M9     1:1  0.04000000 8.414806e-01      100
#> 10    M10     1:1  0.36000000 5.485062e-01      100
#> 11    M11     1:1  0.16000000 6.891565e-01      100
#> 12    M12 1:1:1:1  6.48000000 9.045460e-02      100
#> 13    M13     3:1  0.00000000 1.000000e+00      100
#> 14    M14 1:1:1:1  0.40000000 9.402425e-01      100
#> 15    M15 1:1:1:1  2.24000000 5.241127e-01      100
#> 16    M16     1:1  1.44000000 2.301393e-01      100
#> 17    M17   1:2:1 35.58000000 1.878889e-08      100
#> 18    M18 1:1:1:1  1.44000000 6.961859e-01      100
#> 19    M19   1:2:1 37.98000000 5.659105e-09      100
#> 20    M20 1:1:1:1  4.88000000 1.807980e-01      100
#> 21    M21     1:1  1.44000000 2.301393e-01      100
#> 22    M22     1:1  1.00000000 3.173105e-01      100
#> 23    M23     3:1  0.48000000 4.884223e-01      100
#> 24    M24   1:2:1  1.50000000 4.723666e-01      100
#> 25    M25   1:2:1 35.04000000 2.461278e-08      100
#> 26    M26 1:1:1:1  1.52000000 6.776621e-01      100
#> 27    M27     1:1  1.00000000 3.173105e-01      100
#> 28    M28 1:1:1:1  1.20000000 7.530043e-01      100
#> 29    M29     1:1  0.00000000 1.000000e+00      100
#> 30    M30   1:2:1  3.42000000 1.808658e-01      100
#> 31   SNP1   1:2:1  3.73913043 1.541907e-01       92
#> 32   SNP2   1:2:1  4.76086957 9.251035e-02       92
#> 33   SNP3   1:2:1  4.76086957 9.251035e-02       92
#> 34   SNP5   1:2:1  4.95652174 8.388899e-02       92
#> 35   SNP6   1:2:1  1.80434783 4.056868e-01       92
#> 36   SNP7   1:2:1  1.45652174 4.827478e-01       92
#> 37   SNP8   1:2:1  0.26086957 8.777137e-01       92
#> 38   SNP9   1:2:1  1.39130435 4.987491e-01       92
#> 39  SNP10   1:2:1  0.06521739 9.679172e-01       92
#> 40  SNP11   1:2:1  0.52173913 7.703814e-01       92
#> 41  SNP12   1:2:1  0.17391304 9.167170e-01       92
#> 42  SNP13   1:2:1  0.08695652 9.574534e-01       92
#> 43  SNP14     1:1  0.69565217 4.042485e-01       92
#> 44  SNP16   1:2:1  0.00000000 1.000000e+00       92
#> 45  SNP17     1:1  0.00000000 1.000000e+00       92
#> 46  SNP18     1:1  0.17391304 6.766573e-01       92
#> 47  SNP20     1:1  0.04347826 8.348273e-01       92
#> 48  SNP21     1:1  0.00000000 1.000000e+00       92
#> 49  SNP22   1:2:1  1.10869565 5.744468e-01       92
#> 50  SNP23   1:2:1  2.15217391 3.409270e-01       92
#> 51  SNP24   1:2:1  2.86956522 2.381671e-01       92
#> 52  SNP25   1:2:1  2.15217391 3.409270e-01       92

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.

select_segreg(segreg_test, distorted = TRUE) #to show the markers names with segregation distortion
#> [1] "M17" "M19" "M25"

select_segreg(segreg_test, distorted = FALSE) #to show the markers names without segregation distortion
#>  [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:

dist <- select_segreg(segreg_test, distorted = TRUE, numbers = TRUE) #to show the markers numbers with segregation distortion
dist
#> [1] 17 19 25

no_dist <- select_segreg(segreg_test, distorted = FALSE, numbers = TRUE) #to show the markers numbers without segregation distortion
no_dist
#>  [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:

plot(segreg_test)

# 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.

The function rf_2pts uses as default values of LOD Score 3 and maximum recombination fraction 0.50. You can change this values according with your dataset. Also, you can use the function suggest_lod to calculate a suggested LOD score considering that multiple tests are being performed.

LOD_sug <- suggest_lod(bins_example)
LOD_sug
#> [1] 3.688802

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

twopts <- rf_2pts(bins_example, LOD = LOD_sug, max.rf = 0.5)

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

twopts

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 = 3.688802 , 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:

print(twopts, c("M1", "M3"))
#>   Results of the 2-point analysis for markers: M1 and M3
#>   Criteria: LOD =  3.688802 , 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.

mark_no_dist <- make_seq(twopts, c(no_dist))

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

marker_type(mark_no_dist)
#>   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:

LGs <- group(mark_no_dist)
#>    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), criteria previously defined for the object twopts are used.

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

LGs

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 = 3.688802 , Maximum recombination fraction = 0.5
#>
#>   No. markers:            49
#>   No. groups:             3
#>
#>   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

print(LGs, detailed = FALSE)
#>   This is an object of class 'group'
#>   It was generated from the object "mark_no_dist"
#>
#>   Criteria used to assign markers to groups:
#>     LOD = 3.688802 , Maximum recombination fraction = 0.5
#>
#>   No. markers:            49
#>   No. groups:             3
#>   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:

LGs <- group(mark_no_dist, LOD = 6)
#>    Selecting markers:
#>    group    1
#>     ........................
#>    group    2
#>     ..........
#>    group    3
#>     .....
#>    group    4
#>     ....
LGs
#>   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
#>
#>   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
#>
#>     M7 M29

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

LGs <- group(mark_no_dist, LOD = LOD_sug, max.rf = 0.4)
#>    Selecting markers:
#>    group    1
#>     ........................
#>    group    2
#>     ................
#>    group    3
#>     ......
LGs
#>   This is an object of class 'group'
#>   It was generated from the object "mark_no_dist"
#>
#>   Criteria used to assign markers to groups:
#>     LOD = 3.688802 , Maximum recombination fraction = 0.4
#>
#>   No. markers:            49
#>   No. groups:             3
#>
#>   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

set_map_fun(type = "haldane")

To use Kosambi

set_map_fun(type = "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:

LG3 <- make_seq(LGs, 3)

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

LG3

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):

LG3_ser <- seriation(LG3)
LG3_rcd <- rcd(LG3)
LG3_rec <- record(LG3)
LG3_ug <- ug(LG3)

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

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

LG3_comp <- compare(LG3)

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 or mds_onemap.

In the example, LG3 contains only six 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

LG3_comp
#>
#> Number of orders: 50
#> Best 50 unique orders                         LOD    Nested LOD
#> --------------------------------------------------------------
#> order  1:    43  22   7  18   8  13  44
#>         CC  CC  CC  RR  RR  RR         0.00       0.00
#> --------------------------------------------------------------
#> order  2:    43   7  22  18   8  13  44
#>         CC  CC  CC  RR  RR  RR        -0.01       0.00
#> --------------------------------------------------------------
#> order  3:     7  43  22  18   8  13  44
#>         CC  CC  CC  RR  RR  RR        -0.20       0.00
#> --------------------------------------------------------------
#> order  4:    22  43   7  18   8  13  44
#>         CC  CC  CC  RR  RR  RR        -0.20       0.00
#> --------------------------------------------------------------
#> order  5:    22   7  43  18   8  13  44
#>         CC  CC  CC  RR  RR  RR        -0.21       0.00
#> --------------------------------------------------------------
#> order  6:     7  22  43  18   8  13  44
#>         CC  CC  CC  RR  RR  RR        -0.41       0.00
#> --------------------------------------------------------------
#> order  7:     7  18   8  13  44  22  43
#>         CC  RR  RR  RR  RC  CC        -0.49       0.00
#> --------------------------------------------------------------
#> order  8:     7  44  13   8  18  22  43
#>         CR  RR  RR  RR  CC  CC        -0.61       0.00
#> --------------------------------------------------------------
#> order  9:     7  44  13   8  18  43  22
#>         CR  RR  RR  RR  CC  CC        -0.79       0.00
#> --------------------------------------------------------------
#> order 10:     7  18   8  13  44  43  22
#>         CC  RR  RR  RR  RC  CC        -0.81       0.00
#> --------------------------------------------------------------
#> order 11:    43  22   7  13  18   8  44
#>         CC  CC  CC  CC  RR  CC        -0.98       0.00
#> --------------------------------------------------------------
#> order 12:    43   7  22  13  18   8  44
#>         CC  CC  CC  CC  RR  CC        -0.98       0.00
#> --------------------------------------------------------------
#> order 13:    43  22   7  13  44   8  18
#>         CC  CC  CC  RR  CC  RR        -1.07       0.00
#> --------------------------------------------------------------
#> order 14:    43   7  22  13  44   8  18
#>         CC  CC  CC  RR  CC  RR        -1.08       0.00
#> --------------------------------------------------------------
#> order 15:    43  22   7  44  13   8  18
#>         CC  CC  RR  RR  RR  RR        -1.14       0.00
#> --------------------------------------------------------------
#> order 16:    43   7  22  44  13   8  18
#>         CC  CC  RR  RR  RR  RR        -1.15       0.00
#> --------------------------------------------------------------
#> order 17:     7  43  22  13  18   8  44
#>         CC  CC  CC  CC  RR  CC        -1.21       0.00
#> --------------------------------------------------------------
#> order 18:    43  22   7  18  13   8  44
#>         CC  CC  CC  CC  RR  CC        -1.25       0.00
#> --------------------------------------------------------------
#> order 19:    43   7  22  18  13   8  44
#>         CC  CC  CC  CC  RR  CC        -1.26       0.00
#> --------------------------------------------------------------
#> order 20:     7  43  22  44  13   8  18
#>         CC  CC  RR  RR  RR  RR        -1.30       0.00
#> --------------------------------------------------------------
#> order 21:     7  43  22  13  44   8  18
#>         CC  CC  CC  RR  CC  RR        -1.36       0.00
#> --------------------------------------------------------------
#> order 22:     7  43  22  18  13   8  44
#>         CC  CC  CC  CC  RR  CC        -1.45       0.00
#> --------------------------------------------------------------
#> order 23:    22  43   7  18  13   8  44
#>         CC  CC  CC  CC  RR  CC        -1.45       0.00
#> --------------------------------------------------------------
#> order 24:    22   7  43  18  13   8  44
#>         CC  CC  CC  CC  RR  CC        -1.46       0.00
#> --------------------------------------------------------------
#> order 25:    22  43   7  44  13   8  18
#>         CC  CC  RR  RR  RR  RR        -1.59       0.00
#> --------------------------------------------------------------
#> order 26:    22   7  43  44  13   8  18
#>         CC  CC  RR  RR  RR  RR        -1.60       0.00
#> --------------------------------------------------------------
#> order 27:     7  22  43  18  13   8  44
#>         CC  CC  CC  CC  RR  CC        -1.66       0.00
#> --------------------------------------------------------------
#> order 28:     7  13  44   8  18  22  43
#>         CC  RR  CC  RR  CC  CC        -1.69       0.00
#> --------------------------------------------------------------
#> order 29:     7  18  13   8  44  22  43
#>         CC  CC  RR  CC  RC  CC        -1.72       0.00
#> --------------------------------------------------------------
#> order 30:     7  22  43  44  13   8  18
#>         CC  CC  RR  RR  RR  RR        -1.77       0.00
#> --------------------------------------------------------------
#> order 31:     7  44   8  13  18  22  43
#>         CR  CC  RR  CC  CC  CC        -1.83       0.00
#> --------------------------------------------------------------
#> order 32:     7  13  44   8  18  43  22
#>         CC  RR  CC  RR  CC  CC        -1.88       0.00
#> --------------------------------------------------------------
#> order 33:    22  43   7  13  18   8  44
#>         CC  CC  CC  CC  RR  CC        -1.89       0.00
#> --------------------------------------------------------------
#> order 34:    22   7  43  13  18   8  44
#>         CC  CC  CC  CC  RR  CC        -1.90       0.00
#> --------------------------------------------------------------
#> order 35:    22  43   7  13  44   8  18
#>         CC  CC  CC  RR  CC  RR        -1.90       0.00
#> --------------------------------------------------------------
#> order 36:    22   7  43  13  44   8  18
#>         CC  CC  CC  RR  CC  RR        -1.91       0.00
#> --------------------------------------------------------------
#> order 37:     7  18   8  44  13  22  43
#>         CC  RR  CC  RR  CC  CC        -1.96       0.00
#> --------------------------------------------------------------
#> order 38:     7  44   8  13  18  43  22
#>         CR  CC  RR  CC  CC  CC        -2.01       0.00
#> --------------------------------------------------------------
#> order 39:     7  18  13   8  44  43  22
#>         CC  CC  RR  CC  RC  CC        -2.05       0.00
#> --------------------------------------------------------------
#> order 40:     7  13  18   8  44  22  43
#>         CC  CC  RR  CC  RC  CC        -2.16       0.00
#> --------------------------------------------------------------
#> order 41:     7  22  43  13  18   8  44
#>         CC  CC  CC  CC  RR  CC        -2.18       0.00
#> --------------------------------------------------------------
#> order 42:     7  22  43  13  44   8  18
#>         CC  CC  CC  RR  CC  RR        -2.21       0.00
#> --------------------------------------------------------------
#> order 43:     7  44   8  18  13  22  43
#>         CR  CC  RR  CC  CC  CC        -2.28       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        -2.33       0.00
#> --------------------------------------------------------------
#> order 46:     7  13  18   8  44  43  22
#>         CC  CC  RR  CC  RC  CC        -2.47       0.00
#> --------------------------------------------------------------
#> order 47:     7  43  22  44   8  13  18
#>         CC  CC  RR  CC  RR  CC        -2.48       0.00
#> --------------------------------------------------------------
#> order 48:    43  22   7  18   8  44  13
#>         CC  CC  CC  RR  CC  RR        -2.49       0.00
#> --------------------------------------------------------------
#> order 49:    43   7  22  18   8  44  13
#>         CC  CC  CC  RR  CC  RR        -2.50       0.00
#> --------------------------------------------------------------
#> order 50:     7  18   8  44  13  43  22
#>         CC  RR  CC  RR  CC  CC        -2.52       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

LG3_final <- make_seq(LG3_comp, 1, 1)

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

LG3_final <- make_seq(LG3_comp)

have the same effect.

To see the final map, type

LG3_final
#>
#> Printing map:
#>
#> Markers           Position           Parent 1       Parent 2
#>
#> 43 SNP14              0.00           a |  | b       a |  | a
#> 22 M22               13.35           a |  | b       a |  | a
#>  7 M7                13.35           a |  | a       a |  | b
#> 18 M18               57.71           a |  | b       c |  | d
#>  8 M8                63.40           b |  | a       b |  | a
#> 13 M13               66.06           a |  | o       a |  | o
#> 44 SNP16             71.94           b |  | a       b |  | a
#>
#> 7 markers            log-likelihood: -398.922

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:

rf_graph_table(LG3_final)

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 pallete with the argument n.colors. Hot colors (more close to red) represents lower values of recombination fractions, as showed 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.

rf_graph_table(LG3_final, 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 plolty graphic. If you hover the mouse cursor over the cells it shows some extra information about cells, as percentagem of missing data, marker name and type. The output html file is generated in your work directory and opens automatically in your internet browser.

rf_graph_table(LG3_final, inter = TRUE, html.file = "LG3.html")

For example, passing on the cell corresponding to markers M8 and M13, 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.

rf_graph_table(LG3_final, inter = FALSE, mrk.axis = "numbers")

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 probabily 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’).

rf_graph_table(LG3_final, main = "LG3", inter = FALSE, n.colors = 7, lab.xy = c("markers", "markers"))

## 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:

LG2 <- make_seq(LGs, 2)
LG2
#>
#> 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:

LG2_rcd <- rcd(LG2)
#>
#> order obtained using RCD algorithm:
#>
#>  27 21 29 16 48 9 46 45 23 4 20 47 50 24 49 52 51
#>
#> calculating multipoint map using tol =  1e-04 .
LG2_rcd
#>
#> Printing map:
#>
#> Markers           Position           Parent 1       Parent 2
#>
#> 27 M27                0.00           b |  | o       a |  | a
#> 21 M21              114.87           o |  | o       a |  | b
#> 29 M29              114.87           o |  | a       o |  | o
#> 16 M16              151.19           a |  | a       b |  | o
#> 48 SNP21            151.98           a |  | b       a |  | a
#>  9 M9               158.38           a |  | b       a |  | a
#> 46 SNP18            164.35           a |  | b       a |  | a
#> 45 SNP17            178.43           a |  | b       a |  | a
#> 23 M23              194.75           a |  | o       a |  | o
#>  4 M4               211.70           a |  | o       o |  | b
#> 20 M20              224.47           a |  | b       c |  | d
#> 47 SNP20            260.40           a |  | b       a |  | a
#> 50 SNP23            299.77           a |  | b       b |  | a
#> 24 M24              304.82           a |  | b       b |  | a
#> 49 SNP22            308.11           a |  | b       b |  | a
#> 52 SNP25            313.00           a |  | b       b |  | a
#> 51 SNP24            323.94           a |  | b       b |  | a
#>
#> 17 markers            log-likelihood: -963.6245

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

marker_type(LG2)
#>   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:

LG2_init <- make_seq(twopts, c(4, 20, 24, 49,50,51))

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.

LG2_comp <- compare(LG2_init)

Select the best order:

LG2_frame <- make_seq(LG2_comp)

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

rf_graph_table(LG2_frame, mrk.axis = "numbers")

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:

LG2_extend <- try_seq(LG2_frame, 52)
LG2_extend
#>
#> 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

print(LG2_extend, 7)
#>
#> 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) could be in reverse order (SNP22, M24, SNP23, SNP24, M4 and M20) 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 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.

LG2_test <- make_seq(LG2_extend, 7, 1)

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).

rf_graph_table(LG2_test, mrk.axis = "numbers")

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:

LG2_frame <- LG2_test

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

LG2_extend <- try_seq(LG2_frame, 9)
LG2_frame <- make_seq(LG2_extend, 3)
LG2_extend <- try_seq(LG2_frame, 16)
LG2_frame <- make_seq(LG2_extend, 1)
LG2_extend <- try_seq(LG2_frame, 21)
LG2_frame <- make_seq(LG2_extend, 4)
LG2_extend <- try_seq(LG2_frame, 23)
LG2_frame <- make_seq(LG2_extend, 5)
LG2_extend <- try_seq(LG2_frame, 27)
LG2_frame <- make_seq(LG2_extend, 1)
LG2_extend <- try_seq(LG2_frame, 29)
LG2_frame <- make_seq(LG2_extend, 12)
LG2_extend <- try_seq(LG2_frame, 45)
LG2_frame <- make_seq(LG2_extend, 8)
LG2_extend <- try_seq(LG2_frame, 46)
LG2_frame <- make_seq(LG2_extend, 7)
LG2_extend <- try_seq(LG2_frame, 47)
LG2_frame <- make_seq(LG2_extend, 7)
LG2_extend <- try_seq(LG2_frame, 48)
LG2_final <- make_seq(LG2_extend, 10)

Checking graphically:

rf_graph_table(LG2_final)

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

LG2_ord <- order_seq(LG2, n.init = 5, THRES = 3)
#>
#> 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 20 4 21 23 45 50 24 49
#>
#> Markers not placed on the map: 9 16 29 46 47 48 51 52
#>
#>
#> Calculating LOD-Scores
#>  9 --> M9    : ..........
#> 16 --> M16   : ..........
#> 29 --> M29   : ..........
#> 46 --> SNP18 : ..........
#> 47 --> SNP20 : ..........
#> 48 --> SNP21 : ..........
#> 51 --> SNP24 : ..........
#> 52 --> SNP25 : ..........
#>
#>
#> Placing remaining marker(s) at most likely position
#> 52 --> SNP25 : ..........
#> 46 --> SNP18 : ...........
#> 48 --> SNP21 : ............
#>  9 --> M9    : .............
#> 29 --> M29   : ..............
#> 47 --> SNP20 : ...............
#> 51 --> SNP24 : ................
#> 16 --> M16   : .................
#>
#> Estimating final genetic map using tol = 10E-5.

Basically, this function automates what the try_seq function does, using some pre-defined 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:

LG2_ord
#>
#> Best sequence found.
#> Printing map:
#>
#> Markers           Position           Parent 1       Parent 2
#>
#> 27 M27                0.00           b |  | o       a |  | a
#> 20 M20               21.18           a |  | b       c |  | d
#>  4 M4                33.95           a |  | o       o |  | b
#> 21 M21               47.95           o |  | o       a |  | b
#> 23 M23               53.59           a |  | o       a |  | o
#> 45 SNP17             72.79           a |  | b       a |  | a
#> 50 SNP23            101.92           a |  | b       b |  | a
#> 24 M24              106.95           a |  | b       b |  | a
#> 49 SNP22            110.83           a |  | b       b |  | a
#>
#> 9 markers            log-likelihood: -548.6658
#>
#>
#>
#> The following markers could not be uniquely positioned.
#> Printing most likely positions for each unpositioned marker:
#>
#> ------------------------------------------------------
#> |    |   9 |  16 |  29 |  46 |  47 |  48 |  51 |  52 |
#> |----|-----|-----|-----|-----|-----|-----|-----|-----|
#> |    |     | **  |     |     |     |     |     |     |
#> | 27 |     |     |     |     |     |     |     |     |
#> |    |     | *** |     |     |     |     |     |     |
#> | 20 |     |     |     |     |     |     |     |     |
#> |    |     |     |     |     |     |     |     |     |
#> |  4 |     |     |     |     |     |     |     |     |
#> |    |     |     |     |     |     | *   |     |     |
#> | 21 |     |     |     |     |     |     |     |     |
#> |    |     |     |     |     |     | *   |     |     |
#> | 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, 16, 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, 16, 29, 46, 47, 48, 51 and 52), use

LG2_safe <- make_seq(LG2_ord, "safe")

and to get the order with all markers, use

LG2_all <- make_seq(LG2_ord, "force")
LG2_all
#>
#> Printing map:
#>
#> Markers           Position           Parent 1       Parent 2
#>
#> 27 M27                0.00           b |  | o       a |  | a
#> 16 M16               11.74           a |  | a       b |  | o
#> 20 M20               22.93           a |  | b       c |  | d
#>  4 M4                35.70           a |  | o       o |  | b
#> 21 M21               49.45           o |  | o       a |  | b
#> 23 M23               55.14           a |  | o       a |  | o
#> 48 SNP21             67.95           a |  | b       a |  | a
#>  9 M9                74.08           a |  | b       a |  | a
#> 45 SNP17             82.64           a |  | b       a |  | a
#> 46 SNP18             97.89           a |  | b       a |  | a
#> 47 SNP20            114.31           a |  | b       a |  | a
#> 50 SNP23            143.74           a |  | b       b |  | a
#> 24 M24              148.75           a |  | b       b |  | a
#> 49 SNP22            152.08           a |  | b       b |  | a
#> 52 SNP25            157.05           a |  | b       b |  | a
#> 51 SNP24            168.11           a |  | b       b |  | a
#> 29 M29              198.00           o |  | a       o |  | o
#>
#> 17 markers            log-likelihood: -869.83

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:

LG2_ord <- order_seq(LG2, n.init = 5, THRES = 3, touchdown = TRUE)
LG2_ord
#>
#> Best sequence found.
#> Printing map:
#>
#> Markers           Position           Parent 1       Parent 2
#>
#> 27 M27                0.00           b |  | o       a |  | a
#> 20 M20               21.18           a |  | b       c |  | d
#>  4 M4                33.95           a |  | o       o |  | b
#> 21 M21               47.96           o |  | o       a |  | b
#> 23 M23               53.62           a |  | o       a |  | o
#> 45 SNP17             72.17           a |  | b       a |  | a
#> 46 SNP18             87.10           a |  | b       a |  | a
#> 50 SNP23            115.03           a |  | b       b |  | a
#> 24 M24              120.05           a |  | b       b |  | a
#> 49 SNP22            123.35           a |  | b       b |  | a
#> 52 SNP25            128.36           a |  | b       b |  | a
#>
#> 11 markers            log-likelihood: -625.2533
#>
#>
#>
#> The following markers could not be uniquely positioned.
#> Printing most likely positions for each unpositioned marker:
#>
#> ------------------------------------------
#> |    |   9 |  16 |  29 |  47 |  48 |  51 |
#> |----|-----|-----|-----|-----|-----|-----|
#> |    |     | **  |     |     |     |     |
#> | 27 |     |     |     |     |     |     |
#> |    |     | *** |     |     |     |     |
#> | 20 |     |     |     |     |     |     |
#> |    |     |     |     |     |     |     |
#> |  4 |     |     |     |     |     |     |
#> |    |     |     |     |     | *   |     |
#> | 21 |     |     |     |     |     |     |
#> |    |     |     |     |     | *   |     |
#> | 23 |     |     |     |     |     |     |
#> |    |     |     |     | *   | *** |     |
#> | 45 |     |     |     |     |     |     |
#> |    | *** |     |     | *   | **  |     |
#> | 46 |     |     |     |     |     |     |
#> |    |     |     | **  | *** | **  | **  |
#> | 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.

rf_graph_table(LG2_all, mrk.axis = "numbers")

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

ripple_seq(LG2_all, ws = 4, LOD = LOD_sug)
#> 27-16-20-4-|-21-...
#>   Alternative orders:
#>    27 16 20 4 21 ... :    0.00 ( linkage phases: 1 1 2 2 ... )
#>    16 27 20 4 21 ... :   -0.02 ( linkage phases: 1 1 2 2 ... )
#>
#> ...-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 ... :   -2.62 ( 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 ... :   -2.62 ( linkage phases: ... 2 2 1 1 1 ... )
#>
#> ...-4-|-21-23-48-9-|-45-...
#>   Alternative orders:
#>   ... 4 21 23 48 9 45 ... :    0.00 ( linkage phases: ... 2 1 1 1 1 ... )
#>   ... 4 23 21 48 9 45 ... :   -2.62 ( linkage phases: ... 2 1 1 1 1 ... )
#>
#> ...-21-|-23-48-9-45-|-46-...
#>   Alternative orders:
#>   ... 21 23 48 9 45 46 ... :    0.00 ( linkage phases: ... 1 1 1 1 1 ... )
#>   ... 21 23 48 45 9 46 ... :   -0.31 ( linkage phases: ... 1 1 1 1 1 ... )
#>   ... 21 23 45 48 9 46 ... :   -0.31 ( linkage phases: ... 1 1 1 1 1 ... )
#>   ... 21 23 45 9 48 46 ... :   -0.68 ( linkage phases: ... 1 1 1 1 1 ... )
#>   ... 21 48 23 45 9 46 ... :   -1.97 ( linkage phases: ... 1 1 1 1 1 ... )
#>
#> ...-23-|-48-9-45-46-|-47-...
#>   Alternative orders:
#>   ... 23 48 9 46 45 47 ... :   0.00 ( linkage phases: ... 1 1 1 1 1 ... )
#>   ... 23 48 9 45 46 47 ... :  -0.81 ( linkage phases: ... 1 1 1 1 1 ... )
#>   ... 23 48 46 9 45 47 ... :  -0.83 ( linkage phases: ... 1 1 1 1 1 ... )
#>   ... 23 48 45 9 46 47 ... :  -1.12 ( linkage phases: ... 1 1 1 1 1 ... )
#>   ... 23 45 48 9 46 47 ... :  -1.12 ( linkage phases: ... 1 1 1 1 1 ... )
#>   ... 23 45 46 9 48 47 ... :  -1.12 ( linkage phases: ... 1 1 1 1 1 ... )
#>   ... 23 45 9 48 46 47 ... :  -1.49 ( linkage phases: ... 1 1 1 1 1 ... )
#>   ... 23 45 9 46 48 47 ... :  -1.49 ( linkage phases: ... 1 1 1 1 1 ... )
#>   ... 23 48 45 46 9 47 ... :  -3.44 ( linkage phases: ... 1 1 1 1 1 ... )
#>
#> ...-48-|-9-45-46-47-|-50-...
#>   Alternative orders:
#>   ... 48 9 46 45 47 50 ... :    0.00 ( linkage phases: ... 1 1 1 1 2 ... )
#>   ... 48 9 46 47 45 50 ... :   -0.56 ( linkage phases: ... 1 1 1 1 2 ... )
#>   ... 48 9 45 46 47 50 ... :   -0.81 ( linkage phases: ... 1 1 1 1 2 ... )
#>   ... 48 46 9 45 47 50 ... :   -0.83 ( linkage phases: ... 1 1 1 1 2 ... )
#>   ... 48 45 9 46 47 50 ... :   -1.12 ( linkage phases: ... 1 1 1 1 2 ... )
#>   ... 48 47 46 9 45 50 ... :   -1.93 ( linkage phases: ... 1 1 1 1 2 ... )
#>   ... 48 9 45 47 46 50 ... :   -2.39 ( linkage phases: ... 1 1 1 1 2 ... )
#>   ... 48 47 45 9 46 50 ... :   -3.02 ( linkage phases: ... 1 1 1 1 2 ... )
#>   ... 48 45 46 9 47 50 ... :   -3.44 ( linkage phases: ... 1 1 1 1 2 ... )
#>   ... 48 9 47 46 45 50 ... :   -3.49 ( linkage phases: ... 1 1 1 1 2 ... )
#>   ... 48 46 9 47 45 50 ... :   -3.51 ( linkage phases: ... 1 1 1 1 2 ... )
#>
#> ...-9-|-45-46-47-50-|-24-...
#>   Alternative orders:
#>   ... 9 46 45 47 50 24 ... :    0.00 ( linkage phases: ... 1 1 1 2 1 ... )
#>   ... 9 46 47 45 50 24 ... :   -0.56 ( linkage phases: ... 1 1 1 2 1 ... )
#>   ... 9 45 46 47 50 24 ... :   -0.81 ( linkage phases: ... 1 1 1 2 1 ... )
#>   ... 9 45 47 46 50 24 ... :   -2.39 ( linkage phases: ... 1 1 1 2 1 ... )
#>   ... 9 47 46 45 50 24 ... :   -3.49 ( linkage phases: ... 1 1 1 2 1 ... )
#>
#> ...-45-|-46-47-50-24-|-49-...
#>   Alternative orders:
#>   ... 45 46 47 50 24 49 ... :    0.00 ( linkage phases: ... 1 1 2 1 1 ... )
#>   ... 45 47 46 50 24 49 ... :   -1.58 ( linkage phases: ... 1 1 2 1 1 ... )
#>
#> ...-46-|-47-50-24-49-|-52-... OK
#>
#> ...-47-|-50-24-49-52-|-51-...
#>   Alternative orders:
#>   ... 47 50 24 49 52 51 ... :    0.00 ( linkage phases: ... 2 1 1 1 1 ... )
#>   ... 47 52 49 24 50 51 ... :   -0.55 ( linkage phases: ... 2 1 1 1 1 ... )
#>   ... 47 50 24 52 49 51 ... :   -2.75 ( linkage phases: ... 2 1 1 1 1 ... )
#>   ... 47 49 52 24 50 51 ... :   -2.81 ( linkage phases: ... 2 1 1 1 1 ... )
#>   ... 47 50 52 49 24 51 ... :   -3.11 ( linkage phases: ... 2 1 1 1 1 ... )
#>   ... 47 50 49 52 24 51 ... :   -3.62 ( linkage phases: ... 2 1 1 1 1 ... )
#>
#> ...-50-|-24-49-52-51-|-29-...
#>   Alternative orders:
#>   ... 50 24 49 52 51 29 :    0.00 ( linkage phases: ... 1 1 1 1 3 )
#>   ... 50 24 52 49 51 29 :   -2.75 ( linkage phases: ... 1 1 1 1 3 )
#>   ... 50 51 24 49 52 29 :   -2.86 ( linkage phases: ... 1 1 1 1 3 )
#>   ... 50 52 49 24 51 29 :   -3.11 ( linkage phases: ... 1 1 1 1 3 )
#>   ... 50 49 52 24 51 29 :   -3.62 ( linkage phases: ... 1 1 1 1 3 )
#>
#> 24-|-49-52-51-29
#>   Alternative orders:
#>   ... 24 49 52 51 29 :    0.00 ( linkage phases: ... 1 1 1 3 )
#>   ... 24 52 49 51 29 :   -2.75 ( linkage phases: ... 1 1 1 3 )

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 permutated 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.

LG2_test_seq <- drop_marker(LG2_all, c(23,29))

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. For this we use the map function:

(LG2_test_map <- map(LG2_test_seq))
#>
#> Printing map:
#>
#> Markers           Position           Parent 1       Parent 2
#>
#> 27 M27                0.00           b |  | o       a |  | a
#> 16 M16                0.00           a |  | a       b |  | o
#> 20 M20               16.03           a |  | b       c |  | d
#>  4 M4                28.80           a |  | o       o |  | b
#> 21 M21               46.26           o |  | o       a |  | b
#> 48 SNP21             46.26           a |  | b       a |  | a
#>  9 M9                52.74           a |  | b       a |  | a
#> 45 SNP17             61.27           a |  | b       a |  | a
#> 46 SNP18             76.48           a |  | b       a |  | a
#> 47 SNP20             92.85           a |  | b       a |  | a
#> 50 SNP23            123.18           a |  | b       b |  | a
#> 24 M24              128.19           a |  | b       b |  | a
#> 49 SNP22            131.47           a |  | b       b |  | a
#> 52 SNP25            136.37           a |  | b       b |  | a
#> 51 SNP24            147.31           a |  | b       b |  | a
#>
#> 15 markers            log-likelihood: -777.7371

Now we have the map without markers 23 and 51.

rf_graph_table(LG2_test_map, mrk.axis = "numbers")

We use try_seq function to positioned them again:

LG2_test_seq <- try_seq(LG2_test_map, 23)
#> 23 --> M23   : ................
LG2_test_23 <- make_seq(LG2_test_seq, 6)
LG2_test_seq <- try_seq(LG2_test_23, 29)
#> 29 --> M29   : .................
LG2_test_23_29 <- make_seq(LG2_test_seq, 12)

rf_graph_table(LG2_test_23_29, mrk.axis = "numbers")

Marker 23 keeped 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:

LG2_final <- LG2_test_23
LG2_final
#>
#> Printing map:
#>
#> Markers           Position           Parent 1       Parent 2
#>
#> 27 M27                0.00           b |  | o       a |  | a
#> 16 M16                0.10           a |  | a       b |  | o
#> 20 M20               16.13           a |  | b       c |  | d
#>  4 M4                28.90           a |  | o       o |  | b
#> 21 M21               43.66           o |  | o       a |  | b
#> 23 M23               48.13           a |  | o       a |  | o
#> 48 SNP21             63.84           a |  | b       a |  | a
#>  9 M9                70.14           a |  | b       a |  | a
#> 45 SNP17             78.66           a |  | b       a |  | a
#> 46 SNP18             93.83           a |  | b       a |  | a
#> 47 SNP20            110.16           a |  | b       a |  | a
#> 50 SNP23            140.31           a |  | b       b |  | a
#> 24 M24              145.31           a |  | b       b |  | a
#> 49 SNP22            148.60           a |  | b       b |  | a
#> 52 SNP25            153.50           a |  | b       b |  | a
#> 51 SNP24            164.44           a |  | b       b |  | a
#>
#> 16 markers            log-likelihood: -809.1263

rf_graph_table(LG2_final, mrk.axis = "numbers")

## Genetic mapping of linkage group 1

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

LG1 <- make_seq(LGs, 1)

Construct the linkage map, by automatically using try algorithm:

LG1_ord <- order_seq(LG1, n.init = 6, touchdown = TRUE)

Notice that the second round of try_seq added markers 10, 31, 32, 35, 36, 40 and 42.

LG1_ord
#>
#> 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:

(LG1_frame <- make_seq(LG1_ord, "force"))
#>
#> 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:

rf_graph_table(LG1_frame, mrk.axis = "numbers")

Check for alternative orders:

ripple_seq(LG1_frame)
#> 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.

Alternatively, you can also use mds_onemap function to obtain a first draft for the markers order. The mds_onemap function makes a 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.

LG1_mds <- mds_onemap(LG1)
#> Stress: 0.295520848952197
#> Mean Nearest Neighbour Fit: 25.9634307642159
#> 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. Also, the default method used is the principal curves, know more about using ?mds_onemap and reading the MDSMap vignette. By default, we use the OneMap HMM approach to estimate the distances after the MDSMap ordered the markers, but you can have the default output from MDSMap setting hmm = FALSE.

rf_graph_table(LG1_mds)

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

LG1_test_seq <- drop_marker(LG1_frame, c(10,11,28,42))
LG1_test_map <- map(LG1_test_seq)
rf_graph_table(LG1_test_map, mrk.axis = "numbers")

LG1_extend <- try_seq(LG1_test_map,10)
LG1_test_map <- make_seq(LG1_extend,15)
LG1_extend <- try_seq(LG1_test_map,11)
LG1_test <- make_seq(LG1_extend,23) # We choose to remove this marker
LG1_extend <- try_seq(LG1_test_map,28)
LG1_test_map <- make_seq(LG1_extend,16)
LG1_extend <- try_seq(LG1_test_map,42)
LG1_final <- make_seq(LG1_extend,17) 

Print it:

LG1_final
#>
#> 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
rf_graph_table(LG1_final)

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

LG1_ser <- seriation(LG1)
LG1_rcd <- rcd(LG1)
LG1_rec <- record(LG1)
LG1_ug  <- ug(LG1)

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.

# 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 examplify 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.

CHR1 <- make_seq(twopts, "1")
CHR1
#>
#> Number of markers: 12
#> Markers in the sequence:
#> SNP1 SNP2 SNP3 SNP5 SNP6 SNP7 SNP8 SNP9 SNP10 SNP11 SNP12 SNP13
#>
#> Parameters not estimated.
CHR2 <- make_seq(twopts, "2")
CHR3 <- make_seq(twopts, "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 chromossome informations to them using recombination informations. For this, we can use the function group_seq:

CHR_mks <- group_seq(input.2pts = twopts, seqs = "CHROM", unlink.mks = mark_no_dist,
repeated = FALSE)
#>    Selecting markers:
#>    group    1
#>     ........................
#>    group    2
#>     ......
#>    group    3
#>     ....
#>    group    4
#>     .
#>    Selecting markers:
#>    group    1
#>     ......
#>    group    2
#>     ............
#>    group    3
#>     ......
#>    group    4
#>     .
#>    Selecting markers:
#>    group    1
#>     ................
#>    group    2
#>     ............
#>    group    3
#>     ....

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

CHR_mks <- group_seq(input.2pts = twopts, seqs = list(CHR1=CHR1, CHR2=CHR2, CHR3=CHR3),
unlink.mks = mark_no_dist, repeated = FALSE)

In this case, the command had the same effect of the previous, because we indicate chromossome 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 remining 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 repeateds 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 erros can generate repeated markers. Anyway, they deserves better investigations.

We can access detailed information about the results just printing:

CHR_mks
#>   This is an object of class 'group_seq'
#>   It was generated from the object "bins_example"
#>
#>   Criteria used to assign markers to groups:
#>     LOD = 3.688802 , 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. 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
#>
#>
#>
#>   Repeated markers: 0  markers
#> 

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

CHR_mks$repeated #> [1] NA The same way, we can access the output sequences: CHR_mks$sequences$CHR1 #> #> Number of markers: 25 #> Markers in the sequence: #> SNP1 SNP2 SNP3 SNP5 SNP6 SNP7 SNP8 SNP9 SNP10 SNP11 SNP12 SNP13 M1 M2 M3 M5 M6 #> M10 M11 M12 M14 M15 M26 M28 M30 #> #> Parameters not estimated. # or CHR_mks$sequences[[1]]
#>
#> 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)

CHR1_frame <- mds_onemap(CHR_mks$sequences$CHR1)
# or
CHR1_ord <- order_seq(CHR_mks$sequences$CHR1)
CHR1_frame <- make_seq(CHR1_ord, "force")
rf_graph_table(CHR1_frame) # graphic not showed

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.

CHR1_test_seq <- drop_marker(CHR1_frame, 11)
CHR1_test_map <- map(CHR1_test_seq)
#> 11 --> M11   : .........................
CHR1_add11 <- make_seq(CHR1_add11_seq, 25) # marker 11 was placed at the same position as before

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

CHR1_test_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
rf_graph_table(CHR1_test_map) 

CHR1_final <- CHR1_test_map

Checking for better orders:

ripple_seq(CHR1_final)
#> 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)

CHR2_frame <- mds_onemap(CHR_mks$sequences$CHR2)
# or
CHR2_ord <- order_seq(CHR_mks$sequences$CHR2)
CHR2_frame <- make_seq(CHR2_ord, "force")
rf_graph_table(CHR2_frame) # graphic not showed

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

CHR2_final <- CHR2_frame

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

CHR3_frame <- mds_onemap(CHR_mks$sequences$CHR3)
# or
CHR3_ord <- order_seq(CHR_mks$sequences$CHR3)
CHR3_frame <- make_seq(CHR3_ord, "force")
rf_graph_table(CHR3_frame, mrk.axis = "numbers") # graphic not showed

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.

CHR3_test_seq <- drop_marker(CHR3_frame, c(29))
CHR3_test_ord <- order_seq(CHR3_test_seq)
CHR3_test_map <- make_seq(CHR3_test_ord, "force")
rf_graph_table(CHR3_test_map, mrk.axis = "numbers") #graphic not showed

Trying to add markers 23, 27 and 29 again.

CHR3_add29_seq <- try_seq(CHR3_test_map, 29)
CHR3_add29 <- make_seq(CHR3_add29_seq, 12) # Marker 29 increase the map size disproportionately, it was removed from the map
CHR3_final <- CHR3_test_map
rf_graph_table(CHR3_final, inter = FALSE)

Checking for better orders:

ripple_seq(CHR3_final)
#> 27-16-20-4-|-21-...
#>   Alternative orders:
#>    27 16 20 4 21 ... :    0.00 ( linkage phases: 1 1 2 2 ... )
#>    16 27 20 4 21 ... :   -0.02 ( linkage phases: 1 1 2 2 ... )
#>
#> ...-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 ... :   -2.62 ( 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 ... :   -2.62 ( linkage phases: ... 2 2 1 1 1 ... )
#>
#> ...-4-|-21-23-48-9-|-45-...
#>   Alternative orders:
#>   ... 4 21 23 48 9 45 ... :    0.00 ( linkage phases: ... 2 1 1 1 1 ... )
#>   ... 4 23 21 48 9 45 ... :   -2.62 ( linkage phases: ... 2 1 1 1 1 ... )
#>
#> ...-21-|-23-48-9-45-|-46-...
#>   Alternative orders:
#>   ... 21 23 48 9 45 46 ... :    0.00 ( linkage phases: ... 1 1 1 1 1 ... )
#>   ... 21 23 48 45 9 46 ... :   -0.27 ( linkage phases: ... 1 1 1 1 1 ... )
#>   ... 21 23 45 48 9 46 ... :   -0.28 ( linkage phases: ... 1 1 1 1 1 ... )
#>   ... 21 23 45 9 48 46 ... :   -0.68 ( linkage phases: ... 1 1 1 1 1 ... )
#>   ... 21 48 23 45 9 46 ... :   -1.87 ( linkage phases: ... 1 1 1 1 1 ... )
#>
#> ...-23-|-48-9-45-46-|-47-...
#>   Alternative orders:
#>   ... 23 48 9 46 45 47 ... :   0.00 ( linkage phases: ... 1 1 1 1 1 ... )
#>   ... 23 48 46 9 45 47 ... :  -0.80 ( linkage phases: ... 1 1 1 1 1 ... )
#>   ... 23 48 9 45 46 47 ... :  -0.81 ( linkage phases: ... 1 1 1 1 1 ... )
#>   ... 23 48 45 9 46 47 ... :  -1.08 ( linkage phases: ... 1 1 1 1 1 ... )
#>   ... 23 45 48 9 46 47 ... :  -1.09 ( linkage phases: ... 1 1 1 1 1 ... )
#>   ... 23 45 46 9 48 47 ... :  -1.09 ( linkage phases: ... 1 1 1 1 1 ... )
#>   ... 23 45 9 48 46 47 ... :  -1.49 ( linkage phases: ... 1 1 1 1 1 ... )
#>   ... 23 45 9 46 48 47 ... :  -1.49 ( linkage phases: ... 1 1 1 1 1 ... )
#>
#> ...-48-|-9-45-46-47-|-50-...
#>   Alternative orders:
#>   ... 48 9 46 45 47 50 ... :    0.00 ( linkage phases: ... 1 1 1 1 2 ... )
#>   ... 48 9 46 47 45 50 ... :   -0.54 ( linkage phases: ... 1 1 1 1 2 ... )
#>   ... 48 46 9 45 47 50 ... :   -0.80 ( linkage phases: ... 1 1 1 1 2 ... )
#>   ... 48 9 45 46 47 50 ... :   -0.81 ( linkage phases: ... 1 1 1 1 2 ... )
#>   ... 48 45 9 46 47 50 ... :   -1.08 ( linkage phases: ... 1 1 1 1 2 ... )
#>   ... 48 47 46 9 45 50 ... :   -1.81 ( linkage phases: ... 1 1 1 1 2 ... )
#>   ... 48 9 45 47 46 50 ... :   -2.75 ( linkage phases: ... 1 1 1 1 2 ... )
#>
#> ...-9-|-45-46-47-50-|-24-...
#>   Alternative orders:
#>   ... 9 46 45 47 50 24 ... :    0.00 ( linkage phases: ... 1 1 1 2 1 ... )
#>   ... 9 46 47 45 50 24 ... :   -0.54 ( linkage phases: ... 1 1 1 2 1 ... )
#>   ... 9 45 46 47 50 24 ... :   -0.81 ( linkage phases: ... 1 1 1 2 1 ... )
#>   ... 9 45 47 46 50 24 ... :   -2.75 ( linkage phases: ... 1 1 1 2 1 ... )
#>
#> ...-45-|-46-47-50-24-|-49-...
#>   Alternative orders:
#>   ... 45 46 47 50 24 49 ... :    0.00 ( linkage phases: ... 1 1 2 1 1 ... )
#>   ... 45 47 46 50 24 49 ... :   -1.95 ( linkage phases: ... 1 1 2 1 1 ... )
#>
#> ...-46-|-47-50-24-49-|-52-... OK
#>
#> ...-47-|-50-24-49-52-|-51-...
#>   Alternative orders:
#>   ... 47 50 24 49 52 51 :    0.00 ( linkage phases: ... 2 1 1 1 1 )
#>   ... 47 52 49 24 50 51 :   -0.50 ( linkage phases: ... 2 1 1 1 1 )
#>   ... 47 50 24 52 49 51 :   -2.76 ( linkage phases: ... 2 1 1 1 1 )
#>   ... 47 49 52 24 50 51 :   -2.78 ( 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

map1 <- list(LG1_final, LG2_final, LG3_final)
draw_map(map1, names = TRUE, grid = TRUE, cex.mrk = 0.7)

Drawing map builded with reference genome and recombinations informations

map2 <- list(CHR1_final, CHR2_final, CHR3_final)
draw_map(map2, names = TRUE, grid = TRUE, cex.mrk = 0.7)

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

CHR1_comp <- list(LG1_final, CHR1_final)
draw_map(CHR1_comp, names = TRUE, grid = TRUE, cex.mrk = 0.7)

Markers M1 and SNP2 are in different position between the strategies results for CHR1.

CHR2_comp <- list(LG3_final, CHR2_final)
draw_map(CHR2_comp, names = TRUE, grid = TRUE, cex.mrk = 0.7)

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

CHR3_comp <- list(LG2_final, CHR3_final)
draw_map(CHR3_comp, names = TRUE, grid = TRUE, cex.mrk = 0.7)

There are a invertion between markers SNP17 and SNP18 and the marker M29 was removed in te second strategy.

Or groups alone:

draw_map(CHR1_final, names = TRUE, grid = TRUE, cex.mrk = 0.7)

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

draw_map2(LG1_final, LG2_final, LG3_final, main = "Only with linkage information",
group.names = c("LG1", "LG2", "LG3"))

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

Drawing map builded with reference genome and recombinations informations

draw_map2(CHR1_final, CHR2_final, CHR3_final, output= "map_ref.pdf",
col.group = "#58A4B0",
col.mark= "#335C81")

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, respctivelly.

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

draw_map2(LG1_final, CHR1_final, output = "map_comp.pdf", tag = c("M1","SNP2"))

Markers M1 and SNP2 are in different position between the strategies results for CHR1. When defining marker names in tag argument, all markers with these name will be highlighted no matter in which group it/they is/are.

draw_map2(LG2_final, CHR3_final, tag= c("SNP17", "SNP18", "M29"), main = "Chromosome 3",
group.names = c("Only linkage", "With genome"), centered = TRUE, output = "map_comp2.pdf")

There are a invertion between markers SNP17 and SNP18 and the marker M29 was removed in te second strategy.

# 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

any_seq <- make_seq(twopts, c(30, 12, 3, 14, 2))
(any_seq_map <- map(any_seq))
#>
#> 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

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.

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

any_seq <- make_seq(twopts, c(30, 12, 3, 14, 2), phase = c(4, 1, 4, 3))
(any_seq_map <- map(any_seq))

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.

(any_seq <- add_marker(any_seq, 4:8))
#>
#> 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:

(any_seq <- drop_marker(any_seq, c(3, 4, 5, 12, 30)))
#>
#> 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.

# Session Info

sessionInfo()
#> R version 3.6.1 (2019-07-05)
#> Platform: x86_64-pc-linux-gnu (64-bit)
#> Running under: Ubuntu 18.04.3 LTS
#>
#> Matrix products: default
#> BLAS:   /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.7.1
#> LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.7.1
#>
#> locale:
#>  [1] LC_CTYPE=pt_BR.UTF-8       LC_NUMERIC=C
#>  [3] LC_TIME=pt_BR.UTF-8        LC_COLLATE=C
#>  [5] LC_MONETARY=pt_BR.UTF-8    LC_MESSAGES=en_US.UTF-8
#>  [7] LC_PAPER=pt_BR.UTF-8       LC_NAME=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:
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#>
#> loaded via a namespace (and not attached):
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#>  [13] polynom_1.4-0           jsonlite_1.6.1          nloptr_1.2.1
#>  [16] MDSMap_1.1              broom_0.5.3             cluster_2.1.0
#>  [19] shiny_1.4.0             compiler_3.6.1          backports_1.1.5
#>  [22] assertthat_0.2.1        Matrix_1.2-17           fastmap_1.0.1
#>  [25] lazyeval_0.2.2          later_1.0.0             acepack_1.4.1
#>  [28] htmltools_0.4.0         tools_3.6.1             gtable_0.3.0
#>  [31] glue_1.3.1              reshape2_1.4.3          dplyr_0.8.3
#>  [34] Rcpp_1.0.3              carData_3.0-3           cellranger_1.1.0
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#>  [40] iterators_1.0.12        crosstalk_1.0.0         xfun_0.11
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#>  [46] mime_0.9                miniUI_0.1.1.1          lifecycle_0.1.0
#>  [49] weights_1.0             gtools_3.8.1            princurve_2.1.4
#>  [52] pan_1.6                 candisc_0.8-0           MASS_7.3-51.4
#>  [55] scales_1.1.0            heplots_1.3-5           hms_0.5.2
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#>  [70] foreach_1.4.7           plotrix_3.7-7           checkmate_1.9.4
#>  [73] boot_1.3-23             zip_2.0.4               manipulateWidget_0.10.0
#>  [76] rlang_0.4.4             pkgconfig_2.0.3         rgl_0.100.30
#>  [79] evaluate_0.14           lattice_0.20-38         purrr_0.3.3
#>  [82] htmlwidgets_1.5.1       labeling_0.3            tidyselect_0.2.5
#>  [85] plyr_1.8.5              magrittr_1.5            R6_2.4.1
#>  [88] generics_0.0.2          nnls_1.4                Hmisc_4.3-0
#>  [91] mitml_0.3-7             pillar_1.4.3            haven_2.2.0
#>  [94] foreign_0.8-72          survival_2.44-1.1       abind_1.4-5
#>  [97] nnet_7.3-12             tibble_2.1.3            crayon_1.3.4
#> [100] car_3.0-5               jomo_2.6-10             wordcloud_2.6
#> [106] data.table_1.12.8       forcats_0.4.0           digest_0.6.23
#> [109] webshot_0.5.2           xtable_1.8-4            tidyr_1.0.0
#> [112] httpuv_1.5.2            munsell_0.5.0

# 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.

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.

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.