Outcrossing Populations
The following example is intended to show the usage of OneMap functions for linkage mapping in outcrossing (non-inbred) populations. With basic knowledge of R syntax, one should have no problems using it. If you are not familiar with R, we recommend reading the vignette Introduction to R.
Hopefully, these examples will be clear enough to help any user to understand its functionality and start using it. You do not need to be an expert in R to build your linkage map, but some concepts are necessary and will help you through the process.
There is a GitHub OneMap version which is continuously improved, we strongly recommend all users to try this version. On 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.
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 the 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. 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 with the help of function read_onemap.
Here is an example of such a file for 10 individuals and 5 markers (the three zeros in the second line indicate that there is no chromosome information, physical position information, or phenotypic data, respectively). It is very similar to a MAPMAKER/EXP file, but has additional information about the cross-type.
data type outcross
10 5 0 0 0
I1 I2 I3 I4 I5 I6 I7 I8 I9 I10
*M1 B3.7 ab ab - ab b ab ab - ab b
*M2 D2.18 o - a a - o a - o o
*M3 D1.13 o a a o o - a o a o
*M4 A.4 ab b - ab a b ab b - a
*M5 D2.18 a a o - o o a o o oNotice that once the marker type is identified, no variations of symbols presented on the table for the observed bands are 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")In the session Importing data from VCF file below, you will see how to import VCF files as OneMap objects.
Importing data
Once the input file is created, the data can be loaded and saved into an R onemap object. The function used to import data is named read_onemap. Its usage is quite simple:
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:
## Working...
##
## --Read the following data:
## Type of cross: outcross
## Number of individuals: 100
## Number of markers: 30
## Chromosome information: no
## Position information: no
## Number of traits: 3
## Missing trait values:
## Pheno1: 0
## Pheno2: 3
## Pheno3: 0Because this particular dataset is distributed along with the package, as an alternative you can load it by 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_outyou 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: 0Also, 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 separated by their type. In this case, you can note that the graphic cell size will adapt to the number of markers of the same type. In other words, the higher is the number of markers with the same type, the lower is the cell for this type.
plot(onemap_example_out, all = FALSE)
This function can take quite some time, depending on the number of markers involved. More information about this plot function can be found using ?plot.onemap.
Also, you can see the number of markers by segregation pattern with the plot_by_segreg_type function:
Importing data from VCF file
You can import information from VCF to OneMap using onemap_read_vcfR function.
With the onemap_read_vcfR you can convert the object from vcfR package directly to onemap. The onemap_read_vcfR function keeps chromosome and position information for each marker in the onemap object generated.
We will use the example file vcf_example_out.vcf.gz to show how it works, which contains markers from the same population of onemap_example_out.raw.
Here we use the the vcfR package internally to help this conversion. The vcfR authors mentioned in their tutorials that RAM memory use is an important consideration when using the package. Depending of your dataset, the object created can be huge and occupy a lot of memory.
You can use onemap_read_vcfR function to convert the VCF file to onemap object. The parameters used are the vcf with the VCF file path, 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(vcf = system.file("extdata/vcf_example_out.vcf.gz", package = "onemap"),
parent1 = "P1",
parent2 = "P2",
cross = "outcross")Depending on your dataset, this function can take some time to run.
Note that the conversion filter out markers which are not informative for the informed cross type. For example, in outcrossing species, markers that have both parents homozygous (aa x bb) do not inform recombinations and are removed of the data set. Only markers types contained the table at Creating the data file are kept in the onemap object. Function onemap_read_vcfR print at the screen the reason why markers were filtered.
You can also have more missing data in the returned object compared with the VCF because the onemap_read_vcfR replace by missing data the genotypes that are not expected for that marker type. For example, for a marker type D1.10 (ab x aa), we only expect aa and ab genotypes, if there are bb genotypes they will be replaced by missing data. You can see the percentage of missing data at the resulted onemap object with:
vcf_example_out## This is an object of class 'onemap'
## Type of cross: outcross
## No. individuals: 92
## No. markers: 24
## CHROM information: yes
## POS information: yes
## Percent genotyped: 99
##
## Segregation types:
## B3.7 --> 18
## D1.10 --> 6
##
## No. traits: 0NOTE:From version 2.0.6 to 2.1.1005, OneMap had the vcf2raw function to convert vcf to .raw. Now, this function is defunct, but it can be replaced by a combination of onemap_read_vcfR and write_onemap_raw functions. See Exporting .raw file from onemap object session to further information about write_onemap_raw.
Filter onemap object by missing data
If your onemap object has too many missing genotypes you can face problems during the analysis. Check the percentage of missing genotypes in our data set printing the onemap object:
vcf_example_out## This is an object of class 'onemap'
## Type of cross: outcross
## No. individuals: 92
## No. markers: 24
## CHROM information: yes
## POS information: yes
## Percent genotyped: 99
##
## Segregation types:
## B3.7 --> 18
## D1.10 --> 6
##
## No. traits: 0Our example has 1% of missing genotypes (99% are genotyped). If you want to filter markers according to their percentage of missing data, you can use the function filter_missing:
vcf_filtered <- filter_missing(vcf_example_out, threshold = 0.25)## Number of markers removed from the onemap object: 0Any of our markers were filtered, because, in this example, we do not have much missing data.
Graphical view of genotypes and allele depths (new!)
Function create_depth_profile generates dispersion graphics with x and y-axis representing, respectively, the reference and alternative allele depths. The function is only available for biallelic markers in VCF files with allele counts information. Each dot represents a genotype for mks markers and inds individuals. If both arguments receive NULL, all markers and individuals are considered. Dots are colored according to the genotypes present in the onemap object (GTfrom = onemap) or VCF file (GTfrom = vcf). A rds file is generated with the data in the graphic (rds.file). The alpha argument controls the transparency of the color of each dot. Control this parameter is a good idea when having a large number of markers and individuals. The x_lim and y_lim control the axis scale limits; by default, it uses the maximum value of the counts.
Here is an example for the vcf_example_out dataset.
# For outcrossing population
create_depths_profile(onemap.obj = vcf_example_out,
vcf = system.file("extdata/vcf_example_out.vcf.gz", package = "onemap"),
parent1 = "P1",
parent2 = "P2",
vcf.par = "AD",
recovering = FALSE,
mks = NULL,
inds = NULL,
GTfrom = "vcf",
alpha = 0.1,
rds.file = "depths_out.rds")Because the genotypes are from VCF file, the legend points the VCF codification? ./. represent missing data; 0/0 homozygotes for reference alleles; 0/1 heterozygotes; 1/1 homozygotes for alternative alleles. You can also have phased genotypes represented which have pipe | instead of bar /.
Combining OneMap datasets
If you have more than one dataset of markers, all from the same mapping population, you can use the function combine_onemap to merge them into only one onemap object.
In our example, we have two datasets:
- first:
onemap_example_outwith 30 markers and 100 individuals - second:
vcf_example_outwith 24 biallelic markers and 92 individuals.
The combine_function recognizes the correspondent individuals by the ID, thus, it is important to define the same IDs to respective individuals in both raw files. Compared with the first file, the second file does not have markers information for 8 individuals. The combine_onemap will complete this information with NA.
In our examples, we have only genotypic information, but the function can also merge the phenotypic 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: 0The 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, especially when dealing with too many markers. Redundant markers have the same genotypic information that other markers because they didn’t happen recombination events between each other. They will not increase information on the map but will increase computational effort during the map building. Therefore, it is a good practice to remove them to build the map and, once the map is already built, they can be added again.
First, we use the function find_bins to group the markers into bins according to their genotypic information. In other words, markers with the same genotypic information will be in 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 exactThe first argument is the onemap object and the exact argument specifies if only markers with the same information 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 has only two redundant markers. 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 the 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: 96
##
## Segregation types:
## A.1 --> 3
## A.2 --> 1
## A.4 --> 4
## B1.5 --> 1
## B2.6 --> 2
## B3.7 --> 22
## C.8 --> 2
## D1.10 --> 7
## D1.12 --> 1
## D1.13 --> 2
## D2.15 --> 1
## D2.16 --> 2
## D2.17 --> 2
## D2.18 --> 2
##
## No. traits: 3
## Missing trait values:
## Pheno1: 0
## Pheno2: 3
## Pheno3: 0The arguments for the create_data_bins function are the onemap object and the object created by the 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 manipulate the information of the original .raw file and creates a new dataset. In both cases, you do not have an input file .raw that contains the same information as the analyzed data. If you want to create a new input file with the dataset you are working on after using these functions, you can use the function write_onemap_raw.
write_onemap_raw(bins_example, file.name = "new_dataset.raw")The file new_dataset.raw will be generated in your working directory. In our example, it contains only non-redundant markers from onemap_example_out and vcf_example_out datasets.
Testing segregation pattern
For the map building process, it is also important to know which markers have deviations in the expected segregation pattern. It can be a good practice to remove them from the map building process, because they can adversely affect the map building, and, once the map is built, they can be inserted.
The function test_segregation_of_a_marker performs a chi-square test according to 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] 100The 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 by 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 1.76 0.4147829 100
## 2 M2 1:1 0.04 0.8414806 100
## 3 M3 1:1 0.36 0.5485062 100
## 4 M4 1:1:1:1 2.64 0.4505201 100
## 5 M5 1:1 1.96 0.1615133 100
## 6 M6 1:2:1 1.52 0.4676664 100
## 7 M7 1:1 0.16 0.6891565 100
## 8 M8 1:2:1 0.86 0.6505091 100
## 9 M9 1:1 0.04 0.8414806 100
## 10 M10 1:1 0.36 0.5485062 100
## 11 M11 1:1 0.16 0.6891565 100
## 12 M12 1:1:1:1 6.48 0.0904546 100
## 13 M13 3:1 0.00 1.0000000 100
## 14 M14 1:1:1:1 0.40 0.9402425 100
## 15 M15 1:1:1:1 2.24 0.5241127 100
## [ reached 'max' / getOption("max.print") -- omitted 37 rows ]The only argument of the function is a onemap object.
Once we have the onemap_segreg_testobject, the function select_segreg can be used to show only the markers considered with/without segregation distortion. By default, it uses as a threshold for the test a global \(\alpha=0.05\), corrected for multiple tests with Bonferroni correction.
select_segreg(segreg_test, distorted = TRUE) #to show the markers names with segregation distortion
select_segreg(segreg_test, distorted = FALSE) #to show the markers names without segregation distortionIt is not recommended, but you can define a different threshold value by changing the threshold argument of the function select_segreg.
For the next steps, it will be useful to know the numbers of each marker 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 these 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 25no_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 52You 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 information.
Using the recombinations and also the reference genome information, once our example has
CHROMandPOSinformation for some of the markers.
First, we will apply the strategy using only recombinations information. In the second part of this tutorial, we show a way to use also reference genome information. At the end of our analysis, we will be able to compare these two strategies by drawing the resulted genetic maps.
Using only recombinations information
Estimating two-point recombination fractions
The first step is estimating the recombination fraction between all pairs of markers, using two-point tests.
twopts <- rf_2pts(bins_example)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 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
twoptswill show a message with the criteria used in the analysis and some other information:
## This is an object of class 'rf_2pts'
##
## Criteria: LOD = 3 , Maximum recombination fraction = 0.5
##
## This object is too complex to print
## Type 'print(object, c(mrk1=marker, mrk2=marker))' to see
## the analysis for two markers
## mrk1 and mrk2 can be the names or numbers of both markersIf 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 , 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 1.646878Each line corresponds to a possible linkage phase. CC denotes the 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 the 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 with 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 Marker.name Type
## 1 1 M1 B3.7
## 2 2 M2 D2.18
## 3 3 M3 D1.13
## 4 4 M4 A.4
## 5 5 M5 D2.18
## 6 6 M6 B3.7
## 7 7 M7 D2.15
## 8 8 M8 B3.7
## 9 9 M9 D1.10
## 10 10 M10 D2.17
## 11 11 M11 D2.16
## 12 12 M12 A.2
## 13 13 M13 C.8
## 14 14 M14 A.4
## 15 15 M15 A.4
## 16 16 M16 D2.17
## 17 18 M18 A.1
## 18 20 M20 A.1
## 19 21 M21 D2.16
## 20 22 M22 D1.10
## 21 23 M23 C.8
## 22 24 M24 B3.7
## 23 26 M26 A.1
## 24 27 M27 D1.12
## 25 28 M28 A.4
## [ reached 'max' / getOption("max.print") -- omitted 24 rows ]OneMap has two different functions for grouping markers. The group function:
LGs <- group(mark_no_dist)For this function, optional arguments are LOD and max.rf, which define thresholds to be used when assigning markers to linkage groups. If none is provided (default), it uses as default values of LOD Score 3 and maximum recombination fraction 0.50.
Also, you can use the function suggest_lod to calculate a suggested LOD score considering that multiple tests are being performed.
LOD_sug <- suggest_lod(mark_no_dist)
LOD_sug## [1] 3.639312And apply this suggested value to the two-point tests:
LGs <- group(mark_no_dist, LOD=LOD_sug)## Selecting markers:
## group 1
## ........................
## group 2
## ................
## group 3
## ......The previous command generates an object of class group and the command print for such object has two options. If you type:
LGsyou will get detailed information about the groups, that is, all linkage groups will be printed, displaying the names of markers in each one of them.
## This is an object of class 'group'
## It was generated from the object "mark_no_dist"
##
## Criteria used to assign markers to groups:
## LOD = 3.639312 , Maximum recombination fraction = 0.5
##
## No. markers: 49
## No. groups: 3
## No. linked markers: 49
## No. unlinked markers: 0
##
## Printing groups:
## Group 1 : 25 markers
## M1 M2 M3 M5 M6 M10 M11 M12 M14 M15 M26 M28 M30 SNP1 SNP2 SNP3 SNP5 SNP6 SNP7 SNP8 SNP9 SNP10 SNP11 SNP12 SNP13
##
## Group 2 : 17 markers
## M4 M9 M16 M20 M21 M23 M24 M27 M29 SNP17 SNP18 SNP20 SNP21 SNP22 SNP23 SNP24 SNP25
##
## Group 3 : 7 markers
## M7 M8 M13 M18 M22 SNP14 SNP16However, 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 = 3.639312 , Maximum recombination fraction = 0.5
##
## No. markers: 49
## No. groups: 3
## No. linked markers: 49
## No. unlinked markers: 0You 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)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)(new!)
The other function for grouping is called group_upgma. It is an adapted version of MAPpoly grouping function.
LGs_upgma <- group_upgma(mark_no_dist, expected.groups = 5, inter = F)
plot(LGs_upgma)
You can define the expected number of groups in the expected.groups argument and check how the markers are split in the plotted dendrogram. Using argument inter=TRUE you can change interactively the number of groups defined by the red squares in the graphic.
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, type:
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 other words, a linkage group must be extracted from the object of class group or group.upgma, in order to be mapped. For simplicity, we will start here with the smallest one, which is linkage group 3 (considering the group function). This can be easily done using the following code:
LG3 <- make_seq(LGs, 3)
# or
# LG3 <- make_seq(LGs_upgma,3)The first argument (LGs) is an object of class group or group.upgma 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
LG3you 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, hmm = FALSE))
(LG3_rcd <- rcd(LG3, hmm = FALSE))
(LG3_rec <- record(LG3, hmm = FALSE))
(LG3_ug <- ug(LG3, hmm = FALSE))NOTE: Results are not plotted in this vignette, please check the vignette in GitHub version.
Argument hmm defines if the function should run the HMM chain multipoint approach to estimate the genetic distances given the marker order provided by the two-points ordering algorithm. We set here the argument hmm=FALSE because we just want to obtain the marker order. We are not yet estimating the genetic distances. We suggest to use hmm=TRUE only when you already decided which order is the best because the HMM chain is the most computationally intensive step in the map building. You can use rf_graph_table to check the ordering quality (see details below) and make editions in the marker order using drop_marker. After, you can use map or map_avoid_unlinked functions to estimate the genetic distances (check session #Map-estimation-for-an-arbitrary-order).
Here we can check, there are some differences between each ordering algorithm results (results not shown).
Alternatively, you can also use the mds_onemap function to obtain a first draft for the order of the markers. The mds_onemap is a wrapper function that makes an 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 information 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.
LG3_mds <- mds_onemap(LG3, hmm = FALSE)If you only specify the input sequence, mds_onemap will use the default parameters. It will also generate an MDSMap input file in the out.file file. You can use out.file in the MDSMap package to try other parameters too. The default method used is the principal curves, know more about using ?mds_onemap and reading the MDSMap vignette.
Besides these algorithms use a two-point approach to order the markers, if you set hmm=TRUE a multipoint approach is applied to estimate the genetic distances after the order is estimated. Thus, it can happen that some markers are not considered linked when evaluated by multipoint information, and the function will return an error like this:
ERROR: The linkage between markers 1 and 2 did not reach the OneMap default criteria. They are probably segregating independentlyYou can automatically remove these markers setting argument rm_unlinked = TRUE. The marker will be removed, and the ordering algorithms will be restarted. Warning messages will inform which markers were removed. If you don’t get warning messages, it means that any marker needed to be removed. This is our case in this example, but if you obtain an error or warning running your dataset, you already know what happened.
NOTE: (new!) If your sequence has many markers (more than 60), we suggest to first use hmm=FALSE to check the ordering and after speed up mds, seriation, rcd, record and ug using BatchMap parallelization approach. See section Speed up analysis with parallelization for more information.
To order by comparing all possible orders (exhaustive search), the function compare can be used:
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 on a personal computer, without high capacity, we recommend using a maximum of ten markers.
If you have more markers in your group, we suggest using the following explained approaches order_seq.
In the example, LG3 contains only seven markers. Two of them are of type D1, and one is 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 45 unique orders LOD Nested LOD
## --------------------------------------------------------------
## order 1: 43 22 7 18 8 13 44
## CC CC CC RR RR RR 0.00 0.00
## CC CC RC RR RR RR -1.48 -1.48
## --------------------------------------------------------------
## order 2: 43 7 22 18 8 13 44
## CC CC CC RR RR RR -0.05 0.00
## --------------------------------------------------------------
## order 3: 22 43 7 18 8 13 44
## CC CC CC RR RR RR -0.15 0.00
## CC CC RC RR RR RR -1.48 -1.33
## --------------------------------------------------------------
## order 4: 22 7 43 18 8 13 44
## CC CC CC RR RR RR -0.22 0.00
## --------------------------------------------------------------
## order 5: 7 43 22 18 8 13 44
## CC CC CC RR RR RR -0.25 0.00
## CC CC CR RR RR RR -2.26 -2.01
## --------------------------------------------------------------
## order 6: 7 22 43 18 8 13 44
## CC CC CC RR RR RR -0.42 0.00
## --------------------------------------------------------------
## order 7: 7 18 8 13 44 22 43
## CC RR RR RR RC CC -0.54 0.00
## --------------------------------------------------------------
## order 8: 7 44 13 8 18 22 43
## CR RR RR RR CC CC -0.65 0.00
## --------------------------------------------------------------
## order 9: 7 44 13 8 18 43 22
## CR RR RR RR CC CC -0.80 0.00
## --------------------------------------------------------------
## order 10: 7 18 8 13 44 43 22
## CC RR RR RR RC CC -0.87 0.00
## --------------------------------------------------------------
## order 11: 43 22 7 13 18 8 44
## CC CC CC CC RR CC -0.99 0.00
## --------------------------------------------------------------
## order 12: 43 7 22 13 18 8 44
## CC CC CC CC RR CC -1.03 0.00
## --------------------------------------------------------------
## order 13: 43 22 7 13 44 8 18
## CC CC CC RR CC RR -1.06 0.00
## --------------------------------------------------------------
## order 14: 43 7 22 13 44 8 18
## CC CC CC RR CC RR -1.12 0.00
## --------------------------------------------------------------
## order 15: 43 22 7 44 13 8 18
## CC CC RR RR RR RR -1.13 0.00
## CC CC CR RR RR RR -2.13 -1.00
## --------------------------------------------------------------
## order 16: 43 7 22 44 13 8 18
## CC CC RR RR RR RR -1.19 0.00
## --------------------------------------------------------------
## order 17: 43 22 7 18 13 8 44
## CC CC CC CC RR CC -1.25 0.00
## --------------------------------------------------------------
## order 18: 7 43 22 13 18 8 44
## CC CC CC CC RR CC -1.26 0.00
## --------------------------------------------------------------
## order 19: 43 7 22 18 13 8 44
## CC CC CC CC RR CC -1.30 0.00
## --------------------------------------------------------------
## order 20: 7 43 22 44 13 8 18
## CC CC RR RR RR RR -1.35 0.00
## --------------------------------------------------------------
## order 21: 22 43 7 18 13 8 44
## CC CC CC CC RR CC -1.40 0.00
## --------------------------------------------------------------
## order 22: 7 43 22 13 44 8 18
## CC CC CC RR CC RR -1.41 0.00
## --------------------------------------------------------------
## order 23: 22 7 43 18 13 8 44
## CC CC CC CC RR CC -1.47 0.00
## --------------------------------------------------------------
## order 24: 7 43 22 18 13 8 44
## CC CC CC CC RR CC -1.50 0.00
## --------------------------------------------------------------
## order 25: 22 43 7 44 13 8 18
## CC CC RR RR RR RR -1.54 0.00
## CC CC CR RR RR RR -2.13 -0.60
## --------------------------------------------------------------
## order 26: 22 7 43 44 13 8 18
## CC CC RR RR RR RR -1.66 0.00
## --------------------------------------------------------------
## order 27: 7 22 43 18 13 8 44
## CC CC CC CC RR CC -1.67 0.00
## --------------------------------------------------------------
## order 28: 7 13 44 8 18 22 43
## CC RR CC RR CC CC -1.73 0.00
## --------------------------------------------------------------
## order 29: 7 18 13 8 44 22 43
## CC CC RR CC RC CC -1.76 0.00
## --------------------------------------------------------------
## order 30: 22 43 7 13 18 8 44
## CC CC CC CC RR CC -1.77 0.00
## --------------------------------------------------------------
## order 31: 22 43 7 13 44 8 18
## CC CC CC RR CC RR -1.82 0.00
## --------------------------------------------------------------
## order 32: 7 22 43 44 13 8 18
## CC CC RR RR RR RR -1.84 0.00
## --------------------------------------------------------------
## order 33: 7 44 8 13 18 22 43
## CR CC RR CC CC CC -1.87 0.00
## --------------------------------------------------------------
## order 34: 7 13 44 8 18 43 22
## CC RR CC RR CC CC -1.88 0.00
## --------------------------------------------------------------
## order 35: 22 7 43 13 18 8 44
## CC CC CC CC RR CC -1.90 0.00
## --------------------------------------------------------------
## order 36: 22 7 43 13 44 8 18
## CC CC CC RR CC RR -1.98 0.00
## --------------------------------------------------------------
## order 37: 7 18 8 44 13 22 43
## CC RR CC RR CC CC -2.00 0.00
## --------------------------------------------------------------
## order 38: 7 44 8 13 18 43 22
## CR CC RR CC CC CC -2.02 0.00
## --------------------------------------------------------------
## order 39: 7 18 13 8 44 43 22
## CC CC RR CC RC CC -2.11 0.00
## --------------------------------------------------------------
## order 40: 7 22 43 13 18 8 44
## CC CC CC CC RR CC -2.20 0.00
## --------------------------------------------------------------
## order 41: 7 13 18 8 44 22 43
## CC CC RR CC RC CC -2.21 0.00
## --------------------------------------------------------------
## order 42: 7 22 43 13 44 8 18
## CC CC CC RR CC RR -2.29 0.00
## --------------------------------------------------------------
## order 43: 7 44 8 18 13 22 43
## CR CC RR CC CC CC -2.32 0.00
## --------------------------------------------------------------
## order 44: 43 22 7 44 8 13 18
## CC CC RR CC RR CC -2.32 0.00
## --------------------------------------------------------------
## order 45: 43 7 22 44 8 13 18
## CC CC RR CC RR CC -2.37 0.00
## --------------------------------------------------------------Remember that for outcrossing populations, one needs to estimate marker order and also linkage phases between markers for a given order. However, because two-point analysis provides information about linkage phases, this information is taken into consideration in the compare function, reducing the number of combinations to be evaluated. If a given linkage phase has LOD greater than 0.005 in the two-point analysis, we assume that this phase is very unlikely and so does not need to be evaluated in the multipoint procedure used by compare. We did extensive simulations, which showed that this is a good procedure.
By default, OneMap stores 50 orders, which may or may not be unique. The value of LOD refers to the overall LOD Score, considering all orders tested. Nested LOD refers to LOD Scores within a given order, that is, scores for different combinations of linkage phases for the same marker order.
For example, order 1 has the largest value of log-likelihood and, therefore, its LOD Score is zero for a given combination of linkage phases (CC, CC, RR, RR). For this same order and other linkage phases, LOD Score is -5.20. Analyzing the results for order 2, notice that its highest LOD Score is very close to zero, indicating that this order is also quite plausible. Notice also that Nested LOD will always contain at least one zero value, corresponding to the best combination of phases for markers in a given order. Due to the information provided by a 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 the 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 the 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 13.51 a | | b a | | a
## 7 M7 24.56 a | | a a | | b
## 18 M18 65.59 a | | b c | | d
## 8 M8 71.28 b | | a b | | a
## 13 M13 73.94 a | | o a | | o
## 44 SNP16 79.82 b | | a b | | a
##
## 7 markers log-likelihood: -398.6863At 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. The 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 function plots the recombination fractions between the markers pointed in the axes. You can change the number of colors from the rainbow palette with the argument n.colors. Hot colors (more close to red) represent lower values of recombination fractions, as shown in the scale at the 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 an output HTML file name in html.file. This HTML contains an iterative plot graphic. If you hover the mouse cursor over the cells it shows some extra information about cells, as a percentage of missing data, marker name, and type. The output HTML file is generated in your work directory and opens automatically in your internet browser.
rf_graph_table(LG3_final, inter = TRUE, mrk.axis= "names", html.file = "LG3.html")For example, passing on the cell corresponding to markers 8 and 13, you can see their names (M8 and M13 ), types (B3.7 and C.8), recombination fraction (rf = 0.03) and LOD Scores for each possible linkage phase. This is quite useful in helping to interpret the results.
If you want to see corresponding marker numbers (not the names) in the axis, just change the argument mrk.axis to numbers. It can make the next steps easier.
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.
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 shows linkage with M8, which points that probably it is only a gap. Adding more markers to these 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, hmm = F)
LG2_rcd##
## Number of markers: 17
## Markers in the sequence:
## M27 SNP20 M16 M20 M4 M21 M23 SNP17 SNP18 M9 SNP21 SNP24 SNP23 M24 SNP22 SNP25
## M29
##
## Parameters not estimated.rf_graph_table(LG2_rcd)
Use the marker_type function to check the segregation types of all markers in this group:
marker_type(LG2)## Marker Marker.name Type
## 1 4 M4 A.4
## 2 9 M9 D1.10
## 3 16 M16 D2.17
## 4 20 M20 A.1
## 5 21 M21 D2.16
## 6 23 M23 C.8
## 7 24 M24 B3.7
## 8 27 M27 D1.12
## 9 29 M29 D1.13
## 10 45 SNP17 D1.10
## 11 46 SNP18 D1.10
## 12 47 SNP20 D1.10
## 13 48 SNP21 D1.10
## 14 49 SNP22 B3.7
## 15 50 SNP23 B3.7
## 16 51 SNP24 B3.7
## 17 52 SNP25 B3.7Based 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, 52))Here there is a automatic way of obtain a new sequence only with markers selected by type: (new!)
LG2_init <- seq_by_type(sequence = LG2, mk_type = c("A", "B"))
marker_type(LG2_init)
# If I want to reduce even more the number of markers
# I can use drop_marker function
LG2_init <- drop_marker(LG2_init, 52)
marker_type(LG2_init)NOTE: Some results in this session are not shown in this vignette, please check the vignette in GitHub version.
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 other linkage groups, or they are distant in the same group. Adding more markers will give more information to solve this issue.
Next, let us try to map the remaining markers, one at a time. First, we will try to add the remaining most informative markers. Starting with SNP25:
LG2_extend <- try_seq(LG2_frame, 52)LG2_extendBased on the LOD Scores, marker SNP25 is probably better located after SNP22 (number 49). Detailed results can be seen with:
print(LG2_extend, 7)The second argument indicates the position where to place the marker. Note that the first allele arrangement is the most likely one.
It should be pointed out that the framework created by the function compare (with M20, M4, SNP24, SNP23, M24 and SNP22, or numbers 20, 4, 51,50, 24 and 49) could be in reverse order (SNP22, M24, SNP23, SNP24, M4 and M20, or numbers 49, 24, 50, 51, 4, 20) and still represent the same map. Thus, the positioning of markers with the try_seq command can be different on your computer. For example, here marker SNP25 (number 52) was better placed at position 7; however, if you obtain a reversed order, marker SNP25 would be better placed in position 1. In both cases, the best position for this marker is after SNP22.
We can better evaluate the order with rf_graph_table. It requires an object of the sequence class with mapping information.
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. We will maintain this marker at this position:
LG2_frame <- LG2_testAdding 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)The process of adding markers can be automated with the use of function order_seq.
LG2_ord <- order_seq(LG2, n.init = 5, THRES = 3)##
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|======================================================================| 100%This function automates what the try_seq function does, using some predefined rules. In the function, n.init = 5 means that five markers (the most informative ones) will be used in the compare step; THRES = 3 indicates that the try_seq step will only add markers to the sequence which can be mapped with LOD Score greater than 3.
NOTE: Although very useful, this function can be misleading, especially 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
## 16 M16 11.76 a | | a b | | o
## 20 M20 22.94 a | | b c | | d
## 4 M4 35.71 a | | o o | | b
## 23 M23 53.69 a | | o a | | o
## 45 SNP17 72.86 a | | b a | | a
## 50 SNP23 103.35 a | | b b | | a
## 24 M24 108.37 a | | b b | | a
## 49 SNP22 112.25 a | | b b | | a
##
## 9 markers log-likelihood: -551.4083
##
##
##
## The following markers could not be uniquely positioned.
## Printing most likely positions for each unpositioned marker:
##
## ------------------------------------------------------
## | | 9 | 21 | 29 | 46 | 47 | 48 | 51 | 52 |
## |----|-----|-----|-----|-----|-----|-----|-----|-----|
## | | | | | | | | | |
## | 27 | | | | | | | | |
## | | | | | | | | | |
## | 16 | | | | | | | | |
## | | | | | | | | | |
## | 20 | | | | | | | | |
## | | | | | | | | | |
## | 4 | | | | | | | | |
## | | | *** | | | | | | |
## | 23 | | | | | | | | |
## | | *** | * | | * | | *** | | |
## | 45 | | | | | | | | |
## | | * | | ** | *** | *** | | *** | |
## | 50 | | | | | | | | |
## | | | | | | | | | |
## | 24 | | | | | | | | |
## | | | | | | | | | |
## | 49 | | | | | | | | |
## | | | | *** | | | | ** | *** |
## ------------------------------------------------------
##
## '***' indicates the most likely position(s) (LOD = 0.0)
##
## '**' indicates very likely positions (LOD > -1.0)
##
## '*' indicates likely positions (LOD > -2.0)Note that markers 9, 21, 29, 46, 47, 48, 51 and 52 could not be safely mapped to a single position (LOD Score > THRES in absolute value). The output displays the safe order and the most likely positions for markers not mapped, where *** indicates the most likely position and * corresponds to other plausible positions.
To get the safe order (i.e., without markers 9, 21, 29, 46, 47, 48, 51 and 52), use
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 11.76 a | | a b | | o
## 20 M20 22.94 a | | b c | | d
## 4 M4 35.71 a | | o o | | b
## 21 M21 49.40 o | | o a | | b
## 23 M23 55.18 a | | o a | | o
## 48 SNP21 67.73 a | | b a | | a
## 9 M9 74.32 a | | b a | | a
## 46 SNP18 80.85 a | | b a | | a
## 45 SNP17 96.14 a | | b a | | a
## 47 SNP20 121.33 a | | b a | | a
## 29 M29 170.70 o | | a o | | o
## 50 SNP23 192.38 a | | b b | | a
## 24 M24 197.52 a | | b b | | a
## 49 SNP22 200.80 a | | b b | | a
## 52 SNP25 205.70 a | | b b | | a
## 51 SNP24 216.64 a | | b b | | a
##
## 17 markers log-likelihood: -871.9124Notice that, for this linkage group, the forced map obtained with order_seq is different from that obtained with compare plus try_seq. It depends on which markers we choose to try to 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 a 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
## 16 M16 11.76 a | | a b | | o
## 20 M20 22.94 a | | b c | | d
## 4 M4 35.71 a | | o o | | b
## 23 M23 52.88 a | | o a | | o
## 48 SNP21 65.21 a | | b a | | a
## 45 SNP17 79.22 a | | b a | | a
## 47 SNP20 103.39 a | | b a | | a
## 50 SNP23 143.48 a | | b b | | a
## 24 M24 148.50 a | | b b | | a
## 49 SNP22 151.80 a | | b b | | a
## 52 SNP25 156.80 a | | b b | | a
##
## 12 markers log-likelihood: -670.5
##
##
##
## The following markers could not be uniquely positioned.
## Printing most likely positions for each unpositioned marker:
##
## ------------------------------------
## | | 9 | 21 | 29 | 46 | 51 |
## |----|-----|-----|-----|-----|-----|
## | | | | | | |
## | 27 | | | | | |
## | | | | | | |
## | 16 | | | | | |
## | | | | | | |
## | 20 | | | | | |
## | | | | | | |
## | 4 | | | | | |
## | | | *** | | | |
## | 23 | | | | | |
## | | | | | | |
## | 48 | | | | | |
## | | *** | | | *** | |
## | 45 | | | | | |
## | | | | | * | |
## | 47 | | | | | |
## | | | | *** | | ** |
## | 50 | | | | | |
## | | | | | | |
## | 24 | | | | | |
## | | | | | | |
## | 49 | | | | | |
## | | | | | | |
## | 52 | | | | | |
## | | | | ** | | *** |
## ------------------------------------
##
## '***' indicates the most likely position(s) (LOD = 0.0)
##
## '**' indicates very likely positions (LOD > -1.0)
##
## '*' indicates likely positions (LOD > -2.0)For this particular sequence, the touchdown step could map safely markers 46 and 52, but this depends on the specific dataset.
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-... OK
##
## ...-27-|-16-20-4-21-|-23-... OK
##
## ...-16-|-20-4-21-23-|-48-...
## Alternative orders:
## ... 16 20 4 21 23 48 ... : 0.00 ( linkage phases: ... 1 2 2 1 1 ... )
## ... 16 20 4 23 21 48 ... : -2.21 ( linkage phases: ... 1 2 2 1 1 ... )
##
## ...-20-|-4-21-23-48-|-9-...
## Alternative orders:
## ... 20 4 21 23 48 9 ... : 0.00 ( linkage phases: ... 2 2 1 1 1 ... )
## ... 20 4 23 21 48 9 ... : -2.21 ( linkage phases: ... 2 2 1 1 1 ... )
##
## ...-4-|-21-23-48-9-|-46-...
## Alternative orders:
## ... 4 21 23 48 9 46 ... : 0.00 ( linkage phases: ... 2 1 1 1 1 ... )
## ... 4 23 21 48 9 46 ... : -2.21 ( linkage phases: ... 2 1 1 1 1 ... )
##
## ...-21-|-23-48-9-46-|-45-...
## Alternative orders:
## ... 21 23 48 9 46 45 ... : 0.00 ( linkage phases: ... 1 1 1 1 1 ... )
## ... 21 23 48 46 9 45 ... : -1.05 ( linkage phases: ... 1 1 1 1 1 ... )
##
## ...-23-|-48-9-46-45-|-47-...
## Alternative orders:
## ... 23 48 9 46 45 47 ... : 0.00 ( linkage phases: ... 1 1 1 1 1 ... )
## ... 23 48 46 9 45 47 ... : -1.05 ( linkage phases: ... 1 1 1 1 1 ... )
## ... 23 48 45 9 46 47 ... : -1.80 ( linkage phases: ... 1 1 1 1 1 ... )
## ... 23 48 9 45 46 47 ... : -3.21 ( linkage phases: ... 1 1 1 1 1 ... )
## ... 23 45 48 9 46 47 ... : -3.58 ( linkage phases: ... 1 1 1 1 1 ... )
##
## ...-48-|-9-46-45-47-|-29-...
## Alternative orders:
## ... 48 9 46 45 47 29 ... : 0.00 ( linkage phases: ... 1 1 1 1 3 ... )
## ... 48 46 9 45 47 29 ... : -1.05 ( linkage phases: ... 1 1 1 1 3 ... )
## ... 48 45 9 46 47 29 ... : -1.80 ( linkage phases: ... 1 1 1 1 3 ... )
## ... 48 9 45 46 47 29 ... : -3.21 ( linkage phases: ... 1 1 1 1 3 ... )
##
## ...-9-|-46-45-47-29-|-50-...
## Alternative orders:
## ... 9 46 45 47 29 50 ... : 0.00 ( linkage phases: ... 1 1 1 3 4 ... )
## ... 9 45 46 47 29 50 ... : -3.21 ( linkage phases: ... 1 1 1 3 4 ... )
##
## ...-46-|-45-47-29-50-|-24-... OK
##
## ...-45-|-47-29-50-24-|-49-... OK
##
## ...-47-|-29-50-24-49-|-52-... OK
##
## ...-29-|-50-24-49-52-|-51-...
## Alternative orders:
## ... 29 50 24 49 52 51 : 0.00 ( linkage phases: ... 4 1 1 1 1 )
## ... 29 52 49 24 50 51 : -0.90 ( linkage phases: ... 4 1 1 1 1 )
## ... 29 50 24 52 49 51 : -2.76 ( linkage phases: ... 4 1 1 1 1 )
## ... 29 50 52 49 24 51 : -2.79 ( linkage phases: ... 4 1 1 1 1 )
## ... 29 50 49 52 24 51 : -3.31 ( linkage phases: ... 4 1 1 1 1 )
## ... 29 49 52 24 50 51 : -3.31 ( linkage phases: ... 4 1 1 1 1 )
##
## 50-|-24-49-52-51
## Alternative orders:
## ... 50 24 49 52 51 : 0.00 ( linkage phases: ... 1 1 1 1 )
## ... 50 24 52 49 51 : -2.76 ( linkage phases: ... 1 1 1 1 )
## ... 50 52 49 24 51 : -2.79 ( linkage phases: ... 1 1 1 1 )
## ... 50 51 24 49 52 : -2.85 ( linkage phases: ... 1 1 1 1 )
## ... 50 49 52 24 51 : -3.31 ( linkage phases: ... 1 1 1 1 )We should do this to any of the orders we found, either using try_seq or order_seq. Here, we choose LG2_all for didactic purposes only. The second argument, ws = 4, means that subsets (windows) of four markers will be permuted sequentially (4! orders for each window), to search for other plausible orders. The LOD argument means that only orders with LOD Score smaller than 3.68 will be printed.
The output shows sequences of four numbers, because ws = 4. They are followed by an OK if there is no alternative order with LOD Score smaller than LOD = LOD_sug in absolute value, or by a list of alternative orders. In the example, some sequences showed alternative orders with LOD smaller than LOD = LOD_sug. However, the best order was the original one (LOD = 0.00).
If there were an alternative order more likely than the original, one should check the difference between these orders (and linkage phases).
In some cases, even if there are no better alternative orders suggested by ripple_seq, the graphic showed a color pattern different from the expected. Then, we can remove doubtful markers (for this groups markers 23 and 29) and try to position them again. First, we use the function drop_marker to remove the 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 as the estimated map (LG2_all). After, we should estimate the map again using this predefined order (see section Map estimation for an arbitrary order for further information). For this we use the map function:
(LG2_test_map <- map(LG2_test_seq))Warning: If you find an error message like:
Error in as_mapper(.f, ...) : argument ".f" is missing, with no defaultIt’s because the map function has a very common name, and you can have in your environment other functions with the same name. In the case of the pointed error, R is using the map function from purrr package instead of OneMap, to solve this, simply specify that you want the OneMap function with :: command from stringr package:
library(stringr)
(LG2_test_map <- onemap::map(LG2_test_seq))##
## Printing map:
##
## Markers Position Parent 1 Parent 2
##
## 27 M27 0.00 b | | o a | | a
## 16 M16 11.75 a | | a o | | b
## 20 M20 22.93 a | | b d | | c
## 4 M4 35.70 a | | o b | | o
## 21 M21 52.67 o | | o b | | a
## 48 SNP21 53.59 a | | b a | | a
## 9 M9 60.40 a | | b a | | a
## 46 SNP18 66.83 a | | b a | | a
## 45 SNP17 81.83 a | | b a | | a
## 47 SNP20 106.46 a | | b a | | a
## 50 SNP23 145.68 a | | b a | | b
## 24 M24 150.69 a | | b a | | b
## 49 SNP22 153.97 a | | b a | | b
## 52 SNP25 158.87 a | | b a | | b
## 51 SNP24 169.81 a | | b a | | b
##
## 15 markers log-likelihood: -780.5746NOTE: (new!) If your sequence has many markers (more than 60), we suggest to speed up map using BatchMap parallelization approach. See section Speed up analysis with parallelization for more information.
Now, we have the map without markers 23 and 51.
rf_graph_table(LG2_test_map, mrk.axis = "numbers")
We use the try_seq function to positioned them again:
LG2_test_seq <- try_seq(LG2_test_map, 23)
LG2_test_23 <- make_seq(LG2_test_seq, 6)
LG2_test_seq <- try_seq(LG2_test_23, 29)
LG2_test_23_29 <- make_seq(LG2_test_seq, 12)
rf_graph_table(LG2_test_23_29, mrk.axis = "numbers")
Marker 23 kept its previous position, but marker 29 was re-positioned, configuring now a gap between markers 47 and 50. We removed marker 29 from our map because its color pattern is too different from 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 11.75 a | | a o | | b
## 20 M20 22.93 a | | b d | | c
## 4 M4 35.70 a | | o b | | o
## 21 M21 50.34 o | | o b | | a
## 23 M23 54.87 a | | o o | | a
## 48 SNP21 70.11 a | | b a | | a
## 9 M9 76.77 a | | b a | | a
## 46 SNP18 83.19 a | | b a | | a
## 45 SNP17 98.20 a | | b a | | a
## 47 SNP20 122.83 a | | b a | | a
## 50 SNP23 161.89 a | | b a | | b
## 24 M24 166.89 a | | b a | | b
## 49 SNP22 170.18 a | | b a | | b
## 52 SNP25 175.08 a | | b a | | b
## 51 SNP24 186.02 a | | b a | | b
##
## 16 markers log-likelihood: -811.7886Genetic 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 the try algorithm:
LG1_ord <- order_seq(LG1, n.init = 6, touchdown = TRUE)## Warning in compare_outcross(input.seq = input.seq, n.best = n.best, tol = tol, : This operation may take a VERY long timeNotice that the second round of try_seq added markers 10, 31, 32, 35, 36, and 40.
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: -1554.628Check the map graphically:
rf_graph_table(LG1_frame, mrk.axis = "numbers")Check for alternative orders:
ripple_seq(LG1_frame)No better order was observed.
Let’s check how it behaves with the MDS approach:
LG1_mds <- mds_onemap(LG1, rm_unlinked = TRUE, hmm = F)rf_graph_table(LG1_mds)Based on the drafts from order_seq or/and mds_onemap, we can remove some doubtful markers accordingly with the graphic, try to position 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 <- onemap::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: -1518.748rf_graph_table(LG1_final)
As an option, different algorithms to order markers could be applied:
LG1_ser <- seriation(LG1, hmm = F)
rf_graph_table(LG1_ser)
LG1_rcd <- rcd(LG1, hmm = F)
rf_graph_table(LG1_rcd)
LG1_rec <- record(LG1, hmm = F)
rf_graph_table(LG1_rec)
LG1_ug <- ug(LG1, hmm = F)
rf_graph_table(LG1_ug)NOTE: Results are not plotted in this vignette, please check the vignette in GitHub version.
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 information
In our example, we have reference genome chromosome and position information for some of the markers; here, we will exemplify one method of using this information to help build the genetic map.
With the CHROM information 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 information.
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")Here we use the string "1" because it is our chromosome ID, you can have a different string as ID, check this with:
unique(bins_example$CHROM)## [1] NA "1" "2" "3"We can see that we have markers without chromosome information (NA) and markers with chromosome ID "1", "2" and "3".
Adding markers with no reference genome information
According to CHROM information we have three defined linkage groups, now we can try to group the markers without chromosome information to them using recombination information. 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
## ....
## Selecting markers:
## group 1
## ......
## group 2
## ............
## group 3
## ........
## Selecting markers:
## group 1
## ................
## group 2
## ............
## group 3
## ....The function works as the function group but considering pre-existing sequences. Setting seqs argument with the string "CHROM", it will consider the pre-existing sequences according to CHROM information. You can also indicate other pre-existing sequences if they make sense for your study. For that, you should inform a list of 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 as the previous because we indicate chromosome sequences, but other sequences can be used.
The unlink.mks argument receives an object of class sequence; this defines which markers will be tested to group with the sequences in seqs. In our example, we will indicate only the markers with no segregation distortion, using the sequence mark_no_dist. It is also possible to use the string "all" to test all the remaining markers at the rf_2pts object.
In some cases, the same marker can group into more than one sequence; those markers will be considered repeated. We can choose if we want to remove or not (FALSE/TRUE) them of the output sequences, with the argument repeated. Anyway, their numbers will be informed at the list repeated in the output object. In the example case, there are no repeated markers. However, if they exist, it could indicate that their groups actually constitute the same group. Also, genotyping errors can generate repeated markers. Anyway, they deserve better investigations.
We can access detailed information about the results, just printing:
CHR_mks## This is an object of class 'group_seq'
## Criteria used to assign markers to groups:
## LOD = 3 , Maximum recombination fraction = 0.5
##
## No. markers in input sequences:
## CHR1 : 12 markers
## CHR2 : 2 markers
## CHR3 : 8 markers
##
## No. unlinked input markers: 27 markers
##
## No. markers in output sequences:
## CHR1 : 25 markers
## CHR2 : 7 markers
## CHR3 : 17 markers
## No. unlinked: 0 markers
## No. repeated: 0 markers
##
## Printing output sequences:
## Group CHR1 : 25 markers
## SNP1 SNP2 SNP3 SNP5 SNP6 SNP7 SNP8 SNP9 SNP10 SNP11 SNP12 SNP13 M1 M2 M3 M5 M6 M10 M11 M12 M14 M15 M26 M28 M30
##
## Group CHR2 : 7 markers
## SNP14 SNP16 M7 M8 M13 M18 M22
##
## Group CHR3 : 17 markers
## SNP17 SNP18 SNP20 SNP21 SNP22 SNP23 SNP24 SNP25 M4 M9 M16 M20 M21 M23 M24 M27 M29
##
## Unlinked markers: 0 markers
##
##
## Repeated markers: 0 markers
## Also, we can access the numbers of repeated markers with:
CHR_mks$repeated## [1] NAWe have no repeated markers.
In 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$sequences[[1]]##
## Number of markers: 25
## Markers in the sequence:
## SNP1 SNP2 SNP3 SNP5 SNP6 SNP7 SNP8 SNP9 SNP10 SNP11 SNP12 SNP13 M1 M2 M3 M5 M6
## M10 M11 M12 M14 M15 M26 M28 M30
##
## Parameters not estimated.For this function, optional arguments are LOD and max.rf, which define thresholds to be used when assigning markers to linkage groups. If none is provided (default), criteria previously defined for the object rf_2pts are used.
Now we can order the markers in each group as we made before in (Genetic mapping of linkage group 1,2 and 3). As shown, we can choose different approaches to order the markers.
To order those groups, first, we will use the order_seq function to access a preliminary order, and after, we will edit some marker’s positions or remove some of them according to their color pattern in the rf_graph_table graphic, and other parameters as likelihood and map size.
Genetic mapping of linkage group 1 (with reference genome information)
# CHR1_frame <- mds_onemap(CHR_mks$sequences$CHR1, hmm = F)
# or
CHR1_ord <- order_seq(CHR_mks$sequences$CHR1)
CHR1_frame <- make_seq(CHR1_ord, "force")rf_graph_table(CHR1_frame) # graphic not shownThe group is similar to that built before with only recombinations information. We will better explore differences in the later step. Only marker 11 does not follow the expected color pattern; then, we will try to reposition it.
CHR1_test_seq <- drop_marker(CHR1_frame, 11)
CHR1_test_map <- onemap::map(CHR1_test_seq)
CHR1_add11_seq <- try_seq(CHR1_test_map, 11)
CHR1_add11 <- make_seq(CHR1_add11_seq, 25) # marker 11 was placed at the same position as beforeBased in those results, we decide not to include marker 11 in our map.
CHR1_test_map##
## Printing map:
##
## Markers Position Parent 1 Parent 2
##
## 34 SNP5 0.00 a | | b a | | b
## 33 SNP3 12.27 a | | b a | | b
## 30 M30 15.58 a | | b a | | b
## 12 M12 16.59 b | | a c | | a
## 32 SNP2 20.15 a | | b a | | b
## 31 SNP1 28.31 a | | b a | | b
## 3 M3 51.17 o | | a o | | o
## 14 M14 64.54 a | | o b | | o
## 2 M2 72.44 o | | o o | | a
## 36 SNP7 96.32 b | | a b | | a
## 35 SNP6 109.13 b | | a b | | a
## 1 M1 113.53 b | | a b | | a
## 38 SNP9 119.59 b | | a b | | a
## 37 SNP8 136.22 b | | a b | | a
## 10 M10 149.87 a | | a o | | b
## 28 M28 167.09 a | | o b | | o
## 26 M26 199.46 a | | b d | | c
## 42 SNP13 214.58 b | | a b | | a
## 6 M6 220.93 b | | a b | | a
## 39 SNP10 227.10 b | | a b | | a
## 41 SNP12 243.56 b | | a b | | a
## 40 SNP11 260.69 b | | a b | | a
## 15 M15 302.93 o | | a o | | b
## 5 M5 307.95 o | | o o | | a
##
## 24 markers log-likelihood: -1507.316rf_graph_table(CHR1_test_map) 
CHR1_final <- CHR1_test_mapChecking for better orders:
ripple_seq(CHR1_final)Genetic mapping of linkage group 2 (with reference genome information)
NOTE: Results in this session are not plotted in this vignette, please check the vignette in GitHub version.
# CHR2_frame <- mds_onemap(CHR_mks$sequences$CHR2)
# or
CHR2_ord <- order_seq(CHR_mks$sequences$CHR2)
CHR2_frame <- make_seq(CHR2_ord, "force")rf_graph_table(CHR2_frame) # graphic not shownAs did before, we will not change the positions of the markers of this group.
CHR2_final <- CHR2_frameGenetic mapping of linkage group 2 (with reference genome information)
# CHR2_frame <- mds_onemap(CHR_mks$sequences$CHR2)
# or
CHR2_ord <- order_seq(CHR_mks$sequences$CHR2)
CHR2_frame <- make_seq(CHR2_ord, "force")rf_graph_table(CHR2_frame) # graphic not shownAs did before, we will not change the positions of the markers of this group.
CHR2_final <- CHR2_frameGenetic mapping of linkage group 3 (with reference genome information)
NOTE: Results in this session are not plotted in this vignette, please check the vignette in GitHub version.
# CHR3_frame <- mds_onemap(CHR_mks$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 shownHere, marker 29 has a color pattern too different from the expected, removing it could be influential 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 shownTrying to add marker 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 mapCHR3_final <- CHR3_test_map
rf_graph_table(CHR3_final, inter = FALSE)Checking for better orders:
ripple_seq(CHR3_final)Drawing the genetic maps
Once all linkage groups were obtained using both strategies, we can draw a map for each approach 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 on how to use both of them.
Draw_map
Drawing the map, which was built with only recombinations information.
map1 <- list(LG1_final, LG2_final, LG3_final)
draw_map(map1, names = TRUE, grid = TRUE, cex.mrk = 0.7)
Drawing the map, which built with reference genome and recombinations information
map2 <- list(CHR1_final, CHR2_final, CHR3_final)
draw_map(map2, names = TRUE, grid = TRUE, cex.mrk = 0.7)We also can draw 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)
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 is only inverted).
CHR3_comp <- list(LG2_final, CHR3_final)
draw_map(CHR3_comp, names = TRUE, grid = TRUE, cex.mrk = 0.7)Or groups alone:
draw_map(CHR1_final, names = TRUE, grid = TRUE, cex.mrk = 0.7)
Function draw_map draws a straightforward graphic representation of the genetic map. More recently, we developed a new version called draw_map2 that brings 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 the draw_map2 function. But it has different capacities and arguments. Here are some examples, but you can find more options on the help page ?write_map2.
Drawing the map, which was built with only recombinations information:
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 specifying them in the argument output.
Drawing the map, which was built with reference genome and recombinations information
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 colors. The arguments col.group, col.mark and col.tag can be changed to personalize the color of the groups, the markers, and the highlighted markers, respectively.
We also can draw maps comparing corresponding linkage groups in each strategy:
draw_map2(LG1_final, CHR1_final, output = "map_comp.pdf", tag = c("M1","SNP2"))
When defining marker names in the tag argument, all markers with these names 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")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))NOTE: (new!) If your sequence has many markers (more than 60), we suggest to speed up map using BatchMap parallelization approach. See section Speed up analysis with parallelization for more information.
Warning: If you find an error message like:
Error in as_mapper(.f, ...) : argument ".f" is missing, with no defaultIt’s because the map function has a very common name, and you can have in your environment other functions with the same name. In the case of the pointed error, R is using map function from purrr package instead of OneMap, to solve this, simply specify that you want the OneMap function with :: command from stringr package::
library(stringr)
(any_seq_map <- onemap::map(any_seq))This is a subset of the first linkage group. When used this way, the map function searches for the best combination of phases between markers and prints the results.
(new!)
Warning: It is not our case in this example, but, sometimes, it can happen that some markers in your sequence don’t reach the OneMap linkage criteria when linkage are estimated by HMM multipoint approach using map, it will produce an error like this:
ERROR: The linkage between markers 1 and 2 did not reach the OneMap default criteria. They are probably segregating independentlyYou can evaluate the marker manually, or you can remove them automatically using the map argument rm_unlinked = TRUE. The map function will return a vector with marker numbers excluding the problematic marker; then, you can repeat the process without the marker, using make_seq to create a new sequence and repeat the map. You can also do it automatically using the map_avoid_unlinked function:
LG2_test_map <- map_avoid_unlinked(any_seq)Using this, if map finds a problematic marker, it will print a warning pointing to the marker number, which was removed, and will automatically repeat the analysis without it.
Furthermore, a sequence can also have user-defined linkage phases. The next example shows (incorrect) phases used for the same order of markers:
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))Removing markers 3, 4, 5, 12, and 30 from any_seq:
(any_seq <- drop_marker(any_seq, c(3, 4, 5, 12, 30)))After that, the map needs to be re-estimated.
Speed up analysis with parallelization (new!)
Warning: Only available for outcrossing and f2 intercross populations.
As already mentioned, OneMap uses HMM multipoint approach to estimate genetic distances, a very robust method, but it can take time to run if you have many markers. In 2017, Schiffthaler et al. released an OneMap fork with modifications in CRAN and in GitHub with the possibility of parallelizing the HMM chain dividing markers in batches and use different cores for each phase. Their approach speeds up our HMM and keeps the genetic distance estimation quality. It allows us to divide the job into a maximum of four cores according to the four possible phases for outcrossing mapping populations. We add this parallelized approach to the functions: map, mds_onemap, seriation, rcd, record and ug. For better efficiency, batches must be composed of 50 markers or more; therefore, this approach is only recommended for linkage groups with many markers.
The parallelization is here available for all types of operational systems, however, we suggest setting argument parallelization.type to FORK if you are not using Windows system. It will improve the procedure speed.
Here we will show an example of how to use the BatchMap approach in some functions that requires HMM. For this, we simulated a group with 294 markers (we don’t want this vignette to take too much time to run, but usually maps with markers from high-throughput technologies result in larger groups). Before start, you can see the time spent on each approach (see also Session Info) in this example:
| Without parallelization (h) | With parallelization (h) | |
|---|---|---|
| rcd | 0.6700558 | 0.1612458 |
| record_map | 1.4368436 | 0.2907308 |
| ug_map | 0.7145778 | 0.1884214 |
| mds_onemap | 1.0643083 | 0.2827314 |
| map | 2.0994486 | 0.6107456 |
Reading the simulated dataset:
simParallel <- read_onemap(system.file(package = "onemap", "extdata/simParall_out.raw")) # dataset available only in onemap github version
plot(simParallel, all=FALSE)
# Calculates two-points recombination fractions
twopts <- rf_2pts(simParallel)
seq_all <- make_seq(twopts, "all")
# There are no redundant markers
find_bins(simParallel)
# There are no distorted markers
p <- plot(test_segregation(simParallel))
To prepare the data with a defined bach size, we use the function pick_batch_sizes. It selects a batch size that splits the data into even groups. Argument size defines the batch size next to which an optimum size will be searched. overlap defines the number of markers that overlap between the present batch and next. This is used because pre-defined phases at these overlap markers in the present batch are used to start the HMM in the next batch. The around argument defines how much the function can vary around the defined number in size to search for the optimum batch size.
Some aspects should be considered to define these arguments because if the batch size were set too high, there would be less gain in execution time. If the overlap size were too small, phases would be incorrectly estimated, and large gaps would appear in the map, inflating its size. In practice, these values will depend on many factors such as population size, marker quality, and species. BatchMap authors recommended trying several configurations on a subset of data and select the best performing one.
batch_size <- pick_batch_sizes(input.seq = seq_all,
size = 80,
overlap = 30,
around = 10)
batch_sizeSpeed up two-points ordering approaches
To use parallelized approach you just need to include the arguments when using the functions:
# Without parallelization
rcd_map <- rcd(input.seq = seq_all)
# With parallelization
rcd_map_par <- rcd(input.seq = seq_all,
phase_cores = 4,
size = batch_size,
overlap = 30)
# Without parallelization
record_map <- record(input.seq = seq_all)
# With parallelization
record_map_par <- record(input.seq = seq_all,
phase_cores = 4,
size = batch_size,
overlap = 30)
# Without parallelization
ug_map <- ug(input.seq = seq_all)
# With parallelization
ug_map_par <- ug(input.seq = seq_all,
phase_cores = 4,
size = batch_size,
overlap = 30)
Speed up mds_onemap
# Without parallelization ok
map_mds <- mds_onemap(input.seq = seq_all)
# With parallelization
map_mds_par <- mds_onemap(input.seq = seq_all,
phase_cores = 4,
size = batch_size,
overlap = 30)
Speed up map estimation for an arbitrary order (map function)
Because we simulate this dataset, we know the correct order. We can use map_overlapping_batches to estimate genetic distance in this case. This is equivalent to map, but with a parallelized process.
Similarly, with map, using argument rm_unlinked = TRUE the function will return a vector with marker numbers without the problematic marker. To repeat the analysis removing automatically all problematic markers use map_avoid_unlinked:
# Without parallelization
batch_map <- map_avoid_unlinked(input.seq = seq_all)
# With parallelization
batch_map_par <- map_avoid_unlinked(input.seq = seq_all,
size = batch_size,
phase_cores = 4,
overlap = 30)
As you can see in the above maps, heuristic ordering algorithms do not return an optimal order result, mostly if you don’t have many individuals in your population. Because of the erroneous order, generated map size is not close to the simulated size (100 cM) and their heatmaps don’t present the expected color pattern. Two of them get close to the color pattern, they are the ug and the MDS method. They present the right global ordering but not local. If you have a reference genome, you can use its position information to rearrange the local order.
Export estimated parents haplotypes (new!)
In the older version, users could only access the estimated linkage phase by observing the print in the console:
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: -1518.748Now, you can export this information into a data.frame using:
(parents_haplot <- parents_haplotypes(LG1_final))## group mk.number mk.names dist P1_1 P1_2 P2_1 P2_2
## 1 Group - 1 34 SNP5 0.00000 a b a b
## 2 Group - 1 33 SNP3 12.27061 a b a b
## 3 Group - 1 32 SNP2 18.44978 a b a b
## 4 Group - 1 30 M30 21.21270 a b a b
## 5 Group - 1 12 M12 22.21726 b a c a
## 6 Group - 1 31 SNP1 27.76526 a b a b
## 7 Group - 1 3 M3 51.04932 o a o o
## 8 Group - 1 14 M14 64.17780 a o b o
## 9 Group - 1 2 M2 72.09884 o o o a
## [ reached 'max' / getOption("max.print") -- omitted 15 rows ]write.table(parents_haplot, "parents_haplot.txt")The data.frame contains: group ID (group), marker number (mk.number) and names (mk.names), position in centimorgan (dist) and parents haplotypes (P1_1, P1_2, P2_1, P2_2).
You can also obtain a data.frame with a list of sequences and personalize the group names:
parents_haplotypes(LG1_final,LG2_final, group_names=c("LG1","LG2"))## group mk.number mk.names dist P1_1 P1_2 P2_1 P2_2
## 1 LG1 34 SNP5 0.00000 a b a b
## 2 LG1 33 SNP3 12.27061 a b a b
## 3 LG1 32 SNP2 18.44978 a b a b
## 4 LG1 30 M30 21.21270 a b a b
## 5 LG1 12 M12 22.21726 b a c a
## 6 LG1 31 SNP1 27.76526 a b a b
## 7 LG1 3 M3 51.04932 o a o o
## 8 LG1 14 M14 64.17780 a o b o
## 9 LG1 2 M2 72.09884 o o o a
## [ reached 'max' / getOption("max.print") -- omitted 31 rows ]Export estimated progeny haplotypes (new!)
Function progeny_haplotypes generates a data.frame with progeny phased haplotypes estimated by OneMap HMM. For progeny, the HMM results in probabilities for each possible genotype, then the generated data.frame contains all possible genotypes. If most_likely = TRUE, the most likely genotype receives 1 and the rest 0 (if there are two most likely both receive 0.5), if most_likely = FALSE genotypes probabilities will be according to the HMM results. You can choose which individual to be evaluated in ind. The data.frame is composed by the information: individual (ind) and group (grp) ID, position in centimorgan (pos), progeny homologs (homologs), and from each parent the allele came (parents).
(progeny_haplot <- progeny_haplotypes(LG2_final, most_likely = TRUE, ind = c(1,2), group_names = "LG2_final"))## ind marker grp pos prob parents parents.homologs allele
## 1 IND1 M27 LG2_final 0.00000 0 P1 H1 P1_H1
## 2 IND1 M16 LG2_final 11.74982 1 P1 H1 P1_H1
## 3 IND1 M20 LG2_final 22.93230 1 P1 H1 P1_H1
## 4 IND1 M4 LG2_final 35.70218 1 P1 H1 P1_H1
## 5 IND1 M21 LG2_final 50.34266 1 P1 H1 P1_H1
## 6 IND1 M23 LG2_final 54.87251 1 P1 H1 P1_H1
## 7 IND1 SNP21 LG2_final 70.10843 1 P1 H1 P1_H1
## 8 IND1 M9 LG2_final 76.76818 1 P1 H1 P1_H1
## 9 IND1 SNP18 LG2_final 83.19198 1 P1 H1 P1_H1
## [ reached 'max' / getOption("max.print") -- omitted 119 rows ]You can also have a view of progeny estimated haplotypes using plot. It shows which markers came from each parent’s homologs. position argument defines if haplotypes will be plotted by homologs (stack) or alleles (split). split option is a good way to view the likelihoods of each allele.
plot(progeny_haplot, position = "stack")
plot(progeny_haplot, position = "split")
Session Info
sessionInfo()## R version 4.1.0 (2021-05-18)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows 10 x64 (build 19043)
##
## Matrix products: default
##
## locale:
## [1] LC_COLLATE=English_United States.1252
## [2] LC_CTYPE=English_United States.1252
## [3] LC_MONETARY=English_United States.1252
## [4] LC_NUMERIC=C
## [5] LC_TIME=English_United States.1252
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] stringr_1.4.0 onemap_2.8.0
##
## loaded via a namespace (and not attached):
## [1] minqa_1.2.4 colorspace_2.0-2 ggsignif_0.6.3
## [4] ellipsis_0.3.2 class_7.3-19 rio_0.5.27
## [7] htmlTable_2.3.0 base64enc_0.1-3 rstudioapi_0.13
## [10] proxy_0.4-26 mice_3.13.0 farver_2.1.0
## [13] ggpubr_0.4.0 fansi_0.5.0 codetools_0.2-18
## [16] splines_4.1.0 doParallel_1.0.16 knitr_1.36
## [19] Formula_1.2-4 polynom_1.4-0 jsonlite_1.7.2
## [22] nloptr_1.2.2.2 broom_0.7.9 cluster_2.1.2
## [25] png_0.1-7 httr_1.4.2 compiler_4.1.0
## [28] backports_1.2.1 lazyeval_0.2.2 assertthat_0.2.1
## [31] Matrix_1.3-3 fastmap_1.1.0 htmltools_0.5.2
## [34] tools_4.1.0 rebus.base_0.0-3 gtable_0.3.0
## [37] glue_1.4.2 reshape2_1.4.4 dplyr_1.0.7
## [40] Rcpp_1.0.7 carData_3.0-4 cellranger_1.1.0
## [43] jquerylib_0.1.4 vctrs_0.3.8 ape_5.5
## [46] gdata_2.18.0 nlme_3.1-152 iterators_1.0.13
## [49] pinfsc50_1.2.0 xfun_0.24 rebus.datetimes_0.0-1
## [52] openxlsx_4.2.4 lme4_1.1-27.1 lifecycle_1.0.1
## [55] rebus.numbers_0.0-1 weights_1.0.4 gtools_3.9.2
## [58] rstatix_0.7.0 dendextend_1.15.1 princurve_2.1.6
## [61] candisc_0.8-6 MASS_7.3-54 scales_1.1.1
## [64] heplots_1.3-9 hms_1.1.1 parallel_4.1.0
## [67] smacof_2.1-3 RColorBrewer_1.1-2 yaml_2.2.1
## [70] curl_4.3.2 gridExtra_2.3 ggplot2_3.3.5
## [73] sass_0.4.0 rpart_4.1-15 latticeExtra_0.6-29
## [ reached getOption("max.print") -- omitted 56 entries ]References
Buetow, K. H., Chakravarti, A. Multipoint gene mapping using seriation. I. General methods. American Journal of Human Genetics 41, 180-188, 1987.
Doerge, R.W. Constructing genetic maps by rapid chain delineation. Journal of Agricultural Genomics 2, 1996.
Mollinari, M., Margarido, G. R. A., Vencovsky, R. and Garcia, A. A. F. Evaluation of algorithms used to order markers on genetics maps. Heredity 103, 494-502, 2009.
Schiffthaler, B., Bernhardsson, C., Ingvarsson, P. K., & Street, N. R. BatchMap: A parallel implementation of the OneMap R package for fast computation of F1 linkage maps in outcrossing species. PLoS ONE, 12(12), 1–12, 2017.
Tan, Y., Fu, Y. A novel method for estimating linkage maps. Genetics 173, 2383-2390, 2006.
Van Os H, Stam P, Visser R.G.F., Van Eck H.J. RECORD: a novel method for ordering loci on a genetic linkage map. Theor Appl Genet 112, 30-40, 2005.
Voorrips, R.E. MapChart: software for the graphical presentation of linkage maps and QTLs. Journal of Heredity 93, 77-78, 2002.
Voorrips, R. E., Maliepaard, C. A. The simulation of meiosis in diploid and tetraploid organisms using various genetic models. BMC Bioinformatics, 13(1), 248, 2012.
Wu, R., Ma, C.X., Painter, I. and Zeng, Z.-B. Simultaneous maximum likelihood estimation of linkage and linkage phases in outcrossing species. Theoretical Population Biology 61, 349-363, 2002a.
Wu, R., Ma, C.-X., Wu, S. S. and Zeng, Z.-B. Linkage mapping of sex-specific differences. Genetical Research 79, 85-96, 2002b.