The orthologr package allows users to perform Divergence Stratigraphy for any query and subject organisms of interest.

Divergence Stratigraphy is the process of quantifying the selection pressure (in terms of protein evolutionary rate) acting on orthologous genes between closely related species. The resulting sequence divergence map (short divergence map), stores the divergence stratum in the first column and the query_id of inferred orthologous genes in the second column ( Quint et al., 2012 Nature; Drost et al., 2015 Mol. Biol. Evol.; Drost et al., 2016 Mol. Biol. Evol.; Introduction to myTAI ). Here you can also find a short example and discussion about the usefulness of Divergence Strata.

The following Algorithm implemented in divergence_stratigraphy() defines Divergence Stratigraphy as method (see Drost et al., 2015):

  1. Orthology Inference using BLAST best reciprocal hit (“RBH”) based on blastp

  2. Pairwise global amino acid alignments of orthologous genes using the Needleman-Wunsch algorithm

  3. Codon alignments of orthologous genes using PAL2NAL

  4. dNdS estimation using Comeron’s method (1995)

  5. Categorize estimated dNdS values into divergence strata (= deciles of all dNdS values)

In brief, a Divergence Stratum is defined as a decile (= 10% quantile) retrieved from all Ka/Ks (or dN/dS) values of all orthologs returned by the pairwise genome comparison.

In other words, imagine having 10000 orthologous genes and their corresponding Ka/Ks values after performing a pairwise genome comparison using the dNdS() function. Now, these 10000 Ka/Ks values follow a distribution between 0 and +Inf, where Ka/Ks < 1 reflects purifying selection, Ka/Ks = 1 reflects neutral evolution, and Ka/Ks > 1 reflects positive selection (in reality usually the largest Ka/Ks values I have seen are e.g. 100). Next, you bin these 10000 Ka/Ks values according to their 10% quantile (= decile), meaning that the lowest 10% of Ka/Ks values are in decile one (= Divergence Stratum 1), the lowest Ka/Ks values between the 11%-20% quantile are in decile two (= Divergence Stratum 2), …, and the largest Ka/Ks values between the 91-100% quantile are in decile 10 (= Divergence Stratum 10) (This is what the divergence_map() function does). This way, each Divergence Stratum has (almost) the same number of genes.

In orthologr the Needleman-Wunsch algorithm, PAL2NAL and Comeron’s method (1995) are already included in the orthologr package and do not have to be installed separately. Nevertheless, users need to make sure they have BLAST installed on their machine before using the divergence_stratigraphy()function.

Note: The following examples assume that the BLAST program is installed and stored in the default execution path usr/local/bin. In case users do not have BLAST installed yet or the following command in R produces a different output, please consult the Installation Vignette to corretly set up the BLAST program to perform Divergence Stratigraphy.

system("blastp -version")
blastp: 2.2.30+
Package: blast 2.2.30, build Oct 27 2014 17:10:51

Divergence Map Computations

In Drost et al., 2015 Mol. Biol. Evol. we define a Divergence Map as table storing the degree of selection pressure (= divergence strata) for each protein coding gene of a given query organism. In this case selection pressure was quantified by dNdS estimation (ratio of synonymous versus non-synonymous codon -> amino acid sequence substitution rates). The resulting dNdS values for all protein coding genes of the query organism are then categorized into deciles (10%-quantiles) allowing users to compare the results obtained from Phylostratigraphy with results obtained form Divergence Stratigraphy.

To perform Divergence Stratigraphy using orthologr users need to retrieve the following input files:

  • a CDS file covering all protein coding genes of the query organism of interest
  • a CDS file covering all protein coding genes of the subject organism of interest

Sequence Data Retrieval

In the following example, we will use Arabidopsis thaliana as query organism and Arabidopsis lyrata as subject organism.

First, we need to download the CDS sequences for all protein coding genes of A. thaliana and A. lyrata.

Option 1:

The CDS retrieval can be done using a Terminal or by manual downloading the files

  • Arabidopsis_thaliana.TAIR10.23.cds.all.fa.gz
  • Arabidopsis_lyrata.v.1.0.23.cds.all.fa.gz

# download CDS file of A. thaliana
-o Arabidopsis_thaliana.TAIR10.23.cds.all.fa.gz

# unzip the fasta file
gunzip -d Arabidopsis_thaliana.TAIR10.23.cds.all.fa.gz

# download CDS file of A. lyrata

-o Arabidopsis_lyrata.v.1.0.23.cds.all.fa.gz

# unzip the fasta file
gunzip -d Arabidopsis_lyrata.v.1.0.23.cds.all.fa.gz

When the download is finished you need to unzip the files.

Option 2:

We implemented the biomartr package to automate the process of performing biological data retrieval. The Sequence Retrieval Vignette stored in biomartr provides detailed use cases for the automation of biological sequence retrieval.

Note: Users need to make sure they have biomartr installed before running any biomartr functions.

Computation Time

Please note that performing Divergence Stratigraphy with two large genomes can take (even on a multicore machine) some time -> up to several hours. On a 4 core machine with 3.4 GHz i7 processors the computation time of generating a divergence map between A. thaliana and A. lyrata was 2.5-3 hours.

The comp_cores argument implemented in the divergence_stratigraphy() function allows users to specify the number of cores they would like to use on their machine. The default value is comp_cores = 1 which might take 10-12h to execute. So users need to make sure that they use all cores available on their machine to speed up the computation time.

Running divergence_stratigraphy()

As mentioned earlier the divergence_stratigraphy() function is the main function to perform the Divergence Stratigraphy algorithm.

In divergence_stratigraphy() the query_file and subject_file arguments take an character string storing the path to the corresponding fasta files containing the CDS sequences of these organisms. Here the previously downloaded CDS sequence files of A. thaliana (= query_file) and A. lyrata (= subject_file) need to be specified. The eval is set to 1E-5 (default ; see Quint et al., 2012 Nature) and BLAST best reciprocal hit is used for orthology inference (see Drost et al., 2015). In case `orthologr is running on a multicore machine, users can set the comp_cores argument to any number of cores supported by their machine. The clean_folders argument indicates whether or not the internal folder structure should be deleted (cleaned) after processing is finished. In this case all output files generated by divergence_stratigraphy (stored in tempdir()) will be removed after the Divergence Map was returned. The quiet argument indicates whether or not a successful interface call should be printed out to the console (quiet = FALSE) or not (quiet = TRUE).

Before running divergence_stratigraphy() with two complete genomes, users can first run a test Divergence Stratigraphy with 20 example genes that are stored in the orthologr package:

   divergence_strata    query_id
1                 10 AT1G01010.1
2                  9 AT1G01020.1
3                  5 AT1G01030.1
4                  4 AT1G01040.1
5                  1 AT1G01050.1
6                  9 AT1G01060.3
7                  6 AT1G01070.1
8                  8 AT1G01080.1
9                  2 AT1G01090.1
10                 7 AT1G01110.2
11                 2 AT1G01120.1
12                 3 AT1G01140.3
13                10 AT1G01150.1
14                 8 AT1G01160.1
15                 1 AT1G01170.2
16                 6 AT1G01180.1
17                 7 AT1G01190.1
18                 4 AT1G01200.1
19                 5 AT1G01210.1
20                 3 AT1G01220.1

The resulting output is a Divergence Map of the 20 example genes.

To save corresponding Divergenec Maps to a hard drive users can pass the resulting divergence_stratigraphy() output to a variable and then use the write.table() function implemented in R to store the Divergenec Map as *.csv file.

This way write.table() will store the Divergence Map to the users current working directory (= getwd()).

Specifying the arguments in divergence_stratigraphy()

Several argument combinations can be specified in divergence_stratigraphy() (see Arguments in ?divergence_stratigraphy). This section introduces additional output options of divergence_stratigraphy().

Example: blast_path

Sometimes the machine users are working on does not allow them to install BLAST in the default execution path usr/local/bin. For this purpose the blast_path argument is implemented in divergence_stratigraphy(). This argument takes an character string specifying the PATH to the user’s blastp execution file that is stored in a different place than usr/local/bin.

The following example shows a possible specification of blast_path.

   divergence_strata    query_id
1                 10 AT1G01010.1
2                  9 AT1G01020.1
3                  5 AT1G01030.1
4                  4 AT1G01040.1
5                  1 AT1G01050.1
6                  9 AT1G01060.3
7                  6 AT1G01070.1
8                  8 AT1G01080.1
9                  2 AT1G01090.1
10                 7 AT1G01110.2
11                 2 AT1G01120.1
12                 3 AT1G01140.3
13                10 AT1G01150.1
14                 8 AT1G01160.1
15                 1 AT1G01170.2
16                 6 AT1G01180.1
17                 7 AT1G01190.1
18                 4 AT1G01200.1
19                 5 AT1G01210.1
20                 3 AT1G01220.1

Example: ds.values

As defined earlier, a Divergence Map stores the divergence strata for protein coding genes of a query organism. However, divergence strata are based on dNdS values that were categorized into deciles. For this reason it is not possible to map a divergence stratum value to the exact initial dNdS value. So in case users are interested in the the exact dNdS value of protein coding genes, they can specify the ds.values argument in divergence_stratigraphy() allowing them to retrieve a dNdS Map instead of a Divergence Map. For this purpose users need to set ds.values = FALSE.

      dNdS    query_id
1  0.41950 AT1G01010.1
2  0.38790 AT1G01020.1
3  0.11850 AT1G01030.1
4  0.11560 AT1G01040.1
5  0.00000 AT1G01050.1
6  0.39670 AT1G01060.3
7  0.17280 AT1G01070.1
8  0.32170 AT1G01080.1
9  0.04174 AT1G01090.1
10 0.26620 AT1G01110.2
11 0.02317 AT1G01120.1
12 0.04324 AT1G01140.3
13 0.64120 AT1G01150.1
14 0.37310 AT1G01160.1
15 0.00000 AT1G01170.2
16 0.16830 AT1G01180.1
17 0.17730 AT1G01190.1
18 0.11370 AT1G01200.1
19 0.13420 AT1G01210.1
20 0.10230 AT1G01220.1

The corresponding output now stores dNdS values instead of DS values in the first column.


Although the Divergence Map standard is specified as storing DS values in the first column and GeneIDs in the second column, in some cases it is important to store the GeneIDs of orthologous genes in the subject organism. The argument implemented in divergence_stratigraphy() allows users to retrieve the GeneIDs of the orthologous genes of the subject organism. For this purpose users need to specify = TRUE.

   DS    query_id            subject_id
1  10 AT1G01010.1 333554|PACid:16033839
2   9 AT1G01020.1 470181|PACid:16064328
3   5 AT1G01030.1 470180|PACid:16054974
4   4 AT1G01040.1 333551|PACid:16057793
5   1 AT1G01050.1 909874|PACid:16064489
6   9 AT1G01060.3 470177|PACid:16043374
7   6 AT1G01070.1 918864|PACid:16052578
8   8 AT1G01080.1 909871|PACid:16053217
9   2 AT1G01090.1 470171|PACid:16052860
10  7 AT1G01110.2 333544|PACid:16034284
11  2 AT1G01120.1 918858|PACid:16049140
12  3 AT1G01140.3 470161|PACid:16036015
13 10 AT1G01150.1 918855|PACid:16037307
14  8 AT1G01160.1 918854|PACid:16044153
15  1 AT1G01170.2 311317|PACid:16052302
16  6 AT1G01180.1 909860|PACid:16056125
17  7 AT1G01190.1 311315|PACid:16059488
18  4 AT1G01200.1 470156|PACid:16041002
19  5 AT1G01210.1 311313|PACid:16057125
20  3 AT1G01220.1 470155|PACid:16047984

The resulting output now shows DS values, query GeneIDs, and orthologous subject GeneIDs.

A similar output can be generated for dNdS values instead of DS values by specifying ds.values = FALSE and = TRUE.

      dNdS    query_id            subject_id
1  0.41950 AT1G01010.1 333554|PACid:16033839
2  0.38790 AT1G01020.1 470181|PACid:16064328
3  0.11850 AT1G01030.1 470180|PACid:16054974
4  0.11560 AT1G01040.1 333551|PACid:16057793
5  0.00000 AT1G01050.1 909874|PACid:16064489
6  0.39670 AT1G01060.3 470177|PACid:16043374
7  0.17280 AT1G01070.1 918864|PACid:16052578
8  0.32170 AT1G01080.1 909871|PACid:16053217
9  0.04174 AT1G01090.1 470171|PACid:16052860
10 0.26620 AT1G01110.2 333544|PACid:16034284
11 0.02317 AT1G01120.1 918858|PACid:16049140
12 0.04324 AT1G01140.3 470161|PACid:16036015
13 0.64120 AT1G01150.1 918855|PACid:16037307
14 0.37310 AT1G01160.1 918854|PACid:16044153
15 0.00000 AT1G01170.2 311317|PACid:16052302
16 0.16830 AT1G01180.1 909860|PACid:16056125
17 0.17730 AT1G01190.1 311315|PACid:16059488
18 0.11370 AT1G01200.1 470156|PACid:16041002
19 0.13420 AT1G01210.1 311313|PACid:16057125
20 0.10230 AT1G01220.1 470155|PACid:16047984

Example: dnds.threshold

Divergence Strata are obtained by categorizing dNdS values into deciles. For decilation the range of dNdS values is important. The dnds.threshold defines the upper level cut off of dNdS values. Since dNdS values are in the range [0, +Inf] a upper threshold needs to be specified. The default value for dnds.threshold in divergence_stratigraphy() is dnds.threshold = 2 due to the interpretation of dNdS values for predicting sequence evolution (dNdS < 1 -> negative selection; dNdS = 1 -> neutral selection; dNdS > 1 -> positive selection). Hence, all dNdS values > 1 predict positive selection. In my experience of computing dNdS values between hundreds of pairwise species comparisons covering all evolutionary distances, dNdS values of orthologous genes rarely take values > 2. Nevertheless, in case you wish to extend or reduce the upper threshold for dNdS values, you can specify the dnds.threshold in divergence_stratigraphy().

Example: ortho_detection

According to Drost et al., 2015 Mol. Biol. Evol. the Divergence Stratigraphy algorithm performs BLAST best reciprocal hit (RBH) as orthology inference method. Despite this convention, the ortho_detection argument allows users to perform orthology inference within the Divergence Stratigraphy algorithm that is based on any orthology inference method implemented in orthologr (see ?orthologs or Orthology Inference Vignette for details). For example in Quint et al., 2012 Nature instead of using BLAST best reciprocal hit, the method BLAST best hit (BH) was used to perform orthology inference within the Divergence Stratigraphy algorithm.

   DS    query_id
1  10 AT1G01010.1
2   9 AT1G01020.1
3   5 AT1G01030.1
4   4 AT1G01040.1
5   1 AT1G01050.1
6   9 AT1G01060.3
7   6 AT1G01070.1
8   8 AT1G01080.1
9   2 AT1G01090.1
10  7 AT1G01110.2
11  2 AT1G01120.1
12  3 AT1G01140.3
13 10 AT1G01150.1
14  8 AT1G01160.1
15  1 AT1G01170.2
16  6 AT1G01180.1
17  7 AT1G01190.1
18  4 AT1G01200.1
19  5 AT1G01210.1
20  3 AT1G01220.1

Skip Divergence Stratigraphy and Download Already Published Divergence Maps

Users can find a detailed list of published Phylostratigraphic Maps and Divergence Maps by following the link. This way the computation time of 3-4 h on a local machine for 2 genome comparisions can be skipped.

Combine a Divergence Map with Gene Expression Data

Divergence Maps can be used for a wide range of analyses. One example is to combine Divergence Maps with gene expression data to capture evolutionary signals in developmental transcriptomes (= Phylotranscriptomics; see Drost et al., 2015 Mol. Biol. Evol.). Performing phylotranscriptomic analyses based on an existing Divergence Map can easily be done by using the myTAI package. You can consult the Introduction to the myTAI package Vignette for more details.