# 1 Introduction

The identification of groups of homologous genes within and across species is a powerful tool for evolutionary genomics. The most widely used tools to identify orthogroups (i.e., groups of orthologous genes) are OrthoFinder (Emms and Kelly 2019) and OrthoMCL (Li, Stoeckert, and Roos 2003). However, these tools generate different results depending on the parameters used, such as mcl inflation parameter, E-value, maximum number of hits, and others. Here, we propose a protein domain-aware assessment of orthogroup inference. The goal is to maximize the percentage of shared protein domains for genes in the same orthogroup.

# 2 Installation

if(!requireNamespace('BiocManager', quietly = TRUE))
install.packages('BiocManager')
BiocManager::install("cogeqc")
# Load package after installation
library(cogeqc)

# 3 Data description

Here, we will use orthogroups from the PLAZA 5.0 database (Van Bel et al. 2021), inferred with OrthoFinder (Emms and Kelly 2019). For the purpose of demonstration, the complete dataset was filtered to only keep orthogroups for the Brassicaceae species Arabidopsis thaliana and Brassica oleraceae. Interpro domain annotations were also retrieved from PLAZA 5.0.

# Orthogroups for Arabidopsis thaliana and Brassica oleraceae
data(og)
#>     Orthogroup Species      Gene
#> 1 HOM05D000001     Ath AT1G02310
#> 2 HOM05D000001     Ath AT1G03510
#> 3 HOM05D000001     Ath AT1G03540
#> 4 HOM05D000001     Ath AT1G04020
#> 5 HOM05D000001     Ath AT1G04840
#> 6 HOM05D000001     Ath AT1G05750

# Interpro domain annotations
data(interpro_ath)
data(interpro_bol)

#>        Gene Annotation
#> 1 AT1G01010  IPR036093
#> 2 AT1G01010  IPR003441
#> 3 AT1G01010  IPR036093
#> 4 AT1G01020  IPR007290
#> 5 AT1G01020  IPR007290
#> 6 AT1G01030  IPR003340
#>           Gene Annotation
#> 1 BolC1t00001H  IPR014710
#> 2 BolC1t00001H  IPR018490
#> 3 BolC1t00002H  IPR013057
#> 4 BolC1t00003H  IPR013057
#> 5 BolC1t00004H  IPR005178
#> 6 BolC1t00004H  IPR005178

If you infer orthogroups with OrthoFinder, you can read and parse the output file Orthogroups.tsv with the function read_orthogroups(). For example:

# Path to the Orthogroups.tsv file created by OrthoFinder
og_file <- system.file("extdata", "Orthogroups.tsv.gz", package = "cogeqc")

# Read and parse file
#>     Orthogroup Species      Gene
#> 1 HOM05D000001     Ath AT1G02310
#> 2 HOM05D000001     Ath AT1G03510
#> 3 HOM05D000001     Ath AT1G03540
#> 4 HOM05D000001     Ath AT1G04020
#> 5 HOM05D000001     Ath AT1G04840
#> 6 HOM05D000001     Ath AT1G05750

# 4 Assessing orthogroups

In cogeqc, you can assess orthogroup inference with either a protein domain-based approach or a reference-based approach. Both approaches are described below.

## 4.1 Protein domain-based orthogroup assessment

The protein domain-based assessment of orthogroups is based on the formula below:

\begin{aligned} Scores &= \frac{Homogeneity}{Dispersal} \\ \end{aligned}

The numerator, $$homogeneity$$, is the mean Sorensen-Dice index for all pairwise combinations of genes in an orthogroup. The Sorensen-Dice index measures how similar two genes are, and it ranges from 0 to 1, with 0 meaning that a gene pair does not share any protein domain, and 1 meaning that it shares all protein domains. In a formal definition:

\begin{aligned} Homogeneity &= \frac{1}{N_{pairs}} \sum_{i=1}^{N_{pairs}} SDI_{i} \\ \\ SDI(A,B) &= \frac{2 \left| A \cap B \right|}{ \left|A \right| + \left| B \right|} \end{aligned}

where A and B are the set of protein domains associated to genes A and B. This way, if all genes in an orthogroup have the same protein domains, it will have $$homogeneity = 1$$. If each gene has a different protein domain, the orthogroup will have $$homogeneity = 0$$. If only some gene pairs share the same domain, $$homogeneity$$ will be somewhere between 0 and 1.

The denominator, $$dispersal$$, aims to correct for overclustering (i.e., orthogroup assignments that break “true” gene families into an artificially large number of smaller subfamilies). It is the mean number of orthogroups containing the same protein domain corrected by the number of orthogroup. Formally:

\begin{aligned} Dispersal &= \frac{1}{N_{domains} N_{OG}} \sum_{i=1}^{N_{domains}}D_{i} \\ \\ \end{aligned}

where $$N_{OG}$$ is the number of orthogroups, and $$D_{i}$$ is the number of orthogroups containing the protein domain $$i$$. This term penalizes orthogroup assignments where the same protein domains appears in multiple orthogroups. As orthogroups represent groups of genes that evolved from a common ancestor, a protein domain being present in multiple orthogroups indicates that this domain evolved multiple times in an independent way, which is not reasonable from a phylogenetic point of view, despite convergent evolution.

To calculate scores for each orthogroup, you can use the function assess_orthogroups(). This function takes as input a list of annotation data frames1 NOTE: The names of the list elements must match the species abbreviations in the column Species of the orthogroups data frame. For instance, if your orthogroups data frame contains the species Ath and Bol, the data frames in the annotation list must be named Ath and Bol (not necessarily in that order, but with these exact names). and an orthogroups data frame, and returns the relative homogeneity scores of each orthogroup for each species. Note that if you don’t want to take the dispersal into account, you can set correct_overclustering = FALSE. This will ignore the denominator of the score formula.

# Create a list of annotation data frames
annotation <- list(Ath = interpro_ath, Bol = interpro_bol)
str(annotation) # This is what the list must look like
#> List of 2
#>  $Ath:'data.frame': 131661 obs. of 2 variables: #> ..$ Gene      : chr [1:131661] "AT1G01010" "AT1G01010" "AT1G01010" "AT1G01020" ...
#>   ..$Annotation: chr [1:131661] "IPR036093" "IPR003441" "IPR036093" "IPR007290" ... #>$ Bol:'data.frame': 212665 obs. of  2 variables:
#>   ..$Gene : chr [1:212665] "BolC1t00001H" "BolC1t00001H" "BolC1t00002H" "BolC1t00003H" ... #> ..$ Annotation: chr [1:212665] "IPR014710" "IPR018490" "IPR013057" "IPR013057" ...

og_assessment <- assess_orthogroups(og, annotation)
#>    Orthogroups Ath_score Bol_score Mean_score Median_score
#> 1 HOM05D000001  283.3132  271.9950   277.6541     277.6541
#> 2 HOM05D000002  129.9598  515.2557   322.6078     322.6078
#> 3 HOM05D000003  889.1268  848.1947   868.6607     868.6607
#> 4 HOM05D000004    0.0000  940.5871   470.2935     470.2935
#> 5 HOM05D000005 1135.8799  808.1998   972.0398     972.0398
#> 6 HOM05D000006 2820.8337  899.6528  1860.2433    1860.2433

Now, we can calculate the mean score for this orthogroup inference.

test$Gene[idx_shuffle], size = length(idx_shuffle), replace = FALSE ) # Compare test set to reference set comparison <- compare_orthogroups(ref, test) head(comparison) #> Orthogroup Preserved #> 1 HOM05D000001 FALSE #> 2 HOM05D000002 FALSE #> 3 HOM05D000003 FALSE #> 4 HOM05D000004 TRUE #> 5 HOM05D000005 FALSE #> 6 HOM05D000006 TRUE # Calculating percentage of preservation preserved <- sum(comparison$Preserved) / length(comparison$Preserved) preserved #> [1] 0.2702703 As we can see, 27.03% of the orthogroups in the reference data set are preserved in the shuffled data set. # 5 Visualizing summary statistics Now that you have identified the best combination of parameters for your orthogroup inference, you can visually explore some of its summary statistics. OrthoFinder automatically saves summary statistics in a directory named Comparative_Genomics_Statistics. You can parse this directory in a list of summary statistics with the function read_orthofinder_stats(). To demonstrate it, let’s read the output of OrthoFinder’s example with model species. stats_dir <- system.file("extdata", package = "cogeqc") ortho_stats <- read_orthofinder_stats(stats_dir) ortho_stats #>$stats
#>                   Species N_genes N_genes_in_OGs Perc_genes_in_OGs N_ssOGs
#> 1             Danio_rerio   30313          28236              93.1     569
#> 2 Drosophila_melanogaster   13931          10674              76.6     675
#> 3            Homo_sapiens   23480          22669              96.5     268
#> 4            Mus_musculus   22859          22006              96.3     243
#> 5       Takifugu_rubripes   20545          19403              94.4     135
#> 6      Xenopus_tropicalis   19987          18755              93.8     234
#>   N_genes_in_ssOGs Perc_genes_in_ssOGs Dups
#> 1             3216                10.6 9585
#> 2             3313                23.8 3353
#> 3             1625                 6.9 4527
#> 4             2022                 8.8 4131
#> 5              446                 2.2 2283
#> 6             1580                 7.9 3650
#>
#> $og_overlap #> Danio_rerio Drosophila_melanogaster Homo_sapiens #> Danio_rerio 13472 5872 11365 #> Drosophila_melanogaster 5872 6651 5866 #> Homo_sapiens 11365 5866 14468 #> Mus_musculus 11345 5863 14076 #> Takifugu_rubripes 12100 5810 10994 #> Xenopus_tropicalis 11086 5725 11478 #> Mus_musculus Takifugu_rubripes Xenopus_tropicalis #> Danio_rerio 11345 12100 11086 #> Drosophila_melanogaster 5863 5810 5725 #> Homo_sapiens 14076 10994 11478 #> Mus_musculus 14411 10976 11446 #> Takifugu_rubripes 10976 12649 10776 #> Xenopus_tropicalis 11446 10776 12302 #> #>$duplications
#>                       Node Duplications_50
#> 1  Drosophila_melanogaster            3353
#> 2             Homo_sapiens            4527
#> 3                       N0              73
#> 4        Takifugu_rubripes            2283
#> 5             Mus_musculus            4131
#> 6              Danio_rerio            9585
#> 7                       N1            2458
#> 8                       N2            1530
#> 9                       N3             195
#> 10                      N4             745
#> 11      Xenopus_tropicalis            3650

Now, we can use this list to visually explore summary statistics.

## 5.1 Species tree

To start, one would usually want to look at the species tree to detect possible issues that would compromise the accuracy of orthologs detection. The tree file can be easily read with treeio::read.tree().

data(tree)
plot_species_tree(tree)

You can also include the number of gene duplications in each node.

plot_species_tree(tree, stats_list = ortho_stats)

## 5.2 Species-specific duplications

The species tree above shows duplications per node, but it does not show species-duplications. To visualize that, you can use the function plot_duplications().

plot_duplications(ortho_stats)

## 5.3 Genes in orthogroups

Visualizing the percentage of genes in orthogroups is particularly useful for quality check, since one would usually expect a large percentage of genes in orthogroups, unless there is a very distant species in OrthoFinder’s input proteome data.

plot_genes_in_ogs(ortho_stats)

## 5.4 Species-specific orthogroups

To visualize the number of species-specific orthogroups, use the function plot_species_specific_ogs(). This plot can reveal a unique gene repertoire of a particular species if it has a large number of species-specific OGs as compared to the other ones.

plot_species_specific_ogs(ortho_stats)

## 5.5 All in one

To get a complete picture of OrthoFinder results, you can combine all plots together with plot_orthofinder_stats(), a wrapper that integrates all previously demonstrated plotting functions.

plot_orthofinder_stats(
tree,
xlim = c(-0.1, 2),
stats_list = ortho_stats
)

## 5.6 Orthogroup overlap

You can also visualize a heatmap of pairwise orthogroup overlap across species with plot_og_overlap().

plot_og_overlap(ortho_stats)