OLGenie is a Perl program for estimating d_N/d_S to detect selection and function in overlapping genes (OLGs). It relies on no external dependencies, facilitating maximum portability. Just download and run.

To test the software with the example data, execute the program at the Unix command line or Mac Terminal as follows:

FORMAT:

OLGenie.pl --fasta_file=<alignment>.fasta --frame=<frame> \
--output_file=<OLGenie_codon_results>.tsv --verbose > OLGenie_log.txt

Find some real examples below. For more details, check out our Advance Access paper at Molecular Biology and Evolution.

Contents

• Description
• How it Works
• Options
• Examples
• Output
• Troubleshooting
• Acknowledgments
• Citation
• Contact
• References

Description

Given the codon triplet and antiparallel nature of the genetic code, a single segment of double-stranded nucleic acid has the potential to encode six reading frames: three in the forward (sense) direction and three in the reverse (antisense) direction. This allows for the possibility that two or more genes may overlap the same nucleotide positions in a genome. Indeed, a substantial fraction of genes in taxa ranging from viruses to humans may encode overlapping gene (OLG) pairs, running in either the same (ss; sense-sense) or opposite (sas; sense-antisense) directions (e.g., see Pavesi et al. 2018 and Sabath 2009). We use the nomenclature of Wei and Zhang (2015), referring to these overlapping frames as ss12, ss13, sas11, sas12, or sas13, where the first number refers to the codon position in a reference gene, and the second number refers to the codon position in an alternate (overlapping) gene:

The choice of which gene to consider the reference gene is arbitrary. Typically, the reference gene (mother/ORF1 gene) is the gene whose functional status is known, while the functionality of the alternate gene (daughter/ORF2 gene) may be in question. Thus, in practice, the reference gene is usually larger than the alternate gene, and the alternate gene is either partially or fully embedded within the reference. For example, in sas12, genes overlap in a sense-antisense relationship such that position 1 of codons in the sense (reference) gene correspond to position 2 of codons in the reverse strand (alternate) gene. In other words, the sense gene's first codon position overlaps the antisense gene's second codon position:

It is common to detect natural selection in a DNA sequence alignment using d_N/d_S, i.e., the ratio of nonsynonymous (changes the amino acid) to synonymous (does not change the amino acid) differences per site. While d_N/d_S = 1 implies neutrality (i.e., the null hypothesis of no effect), negative (purifying) selection may lead to d_N/d_S < 1 and positive (Darwinian) selection may lay to d_N/d_S > 1. Thus, d_N/d_S can be used to detect functional protein-coding genes. Unfortunately, standard methods for estimating d_N/d_S do not apply to OLGs, because a mutation that is synonymous in one frame may be nonsynonymous in another, and vice versa. Although some methods for detecting natural selection in OLGs have been developed, they are generally computationally intensive and limited in utility (e.g., Wei and Zhang 2015; Sabath et al. 2008). Thus, it is necessary to develop improved approaches for detecting selection in OLGs that can be implemented with genome-scale data.

OLGenie represents a simplification and extension of the method of Wei and Zhang (2015), utilizing the approach of SNPGenie (Nelson et al. 2015), and tailored for detecting selection in OLGs. The method considers the effects of mutations in the overlapping frame to determine the numerator (number of differences) and denominator (number of sites) of d_N and d_S. For example, d_N is usually calculated as the mean number of nonsynonymous nucleotide differences per nonsynonymous nucleotide site, and d_S is similarly calculated for synonymous differences and sites. In order to control for the possibility that synonymous sites in the frame of interest may be under selection in the alternate overlapping reading frame, Wei-Zhang further considers the expanded measures d_NN, d_SN, d_NS, and d_SS, where the first subscript refers to the reference gene, and the second to the alternate gene. For example, d_SN refers to the mean number of differences per site that are synonymous in the reference frame but nonsynonymous in the alternate frame (i.e., SN). Using these measures, it is possible to estimate d_N/d_S for the reference gene using d_NN/d_SN or d_NS/d_SS, and to estimate d_N/d_S for the alternate gene as d_NN/d_NS or d_SN/d_SS, i.e., the subscript in the alternate OLG is held constant to control for OLG effects.

For more details, please refer to our manuscript.

How it Works

OLGenie is written in Perl with no dependencies for maximum portability (just download and run). The program examines a user-provided FASTA alignment of one protein-coding gene region from the reference gene point of view. This means that the alignment begins at the first site of a reference gene codon, and ends at the last (third) site of a reference gene codon. In practice, depending on the goal of the user, the alignment may contain a reference gene in which a smaller OLG is embedded; just that portion of a reference gene known to contain an OLG; a portion of a reference gene thought not to contain an OLG (i.e., a negative control); or a region in which no OLG is known, but one is being sought.

After reading in the user-provided alignment, OLGenie calculates the number of NN, SN, NS, and SS sites and differences, reporting the mean of all pairwise comparisons. This is done separately for each focal reference codon by considering all unique nonamer (9nt) alleles of which the reference codon is the center, and of which 6nt constitute a minimum overlapping unit: one reference gene codon and its two overlapping alternate gene codons. (Note that sas13 is unique in that one reference codon overlaps exactly one alternate codon.) OLGenie is sufficiently fast that these tasks require no parallelism beyond the level of the single gene alignment. Thus, for datasets with many genes, the user can implement their own parallelization by running numerous alignments (genes) simultaneously.

After results are obtained for each focal codon in the alignment, significant deviations from the null expectation of neutrality (d_N - d_S = 0) may be tested using a Z-test, where the standard error is estimated using bootstrapping (focal codon unit). Don't worry — we provide scripts to do it all!

Options

Call OLGenie using the following options:

• --fasta_file (REQUIRED): a FASTA file containing multiple aligned sequences of one coding sequence. The entire coding sequence will be analyzed as an OLG, even if only part (or none) of the alignment constitues a true OLG. The frame of the alignment must be the frame of the reference gene (see the --frame option). If the user wishes to align their own sequences, it is recommended to translate the gene sequences, align at the amino acid level, and then impose the amino acid alignment on the DNA alignment to preserve complete codons. (If you need a tool to help with this, see align_codon2aa.pl at Evolutionary Bioinformatics Toolkit.)
• --frame (REQUIRED): the frame relationship of the overlapping gene (OLG): ss12, ss13, sas11, sas12, or sas13 (see description above).
• --output_file (OPTIONAL): name of the TAB-delimited output file to be placed in the working directory unless a full path name is given. If not specified, a file will be printed in the working directory by the name OLGenie_codon_results.txt (DEFAULT).
• --verbose (OPTIONAL): tell OLGenie to report all unique nonamers (9nt) overlapping each reference codon, along with their counts, in the output file. May lead to large output files in cases with many and/or divergent sequences. If not specified, verbose output will not be reported (DEFAULT).

EXAMPLES

Example input and output files for OLGenie.pl are available in the EXAMPLE_INPUT and EXAMPLE_OUTPUT directories at this GitHub page, where reproducible examples are numbered (e.g., example1.out). This script produces TAB-delimited output with one row for each (non-terminal) codon, with columns as described in the Codon Results Output File section.

Note that, if your input file(s) (e.g., alignment.fasta) are not in the working directory (i.e., where your Terminal is currently operating), you will need to specify the full path of the file name (e.g., /Users/ohta/Desktop/OLGenie_practice/alignment.fasta). Also note that, in the examples below, a \ is used simply to continue the previous command on the line.

EXAMPLE 1: A SIMPLE RUN

Note that this is a 'real' example and may take up to 60 seconds!

OLGenie.pl --fasta_file=HIV1_env_BLAST.fa --frame=sas12 > example1.out

EXAMPLE 2: VERBOSE OUTPUT TO A USER-SPECIFIED FILE

Remember to replace the --output_file path with a location that exists on your machine.

OLGenie.pl --fasta_file=HIV1_env_BLAST.fa --frame=sas12 \
--output_file=/Users/ohta/Desktop/OLGenie_codon_results_ex2.txt --verbose > example2.out

EXAMPLE 3: TESTING FOR SIGNIFICANCE WITH BOOTSTRAPPING

Use our script OLGenie_bootstrap.R. We provide this script separately so that users can take advantage of the accessible statistical resources offerred by R without having to install Perl modules. Just make sure the R packages readr and boot have been installed (e.g., by calling install.packages("readr") and install.packages("boot") at the R console).

Call the script with the following 3-6 (unnamed) arguments (in this order):

1. CODON RESULTS FILE. The name/path of the file containing the codon results file from the OLGenie analysis. This file must not have been modified, and should only contain the results for one analysis (i.e., one gene product and frame).
2. MINIMUM NUMBER OF DEFINED CODONS PER CODON POSITION (≥2; RECOMMENDED=6). Alignment positions with very few defined (non-gap, non-ambiguous) codons may be prone to erroreous d_N/d_S estimates.
3. NUMBER OF BOOTSTRAP REPLICATES (≥2; RECOMMENDED=10000). The number of bootstrap replicates to perform (typically 1,000 or 10,000).
4. NUMBER OF CPUS (OPTIONAL; ≥1; DEFAULT=1). The number of parallel processes (CPUs) to use when bootstrapping. A typical personal laptop computer can utilize 4-8 CPUs, while a high performance computing cluster might provide access to 10s or 100s.
5. MULTIPLE HITS CORRECTION (OPTIONAL; "NONE" or "JC"; DEFAULT=NONE). When the raw p-distance (mean number of pairwise differences per site) exceeds 0.1, the possibility that sites have undergone multiple hits (recurrent changes at the same hit which cannot be measured) increases. Although no known correction is technically applicable to overlapping genes, we offer Jukes-Cantor as an option.
6. STRING TO PREPEND TO OUTPUT LINES (OPTIONAL; DEFAULT="").

Thus, the format is:

OLGenie_bootstrap.R <CODON RESULTS FILE>.txt <MIN DEFINED CODONS> <NUM BOOTSTRAPS> <NUM CPUS> > <output>.out

For example, try the following using the results from Example 2:

OLGenie_bootstrap.R OLGenie_codon_results_ex2.txt 2 1000 4 > example3.out

This produces TAB-delimited output, as described in the Bootstrap Output section.

EXAMPLE 4: SLIDING WINDOWS WITH BOOTSTRAPPING

Use our script OLGenie_sliding windows.R. Make sure the R packages dplyr, readr, stringr, and boot have been installed (e.g., by calling install.packages("boot") at the R console).

Call the script with the following 5-10 (unnamed) arguments (in this order):

1. CODON RESULTS FILE. The name/path of the file containing the codon results file from the OLGenie analysis (OLGenie_codon_results.txt). This file must not have been modified, and should only contain the results for one analysis (i.e., one gene product and frame).
2. NUMERATOR SITE TYPE. NN, SN, or NS.
3. DENOMINATOR SITE TYPE. SN, NS, or SS.
4. SLIDING WINDOW SIZE. Measured in CODONS; must be ≥2; ≥25 recommended.
5. SLIDING WINDOW STEP SIZE. Measured in CODONS; must be ≥1.
6. NUMBER OF BOOTSTRAP REPLICATES PER WINDOW (OPTIONAL; ≥2; DEFAULT=1000).
7. MINIMUM NUMBER OF DEFINED CODONS PER CODON POSITION (OPTIONAL; ≥2; DEFAULT=6).
8. MULTIPLE HITS CORRECTION (OPTIONAL; "NONE" or "JC", Jukes-Cantor; DEFAULT=NONE). Keep in mind that no correction is truly applicable to OLGs.
9. NUMBER OF CPUS (OPTIONAL; ≥1; DEFAULT=1). A typical personal laptop computer can utilize 4-8 CPUs, while a high performance computing cluster might provide access to 10s or 100s.
10. STRING TO PREPEND TO OUTPUT LINES (OPTIONAL; DEFAULT="").

Thus, the format is:

OLGenie_sliding_windows.R <CODON RESULTS FILE> <NUMERATOR> <DENOMINATOR> <WINDOW SIZE> <WINDOW STEP SIZE> <NUM BOOTSTRAPS> <MIN DEFINED CODONS> <CORRECTION> <NUM CPUS> > <output>.out

For example, a real command might look like the following:

OLGenie_sliding_windows.R OLGenie_codon_results.txt NN NS 25 1 1000 6 NONE 6 > OLGenie_sliding_windows.out

This produces TAB-delimited output, as described in the Sliding Window Output section. The output file is placed within the same directory using the name of the input file as a prefix, but adding the suffix *_WINDOWS_<RATIO>.tsv.

Output

OLGenie outputs the following data:

Standard Output

At the command line (Terminal), OLGenie will first report the date and time, the file and frame relationship used in the analysis, and any warning messages. Following completion of the analysis, OLGenie will report the following summary statistics:

• Mean numbers of sites and differences: the total numbers of NN, SN, NS, and SS sites and differences for the entire alignment, obtained by summing the results for all codons.
• Mean substitution rates (between-species) or nucleotide diversities (within-species):: OLGenie's estimates of d_NN, d_SN, d_NS, and d_SS for the entire alignment, calculated as (*_diffs / *_sites) for each site type.
• dN/dS estimates: OLGenie's estimates of d_N/d_S for the reference gene (d_NN/d_SN, d_NS/d_SS) and alternate gene (d_NN/d_NS and d_SN/d_SS) for the entire alignment.

Codon Results Output File

OLGenie will report codon-by-codon results in the file OLGenie_codon_results.txt (or any file specified with the --output_file option). The columns contain the following information:

• codon_num: the codon position in the alignment, starting at codon 2 and ending at the penultimate codon. The first and last codons are excluded because their values cannot be estimated, as one of their overlapping (alternate gene) codons is unknown, occurring before or after the alignment begins or ends, respectively. (Note that sas13 is an exception.)
• ref_codon_maj: the major (most common) allele for the reference gene codon at this position.
• alt_codon1_maj: the major (most common) allele for the alternate gene codon overlapping the beginning (5' side) of the reference codon at this position.
• alt_codon2_maj: the major (most common) allele for the alternate gene codon overlapping the end (3' side) of the reference codon at this position. Note that only alt_codon1_maj will be reported for the sas13 frame, since OLG codons form one-to-one overlaps in this frame.
• nonamers: only included when using the --verbose option. This column contains all unique nonamer (9nt) alleles occuring at this position, with the reference focal codon at the center. Different alleles are separated using the colon (:) delimiter.
• nonamer_counts: only included when using the --verbose option. This column contains the counts (number of sequences) having each unique nonamer (9nt) allele at this position, in the same order given in the nonamers column. Values for different alleles are separated using the colon (:) delimiter.
• multiple_variants: whether the nonamer at this position contains more than one nucleotide variant. If so, the OLGenie method may underestimate d_S at this position. In this case, the d_N/d_S ratio will constitute a conservative test of purifying (negative) selection, but positive (Darwinian) selection should be inferred with caution.
• NN_sites: the number of sites (i.e., possible nucleotide changes) that are nonsynonymous in both the reference and alternate genes at this reference codon.
• SN_sites: the number of sites (i.e., possible nucleotide changes) that are synonymous in the reference gene but nonsynonymous in the alternate gene at this reference codon.
• NS_sites: the number of sites (i.e., possible nucleotide changes) that are nonsynonymous in the reference gene but synonymous in the alternate gene at this reference codon.
• SS_sites: the number of sites (i.e., possible nucleotide changes) that are synonymous in both the reference and alternate genes at this reference codon.
• NN_diffs: the number of differences (i.e., observed nucleotide changes) that are nonsynonymous in both the reference and alternate genes at this reference codon.
• SN_diffs: the number of differences (i.e., observed nucleotide changes) that are synonymous in the reference gene but nonsynonymous in the alternate gene at this reference codon.
• NS_diffs: the number of differences (i.e., observed nucleotide changes) that are nonsynonymous in the reference gene but synonymous in the alternate gene at this reference codon.
• SS_diffs: the number of differences (i.e., observed nucleotide changes) that are synonymous in both the reference and alternate genes at this reference codon.

Note that any desired estimate of d_N, d_S, or their ratio can be obtained for any subregion of the alignment by summing the appropriate numbers of sites and differences and performing the appropriate calculations. For example, to calculate the alternate gene d_N/d_S = d_SN/d_SS ratio for a 25-codon window within an alignment:

1. Calculate d_SN as sum(SN_diffs)/sum(SN_sites) for those 25 codons;
2. Calculate d_SS as sum(SS_diffs)/sum(SS_sites) for those 25 codons; and
3. Calculate the d_SN/d_SS value.

Bootstrap Output

Significant deviations from neutrality (d_N - d_S = 0) can be detected using a Z-test, where the standard error of d_N - d_S is estimated using bootstrapping (reference codon unit) (Nei and Kumar 2000). Consider using our R script, OLGenie_bootstrap.R (see examples). This produces four lines of output, one for each of the four ratios: d_NN/d_SN, d_NN/d_NS, d_NS/d_SS, and d_SN/d_SS. Columns of values are given in the following order (numbered here for clarity, as these headers do not appear in the output):

1. num_codons: the total number of codons examined.
2. NN_sites: see the description of the codon output file.
3. SN_sites: see the description of the codon output file.
4. NS_sites: see the description of the codon output file.
5. SS_sites: see the description of the codon output file.
6. NN_diffs: see the description of the codon output file.
7. SN_diffs: see the description of the codon output file.
8. NS_diffs: see the description of the codon output file.
9. SS_diffs: see the description of the codon output file.
10. ratio: the ratio being estimated on this line: dNNdSN denotes d_NN/d_SN; dNNdNS denotes d_NN/d_NS; dNSdSS denotes d_NS/d_SS; and dSNdSS denotes d_SN/d_SS.
11. site_rich_ratio: whether this is the most site-rich ratio (TRUE or FALSE). Note that, for sas12, the more accurate ratios (d_NS/d_SS and d_SN/d_SS) are not the most site-rich.
12. gene: whether this line is an estimate of d_N/d_S for the reference gene (ORF1) or the alternate gene (ORF2).
13. num_replicates: number of bootstrap replicates performed.
14. dN: the point estimate of d_N (numerator of ratio).
15. dS: the point estimate of d_S (denominator of ratio).
16. dNdS: the point estimate of d_N/d_S (value of ratio).
17. dN_m_dS: the point estimate of d_N - d_S.
18. boot_dN_SE: the standard error of mean d_N, estimated by bootstrapping.
19. boot_dS_SE: the standard error of mean d_S, estimated by bootstrapping.
20. boot_dN_over_dS_SE: the standard error of mean d_N/d_S, estimated by bootstrapping.
21. boot_dN_over_dS_P: the P value of a deviation from d_N/d_S = 1 (two-sided; Z-test).
22. boot_dN_m_dS_SE: the standard error of mean d_N - d_S, estimated by bootstrapping.
23. boot_dN_m_dS_P: the P value of a deviation from d_N-d_S=0, estimated from the bootstrap SE (two-sided; Z-test). (Recommended test.)
24. boot_dN_gt_dS_count: number of bootstrap replicates in which d_N>d_S.
25. boot_dN_eq_dS_count: number of bootstrap replicates in which d_N=d_S.
26. boot_dN_lt_dS_count: number of bootstrap replicates in which d_N<d_S.
27. ASL_dN_gt_dS_P: one-sided achieved significance level (ASL) P-value of the null hypothesis that d_N>d_S.
28. ASL_dN_lt_dS_P: one-sided achieved significance level (ASL) P-value of the null hypothesis that d_N<d_S.
29. ASL_dNdS_P: two-sided achieved significance level (ASL) P-value of the null hypothesis that d_N=d_S.

Sliding Window Output

The R script OLGenie_sliding_windows.R can be used to compute any of the d_N/d_S ratio estimators and bootstrap them in one feel swoop (see examples). The output includes all the original columns present in the codon results output file, along with additional columns specific to the sliding windows. These are:

• sw_ratio: the overlapping gene d_N/d_S ratio estimator computed in the analysis, i.e., dNNdSN, dNNdNS, dNSdSS, or dSNdSS (denoting d_NN/d_SN, d_NN/d_NS, d_NS/d_SS, and d_SN/d_SS, respectively).
• sw_start: first codon included in the window.
• sw_center: middle codon included in the window.
• sw_end: last codon included in the window.
• sw_num_replicates: number of bootstrap replicates.
• sw_N_diffs: sum of NUMERATOR-type (NN, SN, or NS) differences observed in the window.
• sw_S_diffs: sum of DENOMINATOR-type (SN, NS, or SS) differences observed in the window.
• sw_N_sites: sum of NUMERATOR-type (NN, SN, or NS) sites observed in the window.
• sw_S_sites: sum of DENOMINATOR-type (SN, NS, or SS) sites observed in the window.
• sw_dN: d_N (NUMERATOR) estimate for the window.
• sw_dS: d_S (DENOMINATOR) estimate for the window.
• sw_dNdS: d_N/d_S ratio estimate for the window (neutral null expectation: 1).
• sw_dN_m_dS: d_N-d_S difference estimate for the window (neutral null expectation: 0).
• sw_boot_dN_SE: standard error (SE) of mean d_N, estimated as the standard deviation of the bootstrap replicates.
• sw_boot_dS_SE: standard error (SE) of mean d_S, estimated as the standard deviation of the bootstrap replicates.
• sw_boot_dN_over_dS_SE: standard error (SE) of mean d_N/d_S, estimated as the standard deviation of the bootstrap replicates.
• sw_boot_dN_over_dS_P: Z-test P-value of null hypothesis that d_N/d_S=1, estimated from the bootstrap SE.
• sw_boot_dN_m_dS_SE: standard error (SE) of mean d_N-d_S, estimated as the standard deviation of the bootstrap replicates.
• sw_boot_dN_m_dS_P: the P value of a deviation from d_N-d_S=0, estimated from the bootstrap SE (two-sided; Z-test). (Recommended test.)
• sw_boot_dN_gt_dS_count: number of bootstrap replicates in which d_N>d_S.
• sw_boot_dN_eq_dS_count: number of bootstrap replicates in which d_N=d_S.
• sw_boot_dN_lt_dS_count: number of bootstrap replicates in which d_N<d_S.
• sw_ASL_dN_gt_dS_P: one-sided achieved significance level (ASL) P-value of the null hypothesis that d_N>d_S.
• sw_ASL_dN_lt_dS_P: one-sided achieved significance level (ASL) P-value of the null hypothesis that d_N<d_S.
• sw_ASL_dNdS_P: two-sided achieved significance level (ASL) P-value of the null hypothesis that d_N=d_S.

Troubleshooting

If you have questions about OLGenie, please click on the Issues tab at the top of this page and begin a new thread, so that others might benefit from the discussion. Common questions will be addressed in this section.

Acknowledgments

OLGenie was written with support from a Gerstner Scholars Fellowship from the Gerstner Family Foundation at the American Museum of Natural History to C.W.N. (2016-2019), and is maintained with support from a 中央研究院 Academia Sinica Postdoctoral Research Fellowship (2019-2021). The logo image was designed by Mitch Lin (2019); copyright-free DNA helix obtained from Pixabay. Thanks to Reed Cartwright, Dan Graur, Jim Hussey, Michael Lynch, Sergios Orestis-Kolokotronis, Wen-Hsiung Li, Apurva Narechania, Siegfried Scherer, Sally Warring, Jeff Witmer, Meredith Yeager, Jianzhi (George) Zhang, Martine Zilversmit, and the Sackler Institute for Comparative Genomics workgroup for discussion along the way.

Citation

When using this software, please refer to and cite:

Nelson CW, Ardern Z, Wei X. OLGenie: Estimating Natural Selection to Predict Functional Overlapping Genes. Molecular Biology and Evolution 37(8):2440-2449. DOI: https://doi.org/10.1093/molbev/msaa087

and this page:

https://github.com/chasewnelson/OLGenie

Contact

If you have questions about OLGenie, please click on the Issues tab at the top of this page and begin a new thread, so that others might benefit from the discussion.

Other correspondence should be addressed to Chase W. Nelson:

• cnelson <AT> amnh <DOT> org

References

• Nei M, Gojobori T. 1986. Simple methods for estimating the numbers of synonymous and nonsynonymous nucleotide substitutions. Molecular Biology and Evolution 3(5):418-426.
• Nei M, Kumar S. 2000. Molecular Evolution and Phylogenetics. New York, NY: Oxford University Press.
• Nelson CW, Moncla LH, Hughes AL. 2015. SNPGenie: estimating evolutionary parameters to detect natural selection using pooled next-generation sequencing data. Bioinformatics 31(22):3709-3711.
• Pavesi A, Vianelli A, Chirico N, Bao Y, Blinkova O, Belshaw R, Firth A, Karlin D. 2018. Overlapping genes and the proteins they encode differ significantly in their sequence composition from non-overlapping genes. PLoS ONE 13:e0202513.
• Sabath N. 2009. Molecular Evolution of Overlapping Genes. ProQuest Dissertation #3405062.
• Sabath N, Landan G, Graur D. 2008. A method for the simultaneous estimation of selection intensities in overlapping genes. PLoS One 3(12):e3996.
• Wei X, Zhang J. 2015. A simple method for estimating the strength of natural selection on overlapping genes. Genome Biology and Evolution 7(1):381-390.