Introduction

Statistical inference of the extent at which Darwinian natural selection had impacted on genetic data from multiple populations commands a healthy quota of the phylogenetic literature (Jacques et al. 2023). Validation of these codon-based models relies heavily on simulated data. A search of the entries on the Bioconductor (Gentleman et al. 2004) platform, on 29 July 2024, with keywords codon, mutation, selection, simulate and simulation returned a total of 72 unique (out of the 2300 available Software) packages. None of the retrieved entries was dedicated to codon data simulation for natural selection analyses. Given the ever increasing diverse types of models of natural selection inference from molecular data that exist, there is indeed need for applicable packages on the platform.

Population genomic studies provided the mathematical foundation upon which phylogenetics thrived (Wright 1931; Fisher 1922; Hardy 1908; Weinberg 1908; Darwin 1859). The thirst to bridge the gap between these two genres of evolutionary biology continue to drive the invention of more complex models of evolution (Aris-Brosou and Rodrigue 2012). Consequently, there is need to develop codon sequence simulators to match the growth. scoup is designed on the basis of the mutation-selection (MutSel) framework (Halpern and Bruno 1998) as a contribution to this quest. Only a couple of existing selection-focused simulators in the literature used the MutSel framework (Spielman and Wilke 2015; Arenas and Posada 2014). This is most probably due to the perceived complexity of the methodology. In scoup, the versatility of the Uhlenbeck and Ornstein (1930) algorithm as a framework for evolutionary analyses (Bartoszek et al. 2017) was exploited to circumvent the complexity.

In a bid to identify an appropriate quantifier that permits direct comparison between the degree of selection signatures imposed during simulation and that inferred, the ratio of the variance of the non-synonymous to synonymous selection coefficients (vN/vS) was discovered to be appropriate. The vN/vS statistic is consequently posited as a quality selection discriminant metric. scoup therefore represents an important contribution to the phylogenetic modelling literature. Example code of how to successfully use the package is presented below.

Installation

Use the following code to install scoup from the Bioconductor platform.

if(!requireNamespace("BiocManager", quietly=TRUE))
    install.packages("BiocManager")
BiocManager::install("scoup")

Sample Code

Three primary evolutionary algorithms are available in scoup. These include the frequency-dependent (Jones et al. 2017; Ayala and Campbell 1974), the Ornstein-Uhlenbeck (OU) and the discrete algorithms. Example of R (R Core Team 2024) code where these functions were utilised are presented. The homogeneous (Muse and Gaut 1994; Goldman and Yang 1994) and heterogeneous (site-wise and branch-wise) (Nielsen and Yang 1998; Kosakovsky Pond and Frost 2005) selection inference modelling contexts were explored. Data quality was assessed by comparing the maximum likelihood inferred (ω) and the analytically calculated (dN/dS) estimates to the magnitude of the imposed selection pressure (measured by vN/vS). Template code used to analyse the output data (to obtain ω) with PAML (Álvarez-Carretero, Kapli, and Yang 2023; Yang 2007) and FUBAR (Murrell et al. 2013; Kosakovsky Pond, Frost, and Muse 2005) are presented in the Appendix. The R code presented subsequently, require that the user should have already installed the scoup package.

Ornstein-Uhlenbeck Sensitivity

# Make package accessible in R session
library(scoup)

## Loading required package: Matrix

# Number of extant taxa
## Excluded values contributed to results presented in article
leaves <- 8 # 64

# Number of codon sites
## Excluded values contributed to results presented in article
sSize <- 15 # 250

# Number of data replications for each parameter combination
## Edited count was used for the results presented in article
sims <- 1 # 50

# OU reversion parameter (Theta) value
## Excluded values contributed to results presented in article
eThta <- c(0.01) # c(0.01, 0.1, 1)

# OU asymptotic variance value
## Excluded values contributed to results presented in article 
eVary <- c(0.0001) # c(0.0001, 0.01, 1)

# OU landscape shift parameters
hbrunoStat <- hbInput(c(vNvS=1, nsynVar=0.01))

# Sequence alignment size information
seqStat <- seqDetails(c(nsite=sSize, ntaxa=leaves))

# Iterate over all listed OU variance values
for(g in seq(1,length(eVary))){

    # Iterate over all listed OU reversion parameter values
    for(h in seq(1,length(eThta))){

        # Create appropriate simulation function ("ou") object
        adaptStat <- ouInput(c(eVar=eVary[g],Theta=eThta[h]))

        # Iterate over the specified number of replicates
        for(i in seq(1,sims)){

            # Execute simulation
            simData <- alignsim(adaptStat, seqStat, hbrunoStat, NULL)
        }
    }
}
# Print simulated alignment
seqCOL(simData)

## DNAStringSet object of length 8:
##     width seq                                               names               
## [1]    45 AGGCTGCGCTTTCCACGGGTTGCTCTTAATGCCTTCGGCGCGCTG     S001
## [2]    45 AAGCTGCGCTTTCCACGGGTTGCTCTTAATGCCTTCGGCGCGCTG     S002
## [3]    45 AAGCTGCGCTTTCCACGGGTTGCTTTTAATGCCCTTGGCGCGCTG     S003
## [4]    45 AAGCTGCGCTTTTCACGGGTTGCTCTTAATGCCTTAGGCGCGCTG     S004
## [5]    45 AAGCGGCGTTTTCCACGGGTTGCTCCTAATGCCTGCGGCGGGCTG     S005
## [6]    45 AAGCGGCGTTTTCCACGGGGTGCTCATAATGCCTTCGGCGCGCTG     S006
## [7]    45 AAGCGGTGTTTTTCACGGGTTGCTCATAATGCATTCGGCGCGCTG     S007
## [8]    45 AAGCGGCGTTTTTCACGGGTTGCTCATAATACATTCGGCGCGCCG     S008

As expected, the correlation coefficient estimate was approximately 0.9974 when the means of the inferred (ω) and the calculated (dN/dS) selection effects were compared. The correlation estimation included all the commented values.

vN/vS Sensitivity

# Make package accessible in R session
library(scoup)

# Number of extant taxa
## Omitted value was used for the results presented in article
xtant <- 8 # 64

# Number of codon sites
## Omitted count was used for the results presented in article
siteSize <- 15 # 64

# Number of data replications for each parameter combination
## Omitted count was used for the results presented in article
simSize <- 1 # 50

# Variance of the non-synonymous selection coefficients
## Excluded values contributed to results presented in article
nsynVary <- c(0) # c(0, 0.001, 0.1)

# Ratio of the variance of the non-synonymous to synonymous coeff.
## Excluded values contributed to results presented in article
vNvSvec <- c(0) # c(0, 0.001,  1, 10)

# Sequence alignment size information
seqStat <- seqDetails(c(nsite=siteSize, ntaxa=xtant))

# Iterate over all listed coefficient variance ratios
for(a in seq(1,length(vNvSvec))){

    # Iterate over all listed non-synonymous coefficients variance
    for(b in seq(1,length(nsynVary))){

        # Create appropriate simulation function ("omega") object
        adaptData <- wInput(list(vNvS=vNvSvec[a],nsynVar=nsynVary[b]))
        
        # Iterate over the specified number of replicates
        for(i in seq(1,simSize)){

            # Execute simulation
            simulateSeq <- alignsim(adaptData, seqStat, NA)
        }
    }
}
# Print simulated alignment
cseq(simulateSeq)

##                                            Sequence
##  S001 GCAGGGGCTACGAGCGAGGTTTGTGGTGGAATCGACGGATGTGTA
##  S002 GTACAGTGTACCAGCGAGGTCTGTGGGGGAACCGCCAGATATGGG
##  S003 TTACAGCGTATCAGTGAGATTTGTGGTAGAGCGGTTCGTTGGGTG
##  S004 GTACCGCATATCAGTGAAATCTGTGGTAGAACGGTCCGTTGGGTG
##  S005 GATCAGCTTATCAACAAGGTCTGCGGTCGGGCAGTGCGTTGGGTG
##  S006 GGACAGCTTAGCAACAAGGTCTATGGTAGGACGGTGCGTAGGATG
##  S007 GAACGGTCCAGTAATAAGGTCCGTGGCATGACAGTCCGTTGGATA
##  S008 GAACGGCCTAGTAGTAAGGCCCGTGGCATGATAGTGCGTTGGATA

Sequences generated with the presented code (with the excluded values activated) produced strongly correlated selection inferences (correlation coefficient ≈ 0.9923) when the average dN/dS and the ω values were compared. This implementation is an example of how to execute the frequency-dependent evolutionary technique with the package.

Site-wise Application

# Make package accessible in R session
library(scoup)

# Number of codon sites
## Commented value was used for results presented in article
sitesize<- 15 # 100

# Variance of non-synonymous selection coefficients
nsynVary <- 0.01

# Number of extant taxa
## Commented value was used for results presented in article
taxasize <- 8 # 1024

# Sequence alignment size information
seqsEntry <- seqDetails(c(nsite=sitesize, ntaxa=taxasize))

# Create the applicable ("ou") object for simulation function
## eVar= OU asymptotic variance, Theta=OU reversion parameter
adaptEntry <- ouInput(c(eVar=0.1,Theta=1))

# Ratio of the variance of the non-synonymous to synonymous coeff.
## Excluded values contributed to results presented in article
sratio <- c(0) # c(0, 1e-06, 1e-03, 0.1, 1, 10, 1000)

# Iterate over all listed coefficient variance ratios
for(a0 in seq(1,length(sratio))){

    # OU landscape shift parameters
    mValues <- hbInput(c(vNvS=sratio[a0], nsynVar=nsynVary))
    
    # Execute simulation
    simSeq <- alignsim(adaptEntry, seqsEntry, mValues, NA)
}
# Print simulated codon sequence
cseq(simSeq)

##                                            Sequence
##  S001 AGTCCTTATTCCAGGATAAGACGTCGATACGGAACTAACAACTGG
##  S002 AGACCTTATTCCCGGATAAGGCGTCGGTACGGAGCTAACAACTGG
##  S003 AGTCCTTATTCGCGGATAAGACGTCGGTACGGAGCTGACAACTGG
##  S004 AGTCCTTATTCGCGGATAGGACGTCGGTACGGAGCTAACAATGGG
##  S005 AGTCCCTATTCTTGCTTAAGACGTCGGTACAGCGATAACAACTGG
##  S006 AGCCCTTACTCTCGCTTAAGACGTCGGTACGGCGATAACAACTGG
##  S007 AGTCCTTATTCCCGGACGAGGCTACGGTACGGGGCTAACAACTGG
##  S008 AGTCCTTATTCCCGGACTAGACTTCGGTACGGAGCTGACAACTCG

This is another example of how to call the OU shifting landscape evolutionary approach. The results obtained yielded a pairwise correlation coefficient estimate of approximately 0.9988 between the means of dN/dS and ω. The correlation coefficient estimates were approximately 0.8123 and 0.8305 when the averages were each compared to vN/vS, respectively.

Branch-wise (Episodic) Test

# Make package accessible in R session
library(scoup)

# Number of internal nodes on the desired balanced tree
iNode <- 3

# Number of required codon sites
## Excluded value was used for the results presented in article
siteCount <- 15 # 1000

# Variance of non-synonymous selection coefficients
nsnV <- 0.01

# Number of data replications for each parameter combination
## Edited count was used for the results presented in article
nsim <- 1 # 50

# Ratio of the variance of the non-synonymous to synonymous coeff.
## Excluded values contributed to results presented in article
vNvSvec <- c(0) # c(0, 1e-06, 1e-03, 0.1, 1, 10, 100)

# Sequence alignment size information
seqsBwise <- seqDetails(c(nsite=siteCount, blength=0.10))

# Iterate over all listed coefficient variance ratios
for(h in seq(1,length(vNvSvec))){

    # Iterate over the specified number of replicates
    for(i in seq(1,nsim)){

        # Create the parameter set applicable at each internal tree node
        scInput <- rbind(vNvS=c(rep(0,iNode-1),vNvSvec[h]),
                        nsynVar=rep(nsnV,iNode))
        
        # Create the applicable ("discrete") object for simulation function
        adaptBranch <- discreteInput(list(p02xnodes=scInput))
        
        # Execute simulation
        genSeq <- alignsim(adaptBranch, seqsBwise, NULL)
    }
}
# Print simulated sequence data
seqCOL(genSeq)

## DNAStringSet object of length 8:
##     width seq                                               names               
## [1]    45 GAATGCAGACAGTATCAAGTCCAGAGAGGAAATTCAGCTCATGCG     S001
## [2]    45 GAATGCAGACAGTATCAAGTCCAGCGAGGAAATTCAGCTCATGCG     S002
## [3]    45 GAGTGTAGACAGTATCAAGTTCAGAGAGGGAACTCATTTCACACG     S003
## [4]    45 GACTGCAGACAGTATCGAGTTCAAAGAGGAAACTCATTTCATGCG     S004
## [5]    45 GAATGCCGACAATATCAGGTCCAGAGATGCAACTCATCACATGCG     S005
## [6]    45 AAATGCCGACAATATCAGGTCCAGAGATGTAACTCATCACATGCG     S006
## [7]    45 GAGTGTCGACAGCACCAGGTCCAGAGGGGGAACTCATCACATGCG     S007
## [8]    45 GAGTGCCGACAGCACCAGGTCCAGAGGGGGAACTCGTCACATGCG     S008

The correlation coefficient between the averages of the analytical dN/dS and the inferred ω estimates was approximately 0.9998, obtained from 50 independent iterations of the code for all the listed vN/vS values. The correlation coefficient estimate was approximately 0.6349 for vN/vS vs ω and 0.6360 for vN/vS vs dN/dS.

Conclusion

Reference scoup code were presented to facilitate use of the package. Although not explicitly presented, it is also possible to generate data with signatures of directional selection by setting the aaPlus element of the wInput entry of the alignsim function accordingly. The capacity of the package is expected to be extended in future versions.

Citation

A more appropriate citation will be provided for the package after it has been accepted to the Bioconductor platform and after the corresponding article has been accepted for publication. In the meantime, to cite this package, use Sadiq, H. 2024. “scoup: Simulate Codon Sequences with Darwinian Selection Incorporated as an Ornstein-Uhlenbeck Process”. R Package. doi:10.18129/B9.bioc.scoup.

References

Appendix: Sample Data Analyses (Non-R) Code

CODEML script executed in PAML to infer single alignment-wide ω estimates for data sets generated from 50 independent executions of each of the sensitivity analyses code presented above. The same CODEML script was used to analyse data (also 50 replicates) from the episodic analyses code, with the model entry replaced with 2. The scoup simulated sequence data and tree are seq.nex and seq.tre, respectively.

    seqfile   = seq.nex
    treefile  = seq.tre
    outfile   = seq.out
    noisy     = 0
    verbose   = 0
    seqtype   = 1
    ndata     = 1
    icode     = 0
    cleandata = 0
    model     = 0
    NSsites   = 0
    CodonFreq = 3
    estFreq   = 0
    clock     = 0
    fix_omega = 0
    omega     = 1e-05

FUBAR command executed with HyPhy through the terminal in MacBook. Note that HyPhy was already installed on the computer. The seq.nex input is the scoup simulated codon sequence data that is saved in the same NEXUS file with the tree data. The NEXUS file resides in the working directory.

hyphy fubar --code Universal --alignment seq.nex --tree seq.nex

Session info

The output of sessionInfo() from the computer where this file was generated is provided below.

## R version 4.4.1 (2024-06-14)
## Platform: x86_64-pc-linux-gnu
## Running under: Ubuntu 24.04.1 LTS
## 
## Matrix products: default
## BLAS:   /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3 
## LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.26.so;  LAPACK version 3.12.0
## 
## locale:
##  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
##  [3] LC_TIME=en_US.UTF-8        LC_COLLATE=C              
##  [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
##  [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
##  [9] LC_ADDRESS=C               LC_TELEPHONE=C            
## [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       
## 
## time zone: Etc/UTC
## tzcode source: system (glibc)
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
## [1] scoup_1.1.0      Matrix_1.7-1     BiocStyle_2.35.0
## 
## loaded via a namespace (and not attached):
##  [1] crayon_1.5.3            httr_1.4.7              cli_3.6.3              
##  [4] knitr_1.48              rlang_1.1.4             xfun_0.48              
##  [7] UCSC.utils_1.2.0        jsonlite_1.8.9          S4Vectors_0.44.0       
## [10] buildtools_1.0.0        Biostrings_2.75.0       htmltools_0.5.8.1      
## [13] maketools_1.3.1         sys_3.4.3               stats4_4.4.1           
## [16] sass_0.4.9              rmarkdown_2.28          grid_4.4.1             
## [19] evaluate_1.0.1          jquerylib_0.1.4         fastmap_1.2.0          
## [22] GenomeInfoDb_1.43.0     IRanges_2.41.0          yaml_2.3.10            
## [25] lifecycle_1.0.4         BiocManager_1.30.25     compiler_4.4.1         
## [28] XVector_0.46.0          lattice_0.22-6          digest_0.6.37          
## [31] R6_2.5.1                GenomeInfoDbData_1.2.13 bslib_0.8.0            
## [34] tools_4.4.1             zlibbioc_1.52.0         BiocGenerics_0.53.0    
## [37] cachem_1.1.0

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Bartoszek, Krzysztof, Sylvain Glémin, Ingemar Kaj, and Martin Lascoux. 2017. “Using the Ornstein–Uhlenbeck Process to Model the Evolution of Interacting Populations.” Journal of Theoretical Biology 429: 35–45.

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Fisher, R A. 1922. “On the Dominance Ratio.” Proceedings of the Royal Society of Edinburgh 42: 321–41.

Gentleman, Robert C, Vincent J Carey, Douglas M Bates, Ben Bolstad, Marcel Dettling, Sandrine Dudoit, Byron Ellis, et al. 2004. “Bioconductor: Open Software Development for Computational Biology and Bioinformatics.” Genome Biology 5 (10): R80.

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Murrell, Ben, Sasha Moola, Amandla Mabona, Thomas Weighill, Daniel Sheward, Sergei L Kosakovsky Pond, and Konrad Scheffler. 2013. “FUBAR: A Fast, Unconstrained Bayesian AppRoximation for Inferring Selection.” Molecular Biology and Evolution 30 (5): 1196–1205.

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scoup: Simulate Codons with Darwinian Selection Incorporated as an Ornstein-Uhlenbeck Process