Computer Programs and Methodologies for the Simulation of DNA Sequence Data with Recombination

Abstract

Computer simulations are useful in evolutionary biology for hypothesis testing, to verify analytical methods, to analyze interactions among evolutionary processes, and to estimate evolutionary parameters. In particular, the simulation of DNA sequences with recombination may help in understanding the role of recombination in diverse evolutionary questions, such as the genome structure. Consequently, plenty of computer simulators have been developed to simulate DNA sequence data with recombination. However, the choice of an appropriate tool, among all currently available simulators, is critical if recombination simulations are to be biologically meaningful. This review provides a practical survival guide to commonly used computer programs and methodologies for the simulation of coding and non-coding DNA sequences with recombination. It may help in the correct design of computer simulation experiments of recombination. In addition, the study includes a review of simulation studies investigating the impact of ignoring recombination when performing various evolutionary analyses, such as phylogenetic tree and ancestral sequence reconstructions. Alternative analytical methodologies accounting for recombination are also reviewed.

Full text

MINI REVIEW ARTICLE
published: 01 February 2013
doi: 10.3389/fgene.2013.00009
Computer programs and methodologies for the simulation
of DNA sequence data with recombination
Miguel Arenas*
Centre for Molecular Biology “Severo Ochoa,” Consejo Superior de Investigaciones Científicas, Madrid, Spain
Edited by:
Badri Padhukasahasram, Ford, USA
Reviewed by:
Bjørn Østman, Michigan State
University, USA
Marcos Perez-Losada, Centro de
Investigação em Biodiversidade e
Recursos Genéticos, Portugal
*Correspondence:
Miguel Arenas, Centre for Molecular
Biology “Severo Ochoa,” Consejo
Superior de Investigaciones
Científicas – Universidad Autónoma
de Madrid, C/Nicolás Cabrera, 1,
28049 Cantoblanco, Madrid, Spain.
e-mail: marenas@cbm.uam.es
Computer simulations are useful in evolutionary biology for hypothesis testing, to verify
analytical methods, to analyze interactions among evolutionary processes, and to estimate
evolutionary parameters. In particular, the simulation of DNA sequences with recombina-
tion may help in understanding the role of recombination in diverse evolutionary questions,
such as the genome structure. Consequently, plenty of computer simulators have been
developed to simulate DNA sequence data with recombination. However, the choice of an
appropriate tool, among all currently available simulators, is critical if recombination sim-
ulations are to be biologically meaningful. This review provides a practical survival guide
to commonly used computer programs and methodologies for the simulation of coding
and non-coding DNA sequences with recombination. It may help in the correct design
of computer simulation experiments of recombination. In addition, the study includes a
review of simulation studies investigating the impact of ignoring recombination when per-
forming various evolutionary analyses, such as phylogenetic tree and ancestral sequence
reconstructions. Alternative analytical methodologies accounting for recombination are also
reviewed.
Keywords: simulation, recombination, recombination breakpoints, recombination hotspots, DNA sequences,
recombination phylogenetic bias
INTRODUCTION
Recombination constitutes a basic and dominant mechanism in
molecular evolution, increasing genetic diversity before natural
selection operates on the new sequence. Recombination is wide-
spread across nuclear genomes (e.g.,Awadalla, 2003;Tsaousis et al.,
2005;Fraser et al., 2007;Gaut et al., 2007;Duret and Arndt, 2008)
and the importance of its understanding has been long recog-
nized, with crucial implications for genome structure (Reich et al.,
2001), phenotypic diversity (Zhang et al., 2002), and genetic dis-
eases (Daly et al., 2001). Moreover, ignoring recombination may
bias phylogenetic reconstructions (e.g., Posada, 2001;Posada and
Crandall, 2002;Beiko et al., 2008), and the derived inferences (e.g.,
Schierup and Hein, 2000a;Feil et al., 2001;Anisimova et al., 2003;
Arenas and Posada, 2010a,b,c).
The evolutionary importance of recombination (e.g., Robert-
son et al., 1995;Lukashev, 2005) calls for its accurate detection
and measurement (see, Martin et al., 2011). Although some ana-
lytical methods have shown an overall better performance than
others (Posada and Crandall, 2001;Wiuf et al., 2001), the choice
of an appropriate tool also depends on the particular analysis
(e.g., detection of recombination breakpoints or estimation of
recombination rates), computational costs (some methods are
computationally expensive), and the genetic marker. I recom-
mend the following two reviews for helping users to make choices
for appropriate methods and computer tools for recombination
inference (Posada et al., 2002;Martin et al., 2011).
Computer simulations aim to mimic real world processes. They
allow the study of mechanisms that may alter processes or the
understanding of complex systems that are analytically intractable
(Peck, 2004). Indeed, the simulation of evolutionary histories is
commonly used for hypothesis testing (e.g., Arenas et al., 2008;
Pierron et al., 2011), to verify and compare analytical methods
or programs (e.g., Westesson and Holmes, 2009;Marttinen et al.,
2012), to analyze interactions among evolutionary processes (e.g.,
Arenas et al., 2012, 2013), or to estimate evolutionary parameters
(e.g., Wilson et al., 2009;Beaumont, 2010). Importantly, the choice
of an appropriate simulator is critical because simulations should
be as realistic as possible in order to mimic a given biological sce-
nario. Although several studies have already reviewed computer
simulators in population genetics from global perspectives (e.g.,
Liu et al., 2008;Arenas, 2012;Arenas and Posada, 2012;Hoban
et al., 2012), they have not explored particular methodologies for
the simulation of DNA sequences with recombination.
The present study provides an overview of the capabilities
of available computer tools and methodologies, and suggests
recommendations, for the simulation of DNA sequences with
recombination. It also describes some applications of simulated
datasets with recombination to show the importance of includ-
ing recombination in evolutionary analyses. Alternative analytical
methodologies that consider recombination are also suggested.
COMPUTER PROGRAMS FOR THE SIMULATION OF DNA
DATA UNDER RECOMBINATION
Recombination can be simulated by the two major simulation
approaches commonly used in population genetics, the forward
in time (forward-time, where the evolutionary history of an entire
population is simulated from the past to the present; e.g.,Epperson
et al., 2010) and the coalescent (backward-time, which describes a
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Arenas Simulation of DNA recombination
backward in time genealogical process from a sample of genes to
a single ancestral copy; e.g., Nordborg, 2007;Wakeley, 2008). The
forward-time approach can simulate complex processes, including
gene–gene interactions and complex selection (e.g., Calafell et al.,
2001;Peng et al., 2007), but coalescent simulations are computa-
tionally faster and can be recommended for extensive simulation
studies (e.g., Beaumont et al., 2002). Table 1 shows an overview
of currently available computer programs, for both coalescent
and forward-time approaches, to simulate DNA sequences with
recombination.
SIMULATION OF CODING DNA SEQUENCES WITH RECOMBINATION
Direct simulation of coding DNA sequences with recombination
can be only performed with a few programs. Using the coales-
cent approach, the programs Recodon (Arenas and Posada, 2007),
CodonRecSim (Anisimova et al., 2003), and NetRecodon (Arenas
and Posada, 2010a) allow such simulation, but only the latter pro-
gram does not force recombination breakpoints to occur between
codons, thus allowing more realistic simulations (see Arenas and
Posada, 2010a). Concerning the forward-time approach, only the
programs GenomePop (Carvajal-Rodriguez,2008) and SFS_CODE
(Hernandez, 2008) implement the simulation of coding sequences
with recombination.
Evolutionary scenarios that are not implemented in these pro-
grams can be simulated by the following alternative methodology,
which is based on the concatenation of two different simulators.
First, we simulate an evolutionary history with recombination [an
ancestral recombination graph (ARG, see Figure 1A), which con-
tains a tree for each recombinant fragment; Figures 1B–D]. This
procedure can be carried out using, for example, the program ms
(Hudson, 2002); see also other evolutionary history simulators in
(Hoban et al., 2012). Next, we simulate molecular evolution of each
coding fragment, according to a user-specified codon-substitution
model, along its corresponding simulated tree (further details in
Yang, 2006;Fletcher and Yang, 2009). Finally, we just concate-
nate the simulated coding fragments. The simulation of coding
sequence evolution along given trees can be performed, for exam-
ple, with the program INDELible (Fletcher and Yang, 2009); see
also other software in (Arenas, 2012;Arenas and Posada, 2012).
The limitation of this methodology is that recombination break-
points are always assumed to occur between codons and not within
codons.
SIMULATION OF NUCLEOTIDE SEQUENCES WITH RECOMBINATION
A number of computer programs can directly simulate non-coding
DNA sequences under recombination (see Table 1). Similarly
to the previous subsection, the simulation of non-coding DNA
sequences under other evolutionary scenarios, which are not
described in the Table 1, can be performed by combining two
computer tools. We can use a simulator of recombination evolu-
tionary histories (e.g., ms or msms;Ewing and Hermisson, 2010)
followed by a non-coding DNA sequence evolution simulator (e.g.,
INDELible,Seq-Gen,Rambaut and Grassly, 1997;EVOLVER,Yang,
1997; or indel-Seq-Gen,Strope et al., 2009).
SIMULATION OF GENOMES WITH RECOMBINATION HOTSPOTS
It is known that the recombination rate is not homogeneous
throughout the genome and some regions (hotspot regions)
are more likely to suffer recombination (e.g., Gabriel et al.,
2002;Zhuang et al., 2002). Consequently, recombination hotspots
should be considered for realistic genome simulation.
The simulation of genomes with recombination requires
robust and memory-efficient simulators. Programs like fastsim-
coal (Excoffier and Foll, 2011) or mlcoalsim (Ramos-Onsins and
Mitchell-Olds, 2007) allow for efficient simulations of non-coding
genomic regions under recombination (including recombination
hotspots). However, these tools do not implement a variety of sub-
stitution models (e.g., codon models), or particular evolutionary
mechanisms like selection; this may be problematic if we are trying
to mimic genome-wide data (see, Arbiza et al., 2011).
Again, an alternative methodology consists of the use of two
simulators. A few programs currently implement the simulation
of recombination hotspots, namely, SNPsim (Wiuf and Posada,
2003), cosi (Schaffner et al., 2005), GENOME (Liang et al., 2007),
mbs (Teshima and Innan, 2009), and msHOT (Hellenthal and
Stephens, 2007). Although all these programs simulate particular
genetic markers (such as SNPs or STRs), DNA sequence evolu-
tion can be simulated upon phylogenetic trees produced by these
programs if we use the two-step procedure described above.
SIMULATION OF RECOMBINATION PHYLOGENETIC NETWORKS
In order to represent a full evolutionary history with recombina-
tion, phylogenetic networks should be used instead of forcing the
genealogy onto a single tree (Huson and Bryant, 2006). There are
two commonly used methodologies for the simulation of recom-
bination networks: direct simulation of the ARG (e.g., Figure 1A)
or combining the simulated trees for each recombinant fragment
(e.g., Figures 1B–D). To my knowledge, only two programs can
really output a simulated ARG, namely, Serial NetEvolve (Buen-
dia and Narasimhan, 2006) and NetRecodon (Arenas and Posada,
2010a), where the ARG can be visualized and analyzed using the
NetTest web server (Arenas et al., 2010)1. On the other hand,
trees can be combined to generate a network using tools like
CombineTrees (see for a review, Woolley et al., 2008)2.
RECOMBINATION SIMULATION FOR ANALYZING THE
INFLUENCE OF RECOMBINATION ON PHYLOGENETIC
INFERENCES
This section outlines three computer simulation studies where
ignoring recombination leads to biased phylogenetic inferences.
Alternative phylogenetic inference methodologies considering
recombination are also suggested.
INFLUENCE OF RECOMBINATION ON PHYLOGENETIC TREE
RECONSTRUCTION
Schierup and Hein (2000a) simulated samples under the coa-
lescent with recombination (Hudson, 1983). Then, from the
simulated genealogy, they simulated nucleotide sequence evolu-
tion under the Jukes-Cantor (JC) and Kimura’s two-parameter
(K2P) nucleotide substitution models of evolution. The simu-
lated datasets were analyzed using programs for phylogenetic tree
1http://darwin.uvigo.es/software/nettest/
2http://applications.lanevol.org/combineTrees/
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Arenas Simulation of DNA recombination
Table 1 | Commonly used software for direct simulation of DNA sequences under recombination.
Program Evolutionary
history
Recombination
algorithm
Recombination
hotspots
Other
evolutionary
processes
Substitution
model
Rate
variation
Intracodon
recombination
Indels OS Citation
CodonRecSim Coalescent SCR No No Codb: GY94 No No No SC, W in Anisimova et al. (2003)
Recodon/
NetRecodon
Coalescent SCRaNo D, Pm Nt: All; Codb:
GY94
G, I Yes (NetRecodon) No All Arenas and Posada (2007,
2010a)
SIMCOAL2 Coalescent SCR Yes D, Pm Nt: JC, K2P No No No Linux, Win Laval and Excoffier (2004)
Fastsimcoal Coalescent SMC Yes D, Pm Nt: JC, K2P No No No Linux, Mac,
Win
Excoffier and Foll (2011)
Mlcoalsim Coalescent SCR Yes D, Pm Nt: JC, K2P G, I No No All Ramos-Onsins and
Mitchell-Olds (2007)
TREEEVOLVE Coalescent SCR No D, Pm Nt: All G No No SC, Mac Grassly and Rambaut (1997)
SPLATCHE2 Forward,
coalescent
SCR No D, Pm Nt: JC, K2P No No No Linux, Win Ray et al. (2010)
GenomePop Forward CO Yes D, Pm, S Nt: JC, GTR;
Cod: MG94
No Yes No SC, Linux, Win Carvajal-Rodriguez (2008)
SFS_CODE Forward CO, SB Yes D, Pm, S Nt: All; Cod:
Ntc
G No Yes All Hernandez (2008)
SimuPop Forward CO Yes D, Pm, S Nt: All No No Yes All Peng and Kimmel (2005)
“Recombination algorithm”: “SCR” means the standard coalescent with recombination to simulate the ARG (Hudson, 1983); “SMC” indicates the sequential Markovian coalescent, which is an approximation of the
SCR (further details in, McVean and Cardin, 2005); “CO” means crossing over recombination model (see Padhukasahasram et al., 2008); “SB” indicates sex-biased recombination. “Other evolutionary processes”:
“D,” “Pm,” and “S” mean demographics, population structure with migration, and selection, respectively. “Substitution model” refers to substitution models based on nucleotide “Nt” or codon “Cod” sequences;
“Nt: All” means all nucleotide substitution models (JC, . . ., GTR). “Rate variation” indicates variable substitution rate across sites (G, gamma distribution; I, proportion of invariable sites). “Intracodon recombination”
indicates if recombination breakpoints can occur at any codon position (Yes) or are forced to occur between codons (No). “OS” shows the availability of executable files in different operating systems (“All” means
available for Macintosh,Windows, and Linux), “SC” means that the source code is available.
aThe simulated ARG can be exported from NetRecodon and then can be visualized and analyzed using NetTest (Arenas et al., 2010).
bUnder codon models, dN/dS can vary across codons.
cCoding sequences are simulated by nucleotide substitution models, avoiding stop codons.
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Arenas Simulation of DNA recombination
FIGURE 1 | Example of an ancestral recombination graph (ARG) with the
corresponding embedded trees for each recombinant fragment. (A) ARG
based on two recombination events with breakpoints at positions 100 and
200. Dashed lines indicate branches for recombinant fragments. (B–D)
Embedded tree for each recombinant fragment. Note that topologies and
branch lengths may differ across trees. Finally, the simulation of sequence
evolution can be performed site by site along the corresponding tree (see,
Yang, 2006;Fletcher and Yang, 20 09).
reconstruction by both distance-based methods and maximum-
likelihood (ML) methods. Ignoring recombination biased the
inferred phylogenetic trees toward larger terminal branches,
smaller times to the most recent common ancestor (MRCA) and
incorrect topologies (Schierup and Hein, 2000a). In addition,
ignoring recombination led to overestimation of the substitution
rate heterogeneity, apparent homoplasies and loss of molecular
clock (Schierup and Hein, 2000a,b). Later, Posada (2001) ana-
lyzed the molecular clock hypothesis on four empirical datasets.
In particular, the author applied a triplet likelihood ratio test (test
for equality of evolutionary rates among three species, called a
relative-rate test, RRT), which is independent of topology and
might be unbiased by recombination. Results showed that recom-
binant data did not allow a good fit to the molecular clock when
using classical likelihood ratio tests (LRT). However, the molecu-
lar clock was not rejected when using the RRT test. Thus, this test
could be recommended for testing a molecular clock in the pres-
ence of recombination. In addition, phylogenetic incongruence
in empirical data was also observed as a consequence of ignor-
ing recombination (e.g., Worobey and Holmes, 1999;Feil et al.,
2001).
These findings, consequently, suggest biases in derived evolu-
tionary analyses based on phylogenetic reconstructions that ignore
recombination. As an alternative, there are two methodologies of
phylogenetic reconstruction accounting for recombination:
– Inference of a single phylogenetic network (e.g., Figure 1A;Grif-
fiths and Marjoram, 1997;Huson and Bryant, 2006). Recombi-
nation networks can be inferred by using computer programs
like SplitsTree (Huson, 1998;Huson and Bryant, 2006).
– Inference of a set of phylogenetic trees, where each tree corre-
sponds to the evolutionary history of each recombinant frag-
ment (e.g., Figures 1B–D). The methodology consists of the
detection of recombination breakpoints (see for a review, Mar-
tin et al., 2011) followed by a phylogenetic tree reconstruction
for each recombinant fragment.
Both methodologies correctly account for recombination and
the choice should be based on the posterior application. For exam-
ple, the phylogenetic network may help for an easy visualization of
clades and phylogenetic relationships (e.g., Maughan and Redfield,
2009). By contrast, the simulation of sequence evolution requires
a phylogenetic tree for each recombinant fragment (e.g., Fletcher
and Yang, 2009).
INFLUENCE OF RECOMBINATION ON ANCESTRAL SEQUENCE
RECONSTRUCTION
Recently, Arenas and Posada (2010c) analyzed the effect of consid-
ering recombination on ancestral sequence reconstruction (ASR).
They performed extensive simulations of nucleotide, codon, and
amino acid data by using the coalescent with recombination
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Arenas Simulation of DNA recombination
approach implemented in NetRecodon. They then reconstructed
ancestral sequences with different ASR methods (joint ML, mar-
ginal ML, and empirical Bayes). Results clearly indicated that
ignoring recombination biases the reconstruction of ancestral
sequences, regardless of the method or software used. This ASR
error can be partially reduced if recombination is considered
(Arenas and Posada, 2010c). The methodology consists of four
steps: the detection of recombination breakpoints, the recon-
struction of a phylogenetic tree for each recombinant fragment,
the reconstruction of ancestral fragments by using the corre-
sponding trees and, finally, the concatenation of the ancestral
fragments to generate the entire ancestral sequence. The Data-
monkey web server (Kosakovsky Pond and Frost, 2005)3and the
Hyphy package (Kosakovsky Pond et al., 2005) have automated
the whole procedure described above to infer ancestral sequences
with consideration of recombination.
Arenas and Posada (2010c) also analyzed empirical data, in
particular two datasets of the env region of HIV-1. They inferred
ancestral sequences both ignoring and considering recombination,
using the methodology described above, and observed a different
number of CTL epitopes depending on whether recombination
was considered or not.
INFLUENCE OF RECOMBINATION ON THE DETECTION OF MOLECULAR
ADAPTATION
The detection of molecular adaptation (based on the non-
synonymous/synonymous substitution rate ratio, hereafter
dN/dS) is commonly used at both global (entire sequence) and
local (codon) levels. Indeed, these analyses have commonly been
applied to datasets collected from highly recombinant viruses and
bacteria (e.g., Perez-Losada et al., 2009, 2011;Bozek and Lengauer,
2010). Several studies have shown the impact of recombination
on the estimation of dN/dS (e.g., Anisimova et al., 2003;Are-
nas and Posada, 2010a). After simulating coding data under a
variety of codon-substitution models for heterogeneous selection
pressure (see, Yang et al., 2000) and different levels of recombi-
nation, they selected those heterogeneous codon models that best
fitted the simulated data by using LRTs. Results showed a weak
impact of recombination on the estimation of global dN/dS but
a strong effect on the estimation of local dN/dS, in particular
by increasing the number of false-positively selected sites (PSS).
An alternative methodology to reduce these errors consists of the
detection of recombination breakpoints followed by the recon-
struction of a phylogenetic tree for each recombinant fragment
and, finally, the estimation of dN/dS by using the corresponding
trees (see, Kosakovsky Pond et al., 2006). This methodology was
applied in (Perez-Losada et al., 2009, 2011). Again, the Datamon-
key web server and the Hyphy package have automated this whole
procedure to estimate dN/dS while accounting for recombination.
Recombination might also affect other evolutionary inferences.
For example, it could bias those analytical methods based on
the coalescent without recombination (e.g., BEAST; Drummond
and Rambaut, 2007). However these influences have not yet been
rigorously evaluated.
3http://www.datamonkey.org/
Another interesting question concerns the influence of recom-
bination on genetic diversity. Spencer et al. (2006) studied this
in humans and found that recombination only affects genetic
diversity at recombination hotspots. However, such hotspots
did not alter substitution rates, perhaps because recombination
rates were always low. By contrast, large recombination rates
(common in a variety of viruses and bacteria) may strongly
increase genetic diversity and bring novel lineages (e.g., He et al.,
2010).
At this point, I would suggest the approximate Bayesian com-
putation (ABC) approach (see for a review, Beaumont, 2010) to
estimate evolutionary parameters accounting for recombination.
ABC is based on computer simulations and provides an alter-
native for those analyses where the likelihood function cannot be
computed. Simulations can be performed according to a prior dis-
tribution for recombination rate (among other parameters) and
then, by a rejection or a regression method,a posterior distribution
can be computed to obtain the parameter estimates (Beaumont
et al., 2002). For example,Wilson et al. (2009) applied ABC for joint
estimation of a set of evolutionary parameters, such as substitu-
tion rate, dN/dS and recombination rate. By this methodology, the
influence of recombination on other evolutionary mechanisms is
accounted for, but only if it is indeed implemented in the computer
simulator.
CONCLUSION
This review provides a practical guide to the state of the art in
software, and recommends methodologies, for simulating cod-
ing and non-coding sequence data with recombination, including
recombination hotspots. Currently, only three programs imple-
ment the direct simulation of coding data with recombination.
These programs will not cover every evolutionary scenario, but
this problem can be circumvented by the use of two simulators,
one for the evolutionary history and another for sequence evolu-
tion. It is also important to consider intracodon recombination
(Arenas and Posada, 2010a), because 2/3 of recombination events
are expected to occur within codons. By contrast, the simulation of
non-coding sequences with recombination can be performed by a
variety of programs. Here again, two simulators may be combined
where necessary.
Among many other applications (e.g., Sun et al., 2011;Martti-
nen et al., 2012), the simulation of DNA data with recombination
has been especially important for demonstrating the strong influ-
ence of recombination on phylogenetic tree reconstruction and
derived analyses, such asASR or dN/dS estimation. However,some
alternative methodologies have been developed for phylogenetic
inference accounting for recombination.
The current set of computer tools to simulate DNA sequences
with recombination can cover a wide range of evolutionary scenar-
ios. However, some scenarios are still difficult to simulate and will
require the development of more complex simulators. For exam-
ple, next-generation sequencing (NGS) technologies now deliver
fast and accurate genome sequences (Metzker, 2010) that may
call for simulations of entire genomes accounting for recombi-
nation (including recombination hotspots; e.g., Westesson and
Holmes, 2009;Marttinen et al., 2012), as well as other evolutionary
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Arenas Simulation of DNA recombination
mechanisms like natural selection. Indeed, the simulation of DNA
evolution should be performed by using different substitution
models for each genomic region (Arbiza et al., 2011). Moreover,
I would expect interactions between the different evolutionary
forces, such as joint influences of natural selection and recombi-
nation on dN/dS (e.g., Anisimova et al., 2003;Kryazhimskiy and
Plotkin, 2008) or of structural protein energies on sequence evo-
lution (e.g., Bastolla et al., 2007;Arenas et al., 2009;Grahnen et al.,
2011). To my knowledge, there is currently no tool to simulate
sequences accounting for all these evolutionary features, includ-
ing interactions among them. On the other hand, there is also a
demand for fast simulations, in particular for applying ABC or
Bayesian model-choice approaches that require extensive simula-
tions (see recombination examples in, Wilson et al., 2009;Nunes
and Balding, 2010;Sohn et al., 2012).
In conclusion, there is a need to innovate continuously in fast
and complex simulators of DNA sequences with recombination
and I expect future advances in this area.
ACKNOWLEDGMENTS
I want to thank Badri Padhukasahasram, Guest Associate Edi-
tor of Frontiers in Evolutionary and Population Genetics, for the
invitation to contribute with this review to the Research Topic
“Inference of recombination and gene-conversion from whole genome
sequence variation data.” Indeed, I also want to thank the Journal
Frontiers in Evolutionary and Population Genetics for a waiver to
cover publication costs. I thank Dr Richard M. Gunton for help-
ful comments. I thank two reviewers for insightful comments and
suggestions. I thank the Spanish Government for the “Juan de la
Cierva” fellowship, JCI-2011-10452.
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Conflict of Interest Statement: The
author declares that the research was
conducted in the absence of any
commercial or financial relationships
that could be construed as a potential
conflict of interest.
Received: 20 November 2012; accepted:
17 January 2013; published online: 01
February 2013.
Citation: Arenas M (2013) Computer
programs and methodologies for the sim-
ulation of DNA sequence data with
recombination. Front. Gene. 4:9. doi:
10.3389/fgene.2013.00009
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Evolutionary and Population Genetics, a
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