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\begin{document}

\title{GenAPoPop 1.0: a user-friendly software to analyse genetic diversity and
structure in partially clonal and selfed polyploid organisms}



\author[1]{Solenn Stoeckel}%
\author[2]{Ronan Becheler}%
\author[3]{Ekaterina Bocharova}%
\author[4]{Dominique Barloy}%
\affil[1]{INRA}%
\affil[2]{INRAE}%
\affil[3]{Russian Academy of Sciences}%
\affil[4]{AGROCAMPUS OUEST}%


\vspace{-1em}



  
  \date{May 27, 2024}


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\selectlanguage{english}
\begin{abstract}
Autopolyploidy is quite common in most clades of eukaryotes. The
emergence of sequence-based genotyping methods with individual and
marker tags enables now confident allele dosage, overcoming the main
obstacle to the democratization of the population genetic approaches
when studying ecology and evolution of autopolyploid populations and
species. Reproductive modes, including clonality, selfing and allogamy,
have deep consequences on the ecology and evolution of population and
species. Analysing genetic diversity and its dynamics over generations
is one efficient way to infer the relative importance of clonality,
selfing and allogamy in populations. GENAPOPOP is a user-friendly
solution to compute the specific corpus of population genetic indices,
including indices about genotypic diversity, needed to analyse partially
clonal, selfed and allogamous polysomic populations genotyped with
confident allele dosage. It also easily provides the posterior
probabilities of quantitative reproductive modes in autopolyploid
populations genotyped at two-time steps and a graphical representation
of the minimum spanning trees of the genetic distances between polyploid
individuals, facilitating the interpretation of the genetic coancestry
between individuals in hierarchically structured populations. GENAPOPOP
complements the previously existing solutions, including SPAGEDI and
POLYGENE, to use genotypings to study the ecology and evolution of
autopolyploid populations. It was specially developed with a simple
graphical interface and workflow, and comes with a simulator to
facilitate practical course and teaching of population genetics for
autopolyploid populations.%
\end{abstract}%



\sloppy


\textbf{Title:} GenAPoPop 1.0: a user-friendly software to analyse
genetic diversity and structure in partially clonal and selfed polyploid
organisms

\textbf{Short running title:} Population genetic analyses of
autopolyploids

\textbf{Authors:} Solenn Stoeckel\textsuperscript{1,2}, Ronan
Becheler\textsuperscript{1,2}, Ekaterina Bocharova\textsuperscript{1,3},
Dominique Barloy\textsuperscript{2}

\textbf{Affiliations}

\textsuperscript{1} IGEPP, INRAE, Institut Agro, Universit\selectlanguage{ngerman}é de Rennes,
Le Rheu, France.

\textsuperscript{2} DECOD (Ecosystem Dynamics and Sustainability),
Institut Agro, IFREMER, INRAE, Rennes, France.

\textsuperscript{3} Koltzov Institute of Developmental Biology of
Russian Academy of Sciences (IDB RAS), Moscow, Russia

\textbf{Corresponding author:} solenn.stoeckel@inrae.fr

\textbf{Abstract}

Autopolyploidy is quite common in most clades of eukaryotes. The
emergence of sequence-based genotyping methods with individual and
marker tags enables now confident allele dosage, overcoming the main
obstacle to the democratization of the population genetic approaches
when studying ecology and evolution of autopolyploid populations and
species. Reproductive modes, including clonality, selfing and allogamy,
have deep consequences on the ecology and evolution of population and
species. Analysing genetic diversity and its dynamics over generations
is one efficient way to infer the relative importance of clonality,
selfing and allogamy in populations.

GenAPoPop is a user-friendly solution to compute the specific corpus of
population genetic indices, including indices about genotypic diversity,
needed to analyse partially clonal, selfed and allogamous polysomic
populations genotyped with confident allele dosage. It also easily
provides the posterior probabilities of quantitative reproductive modes
in autopolyploid populations genotyped at two-time steps and a graphical
representation of the minimum spanning trees of the genetic distances
between polyploid individuals, facilitating the interpretation of the
genetic coancestry between individuals in hierarchically structured
populations.

GenAPoPop complements the previously existing solutions, including
SPAGEDI and POLYGENE, to use genotypings to study the ecology and
evolution of autopolyploid populations. It was specially developed with
a simple graphical interface and workflow, and comes with a simulator to
facilitate practical course and teaching of population genetics for
autopolyploid populations.

\textbf{Keywords}

Polyploidy, Genotypic diversity, Genetic differentiation, Unrooted tree
of genetic distances, Bayesian inference of reproductive modes,

\textbf{Introduction}

Population genetics is a robust, cost- and time-efficient framework to
predict, understand and infer the ecology and evolution of species
(Ewens 2004, Ellegren \& Galtier 2016). This paradigm at the center of
biological evolution theory has stood the test of time to predict and
track the ancestral relatedness between individuals at the scale of
studied populations (Wakeley 2005). Using changes of genetic variations
over time and space, population genetic models allow quantifying
evolutionary forces in populations and interpreting them as hypothesized
biological and environmental influences on lineages (Ellegren \& Galtier
2016). Among all the possible biological features driving evolution,
reproductive mode is one of the most significant evolutionary force
impacting the dynamics of genetic diversity and its structure among
populations as it determines the transmission of the hereditary DNA
signal over generations (Duminil \emph{et al.} 2007). In return,
analysing the genetic diversity within populations allows inferring
their reproductive modes, providing a precious knowledge to predict and
understand their ecological and biological evolution. It also helps
better targeting ecological scenarios and more robust inferences of
other evolutionary forces (Fehrer 2010, Yu et al. 2016, Stoeckel et al.
2021). However, to date and despite nearly one century of research,
population genetic models and tools were mostly developed for sexual,
diploid species (Orive \& Krueger-Hadfield 2021, Dufresne et al. 2014).

Eukaryotes with more than two sets of homologous chromosomes
(autopolyploids) or duplicated genomic segments are very common in
ferns, flowering plant and fungi species (Barker et al. 2015, Albertin
\& Marullo 2012, Wood et al. 2009). Polyploidy seems less frequent in
animals albeit significant in a handful of clades such as in fishes,
cnidarians, amphibians and reptiles (Gregory \& Mable 2005,
Mable\emph{et al.} 2011, Boots et al. 2023). It also occurs in some
species only for some chromosomes (aneuploidy), like commonly observed
in partially clonal parasitic protozoa (Tibayrenc \& Ayala 2013,
Rougeron et al. 2015).

Polyploidization influences genetic and phenotypic diversity including
potential ecological adaptations and radiations, with a long-term
dynamic from whole genome duplication to re-diploidization (Baduel et
al. 2018, Wu et al. 2019). Interestingly, polyploidy strongly co-occurs
with reproductive modes involving partial clonality, both in natural and
experimental populations (Herben et al. 2017; Van Drunen \& Husband
2019). It also seems to be an influential complementary factor to the
more classical Baker's hypothesis of the advantage of uniparental
reproductive mode, including selfing and clonality, when peripatric
populations establish in new areas (Pandit et al. 2011, Barrett 2018,
Rutland et al. 2021). Studying the reciprocal influences of reproductive
modes on the ecology and evolution of populations is now usual in
diploid populations using their genetic diversity, favoured by a wide
range of tools adapted to analyse their genetic diversity like Genclone
(Arnaud-Haond \& Belkhir 2007), RMES (David et al. 2007) and Rclone
(Bailleul et al. 2015). However, it is less common in polyploid
populations. The lack of adapted and easily accessible analysis solution
leads previous studies to consider such datasets as haplotypes or
analyse them as diploid.

Indeed, population genetic studies of polyploid organisms were long
limited by two main difficulties (Dufresne et al. 2014, Jighly et al.
2018). First, accessing robust genotyping in such populations has long
been a true challenge due to the problematic allele dosage in
individuals. For example, it was methodologically impractical to
distinguish between \emph{AABB} , \emph{ABBB} and \emph{AAAB}
individuals at a tetraploid genetic marker with two alleles, A and B,
without assuming hypotheses difficult to verify (Dufresne et al. 2014,
Bourke et al. 2019). Allele dosage difficulties intensify with
increasing ploidy and number of possible alleles at the considered
genetic marker, as the number of combinations of alleles determining the
number of possible genotypes itself increases. However, recent advances
in genotyping methods exploiting deep sequencing with low errors rates
combined to individuals and marker tags unlocked the possibility to
genotype polyploid individuals with confident allele dosage, even in
species with large sets of chromosomes (Delord et al. 2018). These
methods benefit both from the advances made on the sequencing process
itself that decrease sequencing errors and from the development of
upstream molecular processing of genetic samples to tag and target
very-specific genomic regions. These processings increase the sequencing
depth of the genotyped marker and allow reproducible replicates. It is
now easier to access for a limited cost to more than 20 to hundreds of
replicated sequences per SNP or microsatellite allele within each
individual in a pool of individuals using genotype-by-sequence method.
For example, Hiplex genotyping method allows genotyping
\textasciitilde{}500 individuals at 100 SNPs using one sequencing run
(\emph{e.g.} , MiSeq 2x150 Heflin), with a sequencing depth of
\textasciitilde{}50 sequences per allele in tetraploids and
\textasciitilde{}33 sequences per allele in hexaploids, resulting in
genotype assignations with a confidence superior to 99\% (Delord et al.
2018, Besnard et al. 2023).

Second, we also long lacked of adapted models and analysis methods to
compute population genetic indices and quantify evolutionary forces in
polyploid populations (Dufresne et al. 2014), especially considering
that partially clonal and selfed populations can result in repeated
genotypes (\emph{i.e.,} the same multi-locus genotype found in different
samples, Arnaud-Haond et al. 2007) or patterns of high probabilities of
identity between genotypes (David et al. 2007; Jullien et al, 2019). Due
to challenges introduced by data formats and difficulties in
generalizing the mathematical formula of population genetic indices
(Ewens 2004), common population genetics softwares, such as Genalex
(Peakall \& Smouse 2012) and GenClone (Arnaud-Haond \& Belkhir 2007) are
not designed to work with partially clonal populations with more than
two allelic copies per gene (Excoffier \& Heckel 2006). A handful of
library and software emerged in the last years, like the command-line
Spagedi (Hardy \& Vekemans 2002), the more user-friendly recent and
multiplateforme Polygene (Huang et al. 2020) or Genodive (Meirmans \&
Tienderen 2004) a software restricted to MacOS X operating system.
However, all these programs do not compute all the population genetic
indices used to understand and interprete all reproductive modes,
including selfing and clonality in populations, such as indices based on
genotypic diversity. Polygene for example cannot handle repeated
genotypes that can be commonly observed in partially clonal populations.
Polysat (Clarck \& Jasieniuk 2011) cannot currently deal with data with
confident allele dosage, which becomes a standard with massive
sequencing \& tagging methods. Some R librairies like Poppr (Kamvar et
al. 2014), RClone and Polysat, and command-line solutions like Spagedi
may help analysing genotypes of polyploid populations with different
modes of reproduction, but they require an exhaustive exploration of
their documentation and some trainings in scripting languages to use
them. During practical courses, they involve a preliminary introduction
about scripting or on the reasons for using some options over another,
complicating teaching population genetics for polyploid species by
dispersing the topic in technical considerations.

\textbf{GenAPoPop software}

Thereby, to provide a user-friendly solution to compute the specific
corpus of population genetic indices needed to analyse partially clonal
and selfed polysomic populations, we developed and packaged a new
portable, multi-operating system, working by itself with no dependency
software, named GenAPoPop (standing for Genetic Analyses of Polyploid
Populations).

GenAPoPop is written combining python, fortran and html with a graphical
user interface coded in Qt. The binary executables for Windows, Linux
and MacOS are provided under the terms of a CC-BY-NC-SA license, version
4, and can be downloaded
at\emph{https://forgemia.inra.fr/solenn.stoeckel/genapopop1.0/}. The
idea of this software is to relieve the users of all scripting tasks,
and simplify as much as possible the infile formatting. To this aim,
GenAPoPop uses a graphical interface organized in a comprehensive
workflow (Fig. 1). This software was also designed to complement the
previously cited softwares that can be used easily using GenAPoPop
dataset export feature.

It enables analysing genotypic dataset with confident allele dosage of
autopolyploid species in which we can neglect double-reduction.
Double-reductions in auto- and allopolypoloids result from multivalent
pairing among homologous chromosomes, when two or more sister chromatids
segregate in a same gamete (Wu et al. 2001, Huang et al. 2019, Jiang et
al. 2021, Ferreira de Carvalho et al. 2021). The main consequence of
double-reduction for population genetics is to increase the probability
of identity-by-descent when compared to random chromosome segregation
model (Hardy 2016). For example, an autotetraploid individual
typed\emph{ABCD} can produce \emph{AA} , \emph{BB} , \emph{CC} ,
\emph{DD}gametes when double-reduction happens. Without
double-reduction, only\emph{AB} , \emph{AC} , \emph{AD} , \emph{BC} ,
\emph{BD} , \emph{CD} gametes are produced.

Users should thus be warned that GenAPoPop doesn't consider yet for
double-reductio as it assumes a \emph{random chromosome segregation
model} (Muller 1914). This model considers that gametes originate from
any combination of homologous chromosomes, thus excluding that two
sister chromatids segregate in a same gamete. This is the most commonly
observed case in polyploids (Wu et al. 2001). GenAPoPop
ignores\emph{pure random chromatid segregation model} where chromatids
randomly segregate into gamete resulting in a rate of double-reduction
of 1/7 for tetrasomic inheritance (Haldane 1930) and \emph{complete and
partial equational segregation model} where whole arms of sister
chromatids are exchanged by recombination into different chromosomes,
resulting in a rate of double-reduction of 1/6 when complete equational
segregation occurs (Mather 1935, Huang et al. 2019).

Each packaged version of GenAPoPop is tested on X64 cpu systems
(including server cpu Intel Xeon E5-2650 v3, AMD Threadripper 3970X and
AMD Ryzen 7 5800u) with a Linux Debian-based distribution and Microsoft
Windows 10 and 11 uptodate versions; The MacOS version is currently
tested on a MacOS Big Sur, Intel version.

\textbf{Format of input data and output results}

GenAPoPop was intentionally designed to accept different genotyping
text-file format as long as each line codes for one individual genotype,
and each allele is reported in one column, with columns separated by
tabulation. It also manages files with multiple header lines. The
advantage of this Genalex-like format text file (Peakall \& Smouse 2012)
is that it is universally handled by spreadsheets and text editors, and
it fits the most commonly-used output format of many SNP-set callers.
GenAPoPop workflow requires to first upload such data file, and then
label the four necessarily present columns in the data file: three
columns indicating population name, generation or date of sampling and
individual identifier (Table 1). Any character can be used in these
columns except tabulation and space. The fourth column indicates the
column with the first allele of the first locus, and implies that all
the following columns until the last one only contains alleles coding
for the individual genotype. Alleles can be SNPs, thus expected to be
coded as upper- or lower-case \emph{a} ,\emph{c} , \emph{g} , \emph{t}
and \emph{n} for missing allele or number\emph{1} , \emph{2} , \emph{3}
, \emph{4} and \emph{0} for missing allele. Alleles can also be sequence
repeat markers (like micro-, mini- and macro-satellites) or sequence
length-based markers, named hereafter SSR-like markers in GenAPoPop
software and documentation. In the case of SSR-like markers, each allele
is expected to be coded as an integer number of repeats or a sequence
size, and, if encountered, missing allele should be coded as zero. For
the moment, GenAPoPop supposes genotypes evolve following a K-allele
mutation model (KAM) in which any allele can mutate in any other allele
with the same probability, which has the advantage of aptly modelling
the mutation of both microsatellites and SNPs (Weir \& Cockerham, 1984),
but does not make it possible to exploit the number of repeated DNA
segment or the sequence sizes for computing population and individual
genetic indices and distances.

GenAPoPop can work on input file with genotypes of one or multiple
populations, with identical ploidy and genotyped with a common
marker-set, to analyse them in mass. GenAPoPop has no limit in the
number of populations, of time-steps and genotypes it can analyse, out
of the classic material and operating system limitations,\emph{i.e.} ,
the quantity of random-access memory (RAM) to upload the datafiles and
the outputs, and the central processing unit clock speed and advancement
of its instruction sets.

\textbf{Implemented methods and workflow}

GenAPoPop is organized by tabs: one homepage, one page to load the
dataset and describe its arrangement, three tabs to perform the three
different types of analyses and one tab of documentation (Fig. 1).

\textbf{* Insert here Figure 1 *}

The software opens on a welcome homepage giving basic information and
enabling opening the attached PDF documentation. This can be done either
using the integrated GenAPoPop's browser, interesting in situations
where the software must be deployed on workstations without
administrator's rights or with restricted access (like during practical
courses at university), or using the default system PDF file reader,
generally more comfortable than basic integrated browsers. Next, users
are directed to a tab dedicated to upload and describe at a minimum the
composition of the genotype dataset. In this tab, users upload the text
file containing the genotypes, inform the header line (after which all
lines code for one genotype of one individual), inform the 4 main
columns (population, generation, individual identifier, and the column
containing the first allele of the first locus), inform the ploidy (from
1 to 50) and the type of markers (SSR-like or SNP-like). Once the
dataset is uploaded and the required lines and columns labelled, users
are invited to check the data format. If troubles, the verification will
report explicit errors to be corrected, returning the problematic line
of the dataset. The verification passed, users are then invited to
launch one of the three types of analyses performed by GenAPoPop by
clicking on the corresponding button opening a dedicated new tab.

\textbf{GenPopPoly tab}

This tab allows users to compute a list of population genetic indices
suitable to analyse genetic diversity and population structure of
polyploid populations with a special focus on reproductive modes. These
indices are useful and efficient to estimate rates of clonality,
autogamy (selfing) and allogamy on genotypes of sampled populations
sampled at one time (Castric et al. 2002, David et al. 2007, Hardy 2016,
Stoeckel et al. 2021). Users select the population(s) to be analysed,
select the analyses to be computed and reported, launch the computation
and can directly browse the results for a first sight in the integrated
calc viewer. The results are also saved in a text-file (separator
tabulation) in the folder containing GenAPoPop executable. Result files
can readily be opened by all spreadsheet applications to be explored and
manipulated to do tables and figures. The output file presents first all
intra-population indices computed per population, then computed overall
populations. It includes genotypic and genetic diversity indices as
recommended in Stoeckel et al. (2021), probabilities of identity for
diploids and autopolyploids (Jacquard 1970, Evett \& Weir 1998, Waits et
al. 2001, Huang et al. 2015), the four first moments (\emph{i.e.,} mean,
variance, skewness and kurtosis) of inbreeding coefficient
F\textsubscript{IS} in populations (Stoeckel \& Masson 2014). It also
provides a list of multi-locus genotypes (commonly named MLG in
literature or genet) with their shared genotype, and in the last column,
the number of repeated genotypes (ramet) found in the considered
population. In each and overall populations, it reports genotypic
diversity indices including the index of clonal diversity (\emph{R} ,
Dorken \& Eckert, 2001) and the size distribution of lineages (D* of
Simpson and \selectlanguage{english}\emph{Pareto ?} , Arnaud-Haond et al., 2007) computed
properly for autopolyploids. We deliberately discarded many other
indices to help users robustly interpreting genotypic diversity in their
populations. Despite \selectlanguage{english}\emph{Pareto ?} is far more robust than the
\emph{R} to assess genotypic diversity in sampled populations (Stoeckel
et al. 2021, Arnaud-Haond et al. 2020), we still compute \emph{R} for
reference, as this one was historically massively reported in past
literature. The output also provides the mean correlation coefficient of
genetic distances between unordered alleles at all loci, usually named
\({\overset{\overline{}}{r}}_{d}\) as an overall measure of linkage disequilibrium per
population and overall populations (Agapow \& Burt, 2001). This index,
ranging from slightly negative or 0 (no correlation) to 1 (maximum
association of alleles over all loci), presents the advantage of
limiting the dependency of the correlation coefficient on the number of
alleles and loci. GenAPoPop also provides per population and overall
populations a table of classical intra-populational genetic indices per
locus: observed heterozygosity, raw and unbiased expected heterozygosity
(also name gene diversity), resulting raw and unbiased inbreeding
coefficient (\emph{Fis} ) accounting for intra-individual genetic
variation as a departure from Hardy-Weinberg assumptions of the
genotyped populations and the raw and effective number of alleles
(\emph{Ae} , Weir 1996). On a side and more experimental part, GenAPoPop
allows computing analysis of molecular variance (AMOVA) computed
following Meirmans \& Liu (2018) and Weir (1996) equations and
recommendations, including the Fis, Fst and Fit per population, over all
populations, per marker and over all markers. These results can already
be obtained using Polygene and Genodive. GenAPoPop also provides in this
section the overall and pairwise-population \emph{rhost} . \emph{rhost}
measures the genetic differentiation between populations as the
\emph{Fst} value that would have the same haploid population sizes
connected with the same migration rate, and present the advantage to be
comparable between species and populations of different ploidy levels
(Ronfort et al. 1998, Meirmans \& Van Tienderen 2013). These indices of
genetic differentiation/structuration are a good complement to the
minimum spanning tree of the genetic distances between individuals when
coloured or tagged by population to get a picture of the genetic
structure of genotyped populations (see below). As these indices are
also computed in Spagedi and Polygene, we invite users to also compare
their results with these softwares.

GenAPoPop was thinked and designed to complement Genodive, Polygene that
performs hierarchical, Bayesian clustering and parentage analysis, and
Spagedi that already performs multiple spatial analyses and that can be
used to estimate selfing rate. In this tab, GenAPoPop users can export
automatically their datasets in a Spagedi-format file that will be
recorded in the same folder under the same imported data name extend
with ``\emph{\_spagedi\_ready.txt} ''. This file that can be easily
imported to extend and access complementary analyses in the previously
cited software, including Spagedi and Polygene, and we greatly encourage
future GenAPoPop users to analyse their data with multiple softwares to
get the most complete view of their dataset.

\textbf{ClonEstiMatePoly tab}

This tab allows users to compute the posterior probabilities of joint
rates of clonality and selfing in polyploid populations genotyped at, at
least, two-time steps. This method was demonstrated to be the most
accurate way to quantitatively assess reproductive modes in diploid
populations over multiple Eukaryotes species, especially for detecting
low rates of clonality (Becheler et al. 2017). It should facilitate the
detection of clonal reproduction, the estimation of the rates of
clonality in polyploid populations, and promote the study of
reproductive modes and their genetic consequences in such species. It
should be a nice addition to the method of estimation of selfing rates
using multilocus standardized identity disequilibrium coefficient found
in spagedi (Hardy 2016).

Here, we extended to autopolyploids the Bayesian formula and method
ClonEstiMate from Becheler et al. (2017). It exploits the likelihood of
transitions of genotype frequencies from one generation to another to
accurately estimate rates of mutation, clonality and selfing, and thus
works well even in the absence of equilibrium between evolutionary
forces (genetic drift, mutation and rates of clonality) which is quite
common in partially clonal populations (Reichel et al. 2016). This
method remains accurate using from about ten polymorphic markers, even
physically linked and mutating with other mutation model, and from 30
sampled individuals. It is however sensitive to erroneous assumed or
restricted prior values of clonal and selfing rates, null alleles and
sampling time interval greater than two generations. Extended equations
for autopolyploids can be found in the documentation in supplementary
material. This discretized Bayesian method needs an analysis plan
listing discretized priors on rates of mutation, clonality and selfing
for each population (Fig. S1). Restricted ranges of prior on each of
these parameters allows better inferences on other targeted parameters.
Analysis plan can be uploaded or prepared (and saved for future use)
using the graphical interface. Analysis plan can be browsed and checked
using the integrated browser before launching the computations. To
speed-up the calculations, computations per locus and population of the
analysis plan were parallelized using the maximum number of threads
available by the operating system. Results are stored in the folder
containing GenAPoPop in a text-file separator tabulation file that can
be readily handled using any spreadsheet application. Results are
presented per population between two time-steps as a list of discrete
joined values of mutation rate, rates of clonality and selfing with the
corresponding posterior probabilities of such joined combination of
priors. This presentation of the results makes it easy to combine the
posterior probability mass functions per population and generations into
table and/or into plots of their distributions. If found in the dataset,
it also returns the list of monomorphic loci at, at least, one sampling
time. Monomorphic loci decrease the inference power of the dataset to
assess rates of mutation, clonality and selfing between the two sampled
generations.

\textbf{Minimum spanning tree of genetic distances between individuals
tab}

This tab allows users to compute the genetic distance between
individuals using their identity-in-state (number of shared alleles) and
provides the corresponding minimum spanning unrooted tree using the
classical equal-angle algorithm (Christopher Meacham in Felsenstein
2004). This network representation is useful to detect multilocus
lineages (named MLL in literature) due to clonality that shape typical
rosettes or small rosaries, \emph{i.e.,} a group of ramets differing by
a limited number of mutations radiating around a main genet (Fig. 2).

\textbf{* Insert here Figure 2 *}

Users can get the computed genetic distances between
pairwise-individuals in an exported text-file to use them with other
software, and they can customize the plot of the minimum spanning
unrooted tree using individual colors and tags. The resulting graph can
be exported at different resolutions into research-standard portable
document format (pdf) file format, raster (portable network graphics,
png) or vector (scalable vector graphics, svg) image formats that can be
processed afterward in dedicated software. The resulting graph can be
previewed and explored using the integrated browser, using mouse
controls (zoom in and out using mouse wheel, move the graph with mouse
grab) before exportation.

\textbf{Consistency and accuracy tests}

To test the consistency and accuracy of our software, we used simulated
data and empirical datasets as control data. To obtain simulated data,
we used the embedded simulator that can also be used for testing and
teaching purposes (Tab Simulation, see Documentation).

First, we perform consistency test of GenAPoPop with the output of
Spagedi reference software (Hardy \& Vekemans 2001) on four basic
population genetic indices (Ae, He, Ho, Rhost). We simulated four test
datasets simple enough to be checked by hand calculations for unit
testing. For further and future unit testing, the raw datasets were
deposited on the European general-purpose open repository Zenodo (Barloy
et al. 2022). These four scenarios correspond respectively to panmictic
(A), highly selfed (B), highly clonal (C) and half-clonal-half-selfed
(D) reproductive modes. Quantitative values are explicitly indicated in
the two first lines of the datasets. In each scenario, we simulated two
connected populations of 100 individuals each with a migration rate of
0.01 and mutating at a rate of 0.01, genotyped at 10 SNPs, 1000
generations after an initial randomly drawing population. For each
scenario, we recorded the populations' genotyping states over two
consecutive generations (generations 1000 and 1001). In addition, we
tested GenAPoPop on two field datasets genotyped with confident allele
dosage, one SNPs set from the autotetraploid genome part of
\emph{Ludwigia grandiflora subsp. hexapetala} (hereafter\emph{Lgh} ,
Genitoni et al. 2020) and one microsatellite set from the autotetraploid
artic sea anemone \emph{Aulactinia stella} (hereafter\emph{As} ,
Bocharova et al. 2018). These two datasets are genetic samples of larger
metapopulations genotyped with confident allele dosage, including
missing alleles and genotypes, and including some loci fixed in one of
the populations. We draw attention of users that the different softwares
present different ways to handle fixed, missing alleles and genotypes.

Second, to analyse how population genetic indices of a snapshot of
genotyped populations behave in autopolyploids and how they compare to
diploids as reported in Stoeckel et al. 2021, we simulated 6300
different datasets following 21 reproductive mode scenarios and three
different ploidies (2,4 and 6). Each reproductive scenario at one ploidy
level was independently simulated a hundred times to get a confident
picture of the range of the possible genetic trajectories. Each of the
21 different reproductive mode scenarios consists on a triplet of values
including one rate of clonality, one rate of selfing and one
complementary rate of allogamy, the three rates necessarily summing to
one. Rates of clonality, selfing and allogamy took complementary values
of all the possible combinations within the set {[}0., 0.2, 0.4, 0.6,
0.8, 1.{]}, constrained to sum to one. For example, one scenario was
(rate of clonality=0.2, rate of selfing=0.4, rate of allogamy=0.4).
Hereafter, for easier representation, we reported couple of rates of
clonality and of selfing in figures and text, implicitly considering
that rate of allogamy was one minus the rates of clonality and selfing.
In each scenario, we simulated two connected populations of 100
individuals each with a migration rate of 0.01 and mutating at a rate of
0.01, genotyped at 30 markers with 4 possible alleles randomly
introduced within individuals in the first generation with the same
frequency. Analysed datasets were recorded 1000 generations after the
initial generation, corresponding to 5 times the overall instantaneous
population size (N=200). Distributions of population genetic indices
obtained with the 21 reproductive modes and 3 ploidy levels were
reported as violin plots, each made from one hundred independent
simulations.

Third, to test the accuracy and precision of ClonEstiMatePoly method to
jointly infer rates of clonality, selfing and allogamy in autopolyploid
populations genotyped at two-time step, we simulated again 6300
different datasets following the same 21 reproductive mode scenarios,
for diploid, tetraploid and hexaploid populations. For each quantitative
reproductive mode (\emph{i.e.} , a precise couple of values of one rate
of clonality and one rate of selfing), we simulated 100 couples of
populations, each of size N=100, mutating at a rate 1/N and exchanging
migrants at a rate of 1/N, over 1000 generations. We submitted the
genotypes found in parents (generation 999) and in their descendants
(generation 1000) to ClonEstiMatePoly with flat priors to get the
inferred posterior distribution of the joint rates of clonality and
selfing. The 100 posterior distributions per couple of rates of
clonality and selfing were summed and reported as a confusion matrix for
ploidy 2, 4 and 6.

All the results were aggregated and deposited in Barloy et al. (2022).

\textbf{Results}

\textbf{Consistency test}

Spagedi and GenAPoPop reported similar values of Ae, He, Ho and Rhost
(Table S1). Ae and He were corrected by sample size in Spagedi but not
in GenAPoPop, explaining the little differences observed. GenAPoPop uses
double-precision floating-point format (64 bits) while, to our
knowledge, Spagedi uses a lower precision that can also add up along the
calculations. GenAPoPop intentionally computes estimators with limited
'correction' to avoid to give more weight to some loci rather than other
which may bias the global picture of a dataset (see formulas in
Documentation).

\textbf{Variations of snapshot population genetic indices with rates of
clonality and selfing, and ploidy}

The principal component analysis on the values of genetic diversity
using a snapshot of genetic diversity of a population showed two main
non-collinear clusters of genetic indices associated with clonality and
selfing (Fig. S2, S3 and S4). Rates of clonality were colinear with
clonal heterogeneity and evenness indices (including R, Pareto Beta, the
complement of the Simpson index and Shannon-Wienner's index), with
variance of Fis and Fit, and linkage disequilibrium. Increasing rates of
clonality increased linkage disequilibrium and variance of Fis among
genotyped loci while it decreased clonal evenness. Rates of selfing were
colinear with indices based on allele diversity (including gene
diversity, probabilities of identity and genetic structure indices) and
heterozygosity. Increasing rates of selfing increased mean Fis and Fit,
and variances of panmictic probabilities of identity, of the number of
alleles per loci, of gene diversity and of pairwise Fst. Conversely, it
decreased the mean number of alleles per loci, the mean gene diversity
and observed heterozygosity.

The distributions of population genetics indices varied with joint rates
of clonality and selfing and with increasing ploidy, except the
distribution of rhost values between the two simulated populations (Fig.
S5). For a fixed ploidy, changes in the range of expected values with
reproductive modes remained quite similar to those observed for
diploids.

\textbf{Accuracy of jointly inferred rates of clonality and selfing with
increasing ploidy}

ClonEstiMatePoly, the Bayesian method we propose here to jointly infer
rates of clonality, selfing and allogamy in autopolyploid populations
genotyped at two-time step showed high accuracy and limited confusion to
jointly infer the true rates of clonality and selfing. The method
inferred in the worst cases the true joint rates of clonality and
selfing with a precision of +-0.2 (Fig. S6). It occurred when populations
reproduced using both intermediate rates of clonality and rates of
selfing. Increasing ploidy showed a slight tendency to overestimate
selfing rates when populations also reproduced using intermediate rates
of clonality.

\textbf{Recommendations and warning}

Most population genetic analyses rely on accurate estimates of real
populational genotype frequencies, including here ClonEstiMatePoly
method. The number of different possible genotypes at one locus
increases with the ploidy and the number of alleles (Reichel et al.
2015). We thus draw users' attention on the fact that sample sizes
should naturally be larger in polyploid organisms to accurately estimate
their genotype frequencies, despite the fact that genotyping more
alleles per individual may help assessing allele frequencies.

Missing values and null alleles compromise comparisons between
individuals, lineages and populations, and are susceptible to create
biases and misinterpretations. Suspected null allele can be coded as
unknow allele with their own specific letters or positive integers, and
should be clearly reported before interpretations. Indeed, no
``correction'' or ``assumptions'' can enhance a blurred and incomplete
genotyping signals without deep consequences on the computed indices and
then their interpretations, whatever the `correction'. We thus recommend
users to rather remove genetic markers and individuals with missing
values and uncertain genotypes.

\textbf{Conclusion}

GenAPoPop provide a user-friendly, multi-operating systems, efficient
mass processing way to analyse autopolyploid (including diploid)
genotypings with a special focus on interpreting the genetic diversity
and its structure within and between populations in regards with their
reproductive modes. It especially allows computing genotypic indices to
analyse clonal heterogeneity and clonal evenness for polyploids due to
repeated multilocus genotypes (MLGs) in samples. It includes an
extension of the robust and efficient ClonEstiMate Bayesian method to
quantitatively infer joint rates of clonality, selfing and allogamy
using populations genotyped at two-time steps. It facilitates the
interpretation of genetic diversity in partially clonal, partially
selfing autopolyploid populations with no or very-limited double
reduction. It has no vocation to include or encompass all methods and
population genetic indices that can be computed when analysing
autopolyploid genotypings. This is why it allows exporting datasets in
format that can be uploaded in other software like Spagedi (Hardy \&
Vekemans 2002), Genodive (Meirmans 2020) and Polygene (Huang \emph{et
al.} 2020). We thus warmly recommend users to use GenAPoPop in
complement to other dedicated analyses that can be found in these other
softwares, depending on the tackled questions. GenAPoPop also answers
the need of a population genetic analysing software for autopolyploid
dataset with confident allele dosage that will come growing with the new
genotyping-by-sequencing methods with individually tagged sample and
locus. It finally answers the need of a user-friendly software for
practical course that doesn't need teaching command-lines or scripting
languages as a prior to introduce students to population genetics for
polyploid species and to the genetic consequences of reproductive modes
on the genetic diversity and structure of populations.

\textbf{Acknowledgements}

We warmly thank Luis Portillo-Lemus for initial discussions during his
PhD thesis that encouraged the development of this software. We thank
three anonymous reviewers for finding a bug in the AMOVA output and for
helping enhancing our manuscript. We globally thank students of the
International Master in Biodiversity Ecology and Evolution and Modelling
in Ecology at The University of Rennes1 and l'Institut Agro for
identifying over the year the need of an adapted and user-friendly
software to correctly teach polyploid population genetics in practical
courses. Finally, we thank participants and organizers of the Polyploidy
and Biodiversity conference (Rennes 11-12 October 2021) for their useful
returns on the first version of GenAPoPop.

This work was supported by Clonix2D ANR-18-CE32-0001; the InvaMat
project (Plant Health and Environment Division of the French National
Institute of Agricultural Research) and the French Embassy in the
Russian Federation, for funding this project by a Metchnikov 2019 grant.
The SNP data on \emph{Ludwigia grandiflora subsp. hexapetala}
populations were acquired using FEDER funds from Region Centre-Val de
Loire and by Agence de l'eau Loire-Bretagne, grant Nature 2045,
programme 9025 (AP 2015 9025). The SSR data on \emph{Aulactinia stella}
was obtained by EB under the IDB RAS Government basic research program \selectlanguage{english}
0088-2021-0019.

\textbf{Authors' contributions}

DB, EB and SS laid the foundation of this work, identifying its need and
were responsible for funding applications. SS formalised the
mathematical equations, formalized the methods, coded the software,
packaged the software and coded the simulator for unit testing and for
testing the consistency with other software. RB and SS contributed the
code testing and interface enhancement, the output exploration, the test
of consistency with other software and performed the literature
researches. SS wrote the core manuscript. All authors read, edited and
approved the final manuscript.

\textbf{Data Accessibility}

The latest packaged binaries of GenAPoPop1.0 can be downloaded on the
long-term academic Gitlab server of INRAE (French National Research
Institute for Agriculture, Food and
Environment):\emph{https://forgemia.inra.fr/solenn.stoeckel/genapopop1.0}

Pseudo-observed and field dataset (\emph{Ludwigia grandiflora subs
hexapetala} and \emph{Aulactinia stella} ) used for consistency tests
are available on Zenodo DOI: 10.5281/zenodo.8164531

\textbf{Conflict of interest}

The authors of this preprint declare that they have no financial
conflicts of interest based on the content of this article.

\textbf{ORCID}

Solenn Stoeckel, 0000-0001-6064-5941

Ronan Becheler, 0000-0001-9322-0771

Ekaterina Bocharova, 0000-0001-9978-3006

Dominique Barloy, 0000-0001-5810-4871

\textbf{References}

Agapow, P.-M., \& Burt, A. (2001). Indices of multilocus linkage
disequilibrium. \emph{Molecular Ecology Notes} , \emph{1} (1--2),
101--102. https://doi.org/10.1046/j.1471-8278.2000.00014.x

Albertin, W., \& Marullo, P. (2012). Polyploidy in fungi: Evolution
after whole-genome duplication. \emph{Proceedings of the Royal Society
B: Biological Sciences} , \emph{279} (1738), 2497--2509.
https://doi.org/10.1098/rspb.2012.0434

Arnaud-Haond, S., \& Belkhir, K. (2007). genclone: A computer program to
analyse genotypic data, test for clonality and describe spatial clonal
organization. \emph{Molecular Ecology Notes} , \emph{7} (1), 15--17.
https://doi.org/10.1111/j.1471-8286.2006.01522.x

Arnaud-Haond, S., Duarte, C. M., Alberto, F., \& Serrao, E. A. (2007).
Standardizing methods to address clonality in population
studies.\emph{Molecular Ecology} , \emph{16} (24), 5115--5139.
https://doi.org/10.1111/j.1365-294X.2007.03535.x

Arnaud-Haond, S., Stoeckel, S., \& Bailleul, D. (2020). New insights
into the population genetics of partially clonal organisms: When
seagrass data meet theoretical expectations. \emph{Molecular Ecology}
,\emph{29} (17), 3248--3260. https://doi.org/10.1111/mec.15532

Baduel, P., Bray, S., Vallejo-Marin, M., Kola\selectlanguage{polish}ř, \selectlanguage{english}F., \& Yant, L. (2018).
The ``Polyploid Hop'': Shifting Challenges and Opportunities Over the
Evolutionary Lifespan of Genome Duplications. \emph{Frontiers in Ecology
and Evolution} , \emph{6} .
https://www.frontiersin.org/articles/10.3389/fevo.2018.00117

Bailleul, D., Stoeckel, S., \& Arnaud-Haond, S. (2016). RClone: A
package to identify MultiLocus Clonal Lineages and handle clonal data
sets in r. \emph{Methods in Ecology and Evolution} , \emph{7} (8),
966--970. https://doi.org/10.1111/2041-210X.12550

Barker, M. S., Arrigo, N., Baniaga, A. E., Li, Z., \& Levin, D. A.
(2016). On the relative abundance of autopolyploids and
allopolyploids.\emph{New Phytologist} , \emph{210} (2),
391--398.\emph{https://doi.org/10.1111/nph.13698}

Barloy, D., Bocharova, E., Harang, M., Portillo, L., \& Stoeckel, S.
(2022). Reference datasets for consistency tests of GENAPOPOP 1.0
software: a user-friendly software to analyse genetic diversity and
structure in partially clonal and selfed polyploid organisms. (1.0)
{[}Data set{]}. \emph{Zenodo} . https://doi.org/10.5281/zenodo.8164531

Barrett SCH (2018) Why reproductive systems matter for the invasion
biology of plants. In: Fifty Years of Invasion Ecology: The Legacy of
Charles Elton (ed. DM Richardson). Oxford University Press, Oxford, UK.

Becheler, R., Masson, J.-P., Arnaud-Haond, S., Halkett, F., Mariette,
S., Guillemin, M.-L., Valero, M., Destombe, C., \& Stoeckel, S. (2017).
ClonEstiMate, a Bayesian method for quantifying rates of clonality of
populations genotyped at two-time steps. \emph{Molecular Ecology
Resources} , \emph{17} (6),
e251--e267.\emph{https://doi.org/10.1111/1755-0998.12698}

Besnard A.-L., Park D. J., Pope B. J., Hammet F., Michon-Coudouel S.,
Biget M., Krueger-Hadfield S.A., Mauger S., Petit E.J. 2023. Workflow
for SNP genotyping using the Hi-Plex method. Protocols.io,
dx.doi.org/10.17504/protocols.io.8epv5jnnnl1b/v1

Bocharova, E. S., Sergeev, A. A., \& Volkov, A. A. (2018).
Identification of microsatellite loci in sea anemones Aulactinia stella
and Cribrinopsis albopunctata (family Actiniidae). \emph{F1000Research}
,\emph{7} , 232.\emph{https://doi.org/10.12688/f1000research.13724.1}

Booth, W., Levine, B. A., Corush J. B., Davis, M. A., Dwyer, Q., De
Plecker, R., \& Schuett, G. W. (2023). Discovery of facultative
parthenogenesis in a new world crocodile. \emph{Biology Letters}
,\emph{19} (6), 20230129. https://doi.org/10.1098/rsbl.2023.0129

Bourke, P. M., Hackett, C. A., Voorrips, R. E., Visser, R. G. F., \&
Maliepaard, C. (2019). Quantifying the Power and Precision of QTL
Analysis in Autopolyploids Under Bivalent and Multivalent Genetic
Models. \emph{G3: Genes\textbar{}Genomes\textbar{}Genetics} ,\emph{9}
(7), 2107--2122.\emph{https://doi.org/10.1534/g3.119.400269}

Castric, V., Bernatchez, L., Belkhir, K., \& Bonhomme, F. (2002).
Heterozygote deficiencies in small lacustrine populations of brook charr
Salvelinus Fontinalis Mitchill (Pisces, Salmonidae): a test of
alternative hypotheses. \emph{Heredity} , 89, 27--35.
https://doi.org/10.1038/sj.hdy.6800089

Clark, L. V., \& Jasieniuk, M. (2011). polysat: An R package for
polyploid microsatellite analysis. \emph{Molecular Ecology Resources}
,\emph{11} (3), 562--566.
https://doi.org/10.1111/j.1755-0998.2011.02985.x

David, P., Pujol, B., Viard, F., Castella, V., \& Goudet, J. (2007).
Reliable selfing rate estimates from imperfect population genetic
data.\emph{Molecular Ecology} , \emph{16} (12), 2474--2487.
https://doi.org/10.1111/j.1365-294X.2007.03330.x

Delord, C., Lassalle, G., Oger, A., Barloy, D., Coutellec, M.-A.,
Delcamp, A., Evanno, G., Genthon, C., Guichoux, E., Le Bail, P.-Y., Le
Quilliec, P., Longin, G., Lorvelec, O., Massot, M., Reveillac, E.,
Rinaldo, R., Roussel, J.-M., Vigouroux, R., Launey, S., \& Petit, E. J.
(2018). A cost-and-time effective procedure to develop SNP markers for
multiple species: A support for community genetics. \emph{Methods in
Ecology and Evolution} , \emph{9} (9),
1959--1974.\emph{https://doi.org/10.1111/2041-210X.13034}

De Mee\selectlanguage{ngerman}ûs, T. \& Balloux, F. (2005), F-statistics of clonal diploids
structured in numerous demes. \emph{Molecular Ecology} , 14, 2695-2702.
https://doi.org/10.1111/j.1365-294X.2005.02643.x

Dorken, M. E., \& Eckert, C. G. (2001). Severely reduced sexual
reproduction in northern populations of a clonal plant,
Decodonverticillatus (Lythraceae). \emph{Journal of Ecology} ,\emph{89}
(3), 339--350. https://doi.org/10.1046/j.1365-2745.2001.00558.x

Dufresne, F., Stift, M., Vergilino, R., \& Mable, B. K. (2014). Recent
progress and challenges in population genetics of polyploid organisms:
An overview of current state-of-the-art molecular and statistical
tools.\emph{Molecular Ecology} , \emph{23} (1), 40--69.
https://doi.org/10.1111/mec.12581

Duminil, J., Fineschi, S., Hampe, A., Jordano, P., Salvini, D.,
Vendramin, G. G., \& Petit, R. J. (2007). Can Population Genetic
Structure Be Predicted from Life\selectlanguage{english}-History Traits? \emph{The American
Naturalist} , \emph{169} (5), 662--672. https://doi.org/10.1086/513490

Ellegren, H., \& Galtier, N. (2016). Determinants of genetic
diversity.\emph{Nature Reviews Genetics} , \emph{17} (7), Article 7.
https://doi.org/10.1038/nrg.2016.58

Ewens, W. J. (2004). \emph{Mathematical Population Genetics} (Vol. 27).
Springer.\emph{https://doi.org/10.1007/978-0-387-21822-9}

Excoffier, L., \& Heckel, G. (2006). Computer programs for population
genetics data analysis: a survival guide. \emph{Nature Reviews Genetics}
, 7, 745--758.\emph{https://doi.org/10.1038/nrg1904}

Evett, I. W., \& Weir, B. S. (1998). Interpreting DNA evidence:
statistical genetics for forensic scientists. Sinaur Associates Inc,
Sunderland, Massachusetts. ISBN 0878931554.

Fehrer, J. (2010). Unraveling the mysteries of
reproduction.\emph{Heredity} , \emph{104} (5), Article
5.\emph{https://doi.org/10.1038/hdy.2010.12}

Felsenstein, J. (2004) Inferring Phylogenies. Sinauer Associates Inc.,
Sunderland. ISBN: 9780878931774

Ferreira de Carvalho, J., Stoeckel, S., Eber, F., Lode-Taburel, M.,
Gilet, M.-M., Trotoux, G., Morice, J., Falentin, C., Chevre, A.-M., \&
Rousseau-Gueutin, M. (2021). Untangling structural factors driving
genome stabilization in nascent Brassica napus allopolyploids. \emph{New
Phytologist} , \emph{230} (5), 2072--2084.
https://doi.org/10.1111/nph.17308

Genitoni, J., Vassaux, D., Delaunay, A., Citerne, S., Portillo Lemus,
L., Etienne, M.-P., Renault, D., Stoeckel, S., Barloy, D., \& Maury, S.
(2020). Hypomethylation of the aquatic invasive plant, Ludwigia
grandiflora subsp. Hexapetala mimics the adaptive transition into the
terrestrial morphotype. \emph{Physiologia Plantarum} , \emph{170} (2),
280--298. https://doi.org/10.1111/ppl.13162

Gregory, T. R., \& Mable, B. K. (2005). CHAPTER 8---Polyploidy in
Animals. In T. R. Gregory (Ed.), \emph{The Evolution of the Genome} (pp.
427--517). Academic Press.
https://doi.org/10.1016/B978-012301463-4/50010-3

Haldane, J. B. S. (1930). Theoretical genetics of
autopolyploids.\emph{Journal of Genetics} , \emph{22} (3), 359--372.
https://doi.org/10.1007/BF02984197

Hardy, O. J. (2016). Population genetics of autopolyploids under a mixed
mating model and the estimation of selfing rate. \emph{Molecular Ecology
Resources} , \emph{16} (1), 103--117.
https://doi.org/10.1111/1755-0998.12431

Hardy, O. J., \& Vekemans, X. (2002). spagedi: A versatile computer
program to analyse spatial genetic structure at the individual or
population levels. \emph{Molecular Ecology Notes} , \emph{2} (4),
618--620. https://doi.org/10.1046/j.1471-8286.2002.00305.x

Herben, T., Suda, J., \& Klime\selectlanguage{polish}š\selectlanguage{english}ov\selectlanguage{ngerman}á, J. (2017). Polyploid species rely on
vegetative reproduction more than diploids: A re-examination of the old
hypothesis. \emph{Annals of Botany} , \emph{120} (2),
341--349.\emph{https://doi.org/10.1093/aob/mcx009}

Huang, K., Guo, S., Shattuck, M., Chen, S. T., Qi, X. G., Zhang, P., \&
Li, B. G. (2015). A maximum-likelihood estimation of pairwise
relatedness for autopolyploids. \emph{Heredity,} \emph{114} , 133--142.
https://doi.org/10.1038/hdy.2014.88

Huang, K., Dunn, D. W., Ritland, K., \& Li, B. (2020). polygene:
Population genetics analyses for autopolyploids based on allelic
phenotypes. \emph{Methods in Ecology and Evolution} , \emph{11} (3),
448--456. https://doi.org/10.1111/2041-210X.13338

Huang, K., Wang, T., Dunn, D. W., Zhang, P., Cao, X., Liu, R., \& Li, B.
(2019). Genotypic Frequencies at Equilibrium for Polysomic Inheritance
Under Double-Reduction. \emph{G3
Genes\textbar{}Genomes\textbar{}Genetics} , \emph{9} (5),
1693--1706.\emph{https://doi.org/10.1534/g3.119.400132}

Jacquard, A. (1970). Structures génétiques des populations. Masson et
cie, Paris. ISBN 9782733220238

Jiang, L., Ren, X., \& Wu, R. (2021). Computational characterization of
double reduction in autotetraploid natural populations. \emph{The Plant
Journal} , \emph{105} (6), 1703--1709. https://doi.org/10.1111/tpj.15126

Jighly, A., Lin, Z., Forster, J. W., Spangenberg, G. C., Hayes, B. J.,
\& Daetwyler, H. D. (2018). Insights into population genetics and
evolution of polyploids and their ancestors. \emph{Molecular Ecology
Resources} , \emph{18} (5),
1157--1172.\emph{https://doi.org/10.1111/1755-0998.12896}

Jullien, M., Navascués, M., Ronfort, J., Loridon, K., \& Gay, L. (2019).
Structure of multilocus genetic diversity in predominantly selfing
populations. \emph{Heredity} , \emph{123} (2), 176-191.
https://doi.org/10.1038/s41437-019-0182-6Kamvar, Z. N., Tabima, J. F.,
\& Grünwald, N. J. (2014). Poppr: An R package for genetic analysis of
populations with clonal, partially clonal, and/or sexual
reproduction.\emph{PeerJ} , \emph{2} , e281.
https://doi.org/10.7717/peerj.281

Mable, B. K., Alexandrou, M. A., \& Taylor, M. I. (2011). Genome
duplication in amphibians and fish: An extended synthesis. \emph{Journal
of Zoology} , \emph{284} (3), 151--182.
https://doi.org/10.1111/j.1469-7998.2011.00829.x

Mather, K. (1935). Reductional and equational separation of the
chromosomes in bivalents and multivalents. \emph{Journal of Genetics}
,\emph{30} (1), 53--78.\emph{https://doi.org/10.1007/BF02982205}

Meirmans, P.G. (2020). GENODIVE version 3.0: Easy-to-use software for
the analysis of genetic data of diploids and polyploids, \emph{Molecular
Ecology Resources} , 20, 1126-1131.
https://doi.org/10.1111/1755-0998.13145

Meirmans, P. G., \& Liu, S. (2018). Analysis of Molecular Variance
(AMOVA) for Autopolyploids. Frontiers in Ecology and Evolution, 6.
https://www.frontiersin.org/articles/10.3389/fevo.2018.00066

Meirmans, P. G., \& Van Tienderen, P. H. (2004). genotype and genodive:
Two programs for the analysis of genetic diversity of asexual
organisms.\emph{Molecular Ecology Notes} , \emph{4} (4), 792--794.
https://doi.org/10.1111/j.1471-8286.2004.00770.x

Meirmans, P. G., \& Van Tienderen, P. H. (2013). The effects of
inheritance in tetraploids on genetic diversity and population
divergence. \emph{Heredity} , \emph{110} (2), 131--137.
https://doi.org/10.1038/hdy.2012.80

Muller, H. J. (1914). A New Mode of Segregation in Gregory's Tetraploid
Primulas. \emph{The American Naturalist} , \emph{48} (572), 508--512.
https://doi.org/10.1086/279426

Orive, M. E., \& Krueger-Hadfield, S. A. (2021). Sex and Asex: A Clonal
Lexicon. \emph{Journal of Heredity} , \emph{112} (1), 1--8.
https://doi.org/10.1093/jhered/esaa058

Pandit, M. K., Pocock, M. J. O., \& Kunin, W. E. (2011). Ploidy
influences rarity and invasiveness in plants. \emph{Journal of Ecology}
,\emph{99} (5), 1108--1115.
https://doi.org/10.1111/j.1365-2745.2011.01838.x

Peakall, R., \& Smouse, P. E. (2012). GenAlEx 6.5: Genetic analysis in
Excel. Population genetic software for teaching and research---an
update. \emph{Bioinformatics} , \emph{28} (19), 2537--2539.
https://doi.org/10.1093/bioinformatics/bts460

Reichel, K., Bahier, V., Midoux, C., Parisey, N., Masson, J.-P., \&
Stoeckel, S. (2015). Interpretation and approximation tools for big,
dense Markov chain transition matrices in population
genetics.\emph{Algorithms for Molecular Biology} , \emph{10} (1), 31.
https://doi.org/10.1186/s13015-015-0061-5

Reichel, K., Masson, J.-P., Malrieu, F., Arnaud-Haond, S., \& Stoeckel,
S. (2016). Rare sex or out of reach equilibrium? The dynamics of FISin
partially clonal organisms. \emph{BMC Genetics} , \emph{17} (1), 76.
https://doi.org/10.1186/s12863-016-0388-z

Ronfort, J., Jenczewski, E., Bataillon, T., \& Rousset, F. (1998).
Analysis of population structure in autotetraploid
species.\emph{Genetics} , \emph{150} (2), 921--930.

Rougeron, V, De Meeûs, T, \& Bañuls, A. L. (2015). A primer for
Leishmania population genetic studies. Trends in Parasitology,\emph{31}
(2), 52-9. https://doi.org/10.1016/j.pt.2014.12.001

Rutland, C. A., Hall, N. D., \& McElroy, J. S. (2021). The Impact of
Polyploidization on the Evolution of Weed Species: Historical
Understanding and Current Limitations. \emph{Frontiers in Agronomy}
,\emph{3} .
https://www.frontiersin.org/articles/10.3389/fagro.2021.626454

Stoeckel, S., Grange, J., Fernández-Manjarres, J. F., Bilger, I.,
Frascaria-Lacoste, N., \& Mariette, S. (2006). Heterozygote excess in a
self-incompatible and partially clonal forest tree species---Prunus
avium L. \emph{Molecular Ecology} , \emph{15} (8),
2109--2118.\emph{https://doi.org/10.1111/j.1365-294X.2006.02926.x}

Stoeckel, S., \& Masson J.P. (2014) The Exact Distributions of
F\textsubscript{IS} under Partial Asexuality in Small Finite Populations
with Mutation. PLOS ONE 9(1): e85228.
https://doi.org/10.1371/journal.pone.0085228

Stoeckel, S., Porro, B., \& Arnaud-Haond, S. (2021). The discernible and
hidden effects of clonality on the genotypic and genetic states of
populations: Improving our estimation of clonal rates. \emph{Molecular
Ecology Resources} , \emph{21} (4),
1068--1084.\emph{https://doi.org/10.1111/1755-0998.13316}

Tibayrenc, M., \& Ayala, F. J. (2013). How clonal are Trypanosoma and
Leishmania?. \emph{Trends in Parasitology} , 29(6), 264--269.
https://doi.org/10.1016/j.pt.2013.03.007

Van Drunen, W. E., \& Husband, B. C. (2019). Evolutionary associations
between polyploidy, clonal reproduction, and perenniality in the
angiosperms. \emph{New Phytologist} , \emph{224} (3), 1266--1277.
https://doi.org/10.1111/nph.15999

Villate, L., Esmenjaud, D., Van Helden, M., Stoeckel, S., \& Plantard,
O. (2010). Genetic signature of amphimixis allows for the detection and
fine scale localization of sexual reproduction events in a mainly
parthenogenetic nematode.\emph{Molecular Ecology} , \emph{19} (5),
856--873. https://doi.org/10.1111/j.1365-294X.2009.04511.x

Waits, L. P., Luikart, G., \& Taberlet, P. (2001). Estimating the
probability of identity among genotypes in natural populations: Cautions
and guidelines.\emph{Molecular Ecology} , \emph{10} (1), 249--256.
https://doi.org/10.1046/j.1365-294x.2001.01185.x

Wakeley, J. (2005). The Limits of Theoretical Population
Genetics.\emph{Genetics} , \emph{169} (1), 1--7.

Weir, B.S. (1996) Genetic Data Analysis II: Methods for Discrete
Population Genetic Data. Sinauer Associates, Inc., Sunderland.

Weir, B. S., \& Cockerham, C. C. (1984). Estimating F-Statistics for the
Analysis of Population Structure. \emph{Evolution} , \emph{38} (6),
1358--1370. https://doi.org/10.2307/2408641

Wood, T. E., Takebayashi, N., Barker, M. S., Mayrose, I., Greenspoon, P.
B., \& Rieseberg, L. H. (2009). The frequency of polyploid speciation in
vascular plants. \emph{Proceedings of the National Academy of Sciences}
,\emph{106} (33), 13875--13879. https://doi.org/10.1073/pnas.0811575106

Wu, R., Gallo-Meagher, M., Littell, R. C., \& Zeng, Z. B. (2001). A
general polyploid model for analyzing gene segregation in outcrossing
tetraploid species. \emph{Genetics} , \emph{159} (2), 869--882.

Wu, S., Cheng, J., Xu, X., Zhang, Y., Zhao, Y., Li, H., \& Qiang, S.
(2019). Polyploidy in invasive Solidago canadensis increased plant
nitrogen uptake, and abundance and activity of microbes and nematodes in
soil. \emph{Soil Biology and Biochemistry} , 138, 107594.
https://doi.org/10.1016/j.soilbio.2019.107594.

Yu, F.-H., Roiloa, S. R., \& Alpert, P. (2016). Editorial: Global
Change, Clonal Growth, and Biological Invasions by
Plants.\emph{Frontiers in Plant Science} , \emph{7} .
https://www.frontiersin.org/articles/10.3389/fpls.2016.01467\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

\textbf{Figure 1:} Workflow in GenAPoPop. Users first import dataset
using the embedded simulator or external datasets, describe the data
structure, and then can launch at least one of the three types of
analyses mediated by the graphical interface. Full connectors indicate
the possible workflows, dashed connectors indicate optional possibility
to consult documentation using the embedded light PDF reader. Results
can be browsed within the software and retrieved in exported files
directly importable into common spreadsheets and text editors.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

\textbf{Figure 2:} Minimum spanning tree of the genetic distance in the
AS dataset. White arrows indicate one rosette of multiple multilocus
genotypes differing from one allele of a central multilocus genotype,
suspected to be recent mutants of a same multilocus lineage. Black arrow
indicates a rosary pattern of multilocus genotypes differing from few
alleles, suspected to be clones of a same multilocus lineage in which
other sampled clones may have accumulated few mutations over
generations.

\textbf{Table1:} An example of formatted triploid dataset ready to be
analysed by GenAPoPop. Bold headers indicate the minimum required
columns per individual; italic headers optional columns expected to
format the minimum spanning tree of the genetic distances between
individuals. One or multiple additional columns with custom information
like ecological, physiological, traits, latitude and longitude, etc. can
figure anywhere before the column containing the first allele of the
first locus.\selectlanguage{english}
\begin{longtable}[]{@{}llllllllll@{}}
\toprule
\textbf{Pop} & \textbf{Gen} & \textbf{ID} & Info & \emph{Col} &
\emph{Tag} & \textbf{1A\_1L} & \textbf{2A\_1L} & \textbf{3A\_1L} &
\textbf{1A\_L2}\tabularnewline
\midrule
\endhead
\textbf{pop1} & \textbf{1} & \textbf{Ind1} & \ldots{} & \emph{Blue} &
\emph{p1\_i1} & \textbf{A} & \textbf{A} & \textbf{G} &
\textbf{T}\tabularnewline
\textbf{pop1} & \textbf{2} & \textbf{Ind2} & \ldots{} & \emph{Red} &
\emph{p1\_i2} & \textbf{A} & \textbf{G} & \textbf{G} &
\textbf{T}\tabularnewline
\ldots{} & \ldots{} & \ldots{} & \ldots{} & \ldots{} & \ldots{} &
\ldots{} & \ldots{} & \ldots{} & \ldots{}\tabularnewline
\textbf{popn} & \textbf{2} & \textbf{Ind30} & \ldots{} & \emph{orange} &
\emph{pn\_i30} & \textbf{A} & \textbf{A} & \textbf{A} &
\textbf{C}\tabularnewline
\bottomrule
\end{longtable}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/2022-11-23-figure1-article/2022-11-23-figure1-article}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/2022-11-25-Figure2/2022-11-25-Figure2}

\end{center}
\end{figure}

\selectlanguage{english}
\FloatBarrier
\end{document}

