```{r, results = "asis", echo = FALSE}

Zhian N. Kamvar, Javier F. Tabima, and Niklaus J. Grünwald

```{r, results = "asis", echo = FALSE}

Journal: **PeerJ**

PO Box 614, Corte Madera, CA 94976, USA

Published 2014-03-04, Issue: **2**:e281,

DOI: [10.7717/peerj.281](https://dx.doi.org/10.7717/peerj.281)

```{r, results = "asis", echo = FALSE}

Many microbial, fungal, or oomcyete populations violate assumptions for

population genetic analysis because these populations are clonal, admixed,

partially clonal, and/or sexual. Furthermore, few tools exist that are

specifically designed for analyzing data from clonal populations, making

analysis difficult and haphazard. We developed the R package poppr providing

unique tools for analysis of data from admixed, clonal, mixed, and/or sexual

populations. Currently, poppr can be used for dominant/codominant and

haploid/diploid genetic data. Data can be imported from several formats

including GenAlEx formatted text files and can be analyzed on a user-defined

hierarchy that includes unlimited levels of subpopulation structure and clone

censoring. New functions include calculation of Bruvo's distance for

microsatellites, batch-analysis of the index of association with several indices

of genotypic diversity, and graphing including dendrograms with bootstrap

support and minimum spanning networks. While functions for genotypic diversity

and clone censoring are specific for clonal populations, several functions found

in poppr are also valuable to analysis of any populations. A manual with

documentation and examples is provided. Poppr is open source and major releases

are available on CRAN: http://cran.r-project.org/package=poppr. More supporting

documentation and tutorials can be found under 'resources' at:

http://grunwaldlab.cgrb.oregonstate.edu/.

The Wright-Fisher model of populations is one of the oldest models utilized in

population genetic theory. Populations in this model are characterized as having

non-overlapping generations with a constant size free from any selective

pressures [@weir1996genetic; @hartl1997principles; @nielsen2013introduction].

Conceptually, these populations are represented as pools of alleles that are

independently assorting where random mating is approximated by randomly sampling

alleles with replacement from one generation to the next. Assumptions of this

model, or related models, are implicitly assumed for common population genetic

analysis tools. In clonal populations, however, alleles are not independently

passed on from one generation to the next, and these assumptions are violated.

Classical textbooks on population genetics do not provide much guidance on how

to analyze clonal or mixed clonal and sexual populations. In reality, many

populations are not strictly clonal or sexual, but can range from completely

sexual to completely clonal and this is commonly observed for fungal, oomycete,

or microbial populations [@anderson1995clonality; @milgroom1996recombination].

Currently, analysis of these populations is not straightforward as we lack the

sophisticated tools and methods developed for model populations that are

typically either haploid or diploid [@grunwald2011evolution].

Inferring population structure with many commonly used model-based clustering

approaches such as the program <span style="font-variant:small-caps;">

Structure</span> [@pritchard2000inference] is inherently problematic for

clonal populations. These approaches cannot be used as clonal populations

violate basic assumptions of panmixia and Hardy-Weinberg equilibrium. Thus,

model free methods such as those relying on k-means clustering, dendrograms

including bootstrap support for clades, or minimum spanning networks are more

appropriate [@goss2009population; @cooke2012genome;

@mascheretti2008reconstruction]. Furthermore, analysis of mixed or clonal

populations traditionally relies on calculation of diversity of genotypes

observed and analysis of clone-censored versus non-censored populations

[@mcdonald1997population; @milgroom1996recombination;

@grunwald2006hierarchical]. Clone censoring involves reduction of any population

sample to a single observation for each multilocus genotype (MLG) in a

population thereby approximating panmictic populations and removing the effect

of genetic linkage [@milgroom1996recombination]. Analysis of diversity, in turn,

involves calculation of the number of genotypes observed (richness), diversity,

and evenness [@grunwald2003analysis]. Typical measures of genotypic diversity

are borrowed from ecology and use either the Shannon-Wiener or Stoddart and

Taylor index [@stoddart1988genotypic; @shannon2001mathematical;

@grunwald2003analysis].

A critical aspect of analyzing clonal or mixed populations is testing a null

hypothesis of panmixia [@milgroom1996recombination]. Testing of this hypothesis

for potentially clonal populations typically relies on assessment of linkage

disequilibrium among loci [@milgroom1996recombination]. This is achieved via

calculation of the index of association or related indices in combination with

resampling of the data to obtain a null distribution for the expectation of

random mating [@burt1996molecular; @brown1980multilocus; @smith1993how;

@milgroom1996recombination]. These approaches have, for example, been applied to

*Pyrenophora teres* [@peever1994genetic] and *Aphanomyces euteiches*

[@grunwald2006hierarchical] and are routinely used in the analyses of clonal

populations although they are not easily calculated given available software

including <span style="font-variant:small-caps;">Multilocus</span>, which is no

longer supported, and <span style="font-variant:small-caps;">LIAN</span>, which

only works for haploids [@Agapow_2001; @Haubold:2000].

Hierarchical sampling adds another layer of complexity to analysis of clonal

populations. With microbial populations, the geographic structure of each

population is not entirely clear, and it is often important to sample temporally

to see if clones persist over time [@grunwald2006hierarchical]. A common

approach when faced with multiple levels of sampling is to create a separate

data set for each level or combination of levels and to analyze them separately.

However, the number of data sets undergo a factorial increase with each

hierarchical level, therefore increasing the chances of human error in data

reformatting or analysis. Thus, tools are needed for analysis of population data

across hierarchies or subsets of data.

Here, we introduce the R package *poppr* that is specifically designed for

analysis of populations that are clonal, admixed and/or sexual. *Poppr*

complements and builds on previously existing R packages including *adegenet*

and *vegan* [@Jombart_2008; @jombart2011adegenet; @oksanen2013vegan] while

implementing tools novel to R significantly facilitating data import, population

genetic analyses, and graphing of clonal or partially clonal populations. These

tools include among others: analysis across hierarchies of populations,

subsetting of populations, clone-censoring, Bruvo's genetic distance

@bruvo2004simple, the index of association and related statistics

[@brown1980multilocus; @smith1993how], and bootstrap support for trees based on

Bruvo's distance. By providing a centralized suite of tools appropriate for many

data types, this package represents a novel and useful resource specifically

tailored for analysis of clonal populations.

*Poppr* allows import of data in several formats for

dominant/codominant, haploid/diploid and geographic data. The R package

*adegenet*, that defines the `genind` data structure that *poppr*

utilizes, allows support for importing data natively from <span

style="font-variant:small-caps;">Structure, Genetix, Genepop</span>, and

<span style="font-variant:small-caps;">Fstat</span>. While these formats

are very common and widely supported, these do not allow for import of

geographic and/or regional data. Furthermore, *adegenet* will only

handle diploids with this format, though manual import is possible. To

aid in importing data, *poppr* has newly added the function

`read.genalex()`, to read data from *GenAlEx* formatted text files into

the `genind` data object of the package *adegenet* [@Jombart_2008;

@jombart2011adegenet; @Peakall:2006]. *GenAlEx* is a popular add-in for <span

style="font-variant:small-caps;">Microsoft Excel</span> that can handle

data including codominant/dominant and haploid/diploid markers as well

as geographic and regional data. This function further facilitates the

import of haploid, geographic, and regional data.

Transferring data to new formats and manipulating data by hand, such as

collapsing data into clones or subsetting data into different

hierarchical levels, is tedious, creates redundancy, and can result in

lost or misrepresented data. *Poppr* includes tools to automate such

repetitive tasks. Many currently available data formats and software

implementations allow analysis of only one or two levels of a population

hierarchy. With *poppr* the user can import a single data set with an

unlimited number of hierarchical levels. This is achieved by having the

user combine the levels using a common delimiter (e.g.

"Year\_Country\_City"). These combined levels are then used as the

defining population factor in the input file and can easily be

manipulated within R.

Once data is imported into R, the user can dynamically access and

manipulate the population hierarchy with the function `splitcombine()`,

subset the data set by population with `popsub()`, and check for cloned

multilocus genotypes using `mlg()`. For data sets that include clones,

the *poppr* function `clonecorrect()` will censor exact clones with

respect to any level of a population hierarchy by creating a new data

set that includes only unique multilocus genotypes (MLGs) per

population. A full list of functions available in *poppr* is provided in

table \@ref(tab:poppr1).

```{r, poptab1, results = 'asis', echo = FALSE}

Typical analyses in *poppr* start with summary statistics for diversity,

rarefaction, evenness, MLG counts, and calculation of distance measures

such as Bruvo's distance, providing a suitable stepwise mutation model

appropriate for microsatellite markers [@bruvo2004simple]. *Poppr* will define

MLGs in your data set, show where they cross populations, and can

produce graphs and tables of MLGs by population that can be used for

further analysis with the R package *vegan* @oksanen2013vegan. Many of the

diversity indices calculated by the *vegan* function `diversity()` are

useful in analyzing the diversity of partially clonal populations. For

this reason, *poppr* features a quick summary table (Table \@ref(tab:poppr2))

that incorporates these indices along with the index of association,

$I_A$ [@brown1980multilocus; @smith1993how], and its standardized form, $\bar{r}_d$,

which accounts for the number of loci sampled [@Agapow_2001]. Both

measures of association can detect signatures of multilocus linkage and

values significantly departing from the null model of no linkage among

markers are detected via permutation analysis utilizing one of four

algorithms described in table \@ref(tab:poppr3) [@Agapow_2001]. The user can

specify the number of samples taken from the observed data set to obtain

the null distribution expected for a randomly mating population.

Detailed examples of these analyses can be found in the *poppr* manual.

```{r, poptab2, results = 'asis', echo = FALSE}

```{r, poptab3, results = 'asis', echo = FALSE}

*Poppr* generates bar charts of MLG counts found within each population

of your data set (Fig. \@ref(fig:poppr1)). Histograms with rug plots for

$I_A$ and $\bar{r}_d$ allow visual assessment of the quality of the

distribution derived from resampling to see if a higher number of

replications are necessary (Fig. \@ref(fig:poppr2)). *Poppr*

automatically produces custom minimum spanning networks for Bruvo's or

other distances using Prim's algorithm, as implemented in the package

*igraph* @csardi2006igraph, with the functions `bruvo.msn()` for Bruvo's distance

(Fig. \@ref(fig:poppr3)) and `poppr.msn()` for any distance matrix. The

combination of data structures from *adegenet* and *igraph* allow

graphing that is color coded by population with vertices grouped by MLG

[@Jombart_2008; @jombart2011adegenet; @csardi2006igraph]. *Poppr* also includes

visualization of dendrograms using UPGMA @phangorn and Neighbor-Joining

@paradis2004ape algorithms with bootstrap support for Bruvo's distance using the

function `bruvo.boot()` (Fig. \@ref(fig:poppr4)). Neither graphing of

minimum spanning networks or dendrograms with bootstrap support are

currently possible for populations in any other R packages.

```{r, poppr1, echo = FALSE, fig.cap = cap1, fig.scap = scap1, results = "asis"}

```{r, poppr2, echo = FALSE, fig.cap = cap2, fig.scap = scap2, results = "asis", out.width = "70%"}

```{r, poppr3, echo = FALSE, fig.cap = cap3, fig.scap = scap3, results = "asis"}

```{r, poppr4, echo = FALSE, fig.cap = cap4, fig.scap = scap4, results = "asis"}

Most of the functions in *Poppr* were written and optimized for

performance in R and are available for inspection and/or download at

<https://github.com/grunwaldlab/poppr>. Algorithms of $\geq O(n^2)$

complexity were written in the byte-compiled C language to optimize

runtime performance.

For comparisons of $I_A$ and Bruvo's distance, we utilized the data set

'nancycats' (237 diploid individuals genotyped at nine microsatellite

loci) from the *adegenet* package. Calculations were run independently

10 times and then averaged. Bruvo's distance was calculated on a machine

with OSX 10.8.4 and a 2.9 GHz intel processor. The $I_A$ and $\bar{r}_d$

calculations were performed on a machine with OSX 10.5.8 and a 2.4 GHz

intel processor due to the inability of the software <span

style="font-variant:small-caps;">multilocus</span> to work on any later

version of OSX.

Several of the methods implemented in *poppr* are described elsewhere.

Users should refer to the original publications for interpretations and

citation. See table \@ref(tab:poppr4) for a full list of citations. As with any

R package, users should always cite the R Core Team [@R2013].

```{r, poptab4, results = 'asis', echo = FALSE}

*Poppr* provides significant, convenient tools for analysis of clonal

and partially clonal populations available in one environment on all

major operating systems. The ability to analyze data for multiple

populations across a user-defined hierarchy and clone-censoring provide

novel functionality in R. Combined with R's graphing abilities,

publication-ready figures are thus obtained conveniently.

**Haploids** **Diploids** $\bar{r}_d$ **All Platforms** **Batch Analysis**

*poppr* Yes Yes Yes Yes Yes

*LIAN* Yes No No Yes Yes

*multilocus* Yes Yes Yes No No

Table: (\#tab:poppr5) Comparison of programs that calculate $I_A$

*Poppr* implements several new functionalities. As of this writing,

aside from *poppr*, there exist two programs that calculate $I_A$: <span

style="font-variant:small-caps;">LIAN</span> [@Haubold:2000] and <span

style="font-variant:small-caps;">multilocus</span> [@Agapow_2001]. <span

style="font-variant:small-caps;">LIAN</span> can calculate $I_A$ for

haploid data and is only available online or for \*nix systems with a C

compiler such as OSX and Linux [@Haubold:2000]. <span

style="font-variant:small-caps;">Multilocus</span> implemented

$\bar{r}_d$, a novel correction for $I_A$, but is no longer supported

[@Agapow_2001]. <span style="font-variant:small-caps;">Multilocus</span>

will only calculate index values for one data set at a time and <span

style="font-variant:small-caps;">LIAN</span> requires the user to

structure the data set with populations in contiguous blocks to analyze

multiple populations within a single file. Thus *poppr* provides

significant improvements for calculation of linkage disequilibrium, and

handles both haploid and diploid data, works on all major operating

systems, and is capable of batch analysis of multiple files and multiple

populations defined within a file including the possibility of clone

correction and sub-setting. A comparison of the capabilities of these

programs are summarized in Table \@ref(tab:poppr5).

To test significance for $I_A$ and $\bar{r}_d$, *poppr* offers four

permutation algorithms. Each one will randomly shuffle data at each

locus, effectively unlinking the loci. The algorithm previously utilized

by <span style="font-variant:small-caps;">mutlilocus</span> is included.

The <span style="font-variant:small-caps;">multilocus</span>-style

algorithm shuffles genotypes, maintaining the associations between

alleles at each locus [@Agapow_2001]. More appropriately, alleles are

expected to assort independently in panmictic populations. *Poppr* thus

provides three new algorithms for permutation that allow for independent

allele assortment at each locus. The default algorithm permutes the

alleles at each locus and the remaining two will randomly sample alleles

from a multinomial distribution parametrically and non-parametrically

[@weir1996genetic]. Details of these algorithms are presented in table

\@ref(tab:poppr3). Because the index of association is calculated using a

binary measure of dissimilarity, we have also made this available as a

distance measure called `diss.dist()`. This pairwise distance is based

on the percent allelic differences.

*Poppr* also newly implements Bruvo's genetic distance that utilizes a stepwise

mutation model appropriate for microsatellite data [@bruvo2004simple]. While this

distance is implemented in the program <span style="font-variant:small-caps;">

GenoDive</span> @meirmans2004genotype and the R package *polysat* @polysat, there are

a few caveats with these two implementations.

<span style="font-variant:small-caps;">GenoDive</span> is closed-source, and

only implemented in OSX. Both *poppr* and *polysat* are open-source and

available on all platforms, but *polysat*, being optimized for polyploid

individuals with ambiguous allelic dosage, is inappropriate for analyzing

diploids. *Polysat* will collapse homozygous individuals into a single allele

and attempt to infer the second allelic state in comparison with heterozygous

individuals. Since haploid and diploid individuals show clear allelic dosage,

this procedure creates a bias misrepresenting the true distance. Not only is

*poppr* not subject to this bias, but it also newly introduces bootstrap support

for this distance as shown in Figure \@ref(fig:poppr4).

**$I_A$ (seconds)** **Bruvo's distance (seconds)**

*poppr* 13.4 0.3

*polysat* - 58.3

*multilocus* 547.2 -

Table: (\#tab:poppr6) Comparison of performance on one data set of 237

individuals over nine loci. Each time point represents an average of 10

independent runs. Calculations of $I_A$ are based on 100 permutations.

*Poppr* reduces the amount of intermediate files and repetitive tasks

needed for basic population genetic analyses and implements

computationally intensive functions, such as Bruvo's distance and the

index of association in C to improve performance. The *polysat* package

calculation of Bruvo's distance took 58.3 seconds on average whereas

*poppr*'s calculation was over 190 times faster, averaging 0.3 seconds

(Table \@ref(tab:poppr6)). For calculation of $I_A$ and $\bar{r}_d$ with 100

permutations and Nei's genotypic diversity [@Nei:1978], <span

style="font-variant:small-caps;">multilocus</span> required around 9.12

minutes on average, as compared to 13.4 seconds with *poppr*.

The R package *poppr* provides new functions and tools specifically tailored for

analysis of data from clonal or partially clonal populations. No software

currently available provides this set of tools. Novel capabilities include

analysis across multiple populations at multiple levels of hierarchies,

clone-censoring, and subsetting. These in combination with R's command line

interface and scripting capabilities makes analyses of these populations more

streamlined and tractable. By implementing computationally expensive algorithms

such as Bruvo's distance and $I_A$ in C, analyses of multiple populations that

would normally take hours to complete can now be finished in a matter of

minutes. This allowed us to expand the utility of these measures to convenient

new graphing abilities such as automatically creating dendrograms with bootstrap

support for Bruvo's distance and minimum spanning networks. While major releases

of *poppr* are available on CRAN, we are continuing to develop this package to

be able to efficiently handle genome-sized SNP data. Development versions are

available on github at <https://github.com/grunwaldlab/poppr>.

The authors would like to thank Sydney Everhart and Corine Schoebel for

invaluable alpha testing and Paul-Michael Agapow for providing the *multilocus*

C++ source code for reference. We thank Sydney Everhart and Brian Knaus for

comments that significantly improved this manuscript. Mention of trade names or

commercial products in this manuscript are solely for the purpose of providing

specific information and do not imply recommendation or endorsement.