# Abstract

Poppr provides open-source, cross-platform tools for quick analysis of population genetic data enabling focus on data analysis and interpretation. While there are a plethora of packages for population genetic analysis, few are able to offer quick and easy analysis of populations with mixed reproductive modes. Poppr’s main advantage is the ease of use and integration with other packages such as adegenet and vegan, including support for novel methods such as clone correction, multilocus genotype analysis, calculation of Bruvo’s distance, and the index of association. New features in version 2.0 include generation of minimum spanning networks with reticulation, calculation of the index of association for genomic data, and filtering multilocus genotypes based on genetic distance.

# Introduction

## Purpose

Poppr is an R package with convenient functions for analysis of genetic data with mixed modes of reproduction including sexual and clonal reproduction. While there are many R packages in CRAN and other repositories with tools for population genetic analyses, few are appropriate for populations with mixed modes of reproduction. There are several stand-alone programs that can handle these types of data sets, but they are often platform specific and often only accept specific data types. Furthermore, a typical analysis often involves switching between many programs, and converting data to each specific format.

Poppr is designed to make analysis of populations with mixed reproductive modes more streamlined and user friendly so that the researcher using it can focus on data analysis and interpretation. Poppr allows analysis of haploid and diploid dominant/co-dominant marker data including microsatellites, Single Nucleotide Polymorphisms (SNP), and Amplified Fragment Length Polymorphisms (AFLP). To avoid creating yet another file format that is specific to a program, poppr was created on the backbone of the popular R package adegenet and can take all the file formats that adegenet can take (Genpop, Genetix, Fstat, and Structure) and newly introduces compatibility with GenAlEx formatted files (exported to CSV). This means that anything you can analyze in adegenet can be further analyzed with poppr.

The real power of poppr is in the data manipulation and analytic tools. Poppr has the ability to bootstrap, clone-censor, and subset data sets. With poppr you can also quickly calculate Bruvo’s distance, the index of association, and easily determine which multilocus genotypes are shared across populations.

In version 2.0, tools for genomic data were introduced (Zhian N Kamvar, Brooks, and Grünwald 2015). These tools allow researchers to define what it means to be a clone lost in a sea of genomic data, generate bootstrapped dendrograms with any genetic distance, and calculate minimum spanning networks with reticulations to reveal the underlying population structure of your clonal data.

## Resources

This vignette will cover all of the material you need to know to efficiently analyze data in poppr. For information on methods of analysis (eg. index of association, distance measures, AMOVA, …), please read the manual pages provided for each function.

As poppr expanded from version 1.0, the vignette also expanded to be 80+ pages. As a result, it became clear that over 22,000 words was less of a manual and more of a novella with a terrible plot. To remedy this, this vignette will focus only on data manipulation and a separate vignette, “algo”, has been written to give algorithmic details of analyses introduced with poppr.

As of spring 2014, Drs. Niklaus J. Grünwald, Sydney E. Everhart, and I have co- authored a primer on using R for population genetic analysis. It is located at http://grunwaldlab.github.io//Population_Genetics_in_R and the source code can be found on our github site.

## Getting Help

If you have any questions or feedback, feel free to send a message to the poppr forum at http://groups.google.com/group/poppr. You can submit bug reports there or on our github site: https://github.com/grunwaldlab/poppr/issues

## Acknowledgments

Much thanks goes to Sydney E. Everhart for alpha testing, beta testing, feature requests, proofreading, data contribution, and moral support throughout the writing of this package and manual. Thanks also to Brian Knaus, Ignazio Carbone, David Cooke, Corine Schoebel, Jane Stewart, and Zaid Abdo for beta testing and feedback.

The following data sets are included in poppr:

• Pinf (SSR, Phytophthora infestans)(Goss et al. 2014)

• monpop (SSR, Monilinia fructicola)(Everhart and Scherm 2015)

• Aeut (AFLP, Aphanomyces eutieches)(Grünwald and Hoheisel 2006)

• Pram (SSR, Phytophthora ramorum)(Z. Kamvar et al. 2015; Goss et al. 2009)

## Citation

citation(package = "poppr")
##
## To cite poppr in publications or presentations, please specify
## poppr version 2.8.2 and with the following citation:
##
##   Kamvar ZN, Tabima JF, Grünwald NJ. (2014) Poppr: an R package
##   for genetic analysis of populations with clonal, partially
##   clonal, and/or sexual reproduction. PeerJ 2:e281. doi:
##   10.7717/peerj.281
##
##   Kamvar ZN, Brooks JC and Grünwald NJ (2015) Novel R tools for
##   analysis of genome-wide population genetic data with emphasis on
##   clonality. Front. Genet. 6:208. doi: 10.3389/fgene.2015.00208
##
## To see these entries in BibTeX format, use 'print(<citation>,
## bibtex=TRUE)', 'toBibtex(.)', or set
## 'options(citation.bibtex.max=999)'.

The formal publication for the first version of poppr was published in the journal PeerJ: http://peerj.com/articles/281/ (Kamvar, Tabima, and Grünwald 2014). The new features in version 2.0 were published in Frontiers https://doi.org/10.3389/fgene.2015.00208 (Zhian N Kamvar, Brooks, and Grünwald 2015).

# Installation and Quick Start

## Installation

This manual assumes you have installed R. If you have not, please refer to The CRAN home page at https://cran.r-project.org/. We also recommend the Rstudio IDE (http://www.rstudio.com/), which allows the user to view the R console, environment, scripts, and plots in a single window.

### From CRAN

To install poppr from CRAN, select “Package Installer” from the menu “Packages & Data” in the GUI or type:

install.packages("poppr", repos = "http://cloud.r-project.org/")

All dependencies will also be installed. In the unfortunate case this does not work, please consult https://cran.r-project.org/doc/manuals/R-admin.html#Installing-packages.

### From GitHub

GitHub is a repository where you can find all stable and development versions of poppr.

Since poppr contains C code, it needs to be compiled, which means that you need a working C compiler. If you are on Linux, you should have that, but if you are on Windows or OSX, you might need to download some special tools:

Windows

OSX

To install from GitHub, you do not need to download the tarball since there is a package called devtools that will download and install the package for you directly from GitHub. After you have installed all dependencies (see above section), you should download devtools:

install.packages("devtools")

Now you can execute the command install_github() with the user and repository name:

devtools::install_github("grunwaldlab/poppr")

## Quick start

The author assumes that if you have reached this point in the manual, then you have successfully installed R and poppr. Before proceeding, you should be aware that R is case sensitive. This means that the words “Case” and “case” are different. You should also know where your R package library is located. In this section, you will learn how to locate a file, import it to R, and make a first analysis using the poppr() function.

What or where is my R package library?

R is as powerful as it is through a community of people who submit extra code called “packages” to help it do specific things. These packages live in a certain place on your computer called an R library. You can find out where this library is by typing .libPaths()

Importing a file into R involves you knowing the path to your file and then typing that into R’s console. getfile() will help provide a point and click interface for selecting a file. This is simply a tool to help you get started. As you get better with R, you might feel that you don"t need it at all.

First, tell your computer to search R’s library, load the poppr package, and use getfile():

library("poppr")
x <- getfile()

A pop up window will appear like this1:

You should navigate to your R library and select the file called “rootrot.csv”. If you don“t know where your the poppr package lives, you can find it by typing find.package("poppr") into the R command line. Once we select a file, the file name and its path will be stored in the variable, x. We can confirm that by typing x into R”s command line.

x
## $files ## [1] "/path/to/R/poppr/files/rootrot.csv" ## ##$path
## [1] "/path/to/R/poppr/files"

Here we can see that x is a list with two entries: $files shows the files you selected and $path shows the path to those files.

We will use x$files to access the file. The file is in the GenAlEx format, so we will import it using read.genalex() and then analyze it with the function poppr() to get a table of diversity indices per population. myData <- read.genalex(x$files)
myData
popdata <- poppr(myData)

The output of poppr() was assigned to the variable popdata, so let"s look at the data.

popdata
##             Pop   N MLG  eMLG    SE     H     G lambda   E.5   Hexp    Ia rbarD   File
## 1      Athena_1   9   7  7.00 0.000 1.889  6.23  0.840 0.932 0.1081  2.92 0.210 myData
## 2      Athena_2  12  12 10.00 0.000 2.485 12.00  0.917 1.000 0.1999  4.16 0.128 myData
## 3      Athena_3  10   2  2.00 0.000 0.325  1.22  0.180 0.571 0.0107  2.00 1.000 myData
## 4      Athena_4  13   9  7.15 0.769 1.946  5.12  0.805 0.687 0.1012  5.49 0.372 myData
## 5      Athena_5  10   7  7.00 0.000 1.834  5.56  0.820 0.866 0.0802  4.53 0.353 myData
## 6      Athena_6   5   5  5.00 0.000 1.609  5.00  0.800 1.000 0.1143  2.46 0.190 myData
## 7      Athena_7  11  10  9.18 0.386 2.272  9.31  0.893 0.955 0.1584  2.13 0.086 myData
## 8      Athena_8   8   6  6.00 0.000 1.667  4.57  0.781 0.831 0.0791  3.86 0.323 myData
## 9      Athena_9  10  10 10.00 0.000 2.303 10.00  0.900 1.000 0.1532  2.82 0.118 myData
## 10    Athena_10   9   8  8.00 0.000 2.043  7.36  0.864 0.948 0.1230  2.85 0.137 myData
## 11 Mt. Vernon_1  10   9  9.00 0.000 2.164  8.33  0.880 0.952 0.1766  7.13 0.276 myData
## 12 Mt. Vernon_2   6   6  6.00 0.000 1.792  6.00  0.833 1.000 0.3940 20.65 0.492 myData
## 13 Mt. Vernon_3   8   6  6.00 0.000 1.667  4.57  0.781 0.831 0.1033  2.12 0.106 myData
## 14 Mt. Vernon_4  12   8  6.83 0.665 1.814  4.50  0.778 0.681 0.0823  3.01 0.255 myData
## 15 Mt. Vernon_5  17   7  5.54 0.828 1.758  5.07  0.803 0.848 0.0544  2.68 0.340 myData
## 16 Mt. Vernon_6  12  11  9.32 0.466 2.369 10.29  0.903 0.958 0.3001 19.50 0.467 myData
## 17 Mt. Vernon_7  12   9  7.82 0.649 2.095  7.20  0.861 0.870 0.0601  1.21 0.153 myData
## 18 Mt. Vernon_8  13   9  7.35 0.764 2.032  6.26  0.840 0.794 0.0430  1.15 0.169 myData
## 19        Total 187 119  9.61 0.612 4.558 68.97  0.986 0.720 0.3651 14.37 0.271 myData

The fields you see in the output include:

• Pop - Population name (Note that “Total” also means “Pooled”).

• N - Number of individuals observed.

• MLG - Number of multilocus genotypes (MLG) observed.

• eMLG - The number of expected MLG at the smallest sample size $$\geq 10$$ based on rarefaction. (Hurlbert 1971)

• SE - Standard error based on eMLG (Heck, Belle, and Simberloff 1975)

• H - Shannon-Wiener Index of MLG diversity. (Shannon 1948)

• G - Stoddart and Taylor"s Index of MLG diversity. (Stoddart and Taylor 1988)

• lambda - Simpson"s index, $$\lambda$$.

• E.5 - Evenness, $$E_5$$. (Pielou 1975)(Ludwig and Reynolds 1988)(Grünwald et al. 2003)

• Hexp - Nei"s 1978 Expected Heterozygosity. (Nei 1978)

• Ia - The index of association, $$I_A$$. (Brown, Feldman, and Nevo 1980) (Smith et al. 1993) (Agapow and Burt 2001)

• rbarD - The standardized index of association, $$\bar{r}_d$$. (Agapow and Burt 2001)

These fields are further described in the function poppr. You can access the help page for poppr by typing ?poppr in your R console.

One thing to note about this output is the NaN in the column labeled SE. In R, NaN means “Not a number”. This is produced from calculation of a standard error based on rarefaction analysis. Occasionally, this calculation will encounter a situation in which it must attempt to take a square root of a negative number. Since the root of any negative number is not defined in the set of real numbers, it must therefore have an imaginary component, $$i$$. Unfortunately, R will not represent the imaginary components of numbers unless you specifically tell it to do so. By default, R represents these as NaN.

# Import and Data types

## Importing data into poppr {Get out of my dreams and into my R}

### How does R represent data? {Objective: data}

Working with data in R means that these data have to be stored inside an “object”, which is stored in the computer“s memory. Because of this, it”s important to know the difference between a file and an object. When anyone talking about importing a file into R, they are referring to a spreadsheet or text file that lives in a folder on your hard drive. Spreadsheet files (saved as *.csv files) are normally imported through the R function read.table(). The output of read.table() is a data.frame. A data.frame is an object represented in your computer’s memory. This means that it only exists for as long as R is running.

The good thing about having objects stored in memory is that you can manipulate them in any way and not affect the source of those data. Since R is a scripted language (instead of point-and-click), any of your manipulations can be saved in a separate R file that can be easily adapted to new data. Of course, most data are not going to be entered into R manually. Usually they will be formatted in a manner that can be read by popular population genetics programs.

As previously mentioned, since poppr is based on adegenet, it’s possible to read in the following file formats into a genind object with the function import2genind():

• Fstat

• Genepop

• Genetix

• Structure

Here, we introduce a new way of importing data into a genind or genclone object from a GenAlEx formatted file.

A very popular program for population genetics is GenAlEx (http://biology.anu.edu.au/GenAlEx/Welcome.html) (Peakall and Smouse 2012, 2006). GenAlEx runs within the Excel environment and can be very powerful in its analyses. Poppr has added the ability to read *.CSV files2 produced in the GenAlEx format. It can handle data types containing regions and geographic coordinates, but currently cannot import allelic frequency data from GenAlEx. Using the poppr function read.genalex() will import your data into adegenet“s genind object or poppr”s genclone object (more information on that below). For ways of formatting a GenAlEx file, see the manual here: http://biology.anu.edu.au/GenAlEx/Download_files/GenAlEx%206.5%20Guide.pdf

Below is an example of the GenAlEx format. We will use the data set called microbov from the adegenet package to generate it. The data contains three demographic factors: Country, Species and Breed contained within the @other slot (detailed in the ‘other’ slot). We will first set these as the population strata, define the population as the combination of the strata, and then save a file to the desktop.

library("poppr")
data(microbov)
strata(microbov) <- data.frame(other(microbov)) # set the strata
microbov
genind2genalex(microbov, file = "~/Desktop/microbov.csv")
## Extracting the table ... Writing the table to ~/Desktop/microbov.csv ... Done.

The GenAlEx format contains individuals in rows and loci in columns. Individual data begins at row 4. Column A always contains individual names and column B defines the population of each individual. Notice here that the three demographic factors from the data have been concatenated with a “_”. This allows us to import more than one population factor to use as hierarchical levels in a genclone object.

The First three rows contain information pertaining to the global data set. The only important information for poppr is the information contained in row 3 and the first three columns of row 1.

A B C D
1 # of Loci # of Individuals # of Populations Pop1 Size
2 - - - Pop1 Name
3 - - Locus 1

Highlighted in red in figure above are definitions of the number of populations and their respective sizes. As this is redundant information, we can remove it. Below is an example of a valid data set that can be imported into poppr.

All GenAlEx formatted data can be imported with the command read.genalex(), detailed below:

read.genalex(genalex, ploidy = 2, geo = FALSE, region = FALSE,
genclone = TRUE, sep = ",", recode = FALSE)
• genalex - a *.CSV file exported from GenAlEx on your disk (For example: my_genalex_file.csv).

• ploidy - a number indicating the ploidy for the data set (eg 2 for diploids, 1 for haploids).

• geo - GenAlEx allows you to have geographic data within your file. To do this for poppr, you will need to follow the first format outlined in the GenAlEx manual and place the geographic data AFTER all genetic and demographic data with one blank column separating it (See the GenAlEx Manual for details). If you have geographic information in your file, set this flag to TRUE and it will be included within the resulting genind object in the @other slot. (If you don“t know what that is, don”t worry. It will be explained later in the ‘other’ slot)

• region - To format your GenAlEx file to include regions, you can choose to include a separate column for regional data, or, since regional data must be in contiguous blocks, you can simply format it in the same way you would any other data (see the GenAlEx manual for details). If you have your file organized in this manner, select this option and the regional information will be stored in the @other slot of the resulting genind object or be incorporated into the hierarchy of the genclone object.

• genclone - This flag will convert your data into a genclone object (see Send in the clones for more info).

• sep - The separator argument for columns in your data. It defaults to “,”.

• recode - If your data is polyploid data, this gives you the option to recode it. (See About Polyploid Data for details)

Note that regional data and geographic data are not mutually exclusive. You can have both in one file, just make sure that they are on the same sheet and that the geographic data is always placed after all genetic and demographic data.

We have a short example of GenAlEx formatted data with no geographic or regional formatting. We will first see where the data is using the command system.file()

system.file("files/rootrot.csv", package="poppr")
## [1] "/path/to/R/library/poppr/files/rootrot.csv"

Now import the data into poppr like so:

rootrot <- read.genalex(system.file("files/rootrot.csv", package="poppr"))

Executing rootrot shows that this file is now in genclone format and can be used with any function in poppr and adegenet

rootrot
##
## This is a genclone object
## -------------------------
## Genotype information:
##
##    119 original multilocus genotypes
##    187 diploid individuals
##     56 dominant loci
##
## Population information:
##
##      1 stratum - Pop
##     18 populations defined -
## Athena_1, Athena_2, Athena_3, ..., Mt. Vernon_6, Mt. Vernon_7, Mt. Vernon_8

### Other ways of importing data

Adegenet already supports the import of FSTAT, Structure, Genpop, and Genetix formatted files, so if you have data in those formats, you can import them using the function import2genind. For sequence data, check if you can use read.dna() from the ape package to import your data. If you can, then you can use the adegenet function DNAbin2genind(). If you don“t have any of these formats handy, you can still import your data using R”s read.table along with df2genind() from adegenet. For more information, see adegenet’s “Getting Started” vignette.

### Function: genind2genalex (exporting data)

Of course, being able to export data is just as useful as being able to import it, so we have this handy little function that will write a GenAlEx formatted file to wherever you desire.
WARNING: This will overwrite any file that exists with the same name.

genind2genalex(gid, filename = "", overwrite = FALSE, quiet = FALSE,
pop = NULL, allstrata = TRUE, geo = FALSE, geodf = "xy",
sep = ",", sequence = FALSE)
• pop - a genind object.

• filename - This is where you specify the path to the new file you wish to create. If you specify only a filename with no path, it will place the file in your current working directory.

• quiet - If this is set to FALSE, a status message will be printed to the console as the extraction progresses.

• pop - A vector specifying a custom population OR a formula specifying the strata to be combined in the new file.

• allstrata - This is TRUE by default and will combine all of the strata in your file unless you have specified a new population factor.

• geo - Set to TRUE, if you have a data frame or matrix in the @other slot of your genind object that contains geographic coordinates for all individuals or all populations. Setting this to TRUE means the resulting file will have two extra columns at the end of your file with geographic coordinates.

• geodf - The name of the data frame or matrix containing the geographic coordinates.

• sep - A separator to separate columns in the resulting file.

First, a simple example for the rootrot data we demonstrated in an earlier section:

genind2genalex(rootrot, "~/Desktop/rootrot.csv")
## Extracting the table ... Writing the table to ~/Desktop/rootrot.csv ... Done.

Here’s an example of exporting the nancycats data set into GenAlEx format with geographic information. If we look at the nancycats geographic information, we can see it"s coordinates for each population, but not each individual:

data(nancycats)
other(nancycats)$xy ## x y ## P01 263.3498 171.10939 ## P02 183.5028 122.40790 ## P03 391.1050 254.70148 ## P04 458.6121 41.72336 ## P05 182.7769 219.08398 ## P06 335.2121 344.83557 ## P07 359.1662 375.36486 ## P08 271.3345 67.89132 ## P09 256.8169 150.02964 ## P10 270.6086 17.00917 ## P11 493.4544 237.25618 ## P12 305.4510 85.33663 ## P13 462.9674 86.79040 ## P14 429.5768 291.04587 ## P15 531.2003 115.13903 ## P16 407.8003 99.87438 ## P17 345.3745 251.79393 To export it: genind2genalex(nancycats, "~/Desktop/nancycats_pop_xy.csv", geo = TRUE) ## Extracting the table ... Writing the table to ~/Desktop/nancycats_pop_xy.csv ... Done. If we wanted to assign a geographic coordinate to each individual, we can use this trick knowing that there are 17 populations in the data set: nan2 <- nancycats other(nan2)$xy <- other(nan2)$xy[pop(nan2), ] tail(other(nan2)$xy)
##            x        y
## P17 345.3745 251.7939
## P17 345.3745 251.7939
## P17 345.3745 251.7939
## P17 345.3745 251.7939
## P17 345.3745 251.7939
## P17 345.3745 251.7939

Now we can export it to a different file.

genind2genalex(nan2, "~/Desktop/nancycats_inds_xy.csv", geo = TRUE)
## Extracting the table ... Writing the table to ~/Desktop/nancycats_inds_xy.csv ... Done.

## Getting to know adegenet"s genind object

Since poppr was built around adegenet"s framework, it is important to know how adegenet stores data in the genind object, as that is the object used by poppr. To create a genind object, adegenet takes a data frame of genotypes (rows) across multiple loci (columns) and converts them into a matrix of individual allelic counts at each locus (Jombart 2008).

For example, Let’s say we had data with 3 diploid individuals each with 3 loci that had 3, 4, and 5 allelic states respectively:

locus1 locus2 locus3
1 101/101 201/201 301/302
2 102/103 202/203 301/303
3 102/102 203/204 304/305

The resulting genind object would contain a matrix that has 3 rows and 12 columns. Below is a schematic of what that would look like. Each column represents a separate allele, each row represents an individual and each color represents a different locus.

When we look at the data derived from table above, we see that we have a matrix of individual allele counts at each locus.

##   locus1.101 locus1.102 locus1.103 locus2.201 locus2.202 locus2.203 locus2.204 locus3.301
## 1          2          0          0          2          0          0          0          1
## 2          0          1          1          0          1          1          0          1
## 3          0          2          0          0          0          1          1          0
##   locus3.302 locus3.303 locus3.304 locus3.305
## 1          1          0          0          0
## 2          0          1          0          0
## 3          0          0          1          1

At each locus, the allele counts for each individual sum to the ploidy, $$p$$. Homozygotes are denoted as having an allele count of $$p$$ at a single allele within a locus, while heterozygotes have their allele counts represented as $$<p$$ where $$p$$ = ploidy across multiple alleles in a single locus. Along with this matrix, are elements that define the names of the individuals, loci, alleles, and populations. If you wish to know more, see the adegenet “Getting Started” manual.

### The other slot

The other slot is a place in the genind object that can be used to store useful information about the data. We saw earlier that it could store demographic information, now let’s explore a different example. Bruvo’s distance is based off of a stepwise mutation model for microsatellites. This requires us to know the length of the repeat of each locus. We could store the repeat lengths in a separate variable in our R environment, but we are at risk of losing that. One way to prevent it from being lost would be to place it in the “other” slot. For the purpose of this example, we will use the “nancycats” data set from the adegenet package and assume that it has di-nucleotide repeats at all of its loci.

data(nancycats) # Load the data
other(nancycats) # geographical coordinates
## $xy ## x y ## P01 263.3498 171.10939 ## P02 183.5028 122.40790 ## P03 391.1050 254.70148 ## P04 458.6121 41.72336 ## P05 182.7769 219.08398 ## P06 335.2121 344.83557 ## P07 359.1662 375.36486 ## P08 271.3345 67.89132 ## P09 256.8169 150.02964 ## P10 270.6086 17.00917 ## P11 493.4544 237.25618 ## P12 305.4510 85.33663 ## P13 462.9674 86.79040 ## P14 429.5768 291.04587 ## P15 531.2003 115.13903 ## P16 407.8003 99.87438 ## P17 345.3745 251.79393 repeats <- rep(2, nLoc(nancycats)) #nLoc = number of loci repeats ## [1] 2 2 2 2 2 2 2 2 2 other(nancycats)$repeat_lengths <- repeats
other(nancycats) # two items named xy and repeat_lengths
## $xy ## x y ## P01 263.3498 171.10939 ## P02 183.5028 122.40790 ## P03 391.1050 254.70148 ## P04 458.6121 41.72336 ## P05 182.7769 219.08398 ## P06 335.2121 344.83557 ## P07 359.1662 375.36486 ## P08 271.3345 67.89132 ## P09 256.8169 150.02964 ## P10 270.6086 17.00917 ## P11 493.4544 237.25618 ## P12 305.4510 85.33663 ## P13 462.9674 86.79040 ## P14 429.5768 291.04587 ## P15 531.2003 115.13903 ## P16 407.8003 99.87438 ## P17 345.3745 251.79393 ## ##$repeat_lengths
## [1] 2 2 2 2 2 2 2 2 2

## The genclone object {send in the clones}

The genclone class was defined in order to make working with clonal organisms more intuitive. It is built off of the genind object and has dedicated slots for defined multilocus genotypes. The name genclone refers to the fact that it has the ability to handle genotypes of clonal organisms (but it is also used for sexual populations).

In previous versions of poppr, the genclone object contained a hierarchy slot as well. This slot was moved to adegenet and its name was changed to “strata”. This slot allows you to carry around several definitions for populations in the same data set.

The function as.genclone allows the user to convert a genind object to a genclone object. The following example will demonstrate that the genclone object is an extension of the genind object as well as the advantages of having populations pre-defined in your data set.

### Function: as.genclone

as.genclone(x, ..., mlg, mlgclass = TRUE)
• x - a genind object to be converted.

• … - any arguments to be passed to the genind constructor.

• mlg - a vector representing the multilocus genotype definitions of your data.

• mlgclass - if TRUE, the MLGs represented in your object will be converted to an MLG class object, which allows for custom MLG definitions.

Let“s show an example of a genclone object. First, we will take an existing genind object and convert it using the function as.genclone (We can also use the function read.genalex()to import as genclone or genind objects). We will use the Aeut data set because it is a clonal data set that has a simple population strata (Grünwald and Hoheisel 2006). The data set is here: https://doi.org/10.6084/m9.figshare.877104 and it is AFLP data of the root rot pathogen Aphanomyces euteiches collected from two different fields in NW Oregon and W Washington, USA. These fields were divided up into subplots from which samples were collected. The fields represent the population and the subplots represent the subpopulation. Let”s take a look at what the genind object looks like:

library("poppr")
data(Aeut)
Aeut
## /// GENIND OBJECT /////////
##
##  // 187 individuals; 56 loci; 56 alleles; size: 68.9 Kb
##
##  // Basic content
##    @tab:  187 x 56 matrix of allele counts
##    @loc.n.all: number of alleles per locus (range: 56-56)
##    @ploidy: ploidy of each individual  (range: 2-2)
##    @type:  PA
##    @call: old2new_genind(object = x, donor = new(class(x)))
##
##  // Optional content
##    @pop: population of each individual (group size range: 90-97)
##    @other: a list containing: population_hierarchy

We can see that there is a data frame in the @other slot called “population_hierarchy”. This is left over from poppr version 1.x behavior. Since the genind object now has a @strata slot, we can use it to set the stratification (previously called “hierarchy”).

strata(Aeut) <- other(Aeut)population_hierarchy[-1] Aeut ## /// GENIND OBJECT ///////// ## ## // 187 individuals; 56 loci; 56 alleles; size: 72.7 Kb ## ## // Basic content ## @tab: 187 x 56 matrix of allele counts ## @loc.n.all: number of alleles per locus (range: 56-56) ## @ploidy: ploidy of each individual (range: 2-2) ## @type: PA ## @call: old2new_genind(object = x, donor = new(class(x))) ## ## // Optional content ## @pop: population of each individual (group size range: 90-97) ## @strata: a data frame with 2 columns ( Pop, Subpop ) ## @other: a list containing: population_hierarchy Now we can convert this to a genclone object, which will store information about our multilocus genotypes for us. agc <- as.genclone(Aeut) agc ## ## This is a genclone object ## ------------------------- ## Genotype information: ## ## 119 original multilocus genotypes ## 187 diploid individuals ## 56 dominant loci ## ## Population information: ## ## 2 strata - Pop, Subpop ## 2 populations defined - Athena, Mt. Vernon If we wanted to, we could also convert it back to a genind object. genclone2genind(agc) ## /// GENIND OBJECT ///////// ## ## // 187 individuals; 56 loci; 56 alleles; size: 83.7 Kb ## ## // Basic content ## @tab: 187 x 56 matrix of allele counts ## @loc.n.all: number of alleles per locus (range: 56-56) ## @ploidy: ploidy of each individual (range: 2-2) ## @type: PA ## @call: genclone2genind(x = agc) ## ## // Optional content ## @pop: population of each individual (group size range: 90-97) ## @strata: a data frame with 2 columns ( Pop, Subpop ) ## @other: a list containing: population_hierarchy ## About polyploid data WARNING Treat polyploid data with care. Please read this section carefully and consult the help pages for all functions mentioned here. With diploid or haploid data, genotypes are unambiguous. It is often clear when it is homozygous or heterozygous. With polyploid data, genotypes can be ambiguous. For example, a tetraploid individual with the apparent genotype of A/B could actually have one of three genotypes: A/A/A/B, A/A/B/B, or A/B/B/B. This ambiguity prevents a researcher from accurately calling all alleles present. In adegenet, it was previously difficult to import polyploid data because of this ambiguity as data was required to be unambiguous or missing. A solution to this problem is to code missing alleles as “0”. An example of this is found within the Pinf data set in poppr (Goss et al. 2014). First, we will look at where we have polyploid allele calls. data(Pinf) Pinf ## ## This is a genclone object ## ------------------------- ## Genotype information: ## ## 72 multilocus genotypes ## 86 tetraploid individuals ## 11 codominant loci ## ## Population information: ## ## 2 strata - Continent, Country ## 2 populations defined - South America, North America ptab <- info_table(Pinf, type = "ploidy", plot = TRUE) We look at the last six samples over two loci, Pi63 (3 alleles, triploid) and Pi70 (3 alleles, diploid) to examine how the data is represented. Pinf[loc = locNames(Pinf)[9:10]] %>% tab() %>% tail() ## Pi63.000 Pi63.148 Pi63.151 Pi63.157 Pi70.000 Pi70.189 Pi70.192 Pi70.195 ## PiPE22 1 1 1 1 2 1 1 0 ## PiPE23 1 1 1 1 2 1 1 0 ## PiPE24 1 1 1 1 2 1 1 0 ## PiPE25 1 1 1 1 2 1 1 0 ## PiPE26 2 0 0 2 2 0 1 1 ## PiPE27 1 1 1 1 2 1 1 0 Each column in this data represents a different allele at a particular locus. Pi63.148 is the allele 148 at locus Pi63. Each row is an individual. The numbers represent the fraction of a given allele that makes up the individual genotype at a particular locus. What we can see here is that the number of columns is 8 when we expect only 6 (2 loci x 3 alleles). The first allele at each locus is 000. Let’s take a look at the data in a human-readable format. Pinfdf <- genind2df(Pinf, sep = "/") tail(Pinfdf[10:11]) ## Pi63 Pi70 ## PiPE22 000/148/151/157 000/000/189/192 ## PiPE23 000/148/151/157 000/000/189/192 ## PiPE24 000/148/151/157 000/000/189/192 ## PiPE25 000/148/151/157 000/000/189/192 ## PiPE26 000/000/157/157 000/000/192/195 ## PiPE27 000/148/151/157 000/000/189/192 It"s more clear now that we have a data set of tetraploid individuals where some genotypes appear diploid (000/000/157/157) and some appear triploid (000/148/151/157). The tetraploid genotype is padded with zeroes to make up the difference in ploidy. This method allows Bruvo’s Distance (Bruvo et al. 2004) and the Index of Association (Brown, Feldman, and Nevo 1980; Smith et al. 1993; Agapow and Burt 2001) to work with polyploids as they specifically recognize the zeroes as being missing data. A side effect, unfortunately is that the extra zeroes appear as extra alleles. As this affects all frequency-based statistics (except for the ones noted above), the user should reformat their data set with the function recode_polyploids, which will remove the zeroes. Pinf_rc <- recode_polyploids(Pinf, newploidy = TRUE) Pinf_rc # Notice that the new ploidy is accounted for. ## ## This is a genclone object ## ------------------------- ## Genotype information: ## ## 72 multilocus genotypes ## 86 diploid (55) and triploid (31) individuals ## 11 codominant loci ## ## Population information: ## ## 2 strata - Continent, Country ## 2 populations defined - South America, North America Pinf_rc[loc = locNames(Pinf_rc)[9:10]] %>% tab() %>% tail ## Pi63.148 Pi63.151 Pi63.157 Pi70.189 Pi70.192 Pi70.195 ## PiPE22 1 1 1 1 1 0 ## PiPE23 1 1 1 1 1 0 ## PiPE24 1 1 1 1 1 0 ## PiPE25 1 1 1 1 1 0 ## PiPE26 0 0 2 0 1 1 ## PiPE27 1 1 1 1 1 0 Below, we show the observed genotypes: Pinfrcdf <- genind2df(Pinf_rc, sep = "/") tail(Pinfrcdf[10:11]) ## Pi63 Pi70 ## PiPE22 148/151/157 189/192 ## PiPE23 148/151/157 189/192 ## PiPE24 148/151/157 189/192 ## PiPE25 148/151/157 189/192 ## PiPE26 157/157 192/195 ## PiPE27 148/151/157 189/192 If you have imported your data as recoded polyploid data, you can use the argument “addzero” to fill out the ploidy: Pinf_rc[loc = locNames(Pinf_rc)[9:10]] %>% recode_polyploids(addzero = TRUE) %>% tab() %>% tail() ## Pi63.0 Pi63.157 Pi63.148 Pi63.151 Pi70.0 Pi70.192 Pi70.189 Pi70.195 ## PiPE22 0 1 1 1 1 1 1 0 ## PiPE23 0 1 1 1 1 1 1 0 ## PiPE24 0 1 1 1 1 1 1 0 ## PiPE25 0 1 1 1 1 1 1 0 ## PiPE26 1 2 0 0 1 1 0 1 ## PiPE27 0 1 1 1 1 1 1 0 # Data Manipulation One tedious aspect of population genetic analysis is the need for repeated data manipulation. Poppr includes novel functions for clone- censoring your data sets, removing genotypes or loci with missing data, removing uninformative loci, and shuffling populations. ## Replace or remove missing data {Inside the golden days of missing data} A data set without missing data is always ideal, but often not achievable. The poppr function missingno exists to handle missing data. Missing data can mean different things based on your data type. For microsatellites, missing data might represent any source of error that could cause a PCR product to not amplify in gel electrophoresis, which may or may not be biologically relevant. For a DNA alignment, missing data could mean something as simple as an insertion or deletion, which is biologically relevant. The choice to exclude or estimate data has very different implications for the type of data you have. Treatment of Missing data is a non-trivial task. You should understand the nature of missing data in your data set before treatment. ### Function: missingno missingno is a function that serves as a way to exclude specific areas that contain systematic missing data. There are four methods available, missingno(pop, type = "loci", cutoff = 0.05, quiet = FALSE, freq = FALSE) pop - a genind object. type - This could be one of five options: 1. “loci” This is to be used for a data set that has systematic problems with certain loci that contain null alleles or simply failed to amplify. This will remove loci with a defined threshold of missing data from the data set. 2. “geno” This is to be used for genotypes (individuals) in your data set where many null alleles are present. Individuals with a defined threshold missing data will be removed. 3. “asis” This argument will retain missing data in your data set. It"s useful for functions that utilize missingno internally, such as mlg.filter(), poppr.amova(), or aboot(). 4. “mean” This replaces missing data with the mean allele frequencies in the entire data set . 5. “zero” or “0” This replaces missing data with zero, signifying a new allele . cutoff - This is a numeric value from 0 to 1 indicating the percent allowable missing data for either loci or genotypes. If you have, for example, two loci containing missing 5% and 10% missing data, respectively and you set cutoff = 0.05, missingno will remove the second locus. Percent missing data for genotypes is considered the percent missing loci over number of total loci. quiet - When this is set to FALSE, the number of missing values replaced will be printed to screen if the method is “zero” or “mean”. It will print the number of loci or individuals removed if the method is “loci” or “geno”. freq - This is used for compatibility with the tab() method for genind object. It will convert counts of alleles to frequencies of alleles, rendering an object that will return warnings. Let’s take a look at what this does by focusing in on areas with missing data. We"ll use the data set nancycats as an example. Using the poppr function info_table, we can assess missing data within populations. library("poppr") data(nancycats) info_table(nancycats, plot = TRUE) ## Locus ## Population fca8 fca23 fca43 fca45 fca77 fca78 fca90 fca96 fca37 Mean ## P01 0.200 . . . . . . . . 0.022 ## P02 . . . . . . . . . . ## P03 . . . . . . . . . . ## P04 . . . . . . . . . . ## P05 . . . . . . . . . . ## P06 . . . . . . . . . . ## P07 0.357 . . . . . . . . 0.040 ## P08 . . . . . . . . . . ## P09 . . . . . . . . . . ## P10 . . . . . . . . . . ## P11 0.150 . . 0.400 . . . 0.050 . 0.067 ## P12 0.214 . . . . . . . . 0.024 ## P13 . . . . . . . . . . ## P14 0.412 . . . . . . . . 0.046 ## P15 . . . . . . . . . . ## P16 . . . . . . . . . . ## P17 . . . 1.000 . . . 0.615 . 0.179 ## Total 0.084 . . 0.089 . . . 0.038 . 0.023 We can see that locus fca8 has a lot of missing data. To demonstrate the function missingno(), we will zoom into the first five individuals at the first locus. tab(nancycats)[1:5, 8:13] ## fca8.133 fca8.135 fca8.137 fca8.139 fca8.141 fca8.143 ## N215 NA NA NA NA NA NA ## N216 NA NA NA NA NA NA ## N217 0 1 0 0 0 1 ## N218 1 1 0 0 0 0 ## N219 1 1 0 0 0 0 When looking at this data set, recall how a genind object is formatted. You have a matrix representing counts of alleles. For diploids, if you see 1, that means it is heterozygous at that allele, and a 2 means it“s homozygous. Here we see three heterozygotes and two individuals with missing data (indicated by NA). Let”s look at what happens when we exclude loci and genotypes with >5% missing data). nanloci <- missingno(nancycats, "loci") nangeno <- missingno(nancycats, "geno") tab(nanloci)[1:5, 8:13] ## fca23.144 fca23.146 fca23.148 fca23.150 fca43.133 fca43.135 ## N215 0 1 0 0 0 0 ## N216 0 2 0 0 0 0 ## N217 0 1 0 0 0 0 ## N218 0 0 0 0 0 0 ## N219 0 1 0 0 0 0 Notice how we now see columns named fca23.128 and fca23.130. This is showing us another locus because we have removed the first. Recall from the summary table that the first locus had 16 alleles, and the second had 11. Now that we’ve removed loci containing missing data, all others have shifted over. Let’s look at the loci names and number of individuals. nInd(nanloci) # Individuals ## [1] 237 locNames(nanloci) # Names of the loci ## [1] "fca23" "fca43" "fca77" "fca78" "fca90" "fca96" "fca37" You can see that the number of individuals stayed the same but the loci “fca8”, “fca45”, and “fca96” were removed. Let’s look at what happened when we removed individuals. tab(nangeno)[1:5, 8:13] ## fca8.133 fca8.135 fca8.137 fca8.139 fca8.141 fca8.143 ## N217 0 1 0 0 0 1 ## N218 1 1 0 0 0 0 ## N219 1 1 0 0 0 0 ## N220 0 1 0 0 0 1 ## N221 0 2 0 0 0 0 nInd(nangeno) # Individuals ## [1] 199 locNames(nangeno) # Names of the loci ## [1] "fca8" "fca23" "fca43" "fca45" "fca77" "fca78" "fca90" "fca96" "fca37" We can see here that the number of individuals decreased, yet we have the same number of loci. Notice how the frequency matrix changes in both scenarios? In the scenario with “loci”, we removed several columns of the data set, and so with our sub-setting, we see alleles from the second locus. In the scenario with “geno”, we removed several rows of the data set so we see other individuals in our sub-setting. ## Extract populations {Divide (populations) and conquer (your analysis)} This poppr function popsub makes subsetting genind or genlight objects by population easier: ### Function: popsub The command popsub is powerful in that it allows you to choose exactly what populations you choose to include or exclude from your analyses. As with many R functions, you can also use this within a function to avoid creating a new variable to keep track of. popsub(gid, sublist = "ALL", blacklist = NULL, mat = NULL, drop = TRUE) • pop - a genind object. • sublist - vector of populations or integers representing the populations in your data set you wish to retain. For example: sublist = c(pop_z, pop_y) or sublist = 1:2. • blacklist - vector of populations or integers representing the populations in your data set you wish to exclude. This can take the same type of arguments as sublist, and can be used in conjunction with sublist for when you want a range of populations, but know that there is one in there that you do not want to analyze. For example: sublist = 1:15, blacklist = pop_x. One very useful thing about the blacklist is that it allows the user to be extremely paranoid about the data. You can set the blacklist to contain populations that are not even in your data set and it will still work! • mat - A matrix produced from the mlg.table function. This overrides the pop argument and subsets this table instead. To demonstrate this tool, we’ll use the H3N2 virus data set provided in adegenet. It contains a data frame in the “other” slot called “x” that contains information about the year of epidemic, country, etc. data("H3N2", package = "adegenet") strata(H3N2) <- data.frame(other(H3N2)x)
H3N2
## /// GENIND OBJECT /////////
##
##  // 1,903 individuals; 125 loci; 334 alleles; size: 4.1 Mb
##
##  // Basic content
##    @tab:  1903 x 334 matrix of allele counts
##    @loc.n.all: number of alleles per locus (range: 2-4)
##    @loc.fac: locus factor for the 334 columns of @tab
##    @all.names: list of allele names for each locus
##    @ploidy: ploidy of each individual  (range: 1-1)
##    @type:  codom
##    @call: .local(x = x, i = i, j = j, drop = drop)
##
##  // Optional content
##    @strata: a data frame with 17 columns ( accession, length, host, segment, subtype, country, ... )
##    @other: a list containing: x  xy  epid

We will demonstrate the popsub functionality by setting the population factor to “country”. Note, in this section, I am naming the variables staring with “v” indicating “virus”.

setPop(H3N2) <- ~country
popNames(H3N2) # Only two countries from North America.
##  [1] "Japan"          "USA"            "Finland"        "China"          "South Korea"
##  [6] "Norway"         "Taiwan"         "France"         "Latvia"         "Netherlands"
## [11] "Bulgaria"       "Turkey"         "United Kingdom" "Denmark"        "Austria"
## [21] "Germany"        "Romania"        "Ukraine"        "Czech Republic" "Greece"
## [26] "Iceland"        "Ireland"        "Sweden"         "Nepal"          "Saudi Arabia"
## [31] "Switzerland"    "Iran"           "Mongolia"       "Spain"          "Slovenia"
## [36] "Croatia"        "Algeria"
v_na <- popsub(H3N2, sublist = c("USA", "Canada"))
popNames(v_na)
## [1] "USA"    "Canada"

If we want to see the population size, we can use the adegenet function nInd():

c(NorthAmerica = nInd(v_na), Total = nInd(H3N2))
## NorthAmerica        Total
##          665         1903

You can see that the population factors are correct and that the size of the data set is considerably smaller. Let’s see the data set without the North American countries.

v_na_minus <- popsub(H3N2, blacklist = c("USA", "Canada"))
popNames(v_na_minus)
##  [1] "Japan"          "Finland"        "China"          "South Korea"    "Norway"
##  [6] "Taiwan"         "France"         "Latvia"         "Netherlands"    "Bulgaria"
## [11] "Turkey"         "United Kingdom" "Denmark"        "Austria"        "Italy"
## [16] "Russia"         "Bangladesh"     "Egypt"          "Germany"        "Romania"
## [21] "Ukraine"        "Czech Republic" "Greece"         "Iceland"        "Ireland"
## [26] "Sweden"         "Nepal"          "Saudi Arabia"   "Switzerland"    "Iran"
## [31] "Mongolia"       "Spain"          "Slovenia"       "Croatia"        "Algeria"

Let"s make sure that the number of individuals in both data sets is equal to the number of individuals in our original data set:

(nInd(v_na_minus) + nInd(v_na)) == nInd(H3N2)
## [1] TRUE

Now we have data sets with and without North America. Let’s try something a bit more challenging. Let’s say that we want the first 10 populations in alphabetical order, but we know that we still don"t want any countries in North America. We can easily do this by using the base function sort.

vsort <- sort(popNames(H3N2))[1:10]
vsort
##  [1] "Algeria"        "Austria"        "Bangladesh"     "Bulgaria"       "Canada"
##  [6] "China"          "Croatia"        "Czech Republic" "Denmark"        "Egypt"
valph <- popsub(H3N2, sublist = vsort, blacklist = c("USA", "Canada"))
popNames(valph)
## [1] "China"          "Bulgaria"       "Denmark"        "Austria"        "Bangladesh"
## [6] "Egypt"          "Czech Republic" "Croatia"        "Algeria"

And that, is how you subset your data with poppr!

## Clone-censor data sets {Attack of the clone correction}

Clone correction refers to the ability of keeping one observation of each MLG in a given population (or sub-population). Clone correcting can be hazardous if its done by hand (even on small data sets) and it requires a defined population hierarchy to get relevant results. Poppr has a clone correcting function that that will correct down to the lowest level of any defined population hierarchy. Note that clone correction in poppr is sensitive to missing data, as it treats all missing data as a single extra allele.

This function will create new data sets, but it is also utilized by the functions poppr() and poppr.amova() natively.

### Function: clonecorrect

This function will return a clone corrected data set corrected for the lowest population level. Population levels are specified with the hier flag. You can choose to combine the population hierarchy to analyze at the lowest population level by choosing combine = TRUE.

clonecorrect(pop, strata = 1, combine = FALSE, keep = 1)
• pop - a genclone object with a defined hierarchy or a genind object that has a population hierarchy data frame in the @other slot. Note, the genind object does not necessarily require a population factor to begin with.

• strata - A hierarchical formula (eg. \simPop/Subpop), representing the hierarchical levels in your data.

• combine - Do you want to combine the population hierarchy? If it"s set to FALSE (default), you will be returned an object with the top most hierarchical level as a population factor unless the keep argument is defined. If set to TRUE, the hierarchy will be returned combined.

• keep - This flag is to be used if you set combine = FALSE. This will tell clone correct to return a specific combination of your hierarchy defined as integers. For example, imagine a hierarchy that needs to be clone corrected at three levels: Population by Year by Month. If you wanted to only run an analysis on the Population level, you would set keep = 1 since Population is the first level of the hierarchy. On the other hand, if you wanted to run analysis on Year by Month, you would set keep = 2:3 since those are the second and third levels of the hierarchy.

Let“s look at ways to clone-correct our data. We”ll look at our A. euteichies data that we used in an earlier section since that data set is known to include clonal populations (Grünwald and Hoheisel 2006). Try playing around with the data and see what different combinations of the strata, and keep flags produce. Below, I will give three examples of clone corrections at the sample level with respect to field, at the field level, and finally, at the level of the entire data set.

First, we will examine the original data set.

data(Aeut)
strata(Aeut) <- data.frame(other(Aeut)$population_hierarchy[-1]) Aeut ## /// GENIND OBJECT ///////// ## ## // 187 individuals; 56 loci; 56 alleles; size: 72.7 Kb ## ## // Basic content ## @tab: 187 x 56 matrix of allele counts ## @loc.n.all: number of alleles per locus (range: 56-56) ## @ploidy: ploidy of each individual (range: 2-2) ## @type: PA ## @call: old2new_genind(object = x, donor = new(class(x))) ## ## // Optional content ## @pop: population of each individual (group size range: 90-97) ## @strata: a data frame with 2 columns ( Pop, Subpop ) ## @other: a list containing: population_hierarchy When you read in data with read.genalex(), the default is to represent it in a genclone object. Since the clonecorrect() function works on multilocus genotype definitions, It’s more efficient to convert it to a genclone object first. We will also rename the strata to “field” and “sample” to make the biological relevance of the data clearer. aphan <- as.genclone(Aeut) nameStrata(Aeut) <- ~field/sample Now we correct by sample with respect to field and keep the field as the population. clonecorrect(aphan, strata = ~Pop/Subpop) ## ## This is a genclone object ## ------------------------- ## Genotype information: ## ## 119 original multilocus genotypes ## 141 diploid individuals ## 56 dominant loci ## ## Population information: ## ## 2 strata - Pop, Subpop ## 2 populations defined - Athena, Mt. Vernon # Your turn: Use the same stratification and use combine = TRUE and then # keep = 1:2. Is there any difference? Correcting by field. Notice how the number of MLG is much closer to our census. clonecorrect(aphan, strata = ~Pop) ## ## This is a genclone object ## ------------------------- ## Genotype information: ## ## 119 original multilocus genotypes ## 120 diploid individuals ## 56 dominant loci ## ## Population information: ## ## 2 strata - Pop, Subpop ## 2 populations defined - Athena, Mt. Vernon Correcting over whole data set. Our MLG is equal to our census. clonecorrect(aphan, strata = NA) ## ## This is a genclone object ## ------------------------- ## Genotype information: ## ## 119 original multilocus genotypes ## 119 diploid individuals ## 56 dominant loci ## ## Population information: ## ## 2 strata - Pop, Subpop ## 2 populations defined - Athena, Mt. Vernon ## Permutations and bootstrap resampling {every day I’m shuffling (data sets)} A common null hypothesis for populations with mixed reproductive modes is panmixia, or to put it simply: lots of sex. Poppr randomly shuffles data sets in order to calculate P-values for the index of association ($$I_A$$ and $$\bar{r} _d$$) (Agapow and Burt 2001) using 4 different methods: method strategy units sampled 1 permutation alleles 2 simulation alleles 3 simulation alleles 4 permutation genotypes These methods are detailed below. We will create a dummy data set to be shuffled by each example below. Let"s assume a single diploid locus with four alleles (1, 2, 3, 4) with the frequencies of 0.1, 0.2, 0.3, and 0.4, respectively: Original A1/A2 1 4/4 2 4/1 3 4/3 4 2/2 5 3/3 The 4 methods are detailed below. ### Function: shufflepop shufflepop(pop, method = 1) • pop - a genind object. • method - a number indicating the method of sampling you wish to use. The following methods are available for use: 1. Permute Alleles (default) This is a sampling scheme that will permute alleles within the locus. A1/A2 1 3/4 2 2/3 3 4/4 4 2/1 5 3/4 A1/A2 1 1/3 2 2/4 3 3/4 4 4/3 5 4/2 As you can see, The heterozygosity has changed, yet the allelic frequencies remain the same. Overall this would show you what would happen if the sample you had underwent panmixis within this sample itself. 2. Parametric Bootstrap The previous scheme reshuffled the observed sample, but the parametric bootstrap draws samples from a multinomial distribution using the observed allele frequencies as weights. A1/A2 1 1/3 2 3/3 3 3/2 4 4/4 5 4/2 A1/A2 1 3/4 2 2/3 3 4/2 4 4/4 5 4/2 Notice how the heterozygosity has changed along with the allelic frequencies. The frequencies for alleles 3 and 4 have switched in the first data set, and we"ve lost allele 1 in the second data set purely by chance! This type of sampling scheme attempts to show you what the true population would look like if it were panmictic and your original sample gave you a basis for estimating expected allele frequencies. Since estimates are made from the observed allele frequencies, small samples will produce skewed results. 3. Non-Parametric Bootstrap The third method is sampling with replacement, again drawing from a multinomial distribution, but with no assumption about the allele frequencies. A1/A2 1 1/3 2 3/3 3 3/1 4 2/2 5 3/1 A1/A2 1 1/3 2 3/1 3 2/3 4 2/1 5 4/3 Again, heterozygosity and allele frequencies are not maintained, but now all of the alleles have a 1 in 4 chance of being chosen. 4. Multilocus permutation This is called Multilocus permutation because it does the same thing as the permutation analysis in the program multilocus by Paul Agapow and Austin Burt (Agapow and Burt 2001). This will shuffle the genotypes at each locus. A1/A2 1 3/3 2 4/1 3 2/2 4 4/4 5 4/3 A1/A2 1 4/4 2 2/2 3 3/3 4 4/3 5 4/1 Note that you have the same genotypes after shuffling, so at each locus, you will maintain the same allelic frequencies and heterozygosity. So, in this sample, you will only see a homozygote with allele 2. This also ensures that the P-values associated with $$I_A$$ and $$\bar{r} _d$$ are exactly the same. This method assumes that alleles are not independently assorting within individuals. This strategy is useful if you suspect the population is inbreeding (Jerome Goudet, personal communication). These shuffling schemes have been implemented for the index of association, but there may be other summary statistics you can use shufflepop for. All you have to do is use the function replicate. Let“s use average Bruvo”s distance with the first population of the data set nancycats as an example: data(nancycats) nan1 <- popsub(nancycats, 1) reps <- rep(2, 9) # Assuming dinucleotide repeats. observed <- mean(bruvo.dist(nan1, replen = reps)) observed ## [1] 0.4180619 You could use this method to replicate the resampling 999 times and then create a histogram to visualize a distribution of what would happen under different assumptions of panmixia. set.seed(9999) bd.test <- replicate(999, mean(bruvo.dist(shufflepop(nan1, method = 2), replen = reps))) hist(bd.test, xlab = "Bruvo's Distance", main = "Average Bruvo's distance over 999 randomizations") abline(v = observed, col = "red") legend('topleft', legend="observed", col="red", lty = 1) ## Removing uninformative loci {Cut It Out!} Phylogenetically uninformative loci are those that have only one sample differentiating from the rest. This can lead to biased results when using multilocus analyses such as the index of association (Brown, Feldman, and Nevo 1980; Smith et al. 1993). These nuisance loci can be removed with the following function. ### Function: informloci informloci(pop, cutoff = 2/nInd(pop), MAF = 0.01, quiet = FALSE) • pop - a genind object. • cutoff - this represents the minimum fraction of individuals needed for a locus to be considered informative. The default is set to $$2/n$$ with $$n$$ being the number of individuals in the data set (represented by the adegenet function nInd). Essentially, this means that any locus with fewer than 2 observations differing will be removed. The user can also specify a fraction of observations for the cutoff (eg. 0.05). • MAF - (Minor Allele Frequency), This defaults to 0.01 indicating that loci that contain one allele representing 1 - MAF of the data will be removed. • quiet - if TRUE, nothing will be printed to the screen, if FALSE (default), the cutoff value in percentage and number of individuals will be printed as well as the names of the uninfomrative loci found. Here’s a quick example using the H3N2 virus SNP data set from an earlier section. We will only retain loci that have a minor allele frequency of $$\geq 5\%$$ H.five <- informloci(H3N2, cutoff = 0.05) ## cutoff value: 5 % ( 95 samples ). ## MAF : 0.01 ## ## Found 49 uninformative loci ## ============================ ## 47 loci found with a cutoff of 95 samples : ## 157, 177, 233, 243, 262, 267, 280, 303, 313, 327, 357, 382, 384, 399, 412, 418, ## 424, 425, 429, 433, 451, 470, 529, 546, 555, 557, 564, 576, 592, 595, 597, 602, ## 612, 627, 642, 647, 648, 654, 658, 663, 667, 681, 717, 806, 824, 837, 882 ## 5 loci found with MAF < 0.01 : ## 42, 313, 433, 597, 915 Now what happens when you have all informative loci. We"ll use the nancycats data set, which has microsatellite loci. It is important to note that this is searching for loci with a specified genotype frequency as fixed heterozygous sites are also uninformative: data(nancycats) naninform <- informloci(nancycats, cutoff = 0.05) ## cutoff value: 5 % ( 12 samples ). ## MAF : 0.01 ## ## All sites polymorphic # Multilocus Genotype Analysis In populations with mixed sexual and clonal reproduction, it common to have multiple samples from the same population that have the same set of alleles at all loci. Here, we introduce tools for tracking MLGs within and across populations in genind, and genlight objects from the adegenet package. We will be using the H3N2 data set containing SNP data from isolates of the H3N2 virus from 2002 to 2006. Note that genclone and snpclone objects are optimal for these analyses. For a more in-depth document on methods for multilocus genotypes in poppr, see the “Multilocus Genotype Analysis” vignette by typing vignette("mlg", package = "poppr") ## How many multilocus genotypes are in our data set? {Just a peek} Counting the number of MLGs in a population is the first step for these analyses as they allow us to see how many clones exist. With the genclone object, This information is already displayed when we view the object. H3N2 ## /// GENIND OBJECT ///////// ## ## // 1,903 individuals; 125 loci; 334 alleles; size: 4.1 Mb ## ## // Basic content ## @tab: 1903 x 334 matrix of allele counts ## @loc.n.all: number of alleles per locus (range: 2-4) ## @loc.fac: locus factor for the 334 columns of @tab ## @all.names: list of allele names for each locus ## @ploidy: ploidy of each individual (range: 1-1) ## @type: codom ## @call: .local(x = x, i = i, j = j, drop = drop) ## ## // Optional content ## @pop: population of each individual (group size range: 1-646) ## @strata: a data frame with 17 columns ( accession, length, host, segment, subtype, country, ... ) ## @other: a list containing: x xy epid If we need to store the number of MLGs as a variable, we can simply run the mlg() command. H3N2_mlg <- mlg(H3N2) ## ############################# ## # Number of Individuals: 1903 ## # Number of MLG: 752 ## ############################# H3N2_mlg ## [1] 752 Since the number of individuals exceeds the number of multilocus genotypes, we conclude that this data set contains clones. Let"s examine what populations these clones belong to. ## MLGs across populations {clone-ing around} Since you have the ability to define hierarchical levels of your data set freely, it is quite possible to see some of the same MLGs across different populations. Tracking them by hand can be a nightmare with large data sets. Luckily, mlg.crosspop has you covered in that regard. ### Function: mlg.crosspop Analyze the MLGs that cross populations within your data set. This has three output modes. The default one gives a list of MLGs, and for each MLG, it gives a named numeric vector indicating the abundance of that MLG in each population. Alternate outputs are described with indexreturn and df. mlg.crosspop(gid, strata = NULL, sublist = "ALL", blacklist = NULL, mlgsub = NULL, indexreturn = FALSE, df = FALSE, quiet = FALSE) • pop - a genind object. • sublist - Populations to include (Defaults to “ALL”). see popsub() • blacklist - Populations to exclude. see popsub() • mlgsub - see mlg.table() Only analyze specified MLGs. The vector for this flag can be produced by this function as you will see later in this vignette. • indexreturn - return a vector of indices of MLGs. (You can use these in the mlgsub flag, or you can use them to subset the columns of an MLG table). • df - return a data frame containing the MLGs, the populations they cross, and the number of copies you find in each population. This is useful for making graphs in ggplot2. • quiet - TRUE or FALSE. Should the populations be printed to screen as they are processed? (will print nothing if indexreturn is TRUE) We can see what MLGs cross different populations and then give a vector that shows how many populations each one of those MLGs crosses. setPop(H3N2) <- ~country v.dup <- mlg.crosspop(H3N2, quiet=TRUE) Here is a snippet of what the output looks like when quiet is FALSE. It will print out the MLG name, the total number of individuals that make up that MLG, and the populations where that MLG can be found. ## MLG.3: (12 inds) USA Denmark ## MLG.9: (16 inds) Japan USA Finland Denmark ## MLG.31: (9 inds) Japan Canada ## MLG.75: (23 inds) Japan USA Finland Norway Denmark Austria Russia Ireland ## MLG.80: (2 inds) USA Denmark ## MLG.86: (7 inds) Denmark Austria ## MLG.95: (2 inds) USA Bangladesh ## MLG.97: (8 inds) USA Austria Bangladesh Romania ## MLG.104: (3 inds) USA France ## MLG.110: (16 inds) Japan USA China The output of this function is a list of MLGs, each containing a vector indicating the number of copies in each population. We"ll count the number of populations each MLG crosses using the function sapply to loop over the data with the function length. head(v.dup) ##$MLG.3
##     USA Denmark
##       4       8
##
## $MLG.9 ## Japan USA Finland Denmark ## 1 13 1 1 ## ##$MLG.31
##      2      7
##
## $MLG.75 ## Japan USA Finland Norway Denmark Austria Russia Ireland ## 2 8 2 1 6 2 1 1 ## ##$MLG.80
##     USA Denmark
##       1       1
##
## $MLG.86 ## Denmark Austria ## 3 4 v.num <- sapply(v.dup, length) # count the number of populations each MLG crosses. head(v.num) ## MLG.3 MLG.9 MLG.31 MLG.75 MLG.80 MLG.86 ## 2 4 2 8 2 2 ## Producing MLG tables and graphs {bringing something to the table} We can also create a table of MLGs per population as well as bar graphs to give us a visual representation of the data. This is achieved through the function mlg.table ### Function: mlg.table This function will produce a matrix containing counts of MLGs (columns) per population (rows). If there are not populations defined in your data set, a vector will be produced instead. mlg.table(gid, strata = NULL, sublist = "ALL", blacklist = NULL, mlgsub = NULL, bar = TRUE, plot = TRUE, total = FALSE, color = FALSE, background = FALSE, quiet = FALSE) • pop - a genind object. • sublist - Populations to include (Defaults to “ALL”). see popsub() • blacklist - Populations to exclude. see popsub() • mlgsub - a vector containing the indices of MLGs you wish to subset your table with. • plot - TRUE or FALSE. If TRUE, a bar plot will be printed for each population with more than one individual. • total - When set to TRUE, the pooled data set will be added to the table. Defaults to FALSE. • quiet - Defaults to FALSE: population names will be printed to the console as they are processed. v.tab <- mlg.table(H3N2, plot = TRUE) v.tab[1:10, 1:10] # Showing the first 10 columns and rows of the table. ## MLG.1 MLG.2 MLG.3 MLG.4 MLG.5 MLG.6 MLG.7 MLG.8 MLG.9 MLG.10 ## Japan 0 0 0 0 0 0 1 2 1 0 ## USA 0 2 4 1 1 0 0 0 13 0 ## Finland 0 0 0 0 0 0 0 0 1 0 ## China 0 0 0 0 0 0 0 0 0 0 ## South Korea 0 0 0 0 0 1 0 0 0 0 ## Norway 1 0 0 0 0 0 0 0 0 0 ## Taiwan 0 0 0 0 0 0 0 0 0 0 ## France 0 0 0 0 0 0 0 0 0 0 ## Latvia 0 0 0 0 0 0 0 0 0 0 ## Netherlands 0 0 0 0 0 0 0 0 0 0 mlg.table(H3N2, sublist = "Norway", plot = TRUE) The MLG table is not limited to use with poppr. In fact, one of the main advantages of mlg.table() is that it allows easy access to diversity functions present in the package vegan (Oksanen et al. 2012). One example is to create a rarefaction curve for each population in your data set giving the number of expected MLGs for a given sample size. For more information, type help(diversity, package=vegan) in your R console. For the sake of this example, instead of drawing a curve for each of the 37 countries represented in this sample, let"s set the hierarchical level to year. setPop(H3N2) <- ~year summary(H3N2) # Check the data to make sure it's correct. ## ## // Number of individuals: 1903 ## // Group sizes: 158 415 399 469 462 ## // Number of alleles per locus: 3 3 4 2 4 2 3 2 4 3 4 2 4 3 2 2 3 3 2 2 3 3 3 2 2 2 2 2 2 2 2 2 2 4 4 3 3 3 4 2 2 2 4 3 2 3 4 2 3 2 3 2 2 2 4 2 2 2 2 2 2 2 4 4 4 3 3 2 3 4 3 2 3 3 3 3 2 3 2 4 2 3 2 2 3 3 3 3 2 2 2 2 3 2 3 2 3 2 3 2 3 3 2 2 2 3 2 2 2 3 3 3 2 2 3 3 3 3 4 2 3 3 4 3 2 ## // Number of alleles per group: 203 255 232 262 240 ## // Percentage of missing data: 2.36 % ## // Observed heterozygosity: 0 library("vegan") H.year <- mlg.table(H3N2, plot = FALSE) rarecurve(H.year, ylab="Number of expected MLGs", sample=min(rowSums(H.year)), border = NA, fill = NA, font = 2, cex = 1, col = "blue") The minimum value from the base function rowSums() of the table represents the minimum common sample size of all populations defined in the table. Setting the “sample” flag draws the horizontal and vertical lines you see on the graph. The intersections of these lines correspond to the numbers you would find if you ran the function poppr on this data set (under the column “eMLG”). ## Combining MLG functions {getting into the mix} Alone, the different functionalities are neat. Combined, we can create interesting data sets. Let"s say we wanted to know which MLGs were duplicated across the regions of the United Kingdom, Germany, Netherlands, and Norway. All we have to do is use the sublist flag in the function: setPop(H3N2) <- ~country UGNN.list <- c("United Kingdom", "Germany", "Netherlands", "Norway") UGNN <- mlg.crosspop(H3N2, sublist=UGNN.list, indexreturn=TRUE) OK, the output tells us that there are three MLGs that are crossing between these populations, but we do not know how many are in each. We can easily find that out if we subset our original table, v.tab. UGNN # Note that we have three numbers here. This will index the columns for us. ## [1] 315 317 620 UGNN.list # And let's not forget that we have the population names. ## [1] "United Kingdom" "Germany" "Netherlands" "Norway" v.tab[UGNN.list, UGNN] ## MLG.315 MLG.317 MLG.620 ## United Kingdom 1 0 0 ## Germany 0 1 1 ## Netherlands 0 0 0 ## Norway 2 3 1 Now we can see that Norway has a higher incidence of nearly all of these MLGs. We can investigate the incidence of these MLGs throughout our data set. One thing that the genclone object keeps track of is a single vector defining the unique multilocus genotypes within the data. These are represented as integers and can be accessed with mlg.vector. This is useful for finding MLGs that correspond to certain individuals or populations. Let“s use mlg.vector to find individuals corresponding to the MLGs. First we”ll investigate what the output of this function looks like. v.vec <- mlg.vector(H3N2) str(v.vec) # Analyze the structure. ## int [1:1903] 605 605 672 675 674 673 670 671 670 678 ... The integers produced are the MLG assignment of each individual in the same order as the data set. This means that the first two individuals have the exact same set of alleles at each locus, so they have the same MLG: 605. If we look at the number of unique integers in the vector, it corresponds to the number of observed multilocus genotypes: length(unique(v.vec)) # count the number of MLGs ## [1] 752 H3N2 # equal to the first number in this output. ## /// GENIND OBJECT ///////// ## ## // 1,903 individuals; 125 loci; 334 alleles; size: 4.1 Mb ## ## // Basic content ## @tab: 1903 x 334 matrix of allele counts ## @loc.n.all: number of alleles per locus (range: 2-4) ## @loc.fac: locus factor for the 334 columns of @tab ## @all.names: list of allele names for each locus ## @ploidy: ploidy of each individual (range: 1-1) ## @type: codom ## @call: .local(x = x, i = i, j = j, drop = drop) ## ## // Optional content ## @pop: population of each individual (group size range: 1-646) ## @strata: a data frame with 17 columns ( accession, length, host, segment, subtype, country, ... ) ## @other: a list containing: x xy epid We will take UGNN (MLGs crossing UK, Germany, Netherlands, and Norway) and compare its elements to the MLG vector (v.vec) to see where else they occur. UGNN # Show what we are looking for ## [1] 315 317 620 UGNN_match <- v.vec %in% UGNN table(UGNN_match) # How many individuals matched to those three MLGs? ## UGNN_match ## FALSE TRUE ## 1881 22 22 individuals matched to those three MLGs. We can use this vector to show us the 22 individuals. indNames(H3N2)[UGNN_match] ## 0329 0330 0331 0332 0341 0342 0345 0556 ## "CY026119" "CY026120" "CY026121" "CY026122" "CY026131" "CY026132" "CY026135" "EU502462" ## 0557 0558 0870 0974 1112 1113 1114 1122 ## "EU502463" "EU502464" "EU501513" "AB243868" "DQ883618" "DQ883619" "DQ883620" "DQ883628" ## 1193 1209 1210 1281 1288 1426 ## "EU501609" "EU501642" "EU501643" "EU501735" "EU501742" "EU502513" Note that there is an alternative way to list individuals matching specific MLGs using the function mlg.id. This function will return a list where each element represents a unique MLG. You can use this data to find out which individuals correspond to specific MLGs. Each element in the list is named with the MLG, but the index does not necessarily match up, so it is important to convert your query MLGs to strings: H3N2.id <- mlg.id(H3N2) H3N2.id[as.character(UGNN)] ##$315
##       0974       1112       1122       1209       1210       1281       1288
## "AB243868" "DQ883618" "DQ883628" "EU501642" "EU501643" "EU501735" "EU501742"
##
## $317 ## 0870 1113 1114 1193 1426 ## "EU501513" "DQ883619" "DQ883620" "EU501609" "EU502513" ## ##$620
##       0329       0330       0331       0332       0341       0342       0345       0556
## "CY026119" "CY026120" "CY026121" "CY026122" "CY026131" "CY026132" "CY026135" "EU502462"
##       0557       0558
## "EU502463" "EU502464"

We can also use the vector of MLGs to subset mlg.table() with the mlgsub flag.

mlg.table(H3N2, mlgsub = UGNN)

That showed us exactly which populations these three MLGs came from in our data set.

# Appendix

## Manipulating Graphics

Poppr utilizes ggplot2 to produce many of its graphs. One advantage it gives the user is the ability to manipulate these graphs. With base R graphs, the only manipulation that can be performed is by adding elements to the graph. It is a static image. The ggplot graphs are actually represented as objects in your R environment. We can use the function last_plot() from ggplot2 to be able to grab the plot that was plotted last in our window. Let’s illustrate this using a MLG bar graph from the Aeut data set.

library("poppr")
library("ggplot2")
data(Aeut)
Aeut.tab <- mlg.table(Aeut)

p <- last_plot()

We’ve captured our plot using last_plot() and now we can manipulate it. One common need is to change the title. We can easily do that with the function ggtitle(). Let“s say we wanted to label it”Aphanomyces euteiches multilocus genotype distribution". We would use ggtitle(Aphanomyces euteiches multilocus genotype distribution). Unfortunately, we need italics for a latin binomial. One way to acheive this is by using the expression() function and declaring which text needs to be italicized.

myTitle <- expression(paste(italic("Aphanomyces euteiches"),
" multilocus genotype distribution"))
(pt <- p +
ggtitle(myTitle) +
xlab("Multilocus genotype")) # We can label the x axis, too

Let"s say we wanted to remove the grey background. We could use the theme() function to do this, or we could use a theme already implemented in ggplot2 called theme_bw().

(ptt <- pt + theme_bw())

Uh-oh. The x axis labels are now horizontal when they should be vertical. Since it"s the overall distribution we’re interested in, we don’t really need them anyways. We can remove them with axis.text.x and axis.ticks.x (we’ll also remove the x axis gridlines because they’re ugly).

(ptta <- ptt + theme(axis.text.x = element_blank()) +
theme(axis.ticks.x = element_blank()) +
theme(panel.grid.major.x = element_blank()))