Paul J. McMurdie and Susan Holmes
Statistics Department, Stanford University
Stanford, CA 94305, USA
phyloseq Home Page
The analysis of microbiological communities brings many challenges: the integration of many different types of data with methods from ecology, genetics, phylogenetics, network analysis, visualization and testing. The data itself may originate from widely different sources, such as the microbiomes of humans, soils, surface and ocean waters, wastewater treatment plants, industrial facilities, and so on; and as a result, these varied sample types may have very different forms and scales of related data that is extremely dependent upon the experiment and its question(s). The phyloseq package is a tool to import, store, analyze, and graphically display complex phylogenetic sequencing data that has already been clustered into Operational Taxonomic Units (OTUs), especially when there is associated sample data, phylogenetic tree, and/or taxonomic assignment of the OTUs. This package leverages many of the tools available in R for ecology and phylogenetic analysis (vegan, ade4, ape, picante), while also using advanced/flexible graphic systems (ggplot2) to easily produce publication-quality graphics of complex phylogenetic data. phyloseq uses a specialized system of S4 classes to store all related phylogenetic sequencing data as single experiment-level object, making it easier to share data and reproduce analyses. In general, phyloseq seeks to facilitate the use of R for efficient interactive and reproducible analysis of OTU-clustered high-throughput phylogenetic sequencing data.
An overview of phyloseq's intended functionality, goals, and design can be found with free and open access the phyloseq article in PLoS ONE
The most updated examples are posted in our online tutorials from the phyloseq home page
A separate vignette describes analysis tools included in phyloseq along with various examples using included example data. A quick way to load it is:
By contrast, this vignette is intended to provide functional examples of the basic data import and manipulation infrastructure included in phyloseq. This includes example code for importing OTU-clustered data from different clustering pipelines, as well as performing clear and reproducible filtering tasks that can be altered later and checked for robustness. The motivation for including tools like this in phyloseq is to save time, and also to build-in a structure that requires consistency across related data tables from the same experiment.This not only reduces code repetition, but also decreases the likelihood of mistakes during data filtering and analysis. For example, it is intentionally difficult in phyloseq to create an experiment-level object in which a component tree and OTU table have different OTU names. The import functions, trimming tools, as well as the main tool for creating an experiment-level object,
phyloseq, all automatically trim the OTUs and samples indices to their intersection, such that these component data types are exactly coherent.
The class structure in the phyloseq package follows the inheritance diagram shown in the figure below. The phyloseq package contains multiple inherited classes with incremental complexity so that methods can be extended to handle exactly the data types that are present in a particular object. Currently, phyloseq uses 4 core data classes. They are the OTU abundance table (
otu_table), a table of sample data (
sample_data), a table of taxonomic descriptors (
taxonomyTable), and a phylogenetic tree (
"phylo"-class, ape package). The
otu_table class can be considered the central data type, as it directly represents the number and type of sequences observed in each sample.
otu_table extends the numeric matrix class in the
R base, and has a few additonal feature slots. The most important of these feature slots is the
taxa_are_rows slot, which holds a single logical that indicates whether the table is oriented with taxa as rows (as in the genefilter package in Bioconductor) or with taxa as columns (as in vegan and picante packages). In phyloseq methods, as well as its extensions of methods in other packages, the
taxa_are_rows value is checked to ensure proper orientation of the
otu_table. A phyloseq user is only required to specify the
otu_table orientation during initialization, following which all handling is internal.
sample_data class directly inherits
data.frame class, and thus effectively stores both categorical and numerical data about each sample. The orientation of a
data.frame in this context requires that samples/trials are rows, and variables are columns (consistent with vegan and other packages). The
taxonomyTable class directly inherits the
matrix class, and is oriented such that rows are taxa/OTUs and columns are taxonomic levels (e.g. Phylum).
The phyloseq-class can be considered an “experiment-level class” and should contain two or more of the previously-described core data classes. We assume that phyloseq users will be interested in analyses that utilize their abundance counts derived from the phylogenetic sequencing data, and so the
phyloseq() constructor will stop with an error if the arguments do not include an
otu_table. There are a number of common methods that require either an
sample_data combination, or an
otu_table and phylogenetic tree combination. These methods can operate on instances of the phyloseq-class, and will stop with an error if the required component data is missing.
Now let's get started by loading phyloseq, and describing some methods for importing data.
To use phyloseq in a new R session, it will have to be loaded. This can be done in your package manager, or at the command line using the
An important feature of phyloseq are methods for importing phylogenetic sequencing data from common taxonomic clustering pipelines. These methods take file pathnames as input, read and parse those files, and return a single object that contains all of the data.
Some additional background details are provided below. The best reproducible examples on importing data with phyloseq can be found on the official data import tutorial page:
New versions of QIIME (see below) produce a more-comprehensive and formally-defined JSON file format, called biom file format:
“The biom file format (canonically pronounced biome') is designed to be a general-use format for representing counts of observations in one or more biological samples. BIOM is a recognized standard for the Earth Microbiome Project and is a Genomics Standards Consortium candidate project.”
See the biom-format home page for details.
QIIME is a free, open-source OTU clustering and analysis pipeline written for Unix (mostly Linux). It is distributed in a number of different forms (including a pre-installed virtual machine). See the QIIME home page for details.
One QIIME input file (sample map), and two QIIME output files (
.tre) are recognized by the
import_qiime() function. Only one of the three input files is required to run, although an
"otu_table.txt" file is required if
import_qiime() is to return a complete experiment object.
In practice, you will have to find the relevant QIIME files among a number of other files created by the QIIME pipeline. A screenshot of the directory structure created during a typical QIIME run is shown in the QIIME Directory Figure.
sample_dataobject and can be extremely useful for certain analyses.
The class of the object returned by
import_qiime() depends upon which filenames are provided. The most comprehensive class is chosen automatically, based on the input files listed as arguments. At least one argument needs to be provided.
The open-source, platform-independent, locally-installed software package, mothur, can also process barcoded amplicon sequences and perform OTU-clustering. It is extensively documented on the mothur wiki
Currently, there are three different files produced by the mothur package (Ver
1.22+) that can be imported by phyloseq. At minimum, a user must supply a “
.list” file, and at least one of the following two files:
.tree. The group file is produced by mothur's
make.group() function. Details can be found at its wiki page. The tree file is a phylogenetic tree calculated by mothur.
The output from
import_mothur() depends on which file types are provided. If all three file types are provided, an instance of the phyloseq-class is returned that contains both an OTU abundance table and its associated phylogenetic tree.
PyroTagger is an OTU-clustering pipeline for barcoded 16S rRNA amplicon sequences, served and maintained by the Department of Energy's (DOE's) Joint Genome Institute (JGI). It can be used through a straightforward web interface at the PyroTagger home page
PyroTagger takes as input the untrimmed sequence (
.fasta) and sequence-quality (
.qual) files, as well as a sample mapping file that contains the bar code sequence for each sample and its name. It uses a 97\% identity threshold for defining OTU clusters (approximately species-level of taxonomic distinction), and provides no options for specifying otherwise. It does allow users to modify the threshold setting for low-quality bases.
PyroTagger returns a single excel spreadsheet file (
.xls) containing both abundance and taxonomy data, as well as some associated confidence information related to each taxonomic assignment. This spreadsheet also reports on potential chimeric sequences. This single output file is sufficient for
import_RDP_tab(), provided the file has been converted to a tab-delimited plain-text format. Any spreadsheet application should suffice. No other changes should be made to the
import_RDP_tab() returns an instance of the phyloseq-class that contains the OTU abundance table and taxonomy table. To my knowledge, PyroTagger does not calculate a tree of the representative sequences from each OTU cluster, nor a distance object, so analyses like
UniFrac are not applicable.
The Ribosomal Database Project (RDP) provides a web-based barcoded 16S rRNA amplicon sequence processing pipeline called the RDP Pyrosequencing Pipeline. A user must run all three of the “Data Processing” steps sequentially through the web interface in order to acquire the output from Complete Linkage Clustering, the approach to OTU clustering used by the RDP Pipeline. Note that this import function assumes that the sequence names in the resulting cluster file follow a particular naming convention with underscore delimiter (see below).
The output from the Complete Linkage Clustering,
.clust, is the only input to the RDP pipeline importer:
myOTU1 <- import_RDP_cluster("path/to/my/filename.clust")
This importer returns an
The RDP cluster pipeline (specifically, the output of the complete linkage clustering step) has no formal documentation for the “.clust” file structure or its apparent sequence naming convention.
The cluster file itself contains the names of all sequences contained in the input alignment. If the upstream barcode and aligment processing steps are also done with the RDP pipeline, then the sequence names follow a predictable naming convention wherein each sequence is named by its sample and sequence ID, separated by a
"_" as delimiter:
This import function assumes that the sequence names in the cluster file follow this convention, and that the sample name does not contain any
"_". It is unlikely to work if this is not the case. It is likely to work if you used the upstream steps in the RDP pipeline to process your raw (barcoded, untrimmed) fasta/fastq data.
There are multiple example data sets included in phyloseq. Many are from published investigations and include documentation with a summary and references, as well as some example code representing some aspect of analysis available in phyloseq. In the package index, go to the names beginning with “data-” to see the documentation of currently available example datasets.
To load example data into the working environment, use the
data(GlobalPatterns) data(esophagus) data(enterotype) data(soilrep)
?enterotype will reveal the documentation for the so-called “enterotype” dataset. For details examples, see the Example Data tutorial
In small font, the following is the summary of the
GlobalPatterns dataset that prints to the terminal. These summaries are consistent among all
phyloseq-class objects. Although the components of
GlobalPatterns have many thousands of elements, the command-line returns only a short summary of each component. This encourages you to check that an object is still what you expect, without needing to let thousands of elements scroll across the terminal. In the cases in which you do want to see more of a particular component, use an accessor function (see table below).
## phyloseq-class experiment-level object ## otu_table() OTU Table: [ 19216 taxa and 26 samples ] ## sample_data() Sample Data: [ 26 samples by 7 sample variables ] ## tax_table() Taxonomy Table: [ 19216 taxa by 7 taxonomic ranks ] ## phy_tree() Phylogenetic Tree: [ 19216 tips and 19215 internal nodes ]
Suppose you have already imported raw data from an experiment into
R, and their indices are labeled correctly. How do you get phyloseq to recognize these tables as the appropriate class of data? And further combine them together? Table Table of Component Constructor Functions lists key functions for converting these core data formats into specific component data objects recognized by phyloseq. These will also
|Function||Input Class||Output Description|
||file path char||phylo-class tree, read from file|
||table file path||A matrix or data.frame (Std
|Function||Input Class||Output Description|
||Two or more component objects||phyloseq-class, experiment-level object|
||Two or more component or phyloseq-class objects||Combined instance of phyloseq-class|
The following example illustrates using the constructor methods for component data tables.
otu1 <- otu_table(raw_abundance_matrix, taxa_are_rows=FALSE) sam1 <- sample_data(raw_sample_data.frame) tax1 <- tax_table(raw_taxonomy_matrix) tre1 <- read_tree(my_tree_file)
Once you've converted the data tables to their appropriate class, combining them into one object requires only one additional function call,
ex1b <- phyloseq(my_otu_table, my_sample_data, my_taxonomyTable, my_tree)
You do not need to have all four data types in the example above in order to combine them into one validity-checked experiment-level phyloseq-class object. The
phyloseq() method will detect which component data classes are present, and build accordingly. Downstream analysis methods will access the required components using phyloseq's accessors, and throw an error if something is missing. For most downstream methods you will only need to supply the combined, phyloseq-class object (the output of
phyloseq() ), usually as the first argument.
ex1c <- phyloseq(my_otu_table, my_sample_data)
Whenever an instance of the phyloseq-class is created by phyloseq — for example, when we use the
import_qiime() function to import data, or combine manually imported tables using
phyloseq() — the row and column indices representing taxa or samples are internally checked/trimmed for compatibility, such that all component data describe exactly (and only) the same OTUs and samples.
The phyloseq project includes support for two complete different categories of merging.
For further details, see the reproducible online tutorial at:
Once you have a phyloseq object available, many accessor functions are available to query aspects of the data set. The function name and its purpose are summarized in the Accessor Functions Table.
||Standard extraction operator. Works on
||General slot accessor function for phyloseq-package|
||Abundance values of all taxa in sample i'|
||Abundance values of taxa i' for all samples|
||A unique vector of the observed taxa at a particular taxonomic rank|
||An individual sample variable vector/factor|
||Get the number of samples described by an object|
||Get the number of OTUs (taxa) described by an object|
||Build or access otu_table objects|
||Get the names of the available taxonomic ranks|
||Build or access
||The names of all samples|
||The names of all taxa|
||The sum of the abundance values of each sample|
||The names of sample variables|
||The sum of the abundance values of each taxa|
||A taxonomy table|
||Access the tree contained in a phyloseq object|
Trimming high-throughput phylogenetic sequencing data can be useful, or even necessary, for certain types of analyses. However, it is important that the original data always be available for reference and reproducibility; and that the methods used for trimming be transparent to others, so they can perform the same trimming or filtering steps on the same or related data. To facilitate this, phyloseq contains many ways to trim/filter the data from a phylogenetic sequencing project. Because matching indices for taxa and samples is strictly enforced, subsetting one of the data components automatically subsets the corresponding indices from the others. Variables holding trimmed versions of your original data can be declared, and further trimmed, without losing track of the original data.
In general, most trimming should be accomplished using the S4 methods
For example, lets make a new object that only holds the most abundant 20 taxa in the experiment. To accomplish this, we will use the
data(GlobalPatterns) most_abundant_taxa <- sort(taxa_sums(GlobalPatterns), TRUE)[1:topN] ex2 <- prune_taxa(names(most_abundant_taxa), GlobalPatterns)
Now we can ask the question, “what taxonomic Family are these OTUs?” (Subsetting still returns a
taxonomyTable object, which is summarized. We will need to convert to a vector)
topFamilies <- tax_table(ex2)[, "Family"] as(topFamilies, "vector")
##  NA "ACK-M1" "ACK-M1" ##  "Bifidobacteriaceae" NA NA ##  "Nostocaceae" NA "Neisseriaceae" ##  "Neisseriaceae" "Pasteurellaceae" "Enterobacteriaceae" ##  "Bacteroidaceae" "Bacteroidaceae" "Bacteroidaceae" ##  "Clostridiaceae" "Ruminococcaceae" "Ruminococcaceae" ##  "Ruminococcaceae" "Streptococcaceae"
The previous example was a relatively simple filtering in which we kept only the most abundant 20 in the whole experiment. But what if we wanted to keep the most abundant 20 taxa of each sample? And of those, keep only the taxa that are also found in at least one-third of our samples? What if we wanted to keep only those taxa that met some across-sample criteria?
For this more complicated filtering phyloseq contains a function,
genefilter_sample, that takes as an argument a phyloseq object, as well as a list of one or more filtering functions that will be applied to each sample in the abundance matrix (
otu_table), as well as an integer argument,
A, that specifies for how many samples the filtering function must return
TRUE for a particular taxa to avoid removal from the object. A supporting function
filterfun_sample is also included in phyloseq to facilitate creating a properly formatted function (enclosure) if more than one function is going to be applied simultaneously.
genefilter_sample returns a logical vector suitable for sending directly to
prune_taxa for the actual trimming.
Here is an example on a completely fabricated
testOTU <- otu_table(matrix(sample(1:50, 25, replace=TRUE), 5, 5), taxa_are_rows=FALSE) f1<- filterfun_sample(topk(2)) wh1 <- genefilter_sample(testOTU, f1, A=2) wh2 <- c(T, T, T, F, F) prune_taxa(wh1, testOTU) prune_taxa(wh2, testOTU)
Here is a second example using the included dataset,
GlobalPatterns. The most abundant taxa are kept only if they are in the most abundant 10\% of taxa in at least half of the samples in dataset
GlobalPatterns. Note that it is not necessary to subset
GlobalPatterns in order to do this filtering. The S4 method
prune_taxa subsets each of the relavent component objects, and returns the complex object back.
data(GlobalPatterns) f1<- filterfun_sample(topp(0.1)) wh1 <- genefilter_sample(GlobalPatterns, f1, A=(1/2*nsamples(GlobalPatterns))) sum(wh1)
##  795
ex2 <- prune_taxa(wh1, GlobalPatterns)
## phyloseq-class experiment-level object ## otu_table() OTU Table: [ 795 taxa and 26 samples ] ## sample_data() Sample Data: [ 26 samples by 7 sample variables ] ## tax_table() Taxonomy Table: [ 795 taxa by 7 taxonomic ranks ] ## phy_tree() Phylogenetic Tree: [ 795 tips and 794 internal nodes ]
If instead of the most abundant fraction of taxa, you are interested in the most abundant fraction of individuals (aka sequences, observations), then the
topf function is appropriate. For steep rank-abundance curves,
topf will seem to be much more conservative (trim more taxa) because it is based on the cumulative sum of relative abundance. It does not guarantee that a certain number or fraction of total taxa (richness) will be retained.
data(GlobalPatterns) f1<- filterfun_sample(topf(0.9)) wh1 <- genefilter_sample(GlobalPatterns, f1, A=(1/3*nsamples(GlobalPatterns))) sum(wh1) prune_taxa(wh1, GlobalPatterns)
filter_taxa function is directly analogous to the
genefilter function for microarray filtering, but is used for filtering OTUs from phyloseq objects. It applies an arbitrary set of functions – as a function list, for instance, created by
genefilter::filterfun – as across-sample criteria, one OTU at a time. It can be thought of as an extension of the genefilter-package (from the Bioconductor repository) for phyloseq objects. It takes as input a phyloseq object, and returns a logical vector indicating whether or not each OTU passed the criteria. Alternatively, if the
prune option is set to FALSE, it returns the already-trimmed version of the phyloseq object.
Inspect the following example. Note that the functions
kOverA are from the genefilter package.
data("enterotype") library("genefilter") flist<- filterfun(kOverA(5, 2e-05)) ent.logi <- filter_taxa(enterotype, flist) ent.trim <- filter_taxa(enterotype, flist, TRUE) identical(ent.trim, prune_taxa(ent.logi, enterotype))
##  TRUE
##  TRUE
filter_taxa(enterotype, flist, TRUE)
## phyloseq-class experiment-level object ## otu_table() OTU Table: [ 416 taxa and 280 samples ] ## sample_data() Sample Data: [ 280 samples by 9 sample variables ] ## tax_table() Taxonomy Table: [ 416 taxa by 1 taxonomic ranks ]
It is possible to subset the samples in a phyloseq object based on the sample variables using the
subset_samples() function. For example to subset
GlobalPatterns such that only certain environments are retained, the following line is needed (the related tables are subsetted automatically as well):
ex3 <- subset_samples(GlobalPatterns, SampleType%in%c("Freshwater", "Ocean", "Freshwater (creek)"))
## phyloseq-class experiment-level object ## otu_table() OTU Table: [ 19216 taxa and 8 samples ] ## sample_data() Sample Data: [ 8 samples by 7 sample variables ] ## tax_table() Taxonomy Table: [ 19216 taxa by 7 taxonomic ranks ] ## phy_tree() Phylogenetic Tree: [ 19216 tips and 19215 internal nodes ]
For this example only a categorical variable is shown, but in principle a continuous variable could be specified and a logical expression provided just as for the
subset function. In fact, because
sample_data component objects are an extension of the data.frame class, they can also be subsetted with the
subset(sample_data(GlobalPatterns), SampleType%in%c("Freshwater", "Ocean", "Freshwater (creek)"))
## Sample Data: [8 samples by 7 sample variables]: ## X.SampleID Primer Final_Barcode Barcode_truncated_plus_T ## LMEpi24M LMEpi24M ILBC_13 ACACTG CAGTGT ## SLEpi20M SLEpi20M ILBC_15 ACAGAG CTCTGT ## AQC1cm AQC1cm ILBC_16 ACAGCA TGCTGT ## AQC4cm AQC4cm ILBC_17 ACAGCT AGCTGT ## AQC7cm AQC7cm ILBC_18 ACAGTG CACTGT ## NP2 NP2 ILBC_19 ACAGTT AACTGT ## NP3 NP3 ILBC_20 ACATCA TGATGT ## NP5 NP5 ILBC_21 ACATGA TCATGT ## Barcode_full_length SampleType ## LMEpi24M CATGAACAGTG Freshwater ## SLEpi20M AGCCGACTCTG Freshwater ## AQC1cm GACCACTGCTG Freshwater (creek) ## AQC4cm CAAGCTAGCTG Freshwater (creek) ## AQC7cm ATGAAGCACTG Freshwater (creek) ## NP2 TCGCGCAACTG Ocean ## NP3 GCTAAGTGATG Ocean ## NP5 GAACGATCATG Ocean ## Description ## LMEpi24M Lake Mendota Minnesota, 24 meter epilimnion ## SLEpi20M Sparkling Lake Wisconsin, 20 meter eplimnion ## AQC1cm Allequash Creek, 0-1cm depth ## AQC4cm Allequash Creek, 3-4 cm depth ## AQC7cm Allequash Creek, 6-7 cm depth ## NP2 Newport Pier, CA surface water, Time 1 ## NP3 Newport Pier, CA surface water, Time 2 ## NP5 Newport Pier, CA surface water, Time 3
It is possible to subset by specific taxonomic category using the
subset_taxa() function. For example, if we wanted to subset
GlobalPatterns so that it only contains data regarding the phylum Firmicutes:
ex4 <- subset_taxa(GlobalPatterns, Phylum=="Firmicutes")
## phyloseq-class experiment-level object ## otu_table() OTU Table: [ 4356 taxa and 26 samples ] ## sample_data() Sample Data: [ 26 samples by 7 sample variables ] ## tax_table() Taxonomy Table: [ 4356 taxa by 7 taxonomic ranks ] ## phy_tree() Phylogenetic Tree: [ 4356 tips and 4355 internal nodes ]
Can also randomly subset, for example a random subset of 100 taxa from the full dataset.
randomSpecies100 <- sample(taxa_names(GlobalPatterns), 100, replace=FALSE) ex5 <- prune_taxa(randomSpecies100, GlobalPatterns)
Sample-wise transformation can be achieved with the
transform_sample_counts() function. It requires two arguments, (1) the phyloseq object that you want to transform, and the function that you want to use to perform the transformation. Any arbitrary function can be provided as the second argument, as long as it returns a numeric vector with the same length as its input. In the following trivial example, we create a second object,
ex2, that has been “transformed” by the identity function such that it is actually identical to
data(GlobalPatterns) ex2 <- transform_sample_counts(GlobalPatterns, I)
For certain kinds of analyis we may want to transform the abundance data. For example, for RDA we want to transform abundance counts to within-sample ranks, and to further include a threshold beyond which all taxa receive the same rank value. The ranking for each sample is performed independently, so that the rank of a particular taxa within a particular sample is not influenced by that sample's total quantity of sequencing relative to the other samples in the project.
The following example shows how to perform such a thresholded-rank transformation of the abundance table in the complex phyloseq object
GlobalPatterns with an arbitrary threshold of 500.
ex4<- transform_sample_counts(GlobalPatterns, threshrankfun(500))
Suppose we are skeptical about the importance of OTU-level distinctions in our dataset. For this scenario, phyloseq includes a taxonomic-agglommeration method,
tax_glom(), which merges taxa of the same taxonomic category for a user-specified taxonomic level. In the following code, we merge all taxa of the same Genus, and store that new object as
ex6 <- tax_glom(GlobalPatterns, taxlevel="Genus")
Similarly, our original example object (
GlobalPatterns) also contains a phlyogenetic tree corresponding to each OTU, which we could also use as a means to merge taxa in our dataset that are closely related. In this case, we specify a threshold patristic distance. Taxa more closely related than this threshold are merged. This is especially useful when a dataset has many taxa that lack a taxonomic assignment at the level you want to investigate, a problem when using
tax_glom(). Note that for datasets with a large number of taxa,
tax_glom will be noticeably faster than
tip_glom. Also, keep in mind that
tip_glom requires that its first argument be an object that contains a tree, while
tax_glom instead requires a
taxonomyTable (See phyloseq classes).
ex7 <- tip_glom(GlobalPatterns, speciationMinLength = 0.05)
Command output not provided here to save time during compilation of the vignette. The user is encouraged to try this out on your dataset, or even this example, if interested. It may take a while to run on the full, untrimmed data.
Please check the phyloseq installation tutorial for help with installation. This is likely to be the first place news and updated information about installation will be posted, as well. Also check out the rest of the phyloseq homepage on GitHub, as this is the best place to post issues, bug reports, feature requests, contribute code, etc.
For running parallel implementation of functions/methods in phyloseq (e.g.
UniFrac(GlobalPatterns, parallel=TRUE)), you will need also to install a function for registering a parallel “backend”. Only one working parallel backend is needed, but there are several options, and the best one will depend on the details of your particular system. The “doParallel” package is a good place to start. Any one of the following lines from an
R session will install a backend package.
install.packages("doParallel") install.packages("doMC") install.packages("doSNOW") install.packages("doMPI")
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