NetCoMi

NetCoMi (Network Construction and Comparison for Microbiome Data) provides functionality for constructing, analyzing, and comparing networks suitable for the application on microbial compositional data. The R package implements the workflow proposed in

Stefanie Peschel, Christian L Müller, Erika von Mutius, Anne-Laure Boulesteix, Martin Depner (2020). NetCoMi: network construction and comparison for microbiome data in R. Briefings in Bioinformatics, bbaa290. https://doi.org/10.1093/bib/bbaa290.

NetCoMi allows its users to construct, analyze, and compare microbial association or dissimilarity networks in a fast and reproducible manner. Starting with a read count matrix originating from a sequencing process, the pipeline includes a wide range of existing methods for treating zeros in the data, normalization, computing microbial associations or dissimilarities, and sparsifying the resulting association/ dissimilarity matrix. These methods can be combined in a modular fashion to generate microbial networks. NetCoMi can either be used for constructing, analyzing and visualizing a single network, or for comparing two networks in a graphical as well as a quantitative manner, including statistical tests. The package furthermore offers functionality for constructing differential networks, where only differentially associated taxa are connected.

Exemplary network comparison using soil microbiome data (‘soilrep’ data from phyloseq package). Microbial associations are compared between the two experimantal settings ‘warming’ and ‘non-warming’ using the same layout in both groups.

Overview of methods included in NetCoMi

Here is an overview of methods available for network construction, together with some information on the implementation in R:

Association measures:

Pearson coefficient (cor() from stats package)
Spearman coefficient (cor() from stats package)
Biweight Midcorrelation bicor() from WGCNA package
SparCC (sparcc() from SpiecEasi package)
CCLasso (R code on GitHub)
CCREPE (ccrepe package)
SpiecEasi (SpiecEasi package)
SPRING (SPRING package)
gCoda (R code on GitHub)
propr (propr package)

Dissimilarity measures:

Euclidean distance (vegdist() from vegan package)
Bray-Curtis dissimilarity (vegdist() from vegan package)
Kullback-Leibler divergence (KLD) (KLD() from LaplacesDemon package)
Jeffrey divergence (own code using KLD() from LaplacesDemon package)
Jensen-Shannon divergence (own code using KLD() from LaplacesDemon package)
Compositional KLD (own implementation following [Martín-Fernández et al., 1999])
Aitchison distance (vegdist() and clr() from SpiecEasi package)

Methods for zero replacement:

Adding a predefined pseudo count
Multiplicative replacement (multRepl from zCompositions package)
Modified EM alr-algorithm (lrEM from zCompositions package)
Bayesian-multiplicative replacement (cmultRepl from zCompositions package)

Normalization methods:

Total Sum Scaling (TSS) (own implementation)
Cumulative Sum Scaling (CSS) (cumNormMat from metagenomeSeq package)
Common Sum Scaling (COM) (own implementation)
Rarefying (rrarefy from vegan package)
Variance Stabilizing Transformation (VST) (varianceStabilizingTransformation from DESeq2 package)
Centered log-ratio (clr) transformation (clr() from SpiecEasi package))

TSS, CSS, COM, VST, and the clr transformation are described in [Badri et al., 2020].

Installation

#install.packages("devtools")

devtools::install_github("stefpeschel/NetCoMi", dependencies = TRUE,
                         repos = c("https://cloud.r-project.org/",
                                   BiocManager::repositories()))

If there are any errors during installation, please install the missing dependencies manually.

Packages that are optionally required in certain settings are not installed together with NetCoMi. These can be automatically installed using:

installNetCoMiPacks()

# Please check:
?installNetCoMiPacks()

If not installed via installNetCoMiPacks(), the required package is installed by the respective NetCoMi function when needed.

Basic Usage

We use the American Gut data from SpiecEasi package to look at some examples of how NetCoMi is applied. NetCoMi’s main functions are netConstruct() for network construction, netAnalyze() for network analysis, and netCompare() for network comparison. As you will see in the following, these three functions must be executed in the aforementioned order. A further function is diffnet() for constructing a differential association network. diffnet() must be applied to the object returned from netConstruct().

First of all, we load NetCoMi and the data from American Gut Project (provided by SpiecEasi, which is automatically loaded together with NetCoMi).

library(NetCoMi)
data("amgut1.filt")
data("amgut2.filt.phy")

Single network with SPRING as association measure

Network construction and analysis

We firstly construct a single association network using the SPRING approach for estimating associations (conditional dependence) between OTUs.

The data are filtered within netConstruct() as follows:

Only samples with a total number of reads of at least 1000 are included (argument filtSamp).
Only the 100 taxa with highest frequency are included (argument filtTax).

measure defines the association or dissimilarity measure, which is "spring" in our case. Additional arguments are passed to SPRING() via measurePar. nlambda and rep.num are set to 10 for a decreased execution time, but should be higher for real data.

Normalization as well as zero handling is performed internally in SPRING(). Hence, we set normMethod and zeroMethod to "none".

We furthermore set sparsMethod to "none" because SPRING returns a sparse network where no additional sparsification step is necessary.

We use the “signed” method for transforming associations into dissimilarities (argument dissFunc). In doing so, strongly negatively associated taxa have a high dissimilarity and, in turn, a low similarity, which corresponds to edge weights in the network plot.

The verbose argument is set to 3 so that all messages generated by netConstruct() as well as messages of external functions are printed.

net_single <- netConstruct(amgut1.filt,
                           filtTax = "highestFreq",
                           filtTaxPar = list(highestFreq = 100),
                           filtSamp = "totalReads",
                           filtSampPar = list(totalReads = 1000),
                           measure = "spring",
                           measurePar = list(nlambda=10, 
                                             rep.num=10),
                           normMethod = "none", 
                           zeroMethod = "none",
                           sparsMethod = "none", 
                           dissFunc = "signed",
                           verbose = 3,
                           seed = 123456)

## Data filtering ...

## 27 taxa removed.

## 100 taxa and 289 samples remaining.

## 
## Calculate 'spring' associations ...

## The input is identified as the covariance matrix.
## Conducting Meinshausen & Buhlmann graph estimation (mb)....done
## The input is identified as the covariance matrix.
## Conducting Meinshausen & Buhlmann graph estimation (mb)....done
## The input is identified as the covariance matrix.
## Conducting Meinshausen & Buhlmann graph estimation (mb)....done
## The input is identified as the covariance matrix.
## Conducting Meinshausen & Buhlmann graph estimation (mb)....done
## The input is identified as the covariance matrix.
## Conducting Meinshausen & Buhlmann graph estimation (mb)....done
## The input is identified as the covariance matrix.
## Conducting Meinshausen & Buhlmann graph estimation (mb)....done
## The input is identified as the covariance matrix.
## Conducting Meinshausen & Buhlmann graph estimation (mb)....done
## The input is identified as the covariance matrix.
## Conducting Meinshausen & Buhlmann graph estimation (mb)....done
## The input is identified as the covariance matrix.
## Conducting Meinshausen & Buhlmann graph estimation (mb)....done
## The input is identified as the covariance matrix.
## Conducting Meinshausen & Buhlmann graph estimation (mb)....done
## The input is identified as the covariance matrix.
## Conducting Meinshausen & Buhlmann graph estimation (mb)....done

## Done.

Analyzing the constructed network

NetCoMi’s netAnalyze() function is used for analyzing the constructed network(s).

Here, centrLCC is set to TRUE meaning that centralities are calculated only for nodes in the largest connected component (LCC).

Clusters are identified using greedy modularity optimization (by cluster_fast_greedy() from igraph package).

Hubs are nodes with an eigenvector centrality value above the empirical 95% quantile of all eigenvector centralities in the network (argument hubPar).

weightDeg and normDeg are set to FALSE so that the degree of a node is simply defined as number of nodes that are adjacent to the node.

props_single <- netAnalyze(net_single, 
                           centrLCC = TRUE,
                           clustMethod = "cluster_fast_greedy",
                           hubPar = "eigenvector",
                           weightDeg = FALSE, normDeg = FALSE)

#?summary.microNetProps
summary(props_single, numbNodes = 5L)

## 
## Component sizes
## ```````````````         
## size: 100
##    #:   1
## ______________________________
## Global network properties
## `````````````````````````
##                                  
## Number of components      1.00000
## Clustering coefficient    0.32020
## Moduarity                 0.51909
## Positive edge percentage 92.01278
## Edge density              0.06323
## Natural connectivity      0.01454
## Vertex connectivity       1.00000
## Edge connectivity         1.00000
## Average dissimilarity*    0.97984
## Average path length**     2.22537
## 
##  *Dissimilarity = 1 - edge weight
## **Path length: Units with average dissimilarity
## 
## ______________________________
## Clusters
## - In the whole network
## - Algorithm: cluster_fast_greedy
## ```````````````````````````````` 
##                       
## name:  1  2  3  4  5 6
##    #: 15 25 14 21 20 5
## 
## ______________________________
## Hubs
## - In alphabetical/numerical order
## - Based on empirical quantiles of centralities
## ```````````````````````````````````````````````       
##  189396
##  191687
##  293896
##  364563
##  544358
## 
## ______________________________
## Centrality measures
## - In decreasing order
## - Computed for the complete network
## ````````````````````````````````````
## Degree (unnormalized):
##          
## 293896 15
## 544358 14
## 174012 13
## 364563 12
## 311477 12
## 
## Betweenness centrality (normalized):
##               
## 175617 0.14533
## 175537 0.11833
## 165261 0.10142
## 185451 0.09462
## 268332 0.08493
## 
## Closeness centrality (normalized):
##               
## 544358 0.71315
## 293896 0.69119
## 191687 0.67098
## 311477 0.66954
## 174012 0.66699
## 
## Eigenvector centrality (normalized):
##               
## 293896 1.00000
## 191687 0.87429
## 364563 0.86119
## 189396 0.83855
## 544358 0.81202

Visualizing the network

We use the determined clusters as node colors and scale the node sizes according to the node’s eigenvector centrality.

# help page
?plot.microNetProps

p <- plot(props_single, 
          nodeColor = "cluster", 
          nodeSize = "eigenvector",
          title1 = "Network on OTU level with SPRING associations", 
          showTitle = TRUE,
          cexTitle = 2.3)

legend(0.7, 1.1, cex = 2.2, title = "estimated association:",
       legend = c("+","-"), lty = 1, lwd = 3, col = c("#009900","red"), 
       bty = "n", horiz = TRUE)

Note that edge weights are (non-negative) similarities, however, the edges belonging to negative estimated associations are colored in red by default (negDiffCol = TRUE).

By default, a different transparency value is added to edges with an absolute weight below and above the cut value (arguments edgeTranspLow and edgeTranspHigh). The determined cut value can be read out as follows:

p$q1$Arguments$cut

## [1] 0.3211104

Single network with Pearson correlation as association measure

Let’s construct another network using Pearson’s correlation coefficient as association measure. The input is now a phyloseq object.

Since Pearson correlations may lead to compositional effects when applied to sequencing data, we use the clr transformation as normalization method. Zero treatment is necessary in this case.

A threshold of 0.3 is used as sparsification method, so that only OTUs with an absolute correlation greater than or equal to 0.3 are connected.

net_single2 <- netConstruct(amgut2.filt.phy,  
                            measure = "pearson",
                            normMethod = "clr", 
                            zeroMethod = "multRepl",
                            sparsMethod = "threshold", 
                            thresh = 0.3,
                            verbose = 3)

## 2 rows with zero sum removed.

## 138 taxa and 294 samples remaining.

## 
## Zero treatment:

## Execute multRepl() ... Done.
## 
## Normalization:
## Execute clr(){SpiecEasi} ... Done.
## 
## Calculate 'pearson' associations ... Done.
## 
## Sparsify associations via 'threshold' ... Done.

Network analysis and plotting:

props_single2 <- netAnalyze(net_single2, clustMethod = "cluster_fast_greedy")

plot(props_single2, 
     nodeColor = "cluster", 
     nodeSize = "eigenvector",
     title1 = "Network on OTU level with Pearson correlations", 
     showTitle = TRUE,
     cexTitle = 2.3)

legend(0.7, 1.1, cex = 2.2, title = "estimated correlation:", 
       legend = c("+","-"), lty = 1, lwd = 3, col = c("#009900","red"), 
       bty = "n", horiz = TRUE)

Let’s improve the visualization a bit by changing the following arguments:

repulsion = 0.8: Place the nodes further apart
rmSingles = TRUE: Single nodes are removed
labelScale = FALSE and cexLabels = 1.6: All labels have equal size and are enlarged to improve readability of small node’s labels
nodeSizeSpread = 3 (default is 4): Node sizes are more similar if the value is decreased. This argument (in combination with cexNodes) is useful to enlarge small nodes while keeping the size of big nodes.

plot(props_single2, 
     nodeColor = "cluster", 
     nodeSize = "eigenvector",
     repulsion = 0.8,
     rmSingles = TRUE,
     labelScale = FALSE,
     cexLabels = 1.6,
     nodeSizeSpread = 3,
     cexNodes = 2,
     title1 = "Network on OTU level with Pearson correlations", 
     showTitle = TRUE,
     cexTitle = 2.3)

legend(0.7, 1.1, cex = 2.2, title = "estimated correlation:",
       legend = c("+","-"), lty = 1, lwd = 3, col = c("#009900","red"),
       bty = "n", horiz = TRUE)

Single association network on genus level

We now construct a further network, where OTUs are agglomerated to genera.

# Agglomerate to genus level
amgut_genus <- phyloseq::tax_glom(amgut2.filt.phy, taxrank = "Rank6")
taxtab <- amgut_genus@tax_table@.Data

# Find undefined taxa (in this data set, unknowns occur only up to Rank5)
miss_f <- which(taxtab[, "Rank5"] == "f__")
miss_g <- which(taxtab[, "Rank6"] == "g__")

# Number unspecified genera
taxtab[miss_f, "Rank5"] <- paste0("f__", 1:length(miss_f))
taxtab[miss_g, "Rank6"] <- paste0("g__", 1:length(miss_g))

# Find duplicate genera
dupl_g <- which(duplicated(taxtab[, "Rank6"]) |
                  duplicated(taxtab[, "Rank6"], fromLast = TRUE))

for(i in seq_along(taxtab)){
  # The next higher non-missing rank is assigned to unspecified genera
  if(i %in% miss_f && i %in% miss_g){
    taxtab[i, "Rank6"] <- paste0(taxtab[i, "Rank6"], "(", taxtab[i, "Rank4"], ")")
  } else if(i %in% miss_g){
    taxtab[i, "Rank6"] <- paste0(taxtab[i, "Rank6"], "(", taxtab[i, "Rank5"], ")")
  }
  
  # Family names are added to duplicate genera
  if(i %in% dupl_g){
    taxtab[i, "Rank6"] <- paste0(taxtab[i, "Rank6"], "(", taxtab[i, "Rank5"], ")")
  }
}

amgut_genus@tax_table@.Data <- taxtab
rownames(amgut_genus@otu_table@.Data) <- taxtab[, "Rank6"]

# Network construction and analysis
net_single3 <- netConstruct(amgut_genus, 
                            measure = "pearson",
                            zeroMethod = "multRepl",
                            normMethod = "clr", 
                            sparsMethod = "threshold", 
                            thresh = 0.3, 
                            verbose = 3)

## 2 rows with zero sum removed.

## 43 taxa and 294 samples remaining.

## 
## Zero treatment:

## Execute multRepl() ... Done.
## 
## Normalization:
## Execute clr(){SpiecEasi} ... Done.
## 
## Calculate 'pearson' associations ... Done.
## 
## Sparsify associations via 'threshold' ... Done.

props_single3 <- netAnalyze(net_single3, clustMethod = "cluster_fast_greedy")

Network plots

Modifications:

Fruchterman-Reingold layout algorithm from igraph package used (passed to plot as matrix)
Shortened labels
Fixed node sizes, where hubs are enlarged
Node color is gray for all nodes (transparancy is lower for hub nodes by default)

# Compute layout
graph3 <- igraph::graph_from_adjacency_matrix(net_single3$adjaMat1, weighted = TRUE)
lay_fr <- igraph::layout_with_fr(graph3)
# Note that row names of the layout matrix must match the node names
rownames(lay_fr) <- rownames(net_single3$adjaMat1)

plot(props_single3,
     layout = lay_fr,
     shortenLabels = "simple",
     labelLength = 10,
     nodeSize = "fix",
     nodeColor = "gray",
     cexNodes = 0.8,
     cexHubs = 1.1,
     cexLabels = 1.2,
     title1 = "Network on genus level with Pearson correlations", 
     showTitle = TRUE,
     cexTitle = 2.3)

legend(0.7, 1.1, cex = 2.2, title = "estimated correlation:",
       legend = c("+","-"), lty = 1, lwd = 3, col = c("#009900","red"), 
       bty = "n", horiz = TRUE)

Since the above visualization is obviously not optimal, we make further adjustments:

This time, the Fruchterman-Reingold layout algorithm is computed within the plot function and thus applied to the “reduced” network without singletons
Leading patterns "g__" are removed
Labels are not scaled to node sizes
Single nodes are removed
Node sizes are scaled to the column sums of clr-transformed data
Node colors represent the determined clusters
Border color of hub nodes is changed from black to darkgray
Label size of hubs is enlarged

set.seed(123456)
graph3 <- igraph::graph_from_adjacency_matrix(net_single3$adjaMat1, weighted = TRUE)
lay_fr <- igraph::layout_with_fr(graph3)
rownames(lay_fr) <- rownames(net_single3$adjaMat1)

plot(props_single3,
     layout = "layout_with_fr",
     shortenLabels = "simple",
     labelLength = 10,
     charToRm = "g__",
     labelScale = FALSE,
     rmSingles = TRUE,
     nodeSize = "clr",
     nodeColor = "cluster",
     hubBorderCol = "darkgray",
     cexNodes = 2,
     cexLabels = 1.5,
     cexHubLabels = 2,
     title1 = "Network on genus level with Pearson correlations", 
     showTitle = TRUE,
     cexTitle = 2.3)

legend(0.7, 1.1, cex = 2.2, title = "estimated correlation:",
       legend = c("+","-"), lty = 1, lwd = 3, col = c("#009900","red"), 
       bty = "n", horiz = TRUE)

Let’s check whether the largest nodes are actually those with highest column sums in the matrix with normalized counts returned from netConstruct().

sort(colSums(net_single3$normCounts1), decreasing = TRUE)[1:10]

##              g__Bacteroides               g__Klebsiella 
##                   1200.7971                   1137.4928 
##         g__Faecalibacterium      g__5(o__Clostridiales) 
##                    708.0877                    549.2647 
##    g__2(f__Ruminococcaceae)    g__3(f__Lachnospiraceae) 
##                    502.1889                    493.7558 
## g__6(f__Enterobacteriaceae)                g__Roseburia 
##                    363.3841                    333.8737 
##          g__Parabacteroides              g__Coprococcus 
##                    328.0495                    274.4082

In order to further improve our plot, we use the following modifications:

This time, we choose the “spring” layout as part of qgraph() (the function is generally used for network plotting in NetCoMi)
A repulsion value below 1 places the nodes further apart
Labels are not shortened anymore
Nodes (bacteria on genus level) are colored according to the respective phylum
Edges representing positive associations are colored in blue, negative ones in orange (just to give an example for alternative edge coloring)
Transparency is increased for edges with high weight to improve the readability of node labels

# Get phyla names from the taxonomic table created before
phyla <- as.factor(gsub("p__", "", taxtab[, "Rank2"]))
names(phyla) <- taxtab[, "Rank6"]
#table(phyla)

# Define phylum colors
phylcol <- c("cyan", "blue3", "red", "lawngreen", "yellow", "deeppink")

plot(props_single3,
     layout = "spring",
     repulsion = 0.84,
     shortenLabels = "none",
     charToRm = "g__",
     labelScale = FALSE,
     rmSingles = TRUE,
     nodeSize = "clr",
     nodeSizeSpread = 4,
     nodeColor = "feature", 
     featVecCol = phyla, 
     colorVec =  phylcol,
     posCol = "darkturquoise", 
     negCol = "orange",
     edgeTranspLow = 0,
     edgeTranspHigh = 40,
     cexNodes = 2,
     cexLabels = 2,
     cexHubLabels = 2.5,
     title1 = "Network on genus level with Pearson correlations", 
     showTitle = TRUE,
     cexTitle = 2.3)

# Colors used in the legend should be equally transparent as in the plot
phylcol_transp <- NetCoMi:::colToTransp(phylcol, 60)

legend(-1.2, 1.2, cex = 2, pt.cex = 2.5, title = "Phylum:", 
       legend=levels(phyla), col = phylcol_transp, bty = "n", pch = 16) 

legend(0.7, 1.1, cex = 2.2, title = "estimated correlation:",
       legend = c("+","-"), lty = 1, lwd = 3, col = c("darkturquoise","orange"), 
       bty = "n", horiz = TRUE)

Network comparison

Now let’s look how two networks are compared using NetCoMi.

Network construction

The covariate "SEASONAL_ALLERGIES" is used for splitting the data set into two groups. The metagMisc package offers a function for splitting phyloseq objects according to a variable. The two resulting phyloseq objects (we ignore the group ‘None’) can directly be passed to NetCoMi.

We select the 50 nodes with highest variance to get smaller networks.

# devtools::install_github("vmikk/metagMisc")

# Split the phyloseq object into two groups
amgut_split <- metagMisc::phyloseq_sep_variable(amgut2.filt.phy, 
                                                "SEASONAL_ALLERGIES")

# Network construction
net_season <- netConstruct(data = amgut_split$no, 
                           data2 = amgut_split$yes,  
                           filtTax = "highestVar",
                           filtTaxPar = list(highestVar = 50),
                           measure = "spring",
                           measurePar = list(nlambda=10, 
                                             rep.num=10),
                           normMethod = "none", 
                           zeroMethod = "none",
                           sparsMethod = "none", 
                           dissFunc = "signed",
                           verbose = 3,
                           seed = 123456)

## Data filtering ...

## 95 taxa removed in each data set.

## 1 rows with zero sum removed in group 1.

## 1 rows with zero sum removed in group 2.

## 43 taxa and 162 samples remaining in group 1.

## 43 taxa and 120 samples remaining in group 2.

## 
## Calculate 'spring' associations ...

## The input is identified as the covariance matrix.
## Conducting Meinshausen & Buhlmann graph estimation (mb)....done
## The input is identified as the covariance matrix.
## Conducting Meinshausen & Buhlmann graph estimation (mb)....done
## The input is identified as the covariance matrix.
## Conducting Meinshausen & Buhlmann graph estimation (mb)....done
## The input is identified as the covariance matrix.
## Conducting Meinshausen & Buhlmann graph estimation (mb)....done
## The input is identified as the covariance matrix.
## Conducting Meinshausen & Buhlmann graph estimation (mb)....done
## The input is identified as the covariance matrix.
## Conducting Meinshausen & Buhlmann graph estimation (mb)....done
## The input is identified as the covariance matrix.
## Conducting Meinshausen & Buhlmann graph estimation (mb)....done
## The input is identified as the covariance matrix.
## Conducting Meinshausen & Buhlmann graph estimation (mb)....done
## The input is identified as the covariance matrix.
## Conducting Meinshausen & Buhlmann graph estimation (mb)....done
## The input is identified as the covariance matrix.
## Conducting Meinshausen & Buhlmann graph estimation (mb)....done
## The input is identified as the covariance matrix.
## Conducting Meinshausen & Buhlmann graph estimation (mb)....done

## Done.
## 
## Calculate associations in group 2 ...

## The input is identified as the covariance matrix.
## Conducting Meinshausen & Buhlmann graph estimation (mb)....done
## The input is identified as the covariance matrix.
## Conducting Meinshausen & Buhlmann graph estimation (mb)....done
## The input is identified as the covariance matrix.
## Conducting Meinshausen & Buhlmann graph estimation (mb)....done
## The input is identified as the covariance matrix.
## Conducting Meinshausen & Buhlmann graph estimation (mb)....done
## The input is identified as the covariance matrix.
## Conducting Meinshausen & Buhlmann graph estimation (mb)....done
## The input is identified as the covariance matrix.
## Conducting Meinshausen & Buhlmann graph estimation (mb)....done
## The input is identified as the covariance matrix.
## Conducting Meinshausen & Buhlmann graph estimation (mb)....done
## The input is identified as the covariance matrix.
## Conducting Meinshausen & Buhlmann graph estimation (mb)....done
## The input is identified as the covariance matrix.
## Conducting Meinshausen & Buhlmann graph estimation (mb)....done
## The input is identified as the covariance matrix.
## Conducting Meinshausen & Buhlmann graph estimation (mb)....done
## The input is identified as the covariance matrix.
## Conducting Meinshausen & Buhlmann graph estimation (mb)....done

## Done.

Alternatively, a group vector could be passed to group, according to which the data set is split into two groups:

# netConstruct() expects samples in rows
countMat <- t(amgut2.filt.phy@otu_table@.Data)
group_vec <- phyloseq::get_variable(amgut2.filt.phy, "SEASONAL_ALLERGIES")

# Select the two groups of interest (level "none" is excluded)
sel <- which(group_vec %in% c("no", "yes"))
group_vec <- group_vec[sel]
countMat <- countMat[sel, ]

net_season <- netConstruct(countMat, 
                           group = group_vec, 
                           filtTax = "highestVar",
                           filtTaxPar = list(highestVar = 50),
                           measure = "spring",
                           measurePar = list(nlambda=10, 
                                             rep.num=10),
                           normMethod = "none", 
                           zeroMethod = "none",
                           sparsMethod = "none", 
                           dissFunc = "signed",
                           verbose = 3,
                           seed = 123456)

Network analysis

The object returned from netConstruct() containing both networks is again passed to netAnalyze(). Network properties are computed for both networks simultaneously.

To demonstrate further functionalities of netAnalyze(), we play around with the available arguments, even if the chosen setting might not be optimal.

centrLCC = FALSE: Centralities are calculated for all nodes (not only for the largest connected component).
avDissIgnoreInf = TRUE: Nodes with an infinite dissimilarity are ignored when calculating the average dissimilarity.
sPathNorm = FALSE: Shortest paths are not normalized by average dissimilarity.
hubPar = c("degree", "between", "closeness"): Hubs are nodes with highest degree, betweenness, and closeness centrality at the same time.
lnormFit = TRUE and hubQuant = 0.9: A log-normal distribution is fitted to the centrality values to identify nodes with “highest” centrality values. Here, a node is identified as hub if for each of the three centrality measures, the node’s centrality value is above the 90% quantile of the fitted log-normal distribution.
The non-normalized centralities are used for all four measures.

Note! The arguments must be set carefully, depending on the research questions. NetCoMi’s default values are not generally preferable in all practical cases!

props_season <- netAnalyze(net_season, 
                           centrLCC = FALSE,
                           avDissIgnoreInf = TRUE,
                           sPathNorm = FALSE,
                           clustMethod = "cluster_fast_greedy",
                           hubPar = c("degree", "between", "closeness"),
                           hubQuant = 0.9,
                           lnormFit = TRUE,
                           normDeg = FALSE,
                           normBetw = FALSE,
                           normClose = FALSE,
                           normEigen = FALSE)

summary(props_season)

## 
## Component sizes
## ```````````````
## Group 1:            
## size: 31 8 1
##    #:  1 1 4
## 
## Group 2:          
## size: 41 1
##    #:  1 2
## ______________________________
## Global network properties
## `````````````````````````
## Largest connected component (LCC):
##                          group '1' group '2'
## Relative LCC size          0.72093   0.95349
## Clustering coefficient     0.27184   0.29563
## Moduarity                  0.51794   0.54832
## Positive edge percentage 100.00000 100.00000
## Edge density               0.11183   0.09512
## Natural connectivity       0.04296   0.03257
## Vertex connectivity        1.00000   1.00000
## Edge connectivity          1.00000   1.00000
## Average dissimilarity*     0.68091   0.67853
## Average path length**      2.23414   2.49352
## 
## Whole network:
##                          group '1' group '2'
## Number of components       6.00000   3.00000
## Clustering coefficient     0.31801   0.29563
## Moduarity                  0.62749   0.54832
## Positive edge percentage 100.00000 100.00000
## Edge density               0.06977   0.08638
## Natural connectivity       0.02979   0.03072
## 
##  *Dissimilarity = 1 - edge weight
## **Path length: Sum of dissimilarities along the path
## 
## ______________________________
## Clusters
## - In the whole network
## - Algorithm: cluster_fast_greedy
## ```````````````````````````````` 
## group '1':                 
## name: 0  1  2 3 4
##    #: 4 10 13 8 8
## 
## group '2':                  
## name: 0 1  2 3 4 5
##    #: 2 6 11 8 8 8
## 
## ______________________________
## Hubs
## - In alphabetical/numerical order
## - Based on log-normal quantiles of centralities
## ```````````````````````````````````````````````
##  group '1' group '2'
##               322235
## 
## ______________________________
## Centrality measures
## - In decreasing order
## - Computed for the complete network
## ````````````````````````````````````
## Degree (unnormalized):
##         group '1' group '2'
##  322235         7         9
##  364563         7         5
##  259569         7         5
##  184983         6         5
##    9715         5         4
##            ______    ______
##  322235         7         9
##  363302         4         9
##  158660         3         6
##   90487         3         5
##  188236         4         5
## 
## Betweenness centrality (unnormalized):
##         group '1' group '2'
##  364563       148        82
##  188236       144        87
##  259569       122        39
##  331820       115         8
##  322235       106       226
##            ______    ______
##  158660         0       317
##  470239         5       256
##   10116         0       233
##  322235       106       226
##  326792         0       161
## 
## Closeness centrality (unnormalized):
##         group '1' group '2'
##  364563  22.67516  25.82886
##  259569  22.19619  23.95399
##  322235   22.1629   30.0221
##  188236   21.1083  26.37517
##  184983   20.0581  22.58796
##            ______    ______
##  322235   22.1629   30.0221
##  158660  17.64634  27.65421
##  363302  17.27059  27.61001
##  326792  17.95234  26.47248
##  188236   21.1083  26.37517
## 
## Eigenvector centrality (unnormalized):
##         group '1' group '2'
##  364563   0.30442    0.2137
##  184983   0.29042   0.26935
##  188236    0.2392   0.23412
##  516022   0.23484   0.14094
##  190464   0.22311   0.21337
##            ______    ______
##  363302   0.21617   0.38157
##  322235   0.14538   0.29676
##  194648   0.17436   0.28061
##  184983   0.29042   0.26935
##  188236    0.2392   0.23412

In the above setting, only one hub node (in the “Seasonal allergies” network) has been identified.

Visual network comparison

First, the layout is computed separately in both groups (qgraph’s “spring” layout in this case).

Node sizes are scaled according to the mclr-transformed data since SPRING uses the mclr transformation as normalization method.

Node colors represent clusters. Note that by default, two clusters have the same color in both groups if they have at least two nodes in common (sameColThresh = 2). Set sameClustCol to FALSE to get different cluster colors.

plot(props_season, 
     sameLayout = FALSE, 
     nodeColor = "cluster",
     nodeSize = "mclr",
     labelScale = FALSE,
     cexNodes = 1.5, 
     cexLabels = 2.5,
     cexHubLabels = 3,
     cexTitle = 3.7,
     groupNames = c("No seasonal allergies", "Seasonal allergies"),
     hubBorderCol  = "gray40")

legend("bottom", title = "estimated association:", legend = c("+","-"), 
       col = c("#009900","red"), inset = 0.02, cex = 4, lty = 1, lwd = 4, 
       bty = "n", horiz = TRUE)

Using different layouts leads to a “nice-looking” network plot for each group, however, it is difficult to identify group differences at a glance.

Thus, we now use the same layout in both groups. In the following, the layout is computed for group 1 (the left network) and taken over for group 2.

rmSingles is set to "inboth" because only nodes that are unconnected in both groups can be removed if the same layout is used.

plot(props_season, 
     sameLayout = TRUE, 
     layoutGroup = 1,
     rmSingles = "inboth", 
     nodeSize = "mclr", 
     labelScale = FALSE,
     cexNodes = 1.5, 
     cexLabels = 2.5,
     cexHubLabels = 3,
     cexTitle = 3.8,
     groupNames = c("No seasonal allergies", "Seasonal allergies"),
     hubBorderCol  = "gray40")

legend("bottom", title = "estimated association:", legend = c("+","-"), 
       col = c("#009900","red"), inset = 0.02, cex = 4, lty = 1, lwd = 4, 
       bty = "n", horiz = TRUE)

In the above plot, we can see clear differences between the groups. The OTU “322235”, for instance, is more strongly connected in the “Seasonal allergies” group than in the group without seasonal allergies, which is why it is a hub on the right, but not on the left.

Since simply taking over the layout of one group to the other usually leads to an “unsightly” plot for one of the groups, NetCoMi (>= 1.0.2) offers a further option (layoutGroup = "union"), where a union of both layouts is used in both groups. In doing so, the nodes are placed as optimal as possible equally for both networks.

The idea and R code for this functionality were provided by Christian L. Müller and Alice Sommer

plot(props_season, 
     sameLayout = TRUE, 
     layoutGroup = "union",
     rmSingles = "inboth", 
     nodeSize = "mclr", 
     labelScale = FALSE,
     cexNodes = 1.5, 
     cexLabels = 2.5,
     cexHubLabels = 3,
     cexTitle = 3.8,
     groupNames = c("No seasonal allergies", "Seasonal allergies"),
     hubBorderCol  = "gray40")

legend("bottom", title = "estimated association:", legend = c("+","-"), 
       col = c("#009900","red"), inset = 0.02, cex = 4, lty = 1, lwd = 4, 
       bty = "n", horiz = TRUE)

Quantitative network comparison

Since runtime is considerably increased if permutation tests are performed, we set the permTest parameter to FALSE. See the tutorial_createAssoPerm file for a network comparison including permutation tests.

comp_season <- netCompare(props_season, permTest = FALSE, verbose = FALSE)

summary(comp_season, 
        groupNames = c("No allergies", "Allergies"),
        showCentr = c("degree", "between", "closeness"), 
        numbNodes = 5)

## 
## Comparison of Network Properties
## ----------------------------------
## CALL: 
## netCompare(x = props_season, permTest = FALSE, verbose = FALSE)
## 
## ______________________________
## Global network properties
## `````````````````````````
## Largest connected component (LCC):
##                          No allergies   Allergies    difference
## Relative LCC size               0.721       0.953         0.233
## Clustering coefficient          0.272       0.296         0.024
## Moduarity                       0.518       0.548         0.030
## Positive edge percentage      100.000     100.000         0.000
## Edge density                    0.112       0.095         0.017
## Natural connectivity            0.043       0.033         0.010
## Vertex connectivity             1.000       1.000         0.000
## Edge connectivity               1.000       1.000         0.000
## Average dissimilarity*          0.681       0.679         0.002
## Average path length**           2.234       2.494         0.259
## 
## Whole network:
##                          No allergies   Allergies    difference
## Number of components            6.000       3.000         3.000
## Clustering coefficient          0.318       0.296         0.022
## Moduarity                       0.627       0.548         0.079
## Positive edge percentage      100.000     100.000         0.000
## Edge density                    0.070       0.086         0.017
## Natural connectivity            0.030       0.031         0.001
## -----
##  *: Dissimilarity = 1 - edge weight
## **Path length: Sum of dissimilarities along the path
## 
## ______________________________
## Jaccard index (similarity betw. sets of most central nodes)
## ``````````````````````````````````````````````````````````
##                     Jacc   P(<=Jacc)     P(>=Jacc)    
## degree             0.286    0.475500      0.738807    
## betweenness centr. 0.077    0.038537 *    0.994862    
## closeness centr.   0.267    0.404065      0.790760    
## eigenvec. centr.   0.667    0.996144      0.018758 *  
## hub taxa           0.000    0.666667      1.000000    
## -----
## Jaccard index ranges from 0 (compl. different) to 1 (sets equal)
## 
## ______________________________
## Adjusted Rand index (similarity betw. clusterings)
## ``````````````````````````````````````````````````
##    ARI       p-value
##  0.327             0
## -----
## ARI in [-1,1] with ARI=1: perfect agreement betw. clusterings,
##                    ARI=0: expected for two random clusterings
## p-value: two-tailed test with null hypothesis ARI=0
## 
## ______________________________
## Centrality measures
## - In decreasing order
## - Computed for the complete network
## ````````````````````````````````````
## Degree (unnormalized):
##        No allergies Allergies abs.diff.
## 363302            4         9         5
## 549871            4         0         4
## 469709            1         4         3
## 158660            3         6         3
## 181016            0         3         3
## 
## Betweenness centrality (unnormalized):
##        No allergies Allergies abs.diff.
## 158660            0       317       317
## 470239            5       256       251
## 10116             0       233       233
## 326792            0       161       161
## 322235          106       226       120
## 
## Closeness centrality (unnormalized):
##        No allergies Allergies abs.diff.
## 181016        0.000    22.880    22.880
## 361496        0.000    22.253    22.253
## 549871       19.787     0.000    19.787
## 278234        0.000    15.093    15.093
## 10116         7.039    20.965    13.925
## 
## _________________________________________________________
## Significance codes: ***: 0.001, **: 0.01, *: 0.05, .: 0.1

Differential networks

We now build a differential association network, where two nodes are connected if they are differentially associated between the two groups.

Due to its very short execution time, we use Pearson’s correlations for estimating associations between OTUs.

Fisher’s z-test is applied for identifying differentially correlated OTUs. Multiple testing adjustment is done by controlling the local false discovery rate.

Note: sparsMethod is set to "none", just to be able to include all differential associations in the association network plot (see below). However, the differential network is always based on the estimated association matrices before sparsification (the assoEst1 and assoEst2 matrices returned by netConstruct()).

net_season_pears <- netConstruct(data = amgut_split$no, 
                                 data2 = amgut_split$yes, 
                                 filtTax = "highestVar",
                                 filtTaxPar = list(highestVar = 50),
                                 measure = "pearson", 
                                 normMethod = "clr",
                                 sparsMethod = "none", 
                                 thresh = 0.2,
                                 verbose = 3)

## Infos about changed arguments:

## Zero replacement needed for clr transformation. 'multRepl' used.

## Data filtering ...

## 95 taxa removed in each data set.

## 1 rows with zero sum removed in group 1.

## 1 rows with zero sum removed in group 2.

## 43 taxa and 162 samples remaining in group 1.

## 43 taxa and 120 samples remaining in group 2.

## 
## Zero treatment in group 1:

## Execute multRepl() ... Done.
## 
## Zero treatment in group 2:
## Execute multRepl() ... Done.
## 
## Normalization in group 1:
## Execute clr(){SpiecEasi} ... Done.
## 
## Normalization in group 2:
## Execute clr(){SpiecEasi} ... Done.
## 
## Calculate 'pearson' associations ... Done.
## 
## Calculate associations in group 2 ... Done.

# Differential network construction
diff_season <- diffnet(net_season_pears,
                       diffMethod = "fisherTest", 
                       adjust = "lfdr")

## Adjust for multiple testing using 'lfdr' ... 
## Execute fdrtool() ...

## Step 1... determine cutoff point
## Step 2... estimate parameters of null distribution and eta0
## Step 3... compute p-values and estimate empirical PDF/CDF
## Step 4... compute q-values and local fdr

## Done.

# Differential network plot
plot(diff_season, 
     cexNodes = 0.8, 
     cexLegend = 3,
     cexTitle = 4,
     mar = c(2,2,8,5),
     legendGroupnames = c("group 'no'", "group 'yes'"),
     legendPos = c(0.7,1.6))

In the differential network shown above, edge colors represent the direction of associations in the two groups. If, for instance, two OTUs are positively associated in group 1 and negatively associated in group 2 (such as ‘191541’ and ‘188236’), the respective edge is colored in cyan.

We also take a look at the corresponding associations by constructing association networks that include only the differentially associated OTUs.

props_season_pears <- netAnalyze(net_season_pears, 
                                 clustMethod = "cluster_fast_greedy",
                                 weightDeg = TRUE,
                                 normDeg = FALSE)

# Identify the differentially associated OTUs
diffmat_sums <- rowSums(diff_season$diffAdjustMat)
diff_asso_names <- names(diffmat_sums[diffmat_sums > 0])

plot(props_season_pears, 
     nodeFilter = "names",
     nodeFilterPar = diff_asso_names,
     nodeColor = "gray",
     highlightHubs = FALSE,
     sameLayout = TRUE, 
     layoutGroup = "union",
     rmSingles = FALSE, 
     nodeSize = "clr",
     edgeTranspHigh = 20,
     labelScale = FALSE,
     cexNodes = 1.5, 
     cexLabels = 3,
     cexTitle = 3.8,
     groupNames = c("No seasonal allergies", "Seasonal allergies"),
     hubBorderCol  = "gray40")

legend(-0.15,-0.7, title = "estimated correlation:", legend = c("+","-"), 
       col = c("#009900","red"), inset = 0.05, cex = 4, lty = 1, lwd = 4, 
       bty = "n", horiz = TRUE)

We can see that the correlation between the aforementioned OTUs ‘191541’ and ‘188236’ is strongly positive in the left group and negative in the right group.

Dissimilarity-based Networks

If a dissimilarity measure is used for network construction, nodes are subjects instead of OTUs. The estimated dissimilarities are transformed into similarities, which are used as edge weights so that subjects with a similar microbial composition are placed close together in the network plot.

We construct a single network using Aitchison’s distance being suitable for the application on compositional data.

Since the Aitchison distance is based on the clr-transformation, zeros in the data need to be replaced.

The network is sparsified using the k-nearest neighbor (knn) algorithm.

net_aitchison <- netConstruct(amgut1.filt,
                              measure = "aitchison",
                              zeroMethod = "multRepl",
                              sparsMethod = "knn", 
                              kNeighbor = 3,
                              verbose = 3)

## Infos about changed arguments:

## Counts normalized to fractions for measure 'aitchison'.

## 127 taxa and 289 samples remaining.

## 
## Zero treatment:

## Execute multRepl() ... Done.
## 
## Normalization:
## Counts normalized by total sum scaling.
## 
## Calculate 'aitchison' dissimilarities ... Done.
## 
## Sparsify dissimilarities via 'knn' ... Done.

For cluster detection, we use hierarchical clustering with average linkage. Internally, k=3 is passed to cutree() from stats package so that the tree is cut into 3 clusters.

props_aitchison <- netAnalyze(net_aitchison,
                              clustMethod = "hierarchical",
                              clustPar = list(method = "average", k = 3),
                              hubPar = "eigenvector")

plot(props_aitchison, 
     nodeColor = "cluster", 
     nodeSize = "eigenvector",
     hubTransp = 40,
     edgeTranspLow = 60,
     charToRm = "00000",
     mar = c(1, 3, 3, 5))

# get green color with 50% transparency
green2 <- colToTransp("#009900", 40)

legend(0.4, 1.1,
       cex = 2.2,
       legend = c("high similarity (low Aitchison distance)",
                  "low similarity (high Aitchison distance)"), 
       lty = 1, 
       lwd = c(3, 1),
       col = c("darkgreen", green2),
       bty = "n")

In this dissimilarity-based network, hubs are interpreted as samples with a microbial composition similar to that of many other samples in the data set.

Soil microbiome example

Here is the code for reproducing the network plot shown at the beginning.

data("soilrep")

soil_warm_yes <- phyloseq::subset_samples(soilrep, warmed == "yes")
soil_warm_no  <- phyloseq::subset_samples(soilrep, warmed == "no")

net_seas_p <- netConstruct(soil_warm_yes, soil_warm_no,
                           filtTax = "highestVar",
                           filtTaxPar = list(highestVar = 500),
                           zeroMethod = "pseudo",
                           normMethod = "clr",
                           measure = "pearson",
                           verbose = 0)

netprops1 <- netAnalyze(net_seas_p, clustMethod = "cluster_fast_greedy")

nclust <- as.numeric(max(names(table(netprops1$clustering$clust1))))
col <- topo.colors(nclust)

plot(netprops1, 
     sameLayout = TRUE, 
     layoutGroup = "union", 
     colorVec = col,
     borderCol = "gray40", 
     nodeSize = "degree", 
     cexNodes = 0.9, 
     nodeSizeSpread = 3, 
     edgeTranspLow = 80, 
     edgeTranspHigh = 50,
     groupNames = c("Warming", "Non-warming"), 
     showTitle = TRUE, 
     cexTitle = 2.8,
     mar = c(1,1,3,1), 
     repulsion = 0.9, 
     labels = FALSE, 
     rmSingles = "inboth",
     nodeFilter = "clustMin", 
     nodeFilterPar = 10, 
     nodeTransp = 50, 
     hubTransp = 30)

References

[Badri et al., 2020] Michelle Badri, Zachary D. Kurtz, Richard Bonneau, and Christian L. Müller (2020). Shrinkage improves estimation of microbial associations under different normalization methods. bioRxiv, doi: 10.1101/406264.

[Martín-Fernández et al., 1999] Josep A Martín-Fernández, Mark J Bren, Carles Barceló-Vidal, and Vera Pawlowsky-Glahn (1999). A measure of difference for compositional data based on measures of divergence. Lippard, Næss, and Sinding-Larsen, 211-216.)

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netcomi's Introduction

NetCoMi

Overview of methods included in NetCoMi

Installation

Basic Usage

Single network with SPRING as association measure

Single network with Pearson correlation as association measure

Single association network on genus level

Network comparison

Differential networks

Dissimilarity-based Networks

Soil microbiome example

References

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