Analyzing Ecological Networks

Description

A collection of advanced tools, methods and models specifically designed for analyzing different types of ecological networks.

Details

econetwork is designed for analyzing different types of ecological networks - especially antagonistic (food webs, host-parasite), mutualistic (plant-pollinator, plant-fungus, etc.) and competitive networks, as well as their variability in time and space. Statistical models are developed to describe and understand the mechanisms that determine species interactions, and to decipher the organization of these (multi-layer) ecological networks.

Author(s)

Authors: Stephane Dray, Catherine Matias, Vincent Miele, Marc Ohlmann, Wilfried Thuiller Maintainer: Vincent Miele <vincent.miele@univ-lyon1.fr>

References

Marc Ohlmann, Vincent Miele, Stephane Dray, Loic Chalmandrier, Louise O'Connor & Wilfried Thuiller, Diversity indices for ecological networks: a unifying framework using Hill numbers. Ecology Letters (2019) <doi:10.1111/ele.13221> Ana M. Martin Gonzalez, Diego P. Vazquez, Rodrigo Ramos-Jiliberto, Sang Hoon Lee & Vincent Miele, Core-periphery structure in mutualistic networks: an epitaph for nestedness? BiorXiv (2020) <doi:10.1101/2020.04.02.021691>

See Also

igraph bipartite

Core-peripheriness measure

Description

Computation of the cpness measure for a bipartite graph/network

Usage

cpness(web, type=c("automatic","binary","integer","float"), plot=TRUE, fastplot=FALSE)

Arguments

Details

In a matrix displaying a core-periphery structure, there is a species ordering (i.e. an ordering in rows and columns) such that interactions are distributed in an L-shape. This L-shape is composed by four blocks of varying connectance: block C11 represents the core; blocks C12 and C21 include the interactions between core and periphery; block C22 includes the interactions that occur between peripheral species.

This fonction computes the core-peripheriness (CPness), as CPness=(E11+E12+E21)/E, where Eij is the number of interactions (edges) or the sum of weights for each block (Eij for block ij) or for the entire network (E). Here, we rely on a stochastic block model (SBM) to detect the four groups/blocks C11, C12, C21 and C22 when they actually exist. However, the SBM can fail in finding these blocks: in these cases, there is no core-periphery partition and the CPness value is set to NA.

This function can deal with binary and weighted networks with the appropriate statistical distribution (Bernouilli for binary data, Poisson for integer weights, and Gaussian for float weights). Note that it is often advisable to log-transform float data before running the cpness function.

Value

cpness returns an object of class list with the following components:

Author(s)

Authors: Vincent Miele Maintainer: Vincent Miele <vincent.miele@univ-lyon1.fr>

References

Ana M. Martin Gonzalez, Diego P. Vazquez, Rodrigo Ramos-Jiliberto, Sang Hoon Lee & Vincent Miele, Core-periphery structure in mutualistic networks: an epitaph for nestedness? BiorXiv (2020) <doi:10.1101/2020.04.02.021691>

Examples

library(bipartite)
data(mosquin1967)
result <- cpness(mosquin1967, type="automatic", plot=TRUE)
print(result)

data(junker2013)
result <- cpness(junker2013, type="automatic", plot=TRUE, fastplot=TRUE)
print(result$cpness)
print(table(result$rowmembership))
print(table(result$colmembership))

Computation of the dissimilarity matrix (pairwise beta-diversity) for a set of networks

Description

Computation of the dissimilarity matrix for a set of networks. Each value of the matrix is the pairwise beta-diversity, computed using Hill numbers. It measures the dissimilarity in terms of groups, links, or probability of links.

Usage

disPairwise(gList, groups=NULL, eta=1,
            type=c('P','L','Pi'), abTable=NULL)

Arguments

Value

Return a dist object whose elements are the pairwise dissimilarities.

Author(s)

Authors: Stephane Dray, Vincent Miele, Marc Ohlmann, Wilfried Thuiller Maintainer: Wilfried Thuiller <wilfried.thuiller@univ-grenoble-alpes.fr>

References

Marc Ohlmann, Vincent Miele, Stephane Dray, Loic Chalmandrier, Louise O'Connor & Wilfried Thuiller, Diversity indices for ecological networks: a unifying framework using Hill numbers. Ecology Letters (2019) <doi:10.1111/ele.13221>

Examples

# Generating a set of Erdos-Renyi graphs and give node names.
library(econetwork)
library(igraph)
nbGraph <- 3
gList <- c()
n <- 57 # number of nodes of each graph
C <- 0.1  # connectance of each graph
for(i in 1:nbGraph){
  graphLocal <- erdos.renyi.game(n, type='gnp', p.or.m=C, directed=TRUE)
  V(graphLocal)$name <- as.character(1:57)
  gList = c(gList,list(graphLocal))
}

# vector that gives the group of each node
groups <- c(rep("a",23),rep("b",34))
names(groups) <- as.character(1:57)
#generating random (non-nul) abundances data
abTable <- sapply(1:nbGraph,function(x) rpois(n,1)+1)
rownames(abTable) = unlist(unique(lapply(gList,function(g) V(g)$name)))

# Dissimilarity matrices based on links beta-diversity
# at a node level
disPairwise(gList, type = 'L')
# at a node level while taking into account node abundances
disPairwise(gList, type = 'L', abTable = abTable)
# at a group level
disPairwise(gList, groups, type = 'L')
# at a group level while taking into account node abundances
disPairwise(gList, groups, type = 'L', abTable = abTable) 

Partitionning network diversity in alpha, beta and gamma diversity

Description

This function computes alpha, beta and gamma diversity of a list of networks. It measures either group, links, or probability of links diversity.

Usage

divPartition(gList, groups, eta=1, framework=c('RLC','Chao'),
             type=c('P','L','Pi'), abTable=NULL)

Arguments

Value

Returns a list the following components:

Author(s)

Authors: Stephane Dray, Vincent Miele, Marc Ohlmann, Wilfried Thuiller Maintainer: Wilfried Thuiller <wilfried.thuiller@univ-grenoble-alpes.fr>

References

Marc Ohlmann, Vincent Miele, Stephane Dray, Loic Chalmandrier, Louise O'Connor & Wilfried Thuiller, Diversity indices for ecological networks: a unifying framework using Hill numbers. Ecology Letters (2019) <doi:10.1111/ele.13221>

Examples

# Generating a set of Erdos-Renyi graphs and give node names.
library(econetwork)
library(igraph)
nbGraph <- 3
gList <- c()
n <- 57 # number of nodes of each graph
C <- 0.1  # connectance of each graph
for(i in 1:nbGraph){
  graphLocal <- erdos.renyi.game(n, type='gnp', p.or.m=C, directed=TRUE)
  V(graphLocal)$name <- as.character(1:57)
  gList = c(gList,list(graphLocal))
}

# vector that gives the group of each node
groups <- c(rep("a",23),rep("b",34)) 
names(groups) <- as.character(1:57)
# generating random (non-nul) abundances data
abTable <- sapply(1:nbGraph,function(x) rpois(n,1)+1)
rownames(abTable) = unlist(unique(lapply(gList,function(g) V(g)$name)))

# Diversities in link abundances
# at a node level
divPartition(gList, framework='Chao', type = 'L')
# at a node level while taking into account node abundances
divPartition(gList, framework='Chao', type = 'L', abTable = abTable)
# at a group level
divPartition(gList, framework='Chao', groups, type = 'L')
# at a group level while taking into account node abundances
divPartition(gList, framework='Chao', groups, type = 'L', abTable = abTable)

Teasing apart the effects of environmental variations and biotic interactions on species distributions

Description

ELGRIN jointly models the presence and absence of all species in a given area in function of environmental covariates and the topological structure of the known metaweb

Usage

elgrin(presence, metaweb, environmentvar, ncores=1)

Arguments

Details

ELGRIN (in reference to Charles Elton and Joseph Grinnell) can handle the effects of both environmental factors and known ecological interactions (aka a metanetwork) on species distributions. We rely on Markov random fields, a family of flexible models that can handle dependencies between variables using a graph.

Value

elgrin returns an object of class list with the following components:

Author(s)

Authors: Vincent Miele Maintainer: Vincent Miele <vincent.miele@univ-lyon1.fr>

References

Vincent Miele, Catherine Matias, Marc Ohlmann, Giovanni Poggiato, St ephane Dray and Wilfried Thuiller, Quantifying the overall effect of biotic1interactions on species communities along2environmental gradients, arXiv <doi:10.48550/arXiv.2103.10433>

Examples

data(virtualComCompetition)
vcom <- virtualComCompetition

result <- elgrin(vcom$presence, vcom$metaweb, vcom$environmentvar)
str(result)

plot(result$betaPres, result$betaAbs, xlab="Co-presence", ylab="Co-absence")
abline(h=0, col=2)
abline(v=0, col=2)

Graph embeddings for comparing trophic network architectures

Description

Computation of different embeddings from a list of directed graphs

Usage

embedding(gList, method="metric2vec", groups=NULL)

Arguments

Details

This function computes a graph embedding from a list of graph.

Comparing the architecture of interaction networks in space or time is essential for understanding the assembly, trajectory, functioning and persistence of species communities. Graph embedding methods, which position networks into a vector space where nearby networks have similar architectures, could be ideal tools for this purposes.

Here, the proposed embedding methods are:

-"metric2vec": each column is a network metric. connectance: network connectance, modularity: network modularity (undirected graph), rangeTL: trophic level range, (trophic level is computed as in Williams & Martinez, 2004), meanTL: mean trophic level, SWTL: shortest weighted trophic level, meanOmni: mean level of omnivory (standard deviation of the trophic levels of the prey), propOmni: proportion of omnivorous species, propCanib: proportion of cannibal species, meanNbPrey: mean number of prey, sdNbPrey: standard deviation of the number of prey, skewNbPrey: skewness of the number of prey, meanNbPred: mean number of predators, sdNbPred: standard deviation of the number of predators, skewNbPred: skewness of the number of predators, propBasal: proportion of basal species (which have no prey), propTop: proportion of top species (which have no predator), propInter: proportion of intermediate species (which have prey and predator), sdVulnerability: standard deviation of the vulnerability (i.e. in-degree), sdGeneralism: standard deviation of the generalism (i.e. out-degree), transitivity: network transitivity, diameter: network diameter, meanSP: mean shortest path, assortativity: network assortativity.

-"motif2vec": Graph motifs are small connected subgraphs with a well-defined structure. Each column is the proportion of each of the 13 connected motifs as enumerated by the 'motifs' function.

-"group2vec": Groups proportion, where the groups are defined previously (e.g. taxonmic groups).

-"shortestpath2vec": Computing the proportion of shortest path lengths. Can use the groups as well, path length proportion is decomposed per source and target group in this case.

Value

embedding returns an object of class matrix where rows corresponds to the differents graphs and columns to the different dimensions in the embedding space.

Author(s)

Authors: Christophe Botella, Stephane Dray, Catherine Matias, Vincent Miele, Wilfried Thuiller

Maintainer: Vincent Miele <vincent.miele@univ-lyon1.fr>

References

Christophe Botella, Stephane Dray, Catherine Matias, Vincent Miele & Wilfried Thuiller, An appraisal of graph embeddings for comparing trophic network architectures. Methods in Ecology and evolution (2021) <doi:10.1111/2041-210X.13738>

Williams, Richard J., and Neo D. Martinez. "Limits to trophic levels and omnivory in complex food webs: theory and data." The American Naturalist 163.3 (2004)

Examples

library(igraph)
# Generating a set of graphs with 3 groups
groups = rep(-1,60)
groups[1:20] = 1
groups[21:40] = 2
groups[41:60] = 3
names(groups) = as.character(1:60)

# A first set with a few links between groups 1 and 3
gList = c()
for(i in 1:5){
    pm <- rbind( c(0, .5, 0.05), c(0, 0, 0.5), c(0,0,0) )
    graphLoc <- sample_sbm(60, pref.matrix=pm, block.sizes=c(20,20,20), directed=TRUE)
    V(graphLoc)$name = as.character(1:60)
    gList = c(gList,list(graphLoc))
}
# A second set with many links between groups 1 and 3
for(i in (6:10)){
    pm <- rbind( c(0, .5, .5), c(0, 0, 0.5), c(0,0,0) )
    graphLoc <- sample_sbm(60, pref.matrix=pm, block.sizes=c(20,20,20), directed=TRUE)
    V(graphLoc)$name = as.character(1:60)
    gList = c(gList,list(graphLoc))
}
names(gList) = LETTERS[1:10]

# Computing different embeddings and
usermfrow <- par()$mfrow
par(mfrow=c(2,2))

embd <- embedding(gList, method="metric2vec")
pca <- prcomp(embd, rank=2)$x
plot(pca, main="metric2vec")
text(x=pca[,1], y=pca[,2], labels=rownames(embd), pos=2, col=c(rep("blue",5),rep("red",5)))

embd <- embedding(gList,  method="motif2vec")
pca <- prcomp(embd, rank=2)$x
plot(pca, main="motif2vec")
text(x=pca[,1], y=pca[,2], labels=rownames(embd), pos=2, col=c(rep("blue",5),rep("red",5)))

embd <- embedding(gList, method="shortestpath2vec")
pca <- prcomp(embd, rank=2)$x
plot(pca, main="shortestpath2vec")
text(x=pca[,1], y=pca[,2], labels=rownames(embd), pos=2, col=c(rep("blue",5),rep("red",5)))

embd <- embedding(gList, method="shortestpath2vec", groups)
pca <- prcomp(embd, rank=2)$x
plot(pca, main="shortestpath2vec_group")
text(x=pca[,1], y=pca[,2], labels=rownames(embd), pos=2, col=c(rep("blue",5),rep("red",5)))

par(mfrow=usermfrow)

Get metaweb

Description

Computation of the binary metaweb from a list of graph

Usage

getMetaweb(gList)

Arguments

Details

This function computes the metaweb from a list of graph. It computes the union (in the sense of graph theory) of the set of graphs.

Value

getMetaweb returns an object of class igraph.

Author(s)

Authors: Stephane Dray, Vincent Miele, Marc Ohlmann, Wilfried Thuiller Maintainer: Wilfried Thuiller <wilfried.thuiller@univ-grenoble-alpes.fr>

References

Marc Ohlmann, Vincent Miele, Stephane Dray, Loic Chalmandrier, Louise O'Connor & Wilfried Thuiller, Diversity indices for ecological networks: a unifying framework using Hill numbers. Ecology Letters (2019) <doi:10.1111/ele.13221>

Examples

# Generating a set of Erdos-Renyi graphs
library(igraph)
gList <- c()
for(i in 1:4){
  graphLocal <- erdos.renyi.game(60, type = 'gnp', p.or.m=0.1, directed=TRUE)
  V(graphLocal)$name <- as.character(1:60)
  gList <- c(gList, list(graphLocal))
}
names(gList) <- c("A","B","C","D")

## building the metaweb
graphMetaweb <- getMetaweb(gList)

Dataset simulated with communities whose composition is driven simultaneously by biotic (competition) and abiotic environmental effects.

Description

50 species in interaction in a metaweb, with presence/absence data for 400 locations and a single enviromental variable.

Usage

data(virtualComCompetition)

Format

A list containing three objects presence, metaweb and environmentvar.