divPartition function

Partitionning network diversity in alpha, beta and gamma diversity

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

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

Arguments

• gList: A list of graph objects of class igraph.
• groups: A named vector of class character indicating the group to which each node belongs to. The length of groups must correspond to the number of different nodes present in gList. The names names(groups) must correspond to the nodes names in gList. If NULL, the groups are the initial nodes.
• eta: A positive number that controls the weight given to abundant groups/links. Default value is 1.
• framework: The framework used to partitionate diversity, either Reeve Leinster Cobbold ('RLC') or Chao ('Chao')
• type: The type of diversity to measure and partitionate. It can be groups diversity ('P'), link diversity ('L') or probability of link diversity ('Pi').
• abTable: A matrix of size the number of nodes of the metanetwork times the number of networks. The rownames of this matrix must be the node names of metanetwork and the columns must be in an order corresponding to gList. The element (i,j) of this matrix is the abundance of species i in network j. Importantly, the non-nul elements in each column of abTalbe must correspond to the nodes present in each element of gList

Returns

Returns a list the following components: - mAlpha: The mean value of alpha-diversity accross all networks.

• Alphas: A vector of numeric containing the local alpha-diversities (i.e. the alpha-diversity value for each network).

• Beta: The value of the overall beta-diversity

• Gamma: The value of the gamma-diversity

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

Author(s)

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

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)