ILSM (version 1.1.0.1)

ig_ddom: Degree of diagonal dominance

Description

Calculating the degree of diagonal dominance for a tripartite network with intra-guild interactions.

Usage

ig_ddom(mat)

Value

Return the average degree of diagonal dominance and a vector of diagonal dominance indices for all nodes.

Arguments

mat

A square block interaction matrix representing a tripartite network including intra-guild and inter-guild interactions. See details.

Details

To calculate degree of diagonal dominance, the input should be a block matrix (\(M\)) to represent three groups of nodes (a-nodes, b-nodes and c-nodes): three intra-guild interaction matrices (\(m_{aa},m_{bb},m_{cc}\)), two inter-guild matrices of a and b-nodes (\(m_{ab},m_{ba}\)), and two inter-guild matrices of b- and c-nodes(\(m_{bc},m_{cb}\)). $$ \left( \begin{array}{ccc} m_{aa} & m_{ab} & 0 \\ m_{ba} & m_{bb} & m_{bc} \\ 0 & m_{cb} & m_{cc} \end{array} \right) $$ This function follows the definition by Garcia-Callejas et al (2023). Diagonal dominance is a matrix property indicating diagonal elements are larger than the sum of non-diagonal elements. In a tripartite network with intra-guild interactions, Garcia-Callejas et al. propose a continuous diagonal dominance index by calculating the difference between the diagonal and the sum of non-diagonal elements for each node. The average degree of diagonal dominance (\(d\)) is calculated by averaging all the nodes' values. $$ d = \frac{1}{S} \sum_{i \in S} \left( M_{ii} - \sum_{\substack{j \in S \\ j \neq i}} M_{ij} \right) $$ Where S is the number of species in the tripartite network \(M\).

References

Garcia-Callejas, D., Godoy, O., Buche, L., Hurtado, M., Lanuza, J.B., Allen-Perkins, A. et al. (2023) Non-random interactions within and across guilds shape the potential to coexist in multi-trophic ecological communities. Ecology Letters, 26, 831-842.

Examples

##A toy tripartite network with intra-guild negative interactions:
##Inter-guild mutualistic interactions and inter-guild antagonistic interactions.
set.seed(12)
## 4 a-nodes, 5 b-nodes, and 3 c-nodes.

##Intra-guild interaction matrices
mat_aa<-matrix(runif(16,-0.8,-0.2),4,4)
mat_bb<-matrix(runif(25,-0.8,-0.2),5,5)
mat_cc<-matrix(runif(9,-0.8,-0.2),3,3)

##Inter-guild interaction matrices between a- and b-nodes.
mat_ab<-mat_ba<-matrix(sample(c(rep(0,8),runif(12,0,0.5))),4,5,byrow=TRUE)
mat_ba[mat_ba>0]<-runif(12,0,0.5);mat_ba<-t(mat_ba)

##inter-guild interaction matrices between b- and c-nodes.
mat_cb<-mat_bc<-matrix(sample(c(rep(0,8),runif(7,0,0.5))),3,5,byrow=TRUE)
mat_bc[mat_bc>0]<-runif(7,0,0.5);mat_bc<--t(mat_bc)
mat<-rbind(cbind(mat_aa,mat_ab,matrix(0,4,3)),cbind(mat_ba,mat_bb,mat_bc))
mat<-rbind(mat,cbind(matrix(0,3,4),mat_cb,mat_cc))

##set the node names
rownames(mat)<-c(paste0("a",1:4),paste0("b",1:5),paste0("c",1:3))
colnames(mat)<-c(paste0("a",1:4),paste0("b",1:5),paste0("c",1:3))
diag(mat)<--1 #assume -1 for diagonal elements

##Visualization of the block matrix.
library(plot.matrix)
pal <- colorRampPalette(c("darkblue", "lightblue", "white", "pink", "darkred"))(100)
par(mar=c(5,5,5,5));plot(mat,col = pal,
    breaks = seq(-max(abs(mat)), max(abs(mat)), length.out = 101),
    main = "Matrix visualization")
    clip(x1 = 0.5,# Left boundary
    x2 = ncol(mat) + 0.5, # Right boundary
    y1 = 0.5,            # Top boundary
    y2 = nrow(mat) + 0.5  )
    abline(v = c(4.5,9.5), h = c(3.5,8.5), lwd = 3, col = "black")

ig_ddom(mat)