In this example of the softnote, we collected two types of tripartite ecological network: 

Plant-herbivore-parasitoid (PHP) and pollinator-plant-herbivore (PPH) networks are two kinds of commonly studied tripartite networks, with antagonistic-antagonistic interactions and mutualistic-antagonistic subnetworks, respectively. They also have different connector nodes, herbivores in PHP networks, and plants in PPH networks.

Description of the data and file structure

The "Example Interaction Data.Zip" contains the interaction network data for all examples, and "ILSM_Function.zip" contains the source function code for the R package. 

Files and variables

File: Example_Interaction_Data.zip

Description: Data for example analyses: 31 Pollinator-Plant-Herbivore networks and 18 Plant-Herbivore-Parasitoid networks.

Data Structure and Contents

Each network is represented as a set of two bipartite interaction matrices that collectively form the complete tripartite ecological network without intra-guild. The dataset includes:

There are two folders: 'PHP_Plant-Herbivore-Parasitoid' and 'PPH_Pollinator-Plant-Herbivore'

Each folder is divided into two subfolders:
\'PHP_Plant-Herbivore-Parasitoid'\ ->'plant-herbivore' and 'heibivore-parasitoid' 
\'PPH_Pollinator-Plant-Herbivore'\ ->'pollinator-plant' and 'plant-heibivore'

The names of subfolders correspond to interaction types of bipartite networks.
Each subfloder contains binary matrices in CSV format.

Variable Definitions

Interaction matrices contain qualitative interaction relation (zero-one integers), with rows and columns representing species from adjacent trophic levels. It should be noted that not all species names are definite; some names use specific labels to indicate them. All matrices follow consistent formatting with proper dimension labels and missing value handling.

File: ILSM_Function.zip

Description: The source function code for the R package:

'icmotif_count.R'

The icmotif_count function calculates the frequency of each defined interconnection motif in a tripartite network. The function takes a graph or two matrices data inputs. The algorithm for counting interconnection motifs uses mathematical operations directly on the bi-adjacency matrix. We drive 48 expressions to enumerate the frequencies of 48 interconnection motifs. For weighted networks, the weight of a given motif is returned as the arithmetic mean of the weights of its links, following previous studies.

'icmotif_role.R'

The icmotif_role function calculates the frequency of each role within interconnection motifs for each connector species using a similar approach as above.

Functions for interconnection patterns

'poc.R'

The poc function calculates the proportion of connector nodes in the shared set of nodes (POC).

'coid.R' and 'cois.R'

The coid function calculates the correlation of interaction degree (CoID) and the cois function calculates the correlation of interaction similarity (CoIS) for connector species. For CoID, two types of degrees (d_P from P and d_Q from Q) are calculated for each connector species, and the correlation of two degrees is calculated for binary networks; the degree is replaced with the Shannon diversity or sum of interaction strengths for weighted networks. For CoIS, the Jaccard index of interaction partners between pairs of connector species in each subnetwork is measured, and then the correlation between Jaccard coefficients in two subnetworks across all pairs of connector species; the generalized Jaccard index is used for weighted networks.

'pc.R'

The pc function calculates the participation coefficient. For each connector node i, pc_i is calculated as two times the ratio between the lowest degree in both interaction subnetworks (d_P and d_Q) divided by the total degree of node i :
                                                                            2*min(d_P, d_Q)/(d_P + d_Q)

Hence, the participation coefficient for all connector nodes (PCc) is represented by the average value of all pc_i. For weighted networks, the degree is replaced with the sum of link weights.

'hc.R'

The hc function counts the proportion of connector nodes in shared node hubs (HC). The connector node hubs are the top x% of shared nodes with the highest degree. The default x% is 20%. For weighted networks, the shared node hubs are determined with the highest sum of link weights instead.

Functions for interconnection centrality

'node_icc.R'

The node_icc function provides three interconnection centrality metrics by modifying centrality algorithms from the R package “igraph” (version: 2.1.1). For binary networks, the interconnection degree for each connector species is defined as the product of its degree values from two subnetworks. Interconnection betweenness is calculated as the number of shortest paths between a-nodes and c-nodes that pass through the connector species

sum(g_ivj / g_ij), where i ∈ a-nodes, j ∈ c-nodes

where g_ij is the total number of shortest paths between node i from a-nodes and 𝑗 from c-nodes while g_ivj~​ ~is the number of those shortest paths that pass through connector species 𝑣. Interconnection closeness is defined as the inverse of the sum of distances from the connector species to both a-nodes and c-nodes

1/sum(d_vi), where i ∈ a-nodes or c-nodes

where d_vi is the distance between connector species v and species i from a-nodes and c-nodes. For weighted networks, interaction strengths are incorporated into the calculations of weighted degree, shortest paths, and distances.

Other functions

'tri_null.R'

The tri_null function generates null models for a tripartite network. It provides two types of null models. The first type shuffles shared nodes following Sauve et al. (2016) without altering subnetwork links. The second type shuffles links in one or both subnetworks using algorithms from the R package “vegan” (version: 2.6-4), applied independently to one or both subnetworks. The null models can be used to test the statistical significance of observed patterns (see examples in the vignettes of this package).

'ig_icmotif_count.R' and 'ig_icmotif_role.R'

The ig_icmotif_count calculates the frequency of each interconnection motif and ig_icmotif_role returns the frequency of each role defined by motifs in an unweighted or weighted tripartite network with intra-guild interactions (see examples in the vignettes of this package). The algorithms for them are provided in the online documentation of this package.

'ig_ddom.R'

The ig_ddom calculates the degree of diagonal dominance for a tripartite network with intra-guild interactions (García-Callejas et al. 2023).

'ig_overlap_guild.R'

The ig_overlap_guild calculates species-level intra-guild and inter-guild interaction overlap for a tripartite network with intra-guild interactions (García-Callejas et al. 2023).

'adjust_net.R'

To optimize the tripartite network structure, this function refines the shared set by eliminating non-connector nodes.

‘Multi_motif.R’

The function represents the dictionary of interconnection motif forms without intra-guild interactions.

'trigraph_from_mat.R'

The function could transform two interaction matrices into an igraph-tripartite object.

Reference

Sauve, A. M. C., et al. 2016. How plants connect pollination and herbivory networks and their contribution to community stability. - Ecology 97: 908-917.

García-Callejas, D., 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.

Access information

Other publicly accessible locations of the data: https://github.com/WeichengSun/ILSM