null_model {ILSM}

Null model of multilayer network

Description

The null model could be generated according to different matrix scrambling algorithms for interconnection patterns in the multilayer network

Usage

null_model(
  network,
  number = NULL,
  null_type = c("subnetwork1", "subnetwork2", "all", "Savue")
)

Arguments

network

A multilayer(tripartite) network of 'igraph' class. The network contains three groups of species and interactions within layers without interactions between each group of species.

number

A numeric value. The number of null model. Default to NULL representing number 1.

null_type

Logical. Four matrix scrambling algorithms. If null_type = NULL, default to "all".

Details

null_type

• For each of the four types of null models, there are corresponding algorithms. The first type, “subnetwork1”, involved scrambling the adjacency matrix of the first and second groups of the multilayer network.

• The second type, “subnetwork2”, focused on scrambling the adjacency matrix of the second and third groups.

• Comprehensively, the third type, “all”, blended the approaches of the first two to disarrange the entire network's adjacency matrix, achieving a thorough perturbation of the network's structure.

• The last type named “Savue” that disarranged inherent structure in terms of the groups of species connected by each interconnecting species of every subnetworks, thus exhibiting different interconnection patterns.

network

About a network of type "igraph", It can be obtained from the connection matrices of subnetworks by the function igraph_from_matrices

Value

Return a list contains one or more elements. Each element represent a null model of multilayer network.

References

Vázquez, D. P., C. J. Melian, N. M. Williams, N. Blüthgen, B. R. Krasnov, and R. Poulin. 2007. Species abundance and asymmetric interaction strength in ecological networks. Oikos 116: 1120-1127.

Sauve, A. M., Thébault, E., Pocock, M. J., & Fontaine, C. (2016). How plants connect pollination and herbivory networks and their contribution to community stability. Ecology, 97(4), 908-917.

Examples

set.seed(12)
d <- build_net(11,22,21,0.2)

set.seed(123)
null_model(d)
set.seed(123)
null_model(d,null_type="subnetwork1")
set.seed(123)
null_model(d,null_type="Savue")
set.seed(123)
null_model(d,number=2,null_type="Savue")