Interaction matrix with Power-Law network adjacency matrix

N is the an Interspecific Interaction matrix with values drawn from a normal distribution H the interaction strength heterogeneity drawn from a power-law distribution with the parameter alpha, and G the adjacency matrix of with out-degree that reflects the heterogeneity of the powerlaw. A scaling factor s may be used to constrain the values of the interaction matrix to be within a desired range. Diagonal elements of A are defined by the parameter d.

Usage

powerlawA(n_species, alpha = 3, stdev = 1, s = 0.1, d = -1, symmetric = FALSE)

Arguments

n_species

integer number of species

alpha

numeric power-law distribution parameter. Should be > 1. (default: alpha = 3.0) Larger values will give lower interaction strength heterogeneity, whereas values closer to 1 give strong heterogeneity in interaction strengths between the species. In other words, values of alpha close to 1 will give Strongly Interacting Species (SIS).

stdev

numeric standard deviation parameter of the normal distribution with mean 0 from which the elements of the nominal interspecific interaction matrix N are drawn. (default: stdev = 1)

s

numeric scaling parameter with which the final global interaction matrix A is multiplied. (default: s = 0.1)

d

numeric diagonal values, indicating self-interactions (use negative values for stability). (default: s = 1.0)

symmetric

logical scalar returning a symmetric interaction matrix (default: symmetric=FALSE)

Value

The interaction matrix A with dimensions (n_species x n_species)

References

Gibson TE, Bashan A, Cao HT, Weiss ST, Liu YY (2016) On the Origins and Control of Community Types in the Human Microbiome. PLOS Computational Biology 12(2): e1004688. https://doi.org/10.1371/journal.pcbi.1004688

Examples

# Low interaction heterogeneity
A_low <- powerlawA(n_species = 10, alpha = 3)
# Strong interaction heterogeneity
A_strong <- powerlawA(n_species = 10, alpha = 1.01)