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PageRank importance of species in a food web following Allesina & Pascual (2009)

Source: R/calc_pagerank_ap.R
calc_pagerank_ap.Rd

Computes the "food-web PageRank" of Allesina & Pascual (2009). Unlike the standard PageRank applied directly to a food web (e.g. igraph::page_rank() with links from prey to predator), which accumulates importance in top predators, this version measures how much other species depend on each species, so that importance flows from consumers to their resources.

Usage

calc_pagerank_ap(g, weights = FALSE, remove_loops = TRUE)

Arguments

g

igraph directed food web with links from prey to predator (the multiweb convention).

weights

logical, if TRUE and g has a weight edge attribute, each consumer splits its importance proportionally to the link weights instead of equally. The links added to/from the root have weight 1 for basal species and, for the detritus links, the mean weight of the network. The original method is unweighted (default FALSE).

remove_loops

logical, remove cannibalistic self-loops (default TRUE).

Value

A data frame sorted by decreasing importance with columns:

Species

species name (or vertex index if the graph has no names).

PageRank

importance, summing 1 over species (root excluded).

Rank

rank of the species (1 = most important; ties get the minimum rank).

Basal

TRUE for species without prey, that are linked to the root.

Details

The algorithm:

  1. Adds a "root" node (external energy/nutrient source) that is the only resource of the basal species (species without prey).

  2. Adds a link from every species to the root, representing loss of matter (detritus/recycling). This makes the graph irreducible and primitive, so no damping factor is needed (damping = 1), as argued by the authors.

  3. Each consumer splits its importance equally (or proportionally to link weights, if weights = TRUE) among its resources; the importance vector is the dominant eigenvector of the resulting column-stochastic matrix.

The root is removed from the output and the scores of the species are rescaled to sum 1.

The method is defined for trophic networks only: the root node represents the flow of matter, which has no meaning for non-trophic layers.

References

Allesina, S. & Pascual, M. (2009). Googling food webs: can an eigenvector measure species' importance for coextinctions? PLoS Computational Biology, 5(9), e1000494. doi:10.1371/journal.pcbi.1000494

See also

calc_centrality()

Examples

# Linear chain: resource -> herbivore -> predator
g <- igraph::graph_from_literal(Resource -+ Herbivore, Herbivore -+ Predator)
calc_pagerank_ap(g)
#>     Species  PageRank Rank Basal
#> 1  Resource 0.5000000    1  TRUE
#> 2 Herbivore 0.3333333    2 FALSE
#> 3  Predator 0.1666667    3 FALSE

# Compare with the standard PageRank, which ranks the predator first
igraph::page_rank(g)$vector
#>  Resource Herbivore  Predator 
#> 0.1844168 0.3411710 0.4744122