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Calc the Quasi Sign Stability measure for antagonistic (predator-prey) or mgraph networks with multiple interactions.

Source: R/calcFunctionalIndices.r
calc_QSS.Rd

The QSS measure is the proportion of matrices that are locally stable, these matrices are created by sampling the values of the community matrix (the Jacobian) from a uniform distribution, preserving the sign structure [1]. If the 'ig' parameter is an mgraph network it needs to have been built with the order c("Competitive", "Mutualistic", "Trophic") It also calculates the mean of the real part of the maximum eigenvalue, which is also a measure of stability [2]. It uses a uniform distribution between 0 and maximum values given by the parameters negative, positive and selfDamping, corresponding to the sign of interactions and self-limitation effect [3,4]. If the edges of the networks have a weight attribute and istrength parameter is true, weight will be used as interaction strength, then the limits of the uniform distribution will be negative*-x, positive*x, selfDamping*x, where x is the value of the weigth for the edge. If the values of these parameters are 0 then there is no interaction of that kind. The default values for negative, positive and selfDumping assume a maximum ecological transfer efficiency of 10%.

Usage

calc_QSS(
  ig,
  nsim = 1000,
  ncores = 0,
  negative = -10,
  positive = 1,
  selfDamping = -1,
  istrength = FALSE,
  returnRaw = FALSE
)

Arguments

ig

igraph or a list of igraph networks or mgraph network

nsim

number of simulations to calculate QSS, if the number of simulations is 1 then it calculates the maximum eingenvalue for the mean of interaction strength, if istrength==FALSE the mean interaction strength are negative/2, positive/2, selfDamping/2.

ncores

number of cores to use in parallel computation if 0 do not set future strategy inside function

negative

the maximum magnitude of the negative interaction (the effect of the predator on the prey) must be <= 0

positive

the maximum magnitude of the positive interaction (the effect of the prey on the predator) must be >= 0

selfDamping

the maximum magnitude of the self-limitation (the effect of the species on itself) must be <= 0, if = 0 or > 0 then the value is a random number between 0 and selfDamping.

istrength

If TRUE takes the weigth attribute of the network as interaction strength.

returnRaw

if TRUE returns all the values of the maximum eingenvalues

Value

if parameter returnRaw is FALSE returns a data.frame with the QSS, and MEing, the mean of the real part of the maximum eingenvalue. If returnRaw is TRUE it returns the values of randomized real part of maximum eingenvalue (maxre)

References

  1. Allesina, S. & Pascual, M. (2008). Network structure, predator - Prey modules, and stability in large food webs. Theor. Ecol., 1, 55–64.

  2. Grilli, J., Rogers, T. & Allesina, S. (2016). Modularity and stability in ecological communities. Nat. Commun., 7, 12031

  3. Monteiro, A.B. & Del Bianco Faria, L. (2017). Causal relationships between population stability and food-web topology. Functional Ecology, 31, 1294–1300.

  4. Borrelli, J. J. 2015. Selection against instability: stable subgraphs are most frequent in empirical food webs. - Oikos 124: 1583–1588.

Examples

if (FALSE) { # \dontrun{

g <- netData[[2]]

tp <- calc_QSS(g)

# Read Multiplex network and calculate QSS

fileName <- c(system.file("extdata",  package = "multiweb"))
dn <- list.files(fileName,pattern = "^Kefi2015.*\\.txt$")
gt <- readMultiplex(dn,types,"inst/extdata", skipColumn = 2)
calc_QSS(gt)

} # }