stability.value {fluxweb}

Estimates network stability

Description

Computes resilience of the system through Jacobian matrix eigenvalues.

Usage

stability.value(val.mat, biomasses, losses, efficiencies, growth.rate,
  bioms.prefs = TRUE, bioms.losses = TRUE, ef.level = "prey",
  full.output = FALSE)

Arguments

val.mat

A matrix describing fluxes between species (usually a result of fluxing function).

biomasses

A vector of species biomasses.

losses

A vector or an array of species energy losses (excluding predation).

efficiencies

A vector or an array of conversion efficiencies of species in the adjacency matrix. These values describe the proportion of consumed energy that is converted to biomass of the consumer.

growth.rate

A vector defining growth rate of basal species.

bioms.prefs

Logical, if TRUE (default) preferences are scaled according to species biomasses.

bioms.losses

Logical, if TRUE (default) losses are scaled with biomass.

ef.level

Set to "prey" if efficiencies are defined by prey, "pred" if they are a property of the predator.

full.output

Logical, if TRUE function return supplementary informations.

Details

• losses: Express species energetic losses not related to consumption. Usually metabolic or death rates. When an array is provided, losses associated to each species correspond to line sums.

• efficiencies: Determines how efficient species are to convert energy (see ef.level for more details). Providing an array will assume values depending on both prey and predator identity.

• growth.rate: Growth rates of basal species defined. Length of the vector should be equal to the number of species. expects positive numeric values for index corresponding to basal species, NA otherwise

• bioms.pref: If TRUE, preferences w_{ij} of predator j on prey i are scaled according to species biomass using the following formula:

  w_{i,j} = \frac{mat[i,j] * biomasses[i]}{\sum_k mat[i,k]* biomasses[k]}

• bioms.losses: If TRUE, function will assume that losses are defined per biomass unit. Thus, total losses will be thereafter multiplied by biomass values for each species.

• ef.level: If "prey" (resp "pred"), the total amount of energy that can be metabolized from a trophic link will be determined by prey (resp pred) identity. "link.specific" assumes that efficiencies are defined for each trophic interaction and implies efficiencies parameter to be a matrix

• full.output: If TRUE, function result is a list of eigenvalues and eigenvectors of the Jacobian matrix.

Value

Maximum eigenvalue of the Jacobian matrix of a Lotka Voltera like system of equations. If full.output, Jacobian eigenvalues and eigenvectors are returned.

Author(s)

Benoit Gauzens, [e-mail]

Examples

losses = 0.15 * groups.level$bodymasses^(-0.25)

# growth rates of basal sppecies
growth.rates = rep(NA, dim(groups.level$mat)[1])
growth.rates[colSums(groups.level$mat) == 0] = 0.5

val.mat = fluxing(groups.level$mat, 
                  groups.level$biomasses, 
                  losses, 
                  groups.level$efficiencies, 
                  bioms.pref = TRUE, 
                  ef.level = "pred")
                  
stability.value(val.mat, 
                groups.level$biomasses, 
                losses, 
                groups.level$efficiencies, 
                growth.rates, 
                ef.level = "pred")