AscInd {NetIndices}

Ascendency network indices

Description

Calculates measures of system growth and development: Ascendency, Overhead and Capacity for several (sub)networks.

Usage

AscInd(Flow = NULL, Tij = t(Flow), Import = NULL, 
       Export = NULL, Dissipation = NULL)

Arguments

Flow

network matrix with Flow[i,j] the flow from i (row) to j (column); component positions in rows and columns must be the same; if present, rownames or columnnames denote the compartment names.

Tij

network matrix where connectance is from column j to row i; component positions in rows and columns must be the same ; if present, rownames or columnnames denote the compartment names.

Import

vector with either the *indices* or the *names* of external compartmens from where flow enters the network; the indices point to the column positions in Tij (and the row positions in Flow).

Export

vector with either the *indices* or the *names* of external compartmens to where flow leaves the network; the indices point to the row positions in Tij (and the column positions in Flow).

Dissipation

vector with either the *indices* or the *names* to external compartments that dissipate flows (e.g. respiration); the indices point to the row positions in Tij (and the column positions in Flow).

Details

The mathematical formulation of these indices can be found in the package vignette - vignette("NetIndices").

The PDF can be found in the subdirectory ‘doc’ of the NetIndices package.

Value

A matrix with ascendency values (columns) for several subnetworks (rows).

The subnetworks (rows) are:

total

network

internal

network (excluding flows from and to external)

import

flows

export

flows; this includes the usuable and unusable flows (i.e. +dissipation)

dissipation

flows

The ascendency indices comprise (columns:)

asc

the ascendency of the network, a measure of growth and development.

overh

the overhead of the network.

cap

the development capacity of the network, an upper bound on ascendency.

ACratio

the ratio of ascendency and capacity.

Author(s)

Karline Soetaert <[e-mail]>, Julius Kipyegon Kones<[e-mail]>

References

Latham LG. 2006. Network flow analysis algorithms. Ecological Modelling 192: 586-600.

Ulanowicz RE. 2000. Ascendency: a measure of ecosystem performacne. Jorgensen SE, Muller F, editors. Handbook of Ecosystem Theories and Management. Lewis Publishers, Boca Raton, p303-315.

Ulanowicz RE, Norden JS. 1990. Symmetrical overhead in flow networks. International Journal of System Science 21: 429-437.

Kones, J.K., Soetaert, K., van Oevelen, D. and J.Owino (2009). Are network indices robust indicators of food web functioning? a Monte Carlo approach. Ecological Modelling, 220, 370-382.

Examples

# The takapoto atoll network
AscInd(Takapoto, Import = "CO2",
       Export = c("CO2", "Sedimentation", "Grazing"),
       Dissipation = "CO2")
       
# Conesprings is the example set 1a from Latham 2006.
as.data.frame(
    AscInd(Tij = Conesprings, Import = "Inflows",
    Export = c("Export","Dissipation"), 
    Dissipation = "Dissipation")
    )