Pathway analysis
Description
Calculates the direct and indirect pathways in a network, i.e. the total system cycled throughflow, Finn's cycling index and average pathlength,...
Based on Finn(1980) (and not Finn (1976))
Usage
1 
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 
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 
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 list with the following items:
TSTC 
total system cycled throughflow. 
TSTS 
noncycled throughflow. 
FCI 
Finn's cycling index (1980). 
FCIb 
revised Finn's cycling index, sensu Allesina and Ulanowicz, 2004. 
APL 
average pathlength, also known as Network Aggradation (Sum of APLc and APLs in Latham 2006). 
Author(s)
Karline Soetaert <karline.soetaert@nioz.nl>, Julius Kipyegon Kones<jkones@uonbi.ac.ke>
References
Finn JT. 1980. Flow analysis of models of the Hubbard Brook ecosystem. Ecology 61: 562571.
Patten BC, Higashi M. 1984. Modified cycling index for ecological applications. Ecological Modelling 25: 6983.
Patten BC, Bosserman RW, Finn JT, Cale WG. 1976. Propagation of cause in ecosystems. Patten BC, editor. Systems Analysis and Simulation in Ecology, vol. 4. Academic Press, New York. p457579.
Allesina and Ulanowicz, 2004. Cycling in ecological netowrks: Finn's index revisited. Computational Biology and Chemistry 28, 227233.
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, 370382.
Examples
1 2 3 4 5 6 7 8 9  # The takapoto atoll network
PathInd(Takapoto, Import = "CO2",
Export = c("CO2", "Sedimentation", "Grazing"))
# Conesprings is the example set 1a from Latham 2006.
as.data.frame(
PathInd(Tij = Conesprings, Import = "Inflows",
Export = c("Export", "Dissipation"))
)
