Calculates the average mutual information (AMI), ascendency, overhead, and capacity of input-output networks. It also returns the ratios of ascendency and overhead to capacity. These metrics describe the organization of flow in an ecological network (Ulanowicz 1997).
Value
- H
Total flow diversity (MacArthur 1955). Uses the Shannon Information measure (aka Boltzmann entropy) applied to the individual flows.
- AMI
Returns the Average Mutual Information (AMI) in a network. AMI provides a measure of the constraints placed on a given peice of energy matter moving through a network (Patricio et al. 2006)
- Hr
Residual uncertainty that remains about the flow distribution once the ecosystem structure is specified (Hr = H - AMI).
- ASC
Returns the ascendnecy of a network. Ascendency is a scaled form of AMI relative to the total system throughput (Ulanowicz 1997; 2004). Total system throughput is the sum of all activity in a network (Kay et al. 1989).
- OH
Returns the overhead of a network. Overhead is the proportion of the capacity in a network that is not used as ascendency (Ulanowicz 2004).
- CAP
Returns the capacity of a network. Capacity is defined as the sum of ascendency and overhead (Ulanowicz 2004).
- ACS.CAP
Returns the proportion of capacity used by ascendency.
- OH.CAP
Returns the proportion of capacity used by overhead.
- robustness
Returns the robustness of the network.
- ELD
Returns the Effective Link Density of the network(c) (Ulanowicz et al. 2014).
- TD
Returns the Trophic Depth of the network(r) (Ulanowicz et al. 2014).
- A.input
Returns the input ascendnecy of a network.
- A.internal
Returns the internal ascendnecy of a network.
- A.export
Returns the export ascendnecy of a network.
- A.respiration
Returns the respiration ascendnecy of a network.
- OH.input
Returns the input overhead of a network.
- OH.internal
Returns the internal overhead of a network.
- OH.export
Returns the export overhead of a network.
- OH.respiration
Returns the respiration overhead of a network.
- CAP.input
Returns the input capacity of a network.
- CAP.internal
Returns the internal capacity of a network.
- CAP.export
Returns the export capacity of a network.
- CAP.respiration
Returns the respiration capacity of a network.
Details
This and other Ulanowicz school functions require that export and respiration components of output be separately quantified.
References
Kay, J.J., Graham, L.A., Ulanowicz, R.E., 1989. A detailed guide to network analysis. p. 15-61 In: Wulff, F., Field, J.G., Man, K.H. (eds.) Network analysis in marine ecology. Coastal Estuarine Study Serries. Springer-Verlag, Berlin.
Patrico, J., Ulanowicz, R.E., Pardal, M.A., Marques J.C., 2004. Ascendency as an ecological indicator: a case study of estuarine pulse eutrophication. Estuar. Coast Shelf S. 60, 23-35.
Ulanowicz, R.E. and Norden, J.S., 1990. Symmetrical overhead in flow networks. International Journal of Systems Science, 21(2), pp.429-437.
Ulanowicz, R.E., 1997. Ecology, The Ascendent Perspective. Columbia University Press, New York.
Ulanowicz, R.E., 2004. Quantitative methods for ecological network analysis. Comput. Biol. Chem. 28, 321-33
Ulanowicz, R.E., Holt, R.D., Barfield, M., 2014. Limits on ecosystem trophic complexity: insights from ecological network analysis. Ecology Letters 17:127-136
Examples
data(troModels)
enaAscendency(troModels[[6]])
#> H AMI Hr CAP ASC OH ASC.CAP OH.CAP
#> [1,] 3.20096 1.336447 1.864513 135864.7 56725.49 79139.25 0.4175144 0.5824856
#> robustness ELD TD A.input A.internal A.export A.respiration
#> [1,] 0.3646722 1.908258 2.525286 19147.85 29331.98 1051.765 7193.894
#> OH.input OH.internal OH.export OH.respiration CAP.input CAP.internal
#> [1,] 6221.751 29832.46 7810.812 35274.22 25369.6 59164.44
#> CAP.export CAP.respiration
#> [1,] 8862.578 42468.11