Quantifying constraint to assess development in ecological networks

[J. Theor. Biol. 85 (1980) 223; Complexity in Ecological System Series (1997) 201] Ascendency index of community growth and development is based, in part, upon the Average Mutual Information (AMI) index of [J. Theor. Biol. 57 (1976) 355]. AMI is an average of mutual constraint on a quantum of material or energy in networks and is reputed to quantify development of ecological systems. The derivation of AMI is explained, and its meaning is illustrated with examples. We compared the AMI to an alternative application of Shannonʹs Theory of Communication to networks. The alternative index, which we have termed the Constraint Efficiency (CE) Index, relies upon a direct quantification of constraint around compartments [sensu Ecology 36 (1955) 536]. Unlike the AMI, where average constraint on a unit of flow in the network is revealed, the CE is based upon a total of the constraints that govern flow out of individual compartments. We compare and contrast the two measures with small networks and discuss their use.