Network optimization model implies strength of average mutual information in ascendency

Abstract

Ulanowicz’s [J. Theor. Biol. 85 (1980) 223; Ulanowicz, R.E., 1997. Ecology, the ascendent perspective. In: Allen, T.F.H., Roberts, D.W. (Eds.), Complexity in Ecological Systems Series. Columbia University Press, New York, p. 201] ascendency ( A) index of community growth and development is based, in part, upon the average mutual information (AMI) index of Rutledge et al. [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. Ascendency is the product of the AMI and the total system throughput ( T). In published calculations of A, the magnitude of T dwarfs the magnitude of the AMI, and A is well correlated with some measures of analysis that are correlated with T [Ecol. Model. 79 (1995) 75]. Investigations have suggested that T is dominant in the calculation of A. Total system throughput could scale AMI in several ways (e.g., nth root, log x ), but AMI has been consistently scaled by T since its original formulation in [J. Theor. Biol. 85 (1980) 223]. We used a network optimization procedure to show that strict selection for networks with a high A produced food webs that were unlike networks selected for either high AMI or high T. The influence of AMI in the A-optimized systems is clearly discernible in a non-metric multidimensional scaling (NMDS) analysis based upon 54 indices that were calculated for the networks. These results suggest that the scaling of AMI by T in the original formulation of A yielded an index wherein the AMI plays an important role in quantifying dimensions of network structure not present when systems are merely optimized for T.