Ulanowicz's ascendency (A) index of community growth and development is based, in part, upon the average mutual information (AMI) index of Rutledge et al. 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. 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. 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), but AMI has been consistently scaled by T since its original formulation. 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.
