The balance between adaptability and adaptation

Abstract

In his 1983 book, Adaptability, Michael Conrad explored the quantitative relationship between adaptability and adaptation using the conditional ‘entropy’ of information theory as his primary tool. The conditional entropy can be used to estimate the connectivity of the network of system exchanges, a key indicator of system stability. In fact, the May-Wigner criterion for the stability of linear dynamical systems can be recast using the conditional entropy to help identify the boundary along which adaptability and adaptation are exactly in balance—the ‘edge of chaos’ as it is popularly known. Real data on networks of ecosystem flows indicate that in general these systems do not exist nigh upon the edge of chaos, but rather they populate a much wider ‘window of vitality’ that exists between the realms of chaotic and deterministic dynamics. It appears that the magnitudes of network flows within this region are distributed in power law fashion. The theory also suggests that an absolute limit to the connectivity of natural self-organizing systems exists, at approximately 3.015 effective connections per node.