Why everything is connected to everything else

Abstract

In Earth surface systems (ESS), everything is connected to everything else, an aphorism often called the First Law of Ecology and of geography. Such linkages are not always direct and unmediated, but many ESS, represented as networks of interacting components, attain or approach full, direct connectivity among components. The question is how and why this happens at the system or network scale. The crowded landscape concept dictates that linkages and connections among ESS components are inevitable. The connection selection concept holds that the linkages among components are (often) advantageous to the network and are selected for, and thereby preserved and enhanced. These network advantages are illustrated via algebraic graph theory. For a given number of components in an ESS, as the number of links or connections increases, spectral radius, graph energy, and algebraic connectivity increase. While the advantages (if any) of increased complexity are unclear, higher spectral radii are directly correlated with higher graph energy. The greater graph energy is associated with more intense feedback in the system, and tighter coupling among components. This in turn reflects advantageous properties of more intense cycling of water, nutrients, and minerals, as well as multiple potential degrees of freedom for individual components to respond to changes. The increase of algebraic connectivity reflects a greater ability or tendency for the network to respond to changes in concert.