Complexity of Earth Surface System Evolutionary Pathways

摘要: Evolution of Earth surface systems (ESS) comprises sequential transitions between system states. Treating these as directed graphs, algebraic graph theory was used to quantify complexity archetypal structures, and empirical examples forest succession alluvial river channel change. Spectral radius measures structural is highest for fully connected, lowest linear cyclic intermediate divergent convergent patterns. The irregularity index \(\beta \) represents the extent which a subgraph representative full graph. Fully connected graphs have = 1\). Lower values are found in cycle patterns, while higher values, such those due few highly nodes. Algebraic connectivity (\(\mu (\mathrm{G}))\) indicates inferential synchronization inversely related historical contingency. Highest associated with strongly mesh whereas forking structures sequences all \(\mu (G)\) 1, cycles slightly higher. Diverging vs. converging same size topology no differences respect complexity, so change dependent on whether development results increased or reduced richness. Convergent-divergent mode switching, however, would generally increase ESS decrease irregularity, connectivity. As evolve, none possible trends reduces can only remain constant increase. may increase, however. improving shortcomings evolution models result elaborating state changes, this produces more structurally complex but less historically contingent models.