Towards a physics of evolution: Critical diversity dynamics at the edges of collapse and bursts of diversification

Systems governed by the standard mechanisms of biological or technological evolution are often described by catalytic evolution equations. We study the structure of these equations and find an analogy with classical thermodynamic systems. In particular, we can demonstrate the existence of several distinct phases of evolutionary dynamics: a phase of fast growing diversity, one of stationary, finite diversity, and one of rapidly decaying diversity. While the first two phases have been subject to previous work, here we focus on the destructive aspects-in particular the phase diagram-of evolutionary dynamics. The main message is that within a critical region, massive loss of diversity can be triggered by very small external fluctuations. We further propose a dynamical model of diversity which captures spontaneous creation and destruction processes fully respecting the phase diagrams of evolutionary systems. The emergent time series show rich diversity dynamics, including power laws as observed in actual economical data, e.g., firm bankruptcy data. We believe the present model presents a possibility to cast the famous qualitative picture of Schumpeterian economic evolution, into a quantifiable and testable framework.