Temporal Griffiths phase: a simple solution to the "savanna problem"

Abstract

We introduce the concepts of temporal Griffiths phases and dynamical phase coexistence. These provide a simple solution for a long-standing problem in theoretical ecology, the so-called "savanna problem". The challenge was to understand why in savanna ecosystems two vegetation forms (trees and grasses) coexist in a robust way with large spatio-temporal variability, but without either of them taking over. We propose a simple model, a variant of the Contact Process, which includes two extra features: varying external (weather) conditions and tree age. The system fluctuates locally between an active (woodland) and an absorbing (grassland) phase of the underlying pure contact process. This leads to a highly variable stable active phase, which we name "temporal Griffiths phase", characterized by active and absorbing patches coexisting dynamically. We expect temporal Griffiths phases to be relevant in other contexts in physics, biology or social sciences.