Phase transitions in two-dimensional daisyworld with small-world effects— A study of local and long-range couplings

• We construct a 2D daisyworld model with small-world effect.
• We use different couplings for temperature and daisies.
• We investigate the role of non-local long-range couplings in daisyworld dynamics.
• We examine the homeostasis emergence of daisyworld.
• We analyse the phase transition region in the small-world regime.

Watson and Lovelock’s daisyworld is a coupled biotic–abiotic feedback loop exhibiting interesting planetary ecodynamics. Previous studies have shown fascinating spatio-temporal dynamics in a 2D daisyworld, with the emergence of complex spatial patterns. We introduce small-world effect into such a system. Even a small fraction of long-range couplings destroys the emergent static pattern formation, leading to completely coherent periodic dominance as observed in fully-connected graphs. This change in daisyworld behaviour depends only on the small-world effect, independent of the means by which they are induced (Watts–Strogatz, Newman–Watts and smallest-world models). The transition from static patterns in grid worlds to periodic coexisting dominance in small-worlds is relatively abrupt, exhibiting a critical region of rapid transition. The behaviours in this transition region are a mix of emergent static spatial patterns and large-scale pattern disruption.