Daisyworld in two dimensional small-world networks

Daisyworld was initially proposed as an abstract model of the self-regulation of planetary ecosystems. The original one-point model has also been extended to one- and two-dimensional worlds. The latter are especially interesting, in that they not only demonstrate the emergence of spatially-stabilised homeostasis but also emphasise dynamics of heterogeneity within a system, in which individual locations in the world experience booms and busts, yet the overall behaviour is stabilised as patches of white and black daisies migrate around the world. We extend the model further, to small-world networks, more realistic for social interaction - and even for some forms of ecological interaction - using the Watts-Strogatz (WS) and Newman-Watts (NW) models. We find that spatially-stabilised homeostasis is able to persist in small-world networks. In the WS model, as the rewiring probabilities increase even far beyond normal small-world limits, there is only a small loss of effectiveness. However as the average number of connections increases in the NW model, we see a gradual breakdown of heterogeneity in patch dynamics, leading to less interesting - more homogenised - worlds.