Fig. 3.

Differences in properties and dynamics of patterns in models with scale-dependent feedbacks (SDFs for short) and density-dependent aggregation (DDA for short). (A, C, and E) Scale-dependent feedbacks result in periodic (regular) patterns that have a characteristic wavelength (A) and are stable over time (C and Movie S1 for its spatiotemporal dynamics). This results in a patch-size distribution that is centered around a characteristic patch size (E). (B, D, and F) Patterns resulting from DDA, in contrast, are irregular and consist of alternate phases coexisting in space (B) and are continuously coarsening over time (D and Movie S2 for its spatiotemporal dynamics). The coarsening dynamics result in a patch-size distribution that is continuously shifting in the direction of larger patches (F). Different patches survival curves at different times overlap perfectly when adjusted to the mean scale of the patches (Inset). Accordingly, the scaled patch-size distribution can be considered an emergent property of underlying phase-separation process. Patch sizes were obtained as described methods in SI Appendix, Text S8.