Multiscale Pattern Complexity in Dry-Land Vegetation: A Simplified Modeling Approach Incorporating Root Augmentation and Stratified Soil Water Dynamics.

Vegetation in arid and semi-arid ecosystems often exhibits self-organized spatial patterns as a collective adaptation to water limitation. While reaction-diffusion models have successfully captured such pattern formation, the influence of individual-level traits, particularly root phenotypic plasticity, whereby plants adjust root architecture in response to environmental conditions, remains underexplored. Here, we develop a minimal reaction-diffusion framework that integrates vertical soil stratification with adaptive root conversion to explain the coexistence of multiple spatial scales commonly observed in dry-land vegetation. Building on the single-layer model of Hardenberg et al. [Phys. Rev. Lett. 87, 198101 (2001)0031-900710.1103/PhysRevLett.87.198101], we introduce a second soil layer and a unidirectional biomass conversion from shallow- to deep-rooted phenotype. Analytical and numerical analyses reveal that strong contrasts in diffusion scales, coupled with adaptive conversion, generate two coexisting Turing modes that give rise to robust multiscale vegetation structures. Shallow-rooted biomass with higher diffusivity forms broad vegetation bands, whereas deep-rooted biomass with lower diffusivity clusters at finer scales. The proposed framework provides a mechanistically transparent and ecologically grounded model for multiscale pattern formation, linking adaptive plant traits with the physics of coupled soil-water interactions.