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Complex topographies exhibit universal properties when fluvial erosion dominates landscape evolution over other geomorphological processes. Similarly, we show that the solutions of a minimalist landscape evolution model display invariant behavior as the impact of soil diffusion diminishes compared to fluvial erosion at the landscape scale, yielding complete self-similarity with respect to a dimensionless channelization index. Approaching its zero limit, soil diffusion becomes confined to a region of vanishing area and large concavity or convexity, corresponding to the locus of the ridge and valley network. We demonstrate these results using one dimensional analytical solutions and two dimensional numerical simulations, supported by real-world topographic observations. Our findings on the landscape self-similarity and the localized diffusion resemble the self-similarity of turbulent flows and the role of viscous dissipation. Topographic singularities in the vanishing diffusion limit are suggestive of shock waves and singularities observed in nonlinear complex systems. 

Abstract An overlooked phenomenon is a potential increase in the distribution and abundance of plants with the highly water-usage-efficient crassulacean acid metabolism (CAM). In the present article, we critically analyze recent research to investigate to what extent and why CAM plants may have recently expanded their range and abundance under global change. We discuss the ecophysiological and evolutionary mechanisms linked with CAM succulence and the drivers underlying potential CAM expansion, including drought, warming, and atmospheric carbon dioxide enrichment. We further map the biogeographic pattern of CAM expansion and show that some CAM plants (e.g., Cylindropuntia, Opuntia, and Agave) are expanding and encroaching within dryland landscapes worldwide. Our results collectively highlight the recent expansion of CAM plants, a trend that could be sustained under increasing aridity with climate change. We recommend that CAM expansion be evaluated in a data-model integrated framework to better understand and predict the ecological and socioeconomic consequences of CAM expansion during the Anthropocene. 

Summary Plant response to water stress involves multiple timescales. In the short term, stomatal adjustments optimize some fitness function commonly related to carbon uptake, while in the long term, traits including xylem resilience are adjusted. These optimizations are usually considered independently, the former involving stomatal aperture and the latter carbon allocation. However, short‐ and long‐term adjustments are interdependent, as ‘optimal’ in the short term depends on traits set in the longer term.An economics framework is used to optimize long‐term traits that impact short‐term stomatal behavior. Two traits analyzed here are the resilience of xylem and the resilience of nonstomatal limitations (NSLs) to photosynthesis at low‐water potentials.Results show that optimality requires xylem resilience to increase with climatic aridity. Results also suggest that the point at which xylem reach 50% conductance and the point at which NSLs reach 50% capacity are constrained to approximately a 2 : 1 linear ratio; however, this awaits further experimental verification.The model demonstrates how trait coordination arises mathematically, and it can be extended to many other traits that cross timescales. With further verification, these results could be used in plant modelling when information on plant traits is limited. 

Turbulent flows are out-of-equilibrium because the energy supply at large scales and its dissipation by viscosity at small scales create a net transfer of energy among all scales. This energy cascade is modelled by approximating the spectral energy balance with a nonlinear Fokker–Planck equation consistent with accepted phenomenological theories of turbulence. The steady-state contributions of the drift and diffusion in the corresponding Langevin equation, combined with the killing term associated with the dissipation, induce a stochastic energy transfer across wavenumbers. The fluctuation theorem is shown to describe the scale-wise statistics of forward and backward energy transfer and their connection to irreversibility and entropy production. The ensuing turbulence entropy is used to formulate an extended turbulence thermodynamics.