Self-Organization and Complex Networks

In this chapter we discuss how the results developed within the theory of fractals and Self-Organized Criticality (SOC) can be fruitfully exploited as ingredients of adaptive network models. In order to maintain the presentation self-contained, we first review the basic ideas behind fractal theory and SOC. We then briefly review some results in the field of complex networks, and some of the models that have been proposed. Finally, we present a self-organized model recently proposed by Garlaschelli et al. [Nat. Phys. 3, 813 (2007)] that couples the fitness network model defined by Caldarelli et al. [Phys. Rev. Lett. 89, 258702 (2002)] with the evolution model proposed by Bak and Sneppen [Phys. Rev. Lett. 71, 4083 (1993)] as a prototype of SOC. Remarkably, we show that the results obtained for the two models separately change dramatically when they are coupled together. This indicates that self-organized networks may represent an entirely novel class of complex systems, whose properties cannot be straightforwardly understood in terms of what we have learnt so far.Comment: Book chapter in "Adaptive Networks: Theory, Models and Applications", Editors: Thilo Gross and Hiroki Sayama (Springer/NECSI Studies on Complexity Series

On the importance of accurate depiction of infiltration processes on modelled soil moisture and vegetation water stress

The description of soil moisture dynamics is a challenging problem for the hydrological community, as it is governed by complex interactions between climate, soil and vegetation. Recent research has achieved significant advances in the description of temporal dynamics of soil water balance through the use of a stochastic differential equation proposed by Laio et al. (2001). The assumptions of the Laio et al. model simplify the mathematical form of the soil water loss functions and the infiltration process. In particular, runoff occurs only for saturation excess, the probability distribution function (PDF) of which is well-represented by a simple expression, but the model does not consider the limited infiltration capacity of soil. In the present work, we extend the soil moisture model to include limitations on soil infiltration capacity with the aim of understanding the impact of varying infiltration processes on the soil water balance and vegetation stress. A comparison between the two models (the original version and the modified one) is carried out via numerical simulations. The limited infiltration capacity influences the soil moisture PDF by reducing its mean and variance. Major changes in the PDFs are found for climates characterized by storms of short duration and high rainfall intensity, as well as in humid climates and in cases where soils have moderate permeability (e.g. loam and clay soils). In the case of limited infiltration capacity, modifications to the dynamics of soil moisture generally lead to higher amounts of vegetation water stress. An investigation of the role of soil texture on vegetation water stress demonstrates that loam soil provides the most favorable condition for plant-growth under arid and semi-arid conditions, while vegetation may benefit from the presence of more permeable soils (e.g. loamy sand) in humid climates

Il ruolo dell’esposizione e della pendenza dei versanti sullo stress idrico della vegetazione

Il presente lavoro si pone l’obiettivo di descrivere gli effetti della morfologia sulle dinamiche di imbibizione del suolo, sull’evapotraspirazione e sullo stato della vegetazione. Questi processi sono strettamente collegati tra loro e influenzati dal bilancio radiativo al suolo. La radiazione solare, infatti, che dipende dalle condizioni climatiche e dalla morfologia, può sensibilmente modificare i processi idrologici alla scala locale. Nel presente lavoro si è fatto ricorso all’approccio proposto da Allen et al. (2006) che consente di descrivere il bilancio radiativo tenendo conto degli effetti dell’esposizione e pendenza dei versanti. Ciò è estremamente utile per descrivere la distribuzione spaziale della radiazione solare e dell’evapotraspirazione potenziale che condiziona le dinamiche di umidità del suolo così come lo stress idrico della vegetazione durante la stagione vegetativa. Le analisi sono state condotte sul bacino Rio Salado (New Mexico-USA) definendo lo stresso idrico della vegetazione attraverso il modello proposto da Porporato et al. (2001). Le analisi hanno evidenziato che la morfologia del bacino influisce in maniera significativa sulla distribuzione spaziale dello stress idrico favorendo una diversità nella composizione della vegetazione. Questa variabilità è condizionata in modo marcato dalle condizioni iniziali del suolo legate al periodo dormiente della vegetazione in cui si osservano maggiori differenze nel bilancio radiativo

Vegetation structure characteristics and relationships of Kalahari woodlands and savannas

The Kalahari Transect is one of several International Geosphere–Biosphere Programme (IGBP) transects designed to address global change questions at the regional scale, in particular by exploiting natural parameter gradients (Koch et al., 1995). In March 2000, we collected near-synoptic vegetation structural data at five sites spanning the Kalahari's large precipitation gradient (about 300–1000 mm yr?1) from southern Botswana (?24°S) to Zambia (?15°S). All sites were within the expansive Kalahari sandsheet. Common parameters, including plant area index (PAI), leaf area index (LAI) and canopy cover (CC), were measured or derived using several indirect instruments and at multiple spatial scales. Results show that CC and PAI increase with increasing mean annual precipitation. Canopy clumping, defined by the deviation of the gap size distribution from that of randomly distributed foliage, was fairly constant along the gradient. We provide empirical relationships relating these parameters to each other and to precipitation. These results, combined with those in companion Kalahari Transect studies, provide a unique and coherent test bed for ecological modeling. The data may be used to parameterize process models, as well as test internally predicted parameters and their variability in response to well-characterized climatological differences.<br/

Understanding the role of ecohydrological feedbacks in ecosystem state change in drylands

Ecohydrological feedbacks are likely to be critical for understanding the mechanisms by which changes in exogenous forces result in ecosystem state change. We propose that in drylands, the dynamics of ecosystem state change are determined by changes in the type (stabilizing vs amplifying) and strength of ecohydrological feedbacks following a change in exogenous forces. Using a selection of five case studies from drylands, we explore the characteristics of ecohydrological feedbacks and resulting dynamics of ecosystem state change. We surmise that stabilizing feedbacks are critical for the provision of plant-essential resources in drylands. Exogenous forces that break these stabilizing feedbacks can alter the state of the system, although such changes are potentially reversible if strong amplifying ecohydrological feedbacks do not develop. The case studies indicate that if amplifying ecohydrological feedbacks do develop, they are typically associated with abiotic processes such as runoff, erosion (by wind and water), and fire. These amplifying ecohydrological feedbacks progressively modify the system in ways that are long-lasting and possibly irreversible on human timescales