Ecohydrological Footprints: Quantitative Response of Ecosystems to Changes in their Hydrological Drivers

Ecohydrological footprints are defined as the response of ecosystem functions or services to changes in their hydrologic drivers. In this thesis, several diverse footprints are addressed: noise-driven effects on storage-discharge relations and catchment streamflow distributions, that are important drivers of biodiversity; soil salinization and its ecohydrological implications; topological effects of the ecological interaction networks on living communities (e.g. on their species persistence); and form and function of the global virtual water trade network. The coherence of the conceptual framework is provided by the study of drivers and controls of ecohydrological variability using methodological approaches based on statistical mechanics. In fact, this thesis work outlines a significant portion of environmental statistical mechanics, an overarching discipline that is emerging in recent years, which applies mathematical tools from statistical mechanics to model several ecohydrological processes. The proposed relevance of this thesis lies in the major effects of hydrologic drivers on ecological process. The view that emerges from current research in ecohydrology, that this thesis supports, is that there exists a definite need for an integrated understanding of ecological and hydrological processes. Because stochasticity is intrinsic to environmental and ecohydrological variability, noise plays an important and constructive role in ecohydrological processes. In this thesis, a stochastic approach is applied to analyze different ecohydrological processes, ranging from green and blue water flows in river basins (part I), ecosystem dynamics affected by the directional dispersal provided by river networks (part II) to water footprints of human society (part III).Methods range from novel exact solutions to stochastic differential equations to random graph theory applications, and imply the analysis of suitable field data. An analytical framework for quantitative analysis is laid out to tackle complex problems and to estimate the effects of environmental change on the interaction of the hydrologic processes with the biota. The main results of this thesis are: i) the achievement of exact solutions for the probability distribution of catchment streamflow, that takes in account stochastic fluctuations in the storage-discharge relation and for the condition of a noise induced phenomena to the streamflows regimes; ii) the stationary solutions of soil salinity under stochastic hydrologic forcing; iii) a novel solution of the Ito-Stratonovich problem in multiplicative Poisson processes; iv) the proper framework for species' persistence time distributions, as a function of topological constraints on the ecosystem, and its connection with other important macroecological laws. A related length-bias sampling problem is also solved. v) A statistical analysis of the global virtual trade network and a semi-analytical model that is able to describe most of the observed properties.

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