This chapter provides an outlook of the issues, born out of the material presented in the book, that will likely be at the center of future developments of the field.They are organized following the scheme set by the preceding chapters.

This chapter illustrates the implications of river network structure for the spread of waterborne diseases. Human mobility is also added as a driver and a network of interaction. The water-related (WR) diseases considered are epidemic cholera, endemic schistosomiasis, and proliferative kidney disease in fish. After reviewing the basic (space-implicit) epidemiological models for micro- and micro-parasites, general space-explicit models for both kinds of parasites are studied. Both the hydrologic and the human mobility network are included, and the general conditions for disease establishment are derived, including also the case of seasonal forcings. Conditions for transient (though possibly large) epidemics are also found. The microparasitic model is applied to several cholera epidemics, including the one that has been devastating Haiti. Spatially explicit macroparasitic models of schistosomiasis are then analyzed and applied to the cases of Senegal and Burkina Faso. Proliferative kidney disease (PKD) in salmonid fish, a pathology linked to global warming, is modeled. The space-explicit approach is used for the study of PKD spread in the basin of the river Wigger (Switzerland).

Three separate appendices, rather technical, compose this chapter. The first deals with the stability of dynamical systems and bifurcation analysis, the second with a background and rationale for optimal channel networks. The third deals with computational tools: Matlab code is explained and run, and results are highlighted. The source codes may be downloaded at www.epfl.ch/labs/echo/.

The chapter explores the problem of species spread in river systems. It introduces the basic quantitative tools for dealing with the topic: first advection-diffusion-reaction traditional equations, then more modern approaches via interacting particle systems and reaction random walks on graphs. The Mississippi-Missouri river system is once again taken as the epitomizing river network: the dramatic invasion of the zebra mussel (Dreissena polymorpha), seeded by the accidental discharge of ballast water from European cargo ships in the Great Lakes region, is studied via a multilayer network model, including not only hydrology but also the displacement due to anthropic activity. Advanced laboratory experiments are then described and modeled in which the response of the alga Euglena gracilis when exposed to controlled light fields is analyzed. This allows insight into the problem of how spatial resource availability shapes the invasion patterns of riverine populations. Finally, a thorough analysis of mixing and dispersion in river systems is the basic tool to tackle a problem of enormous interest, namely, estimating species distribution and abundance using environmental DNA.

The introductory chapter outlines the leit-motiv of the book – dendritic substrates for ecological interactions, chief and foremost river networks in our case, bear important consequences for a number of processes, from patterns of biodiversity to controls of spreading of waterborne disease. In this chapter we discuss important methodological aspects of spatially explicit ecology that are used throughout the book.

The chapter is not a complete review of the subject but rather contains a specific choice of topics relevant to the general concepts of biodiversity in river networks. It first explores the fish diversity of the Mississippi-Missouri river system via a hierarchical metacommunity model that includes river hydrology and habitat suitability. Illustrated is the role of the frequency distribution of shear stresses in determining the spatially explicit probability distribution functions of benthic invertebrate habitat suitability. The viewpoint is then broadened by addressing general metapopulation persistence in river networks; this is achieved by analyzing stage-structured populations that exploit different dispersal pathways, both alongstream and overland. Examples are given with reference to amphibians. Gradients of biodiversity in fluvial landscapes, as determined by changes in elevation, is the next topic. The characteristic features of hump-shaped patterns of species richness along elevational gradients are derived, using both idealized (but realistic) fluvial landscapes and real landscapes of the Swiss Alps. The approach allows also the outline of possible consequences of climate change.

This chapter explores the dependence of plant carbon assimilation on soil moisture. Since the soil–plant–atmosphere dynamics involves different time scales, from the hourly dynamics of stomatal control and transpiration, to the daily-to-seasonal time scales of soil moisture and plant growth dynamics, a temporal upscaling is essential to understand how the short time scale processes actually control the long-term dynamics of the water and carbon fluxes and the related evolution of ecosystems.

The analysis starts at the hourly time scale by coupling the equations of the soil–plant–atmosphere continuum (SPAC) to a parsimonious model of the atmospheric boundary layer, to investigate the role of soil, plant, and boundary layer characteristics on the diurnal courses of soil moisture, transpiration, and carbon assimilation during interstorm periods. The temporal evolution of such variables is then integrated at the daily time scale, yielding very similar results to the empirical relationships used in the previous chapters to relate these variables. Finally, the daily leaf carbon assimilation is coupled to the stochastic soil moisture model of Chapter 2, to obtain a probabilistic description of the carbon assimilation during a growing season. The analysis of the duration and frequency of periods with impaired assimilation provides a measure of plant water stress as a function of the soil, vegetation, and climate characteristics that is in good agreement with (and partly complements) the dynamic water stress defined in Chapter 4.

The aim of this chapter is to provide the bases for the temporal upscaling of the transpiration/assimilation dynamics and then proceed with their stochastic analysis at the daily time scale. For this reason the modeling of the SPAC is simplified to only retain its essential dynamical features.

The reduction of soil moisture content during droughts lowers the plant water potential and leads to a decrease in transpiration. This in turn causes a reduction of cell turgor and relative water content in plants, which brings about a sequence of damages of increasing seriousness. After a discussion of the links between soil moisture and plant conditions, the mean crossing properties of soil moisture, analytically derived in Chapter 3, are used here to define an index of plant water stress that combines the intensity, duration, and frequency of periods of soil-water deficit. Plant water stress is then studied under different climatic conditions, to analyze how the interplay between plant, soil, and environment impacts on vegetation conditions. The analysis of plant water stress presented in this chapter closely follows the paper by Porporato et al. (2001).

Soil-water deficit and plant water stress

From the level of the single plant to that of the entire ecosystem, the action of climate, soil, and vegetation is linked to plant response by two fundamental processes: the first one is centered around the soil moisture dynamics and controls the intensity and duration of the periods of soil-water deficit, while the second one regulates the impacts of water deficit on plant physiology (Figure 4.1).

Since plants get their water from the soil, many of the impacts of climate and soil are felt by plants through the filter of soil moisture dynamics. Effective drought conditions for plants are determined by soil moisture availability and not necessarily by precipitation scarcity (Stephenson, 1990, 1998).

Throughout the book we have described various ways in which plants respond to hydrologic forcing: in this last chapter, these elements are put together to analyze the role of hydrologic variability on the space–time ecosystem structure. Vegetation has been observed to exhibit a degree of spatial organization in a number of ecosystems, including rainforests (Sole and Manrubia, 1995), semi-arid grasslands (Milne, 1992), temperate forests (Mladenoff et al.,1993), and savannas (Couteron and Kokou, 1997; Scholes and Archer, 1997; see also Figure 1.10). The emergence of these organized patterns is attributable to a range of temporal and spatial variations in the interaction among species, localized dispersal abilities, and disturbance regimes as well as in the climate and soil characteristics.

Understanding the temporal and spatial patterns of vegetation in semi-arid ecosystems is perhaps one of the most fascinating aspects of ecohydrology. It is a rapidly evolving topic in which a great deal of research is currently being done. As a consequence, what follows is not to be intended as an exhaustive review of the subject, but rather as a discussion of results arising from simplified models with the same explorative spirit of the previous chapters. We just mention other studies that, though not directly dealing with fluctuating hydrologic conditions, might be of interest here (e.g., Klausmeier, 1999; Hellerislambers et al., 2001; Rietkerk et al., 2002; and references therein). Many of these studies have proposed models in which the pattern-forming component is an activation-inhibition mechanism that generates a Turing-type of instability (e.g., Murray, 1989).

This chapter focuses on the role of the spatial dimension in the dynamics of water balance, with special emphasis on vegetation response and the resulting feedbacks. In fact, notwithstanding the importance of the results obtained in the preceding chapters for the spatially lumped description of soil moisture, there are important cases in which the lateral and vertical fluxes of soil moisture may become essential in the water balance of a site.

The first part of the chapter will discuss the role of the vertical dimension in soil moisture dynamics. Historically, this issue has been the focus of much attention in the ecohydrology context, especially in connection with the vertical partitioning of the water available to vegetation. The well-known Walter hypothesis for tree–grass coexistence in savannas (Walter, 1971; Eagleson and Segarra, 1985) has perhaps contributed to overemphasize the role played by the vertical dimension in soil moisture dynamics on vegetation patterns (see Scholes and Walker, 1993; and also Chapter 11). Although some climate and soil combinations may indeed enhance the importance of the vertical dimension (e.g., as in the case of the Patagonia steppe or the shrublands of Arizona; Burgess, 1995; Paruelo and Sala, 1995; Golluscio et al., 1998), its relevance at the daily and seasonal time scale is usually less dramatic than at the hourly time scale, so that vertically integrated models of soil moisture dynamics can often provide an accurate enough description in what concerns plant stress and ecosystem function. Likewise, the interaction of the active soil layer with the water table is of secondary importance in most water-controlled ecosystems, unless strong topographic gradients or plants with very deep tap roots (phreatotypes) are present.