RIVER NETWORKS AS ECOLOGICAL CORRIDORS: MIGRATION FRONTS,
HYDROCHORY, SPREADING OF WATER-BORNE INFECTIONS
ANDREA RINALDO
Dipartimento IMAGE & International Centre for Hydrology “Dino Tonini”, Università di
Padova, Italy
The Lecture first recalls empirical and theoretical evidence on the structure of river basins, emphasizing
intertwined form and function of such complex adaptive systems [e.g. Rodriguez-Iturbe and Rinaldo,
1997]. Of some importance is arguably the claim, which will be put forward in the Lecture, that river
basins constitute one of the most reliable and fascinating laboratories for the observation of how Nature
works across a wide range of scales. Specific applications discussed in the talk deal with transport
through fractal networks and the transport of matter, species, polupations and infections at basin-scales.
Moving from a recent quantitative model of the US colonization in the 19th century that relies on
analytical and numerical results of reactive-diffusive transport on fractal river networks [Campos et al.,
2006], I shall consider its generalization to include an embedded flow direction which biases transport
[Bertuzzo et al., 2007a] and explore the properties of biased reaction-dispersal models, in which the
reaction rates are described by a logistic equation. The relevance of the work is related to the prediction
of the role of hydrologic controls on invasion processes (of species, populations, propagules or infective
agents, depending on the specifics of reaction and transport) occurring in river basins. Exact solutions
are described along with general numerical solutions, which are applied to fractal constructs like Peano
basins and real rivers. Similarities and departures from different one-dimensional invasion models
where a bias is added to both the diffusion [Bertuzzo et al., 2007a] and the telegraph equations
[Holmes, 1993], considering their respective ecological insight. It is found that the geometrical
constraints imposed by the fractal networks imply strong corrections on the speed of travelling fronts
that can be enhanced or smoothed by the bias. Applications to real river networks show that the chief
morphological parameters affecting the front speed are those characterizing the node-to-node distances
measured along the network structure. The spatial density and number of reactive sites thus prove to be
a vital hydrologic control on invasions. Such solutions are claimed to be relevant to the general study of
species' spreading along ecological corridors defined by the river network structure.
Ecological implications of the distribution of tributaries relate to the availability of flow, slope and riparian
area available in defining an ecological corridor [Bertuzzo et al., 2007a; Banavar et al., 2007;
Muneepeerakul et al., 2007b]. Riparian zones, in fact, play many important roles in regulating
ecosystem function within streams, surrounding environments, and upland areas. They are usually
related to the stream width or to topographically concave areas, features that inevitably relate to
landscape-forming discharges and hence to the distribution of tributary areas. Spreading of species or
infections on river networks also requires flow specifications defining, for instance, the bias affecting
dispersion of water-borne agents or propagules. Moreover, although models of biodiversity in twodimensional landscapes had been extensively studied [e.g. Tilman and Downing, 1994; Hubbell, 2001],
only recently Muneepeerakul et al. [2007a] have shown that the combined effects of directionality of
dispersal produced by the network landscape significantly alter various biodiversity patterns of
vegetation communities obeying the neutral model. Be it metapopulation models coupled with the
strictly hierarchical competition-colonization trade-off model to study the resulting biodiversity patterns in
the river basin [Muneepeerakul et al., 2007b], or patterns of infection or migration spreading [Bertuzzo
et al., 2007b], it is clear the fundamental role played by the network substrate and of its properties on
several ecological processes. About the purported connection with riverine ecology, the Lecture shall
briefly discuss the distribution of distances between tributaries of given size, which recently found
general expression [Convertino et al., 2007]. It defines analytically the distribution of the distance of
mean flowrates, channel width or riparian areas alongstream because all such quantitites are, in fact,
proxies of cumulative basin area, and hence of tributaries' contributing area.
The Lecture finally reports on how river networks, acting as environmental corridors for pathogens,
affect the spreading of cholera epidemics [Bertuzzo et al., 2007b]. Specifically, I shall compare
epidemiological data from the real world with the space-time evolution of infected individuals predicted
by a theoretical scheme based on reactive transport of infective agents through a biased network
portraying actual river pathways. The data pertain to a cholera outbreak in South Africa which started in
2000 and affected in particular the Kwazulu-Natal province. The epidemic lasted for two years and
involved about 140,000 confirmed cholera cases. Physical and other epidemiological data have also
been carefully considered. The theoretical tools relate to recent advances in hydrochory, migration
fronts and infection spreading, and are novel in that nodal reactions describe the dynamics of cholera.
Reactions are, in fact, confined to nodes and transport through network links provides the coupling of
the nodal dynamics of infected, who are assumed to reside at the nodes. This proves a realistic
scheme. The theoretical scheme is remarkably capable of predicting actual outbreaks, and indeed that
network structures play a controlling role in the actual, rather anisotropic propagation of infections, in
analogy to spreading of species or migration processes that also use rivers as ecological corridors.
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