On species persistence-time distributions.

We present new theoretical and empirical results on the probability distributions of species persistence times in natural ecosystems. Persistence times, defined as the timespans occurring between species' colonization and local extinction in a given geographic region, are empirically estimated from local observations of species' presence/absence. A connected sampling problem is presented, generalized and solved analytically. Species persistence is shown to provide a direct connection with key spatial macroecological patterns like species-area and endemics-area relationships. Our empirical analysis pertains to two different ecosystems and taxa: a herbaceous plant community and a estuarine fish database. Despite the substantial differences in ecological interactions and spatial scales, we confirm earlier evidence on the general properties of the scaling of persistence times, including the predicted effects of the structure of the spatial interaction network. The framework tested here allows to investigate directly nature and extent of spatial effects in the context of ecosystem dynamics. The notable coherence between spatial and temporal macroecological patterns, theoretically derived and empirically verified, is suggested to underlie general features of the dynamic evolution of ecosystems.

The role of aquatic reservoir fluctuations in long-term cholera patterns.

We propose and analyze an important extension of standard cholera epidemiological models, explicitly accounting for fluctuations of water availability to the human community under study. The seasonality of water input in the reservoir drives the variation of concentration of Vibrio cholerae. Two compartments are added to the Susceptible-Infected-Bacteria model. First, the recovered individuals, which, over many seasons, lose their immunity to the disease and replenish the Susceptible group. Second, the water volume of the reservoir, which determines bacterial dilution and, consequently, the probability of contracting cholera by ingesting contaminated water. By forcing the model with a seasonally varying hydrologic input, we obtain simulations that can be compared to available data for various regions of the World characterized by different hydrological and epidemiological regimes. The model is shown to satisfactorily reproduce important characteristics of disease insurgence and long-term persistence. Using bifurcation analysis of nonlinear systems, we also explore how different degrees of seasonality and values of the basic reproductive number can change the expected long-term epidemiological time series. We find that there exist parametric conditions where the model shows chaotic patterns - i.e. high unpredictability especially in the amplitude of prevalence peaks - which very much resemble actual data on long-term cholera insurgence.

Modelling cholera epidemics: the role of waterways, human mobility and sanitation.

We investigate the role of human mobility as a driver for long-range spreading of cholera infections, which primarily propagate through hydrologically controlled ecological corridors. Our aim is to build a spatially explicit model of a disease epidemic, which is relevant to both social and scientific issues. We present a two-layer network model that accounts for the interplay between epidemiological dynamics, hydrological transport and long-distance dissemination of the pathogen Vibrio cholerae owing to host movement, described here by means of a gravity-model approach. We test our model against epidemiological data recorded during the extensive cholera outbreak occurred in the KwaZulu-Natal province of South Africa during 2000-2001. We show that long-range human movement is fundamental in quantifying otherwise unexplained inter-catchment transport of V. cholerae, thus playing a key role in the formation of regional patterns of cholera epidemics. We also show quantitatively how heterogeneously distributed drinking water supplies and sanitation conditions may affect large-scale cholera transmission, and analyse the effects of different sanitation policies.

On spatially explicit models of cholera epidemics.

We generalize a recently proposed model for cholera epidemics that accounts for local communities of susceptibles and infectives in a spatially explicit arrangement of nodes linked by networks having different topologies. The vehicle of infection (Vibrio cholerae) is transported through the network links that are thought of as hydrological connections among susceptible communities. The mathematical tools used are borrowed from general schemes of reactive transport on river networks acting as the environmental matrix for the circulation and mixing of waterborne pathogens. Using the diffusion approximation, we analytically derive the speed of propagation for travelling fronts of epidemics on regular lattices (either one-dimensional or two-dimensional) endowed with uniform population density. Power laws are found that relate the propagation speed to the diffusion coefficient and the basic reproduction number. We numerically obtain the related, slower speed of epidemic spreading for more complex, yet realistic river structures such as Peano networks and optimal channel networks. The analysis of the limit case of uniformly distributed population sizes proves instrumental in establishing the overall conditions for the relevance of spatially explicit models. To that extent, the ratio between spreading and disease outbreak time scales proves the crucial parameter. The relevance of our results lies in the major differences potentially arising between the predictions of spatially explicit models and traditional compartmental models of the susceptible-infected-recovered (SIR)-like type. Our results suggest that in many cases of real-life epidemiological interest, time scales of disease dynamics may trigger outbreaks that significantly depart from the predictions of compartmental models.

Inferring plant ecosystem organization from species occurrences.

In this paper, we present an approach capable of extracting insights on ecosystem organization from merely occurrence (presence/absence) data. We extrapolate to the collective behavior by encapsulating some simplifying assumptions within a given set of constraints, and then examine their ecological implications. We show that by using the mean occurrence and co-occurrence of species as constraints, one is able to capture detailed statistics of a plant community distributed across a vast semiarid area of the United States. The approach allows us to quantify the species' effective couplings: Their frequencies exhibit a peak at zero and the minimal pairwise model is able to capture about 80% of the ecosystem structure. Our analysis reveals a relatively stronger impact of the species network on uncommon species and underscores the importance of species pairs experiencing positive couplings. Additionally, we study the associations among species and, interestingly, find that the frequencies of groups of different species, which the approach is able to capture, exhibit a power-law-like distribution.

Hydrologic dynamics and ecosystem structure.

Ecohydrology is the science that studies the mutual interaction between the hydrological cycle and ecosystems. Such an interaction is especially intense in water-controlled ecosystems, where water may be a limiting factor, not only because of its scarcity, but also because of its intermittent and unpredictable appearance. Hydrologic dynamics is shown to be a crucial factor for ecological patterns and processes. The probabilistic structure of soil moisture in time and space is presented as the key linkage between soil, climate and vegetation dynamics. Nutrient cycles, vegetation coexistence and plant response to environmental conditions are all intimately linked to the stochastic fluctuation of the hydrologic inputs driving an ecosystem.

Mean first passage times of processes driven by white shot noise.

We consider mean first passage times in systems driven by white shot noise with exponentially distributed jump heights. Simple interpretable results are obtained and the linkage between those results and the steady-state probability density function of the process is presented. The virtual waiting-time or Takács process (constant losses) and the shot noise process with linear losses are analyzed in depth, along with a more complex process with useful implications for the modeling of the soil moisture dynamics in hydrology.