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Bacterial communities are pivotal to maintaining ecological function and preserving the rich tapestry of biological diversity. The rapid development of environmental sequencing technologies, such as metagenomics, has revolutionized our capacity to probe such diversity. However, despite these advances, a theoretical understanding connecting empirical data with ecosystem modelling, in particular in the framework of disordered systems akin to spin glasses, is still in its infancy. Here, we present a comprehensive framework using theories of disordered systems to decode microbiome data, which offers insight into the ecological forces that shape macroecological states. By employing the quenched disordered generalized Lotka-Volterra model, we analyze species abundance data in healthy and diseased human gut microbiomes. Results reveal the emergence of two distinct patterns of species-interaction networks, elucidating the pathways through which dysbiosis may drive microbiome instability. Interaction patterns thus provide a window into the systemic shifts accompanying the transition from health to disease, offering a new perspective on the dynamics of the microbial community. Our findings suggest the potential of disordered systems theory to characterize microbiomes by capturing the essence of ecological interactions and their consequences on stability and functioning, leveraging our understanding of the linkages of dysbiosis and microbial dynamics., Comment: 10 pages, 4 figures

Metapopulation models have been instrumental in demonstrating the ecological impact of landscape structure on the survival of a focal species in complex environments. However, extensions to multiple species with arbitrary dispersal networks often rely on phenomenological assumptions limiting their scope. Here, we develop a multilayer network model of competitive dispersing metacommunities to investigate how spatially structured environments impact species coexistence and ecosystem stability. We show that homogeneous environments always lead to monodominance unless all species' fitness parameters are in an exact trade-off. However, this precise fine-tuning does not guarantee coexistence in generic heterogeneous environments. By introducing general spatial disorder in the model, we solve it exactly in the mean-field limit, finding that stable coexistence becomes possible in the presence of strong disorder. Crucially, coexistence is supported by the spontaneous localization of species through the emergence of ecological niches. Our results remain qualitatively valid in arbitrary dispersal networks, where topological features can improve species coexistence. Finally, we employ our model to study how correlated disorder promotes spatial ecological patterns in realistic terrestrial and riverine landscapes. Our work provides a novel framework to understand how landscape structure enables coexistence in metacommunities by acting as the substrate for ecological interactions., Comment: 11 pages, 4 figures

We analyze about two hundred naturally occurring networks with distinct dynamical origins to formally test whether the commonly assumed hypothesis of an underlying scale-free structure is generally viable. This has recently been questioned on the basis of statistical testing of the validity of power law distributions of network degrees by contrasting real data. Specifically, we analyze by finite-size scaling analysis the datasets of real networks to check whether purported departures from the power law behavior are due to the finiteness of the sample size. In this case, power laws would be recovered in the case of progressively larger cutoffs induced by the size of the sample. We find that a large number of the networks studied follow a finite size scaling hypothesis without any self-tuning. This is the case of biological protein interaction networks, technological computer and hyperlink networks, and informational networks in general. Marked deviations appear in other cases, especially infrastructure and transportation but also social networks. We conclude that underlying scale invariance properties of many naturally occurring networks are extant features often clouded by finite-size effects due to the nature of the sample data.

In this work, we analyze and model the cholera epidemics that affected South Sudan, the newest country in the world, during 2014 and 2015. South Sudan possibly represents one of the most difficult context in which adapt the deterministic mathematical cholera model, due to the unstable social and political situation that clearly affects the fluxes of people and the sanitary conditions, increasing the risk of large outbreaks. Despite the limitation of a static gravity model in describing the chaotic human mobility of South Sudan, the SIRB model, calibrated with a data assimilation technique (Ensemble Kalman Filter), retrieves the epidemic dynamics in the counties with the largest number of infected cases, showing the potentiality of the methodology in forecasting future outbreaks., Comment: MSc Thesis

Scaling laws in ecology, intended both as functional relationships among ecologically-relevant quantities and the probability distributions that characterize their occurrence, have long attracted the interest of empiricists and theoreticians. Empirical evidence exists of power laws associated with the number of species inhabiting an ecosystem, their abundances and traits. Although their functional form appears to be ubiquitous, empirical scaling exponents vary with ecosystem type and resource supply rate. The idea that ecological scaling laws are linked had been entertained before, but the full extent of macroecological pattern covariations, the role of the constraints imposed by finite resource supply and a comprehensive empirical verification are still unexplored. Here, we propose a theoretical scaling framework that predicts the linkages of several macroecological patterns related to species' abundances and body sizes. We show that such framework is consistent with the stationary state statistics of a broad class of resource-limited community dynamics models, regardless of parametrization and model assumptions. We verify predicted theoretical covariations by contrasting empirical data and provide testable hypotheses for yet unexplored patterns. We thus place the observed variability of ecological scaling exponents into a coherent statistical framework where patterns in ecology embed constrained fluctuations., Comment: S.Z. and A.G. contributed equally to this work

Because of increasing global urbanization and its immediate consequences, including changes in patterns of food demand, circulation and land use, the next century will witness a major increase in the extent of paved roads built worldwide. To model the effects of this increase, it is crucial to understand whether possible self-organized patterns are inherent in the global road network structure. Here, we use the largest updated database comprising all major roads on Earth, together with global urban and cropland inventories, to suggest that road length distributions within croplands are indistinguishable from urban ones, once rescaled to account for the difference in mean road length. Such similarity extends to road length distributions within urban or agricultural domains of given area. We find two distinct regimes for the scaling of the mean road length with the associated area, holding in general at small and at large values of the latter. In suitably large urban and cropland domains, we find that mean and total road lengths increase linearly with their domain area, differently from earlier suggestions. Scaling regimes suggest that simple and universal mechanisms regulate urban and cropland road expansion at the global scale. As such, our findings bear implications for global road infrastructure growth based on land-use change and for planning policies sustaining urban expansions.

Classical models of biological invasions assess species spread in homogeneous landscapes by assuming constant growth rates and random local movement. Mounting evidence suggests, however, that demographic stochasticity, environmental heterogeneity and non-random movement of individuals affect considerably the spread dynamics. Here, we show that the dynamics of biological invasions are controlled by the spatial heterogeneity of the resource distribution. We show theoretically that increasing the landscape resource autocorrelation length causes a reduction in the average speed of species spread. Demographic stochasticity plays a key role in the slowdown, which is streghtened when individuals can actively move towards resources. The reduction in the front propagation speed is verified in laboratory microcosm experiments with the flagellated protist Euglena gracilis by comparing spread in habitats characterized by different resource heterogeneity. Our theoretical and experimental findings highlight the need to account for the intrinsic stochasticity of population dynamics to describe spread in spatially extended landscapes, which are inevitably characterized by heterogeneous spatial distributions of resources controlling vital rates. Our work identifies the resource autocorrelation length as a key modulator and a simple measure of landscape susceptibility to biological invasions, with implications for predicting the characters of biological invasions within naturally heterogeneous environmental corridors.

We explore connections between surficial deltaic processes (e.g. avulsion, deposition) and the stratigraphic record using a simple numerical model of delta-plain evolution, with the aim of constraining these connections and thus improving prediction of subsurface features. The model represents channel dynamics using a simple but flexible cellular approach, and is unique in that it explicitly includes backwater effects that are known to be important in low-gradient channel networks. The patterns of channel deposits in the stratigraphic record vary spatially due to variation in avulsion statistics with radial distance from the delta's source of water and sediment. We introduce channel residence time as an important statistical measure of the surface channel kinematics. The model suggests that the mean channel residence time anywhere within the delta is nicely described by a power law distribution showing a cutoff that depends on radial distance. Thicknesses of channel deposits are not uniquely determined by the residence time of channelization. The channel residence time distributions at given radial distances from the source are found to be approximately lognormally distributed, a finding consistent with the scale-dependent radial structure of channel deposits in the stratigraphic record., Comment: 31 pages, 9 figures

Taylor's law (TL) states that the variance $V$ of a non-negative random variable is a power function of its mean $M$, i.e. $V=a M^b$. The ubiquitous empirical verification of TL, typically displaying sample exponents $b \simeq 2$, suggests a context-independent mechanism. However, theoretical studies of population dynamics predict a broad range of values of $b$. Here, we explain this apparent contradiction by using large deviations theory to derive a generalized TL in terms of sample and populations exponents $b_{jk}$ for the scaling of the $k$-th vs the $j$-th cumulant (conventional TL is recovered for $b=b_{12}$), with the sample exponent found to depend predictably on the number of observed samples. Thus, for finite numbers of observations one observes sample exponents $b_{jk}\simeq k/j$ (thus $b\simeq2$) independently of population exponents. Empirical analyses on two datasets support our theoretical results., Comment: 41 pages, 10 figures, 6 tables

The motility of microorganisms in liquid media is an important issue in active matter and it is not yet fully understood. Previous theoretical approaches dealing with the microscopic description of microbial movement have modeled the propelling force exerted by the organism as a Gaussian white noise term in the equation of motion. We present experimental results for ciliates of the genus Colpidium, which do not agree with the Gaussian white noise hypothesis. We propose a new stochastic model that goes beyond such assumption and displays good agreement with the experimental statistics of motion, such as velocity distribution and velocity autocorrelation.

Population growth is in general constrained by food production, which in turn depends on the access to water resources. At a country level, some populations use more water than they control because of their ability to import food and the virtual water required for its production. Here, we investigate the dependence of demographic growth on available water resources for exporting and importing nations. By quantifying the carrying capacity of nations based on calculations of the virtual water available through the food trade network, we point to the existence of a global water unbalance. We suggest that current export rates will not be maintained and consequently we question the long-run sustainability of the food trade system as a whole. Water rich regions are likely to soon reduce the amount of virtual water they export, thus leaving import-dependent regions without enough water to sustain their populations. We also investigate the potential impact of possible scenarios that might mitigate these effects through (1) cooperative interactions among nations whereby water rich countries maintain a tiny fraction of their food production available for export; (2) changes in consumption patterns; and (3) a positive feedback between demographic growth and technological innovations. We find that these strategies may indeed reduce the vulnerability of water-controlled societies., Comment: 11 pages, 3 figures

We present novel analytical results about ecosystem species diversity that stem from a proposed coarse grained neutral model based on birth-death processes. The relevance of the problem lies in the urgency for understanding and synthesizing both theoretical results of ecological neutral theory and empirical evidence on species diversity preservation. Neutral model of biodiversity deals with ecosystems in the same trophic level where per-capita vital rates are assumed to be species-independent. Close-form analytical solutions for neutral theory are obtained within a coarse-grained model, where the only input is the species persistence time distribution. Our results pertain: the probability distribution function of the number of species in the ecosystem both in transient and stationary states; the n-points connected time correlation function; and the survival probability, definned as the distribution of time-spans to local extinction for a species randomly sampled from the community. Analytical predictions are also tested on empirical data from a estuarine fish ecosystem. We find that emerging properties of the ecosystem are very robust and do not depend on specific details of the model, with implications on biodiversity and conservation biology., Comment: 20 pages, 4 figures. To appear in Journal of Statistichal Mechanics

Natural ecosystems are characterized by striking diversity of form and functions and yet exhibit deep symmetries emerging across scales of space, time and organizational complexity. Species-area relationships and species-abundance distributions are examples of emerging patterns irrespective of the details of the underlying ecosystem functions. Here we present empirical and theoretical evidence for a new macroecological pattern related to the distributions of local species persistence times, defined as the timespans between local colonizations and extinctions in a given geographic region. Empirical distributions pertaining to two different taxa, breeding birds and herbaceous plants, analyzed in a new framework that accounts for the finiteness of the observational period, exhibit power-law scaling limited by a cut-off determined by the rate of emergence of new species. In spite of the differences between taxa and spatial scales of analysis, the scaling exponents are statistically indistinguishable from each other and significantly different from those predicted by existing models. We theoretically investigate how the scaling features depend on the structure of the spatial interaction network and show that the empirical scaling exponents are reproduced once a two-dimensional isotropic texture is used, regardless of the details of the ecological interactions. The framework developed here also allows to link the cut-off timescale with the spatial scale of analysis, and the persistence-time distribution to the species-area relationship. We conclude that the inherent coherence obtained between spatial and temporal macroecological patterns points at a seemingly general feature of the dynamical evolution of ecosystems., Comment: 5 pages, 5 figures. Supplementary materials avaliable on http://www.pnas.org/content/108/11/4346

Generalized Langevin equations (GLE) with multiplicative white Poisson noise pose the usual prescription dilemma leading to different evolution equations (master equations) for the probability distribution. Contrary to the case of multiplicative gaussian white noise, the Stratonovich prescription does not correspond to the well known mid-point (or any other intermediate) prescription. By introducing an inertial term in the GLE we show that the Ito and Stratonovich prescriptions naturally arise depending on two time scales, the one induced by the inertial term and the other determined by the jump event. We also show that when the multiplicative noise is linear in the random variable one prescription can be made equivalent to the other by a suitable transformation in the jump probability distribution. We apply these results to a recently proposed stochastic model describing the dynamics of primary soil salinization, in which the salt mass balance within the soil root zone requires the analysis of different prescriptions arising from the resulting stochastic differential equation forced by multiplicative white Poisson noise whose features are tailored to the characters of the daily precipitation. A method is finally suggested to infer the most appropriate prescription from the data.

Transportation networks are inevitably selected with reference to their global cost which depends on the strengths and the distribution of the embedded currents. We prove that optimal current distributions for a uniformly injected d-dimensional network exhibit robust scale-invariance properties, independently of the particular cost function considered, as long as it is convex. We find that, in the limit of large currents, the distribution decays as a power law with an exponent equal to (2d-1)/(d-1). The current distribution can be exactly calculated in d=2 for all values of the current. Numerical simulations further suggest that the scaling properties remain unchanged for both random injections and by randomizing the convex cost functions., Comment: 5 pages, 5 figures