Emergent encoding of dispersal network topologies in spatial metapopulation models.

We address a generalization of the concept of metapopulation capacity for trees and networks acting as the template for ecological interactions. The original measure had been derived from an insightful phenomenological model and is based on the leading eigenvalue of a suitable landscape matrix. It yields a versatile predictor of metapopulation persistence through a threshold value of the eigenvalue determined by ecological features of the focal species. Here, we present an analytical solution to a fundamental microscopic model that incorporates key ingredients of metapopulation dynamics and explicitly distinguishes between individuals comprising the "settled population" and "explorers" seeking colonization. Our approach accounts for general network characteristics (in particular graph-driven directional dispersal which is known to significantly constrain many ecological estimates) and yields a generalized version of the original model, to which it reduces for particular cases. Through examples, including real landscapes used as the template, we compare the predictions from our approach with those of the standard model. Results suggest that in several cases of practical interest, differences are significant. We also examine, with both models, how changes in habitat fragmentation, including removal, addition, or alteration in size, affect metapopulation persistence. The current approach demonstrates a high level of flexibility, enabling the incorporation of diverse "microscopic" elements and their impact on the resulting biodiversity landscape pattern.

Spatially explicit effective reproduction numbers from incidence and mobility data.

Current methods for near real-time estimation of effective reproduction numbers from surveillance data overlook mobility fluxes of infectors and susceptible individuals within a spatially connected network (the metapopulation). Exchanges of infections among different communities may thus be misrepresented unless explicitly measured and accounted for in the renewal equations. Here, we first derive the equations that include spatially explicit effective reproduction numbers, ℛk(t), in an arbitrary community k. These equations embed a suitable connection matrix blending mobility among connected communities and mobility-related containment measures. Then, we propose a tool to estimate, in a Bayesian framework involving particle filtering, the values of ℛk(t) maximizing a suitable likelihood function reproducing observed patterns of infections in space and time. We validate our tools against synthetic data and apply them to real COVID-19 epidemiological records in a severely affected and carefully monitored Italian region. Differences arising between connected and disconnected reproduction numbers (the latter being calculated with existing methods, to which our formulation reduces by setting mobility to zero) suggest that current standards may be improved in their estimation of disease transmission over time.

Scaling of joint mass and metabolism fluctuations in in silico cell-laden spheroids.

Variations and fluctuations are characteristic features of biological systems and are also manifested in cell cultures. Here, we describe a computational pipeline for identifying the range of three-dimensional (3D) cell-aggregate sizes in which nonisometric scaling emerges in the presence of joint mass and metabolic rate fluctuations. The 3D cell-laden spheroids with size and single-cell metabolic rates described by probability density functions were randomly generated in silico. The distributions of the resulting metabolic rates of the spheroids were computed by modeling oxygen diffusion and reaction. Then, a method for estimating scaling exponents of correlated variables through statistically significant data collapse of joint probability distributions was developed. The method was used to identify a physiologically relevant range of spheroid sizes, where both nonisometric scaling and a minimum oxygen concentration (0.04 mol⋅m-3) is maintained. The in silico pipeline described enables the prediction of the number of experiments needed for an acceptable collapse and, thus, a consistent estimate of scaling parameters. Using the pipeline, we also show that scaling exponents may be significantly different in the presence of joint mass and metabolic-rate variations typically found in cells. Our study highlights the importance of incorporating fluctuations and variability in size and metabolic rates when estimating scaling exponents. It also suggests the need for taking into account their covariations for better understanding and interpreting experimental observations both in vitro and in vivo and brings insights for the design of more predictive and physiologically relevant in vitro models.

True scale-free networks hidden by finite size effects.

We analyze about 200 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. Specifically, we analyze by finite size scaling analysis the datasets of real networks to check whether the purported departures from power law behavior are due to the finiteness of sample size. We find that a large number of the networks follows 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 involving infrastructure and transportation but also in 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.

The Widened Pipe Model of plant hydraulic evolution.

Shaping global water and carbon cycles, plants lift water from roots to leaves through xylem conduits. The importance of xylem water conduction makes it crucial to understand how natural selection deploys conduit diameters within and across plants. Wider conduits transport more water but are likely more vulnerable to conduction-blocking gas embolisms and cost more for a plant to build, a tension necessarily shaping xylem conduit diameters along plant stems. We build on this expectation to present the Widened Pipe Model (WPM) of plant hydraulic evolution, testing it against a global dataset. The WPM predicts that xylem conduits should be narrowest at the stem tips, widening quickly before plateauing toward the stem base. This universal profile emerges from Pareto modeling of a trade-off between just two competing vectors of natural selection: one favoring rapid widening of conduits tip to base, minimizing hydraulic resistance, and another favoring slow widening of conduits, minimizing carbon cost and embolism risk. Our data spanning terrestrial plant orders, life forms, habitats, and sizes conform closely to WPM predictions. The WPM highlights carbon economy as a powerful vector of natural selection shaping plant function. It further implies that factors that cause resistance in plant conductive systems, such as conduit pit membrane resistance, should scale in exact harmony with tip-to-base conduit widening. Furthermore, the WPM implies that alterations in the environments of individual plants should lead to changes in plant height, for example, shedding terminal branches and resprouting at lower height under drier climates, thus achieving narrower and potentially more embolism-resistant conduits.

Optimal control of the spatial allocation of COVID-19 vaccines: Italy as a case study.

While campaigns of vaccination against SARS-CoV-2 are underway across the world, communities face the challenge of a fair and effective distribution of a limited supply of doses. Current vaccine allocation strategies are based on criteria such as age or risk. In the light of strong spatial heterogeneities in disease history and transmission, we explore spatial allocation strategies as a complement to existing approaches. Given the practical constraints and complex epidemiological dynamics, designing effective vaccination strategies at a country scale is an intricate task. We propose a novel optimal control framework to derive the best possible vaccine allocation for given disease transmission projections and constraints on vaccine supply and distribution logistics. As a proof-of-concept, we couple our framework with an existing spatially explicit compartmental COVID-19 model tailored to the Italian geographic and epidemiological context. We optimize the vaccine allocation on scenarios of unfolding disease transmission across the 107 provinces of Italy, from January to April 2021. For each scenario, the optimal solution significantly outperforms alternative strategies that prioritize provinces based on incidence, population distribution, or prevalence of susceptibles. Our results suggest that the complex interplay between the mobility network and the spatial heterogeneities implies highly non-trivial prioritization strategies for effective vaccination campaigns. Our work demonstrates the potential of optimal control for complex and heterogeneous epidemiological landscapes at country, and possibly global, scales.

Spread and dynamics of the COVID-19 epidemic in Italy: Effects of emergency containment measures.

The spread of coronavirus disease 2019 (COVID-19) in Italy prompted drastic measures for transmission containment. We examine the effects of these interventions, based on modeling of the unfolding epidemic. We test modeling options of the spatially explicit type, suggested by the wave of infections spreading from the initial foci to the rest of Italy. We estimate parameters of a metacommunity Susceptible-Exposed-Infected-Recovered (SEIR)-like transmission model that includes a network of 107 provinces connected by mobility at high resolution, and the critical contribution of presymptomatic and asymptomatic transmission. We estimate a generalized reproduction number ([Formula: see text] = 3.60 [3.49 to 3.84]), the spectral radius of a suitable next-generation matrix that measures the potential spread in the absence of containment interventions. The model includes the implementation of progressive restrictions after the first case confirmed in Italy (February 21, 2020) and runs until March 25, 2020. We account for uncertainty in epidemiological reporting, and time dependence of human mobility matrices and awareness-dependent exposure probabilities. We draw scenarios of different containment measures and their impact. Results suggest that the sequence of restrictions posed to mobility and human-to-human interactions have reduced transmission by 45% (42 to 49%). Averted hospitalizations are measured by running scenarios obtained by selectively relaxing the imposed restrictions and total about 200,000 individuals (as of March 25, 2020). Although a number of assumptions need to be reexamined, like age structure in social mixing patterns and in the distribution of mobility, hospitalization, and fatality, we conclude that verifiable evidence exists to support the planning of emergency measures.

Earth and field observations underpin metapopulation dynamics in complex landscapes: Near-term study on carabids.

Understanding risks to biodiversity requires predictions of the spatial distribution of species adapting to changing ecosystems and, to that end, Earth observations integrating field surveys prove essential as they provide key numbers for assessing landscape-wide biodiversity scenarios. Here, we develop, and apply to a relevant case study, a method suited to merge Earth/field observations with spatially explicit stochastic metapopulation models to study the near-term ecological dynamics of target species in complex terrains. Our framework incorporates the use of species distribution models for a reasoned estimation of the initial presence of the target species and accounts for imperfect and incomplete detection of the species presence in the study area. It also uses a metapopulation fitness function derived from Earth observation data subsuming the ecological niche of the target species. This framework is applied to contrast occupancy of two species of carabids (Pterostichus flavofemoratus, Carabus depressus) observed in the context of a large ecological monitoring program carried out within the Gran Paradiso National Park (GPNP, Italy). Results suggest that the proposed framework may indeed exploit the hallmarks of spatially explicit ecological approaches and of remote Earth observations. The model reproduces well the observed in situ data. Moreover, it projects in the near term the two species' presence both in space and in time, highlighting the features of the metapopulation dynamics of colonization and extinction, and their expected trends within verifiable timeframes.

Generalized size scaling of metabolic rates based on single-cell measurements with freshwater phytoplankton.

Kleiber's law describes the scaling of metabolic rate with body size across several orders of magnitude in size and across taxa and is widely regarded as a fundamental law in biology. The physiological origins of Kleiber's law are still debated and generalizations of the law accounting for deviations from the scaling behavior have been proposed. Most theoretical and experimental studies of Kleiber's law, however, have focused on the relationship between the average body size of a species and its mean metabolic rate, neglecting intraspecific variation of these 2 traits. Here, we propose a theoretical characterization of such variation and report on proof-of-concept experiments with freshwater phytoplankton supporting such framework. We performed joint measurements at the single-cell level of cell volume and nitrogen/carbon uptake rates, as proxies of metabolic rates, of 3 phytoplankton species using nanoscale secondary ion mass spectrometry (NanoSIMS) and stable isotope labeling. Common scaling features of the distribution of nutrient uptake rates and cell volume are found to hold across 3 orders of magnitude in cell size. Once individual measurements of cell volume and nutrient uptake rate within a species are appropriately rescaled by a function of the average cell volume within each species, we find that intraspecific distributions of cell volume and metabolic rates collapse onto a universal curve. Based on the experimental results, this work provides the building blocks for a generalized form of Kleiber's law incorporating intraspecific, correlated variations of nutrient-uptake rates and body sizes.

Range of reproduction number estimates for COVID-19 spread.

To monitor local and global COVID-19 outbreaks, and to plan containment measures, accessible and comprehensible decision-making tools need to be based on the growth rates of new confirmed infections, hospitalization or case fatality rates. Growth rates of new cases form the empirical basis for estimates of a variety of reproduction numbers, dimensionless numbers whose value, when larger than unity, describes surging infections and generally worsening epidemiological conditions. Typically, these determinations rely on noisy or incomplete data gained over limited periods of time, and on many parameters to estimate. This paper examines how estimates from data and models of time-evolving reproduction numbers of national COVID-19 infection spread change by using different techniques and assumptions. Given the importance acquired by reproduction numbers as diagnostic tools, assessing their range of possible variations obtainable from the same epidemiological data is relevant. We compute control reproduction numbers from Swiss and Italian COVID-19 time series adopting both data convolution (renewal equation) and a SEIR-type model. Within these two paradigms we run a comparative analysis of the possible inferences obtained through approximations of the distributions typically used to describe serial intervals, generation, latency and incubation times, and the delays between onset of symptoms and notification. Our results suggest that estimates of reproduction numbers under these different assumptions may show significant temporal differences, while the actual variability range of computed values is rather small.

Estimating species distribution and abundance in river networks using environmental DNA.

All organisms leave traces of DNA in their environment. This environmental DNA (eDNA) is often used to track occurrence patterns of target species. Applications are especially promising in rivers, where eDNA can integrate information about populations upstream. The dispersion of eDNA in rivers is modulated by complex processes of transport and decay through the dendritic river network, and we currently lack a method to extract quantitative information about the location and density of populations contributing to the eDNA signal. Here, we present a general framework to reconstruct the upstream distribution and abundance of a target species across a river network, based on observed eDNA concentrations and hydro-geomorphological features of the network. The model captures well the catchment-wide spatial biomass distribution of two target species: a sessile invertebrate (the bryozoan Fredericella sultana) and its parasite (the myxozoan Tetracapsuloides bryosalmonae). Our method is designed to easily integrate general biological and hydrological data and to enable spatially explicit estimates of the distribution of sessile and mobile species in fluvial ecosystems based on eDNA sampling.

Field migration rates of tidal meanders recapitulate fluvial morphodynamics.

The majority of tidal channels display marked meandering features. Despite their importance in oil-reservoir formation and tidal landscape morphology, questions remain on whether tidal-meander dynamics could be understood in terms of fluvial processes and theory. Key differences suggest otherwise, like the periodic reversal of landscape-forming tidal flows and the widely accepted empirical notion that tidal meanders are stable landscape features, in stark contrast with their migrating fluvial counterparts. On the contrary, here we show that, once properly normalized, observed migration rates of tidal and fluvial meanders are remarkably similar. Key to normalization is the role of tidal channel width that responds to the strong spatial gradients of landscape-forming flow rates and tidal prisms. We find that migration dynamics of tidal meanders agree with nonlinear theories for river meander evolution. Our results challenge the conventional view of tidal channels as stable landscape features and suggest that meandering tidal channels recapitulate many fluvial counterparts owing to large gradients of tidal prisms across meander wavelengths.

River landscapes and optimal channel networks.

We study tree structures termed optimal channel networks (OCNs) that minimize the total gravitational energy loss in the system, an exact property of steady-state landscape configurations that prove dynamically accessible and strikingly similar to natural forms. Here, we show that every OCN is a so-called natural river tree, in the sense that there exists a height function such that the flow directions are always directed along steepest descent. We also study the natural river trees in an arbitrary graph in terms of forbidden substructures, which we call k-path obstacles, and OCNs on a d-dimensional lattice, improving earlier results by determining the minimum energy up to a constant factor for every [Formula: see text] Results extend our capabilities in environmental statistical mechanics.

Covariations in ecological scaling laws fostered by community dynamics.

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 has 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 a framework is consistent with the stationary-state statistics of a broad class of resource-limited community dynamics models, regardless of parameterization 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.

Entropy and optimality in river deltas.

The form and function of river deltas is intricately linked to the evolving structure of their channel networks, which controls how effectively deltas are nourished with sediments and nutrients. Understanding the coevolution of deltaic channels and their flux organization is crucial for guiding maintenance strategies of these highly stressed systems from a range of anthropogenic activities. To date, however, a unified theory explaining how deltas self-organize to distribute water and sediment up to the shoreline remains elusive. Here, we provide evidence for an optimality principle underlying the self-organized partition of fluxes in delta channel networks. By introducing a suitable nonlocal entropy rate ([Formula: see text]) and by analyzing field and simulated deltas, we suggest that delta networks achieve configurations that maximize the diversity of water and sediment flux delivery to the shoreline. We thus suggest that prograding deltas attain dynamically accessible optima of flux distributions on their channel network topologies, thus effectively decoupling evolutionary time scales of geomorphology and hydrology. When interpreted in terms of delta resilience, high nER configurations reflect an increased ability to withstand perturbations. However, the distributive mechanism responsible for both diversifying flux delivery to the shoreline and dampening possible perturbations might lead to catastrophic events when those perturbations exceed certain intensity thresholds.

Integrated field, laboratory, and theoretical study of PKD spread in a Swiss prealpine river.

Proliferative kidney disease (PKD) is a major threat to wild and farmed salmonid populations because of its lethal effect at high water temperatures. Its causative agent, the myxozoan Tetracapsuloides bryosalmonae, has a complex lifecycle exploiting freshwater bryozoans as primary hosts and salmonids as secondary hosts. We carried out an integrated study of PKD in a prealpine Swiss river (the Wigger). During a 3-year period, data on fish abundance, disease prevalence, concentration of primary hosts' DNA in environmental samples [environmental DNA (eDNA)], hydrological variables, and water temperatures gathered at various locations within the catchment were integrated into a newly developed metacommunity model, which includes ecological and epidemiological dynamics of fish and bryozoans, connectivity effects, and hydrothermal drivers. Infection dynamics were captured well by the epidemiological model, especially with regard to the spatial prevalence patterns. PKD prevalence in the sampled sites for both young-of-the-year (YOY) and adult brown trout attained 100% at the end of summer, while seasonal population decay was higher in YOY than in adults. We introduce a method based on decay distance of eDNA signal predicting local species' density, accounting for variation in environmental drivers (such as morphology and geology). The model provides a whole-network overview of the disease prevalence. In this study, we show how spatial and environmental characteristics of river networks can be used to study epidemiology and disease dynamics of waterborne diseases.

On the probabilistic nature of the species-area relation.

The Species-Area Relation (SAR), which describes the increase in the number of species S with increasing area A, is under intense scrutiny in contemporary ecology, in particular to probe its reliability in predicting the number of species going extinct as a direct result of habitat loss. Here, we focus on the island SAR, which is measured across a set of disjoint habitat patches, and we argue that the SAR portrays an average trend around which fluctuations are to be expected due to the stochasticity of community dynamics within the patches, external perturbations, and habitat heterogeneity across different patches. This probabilistic interpretation of the SAR, though already implicit in the theory of island biogeography and manifest in the scatter of data points in plots of empirical SAR curves, has not been investigated systematically from the theoretical point of view. Here, we show that the two main contributions to SAR fluctuations, which are due to community dynamics within the patches and to habitat heterogeneity between different patches, can be decoupled and analyzed independently. To investigate the community dynamics contribution to SAR fluctuations, we explore a suite of theoretical models of community dynamics where the number of species S inhabiting a patch emerges from diverse ecological and evolutionary processes, and we compare stationary predictions for the coefficient of variation of S, i.e. the fluctuations of S with respect to the mean. We find that different community dynamics models diverge radically in their predictions. In island biogeography and in neutral frameworks, where fluctuations are only driven by the stochasticity of diversification and extinction events, relative fluctuations decay when the mean increases. Computational evidence suggests that this result is robust in the presence of competition for space or resources. When species compete for finite resources, and mass is introduced as a trait determining species' birth, death and resource consumption rates based on empirical allometric scalings, relative fluctuations do not decay with increasing mean S due to the occasional introduction of new species with large resource demands causing mass extinctions in the community. Given this observation, we also investigate the contribution of external disturbance events to fluctuations of S in neutral community dynamics models and compare this scenario with the community dynamics in undisturbed non-neutral models. Habitat heterogeneity within a single patch, in the context of metapopulation models, causes variability in the number of coexisting species which proves negligible with respect to that caused by the stochasticity of the community dynamics. The second contribution to SAR fluctuations, which is due to habitat heterogeneity among different patches, introduces corrections to the coefficient of variation of S. Most importantly, inter-patches heterogeneity introduces a constant, lower bound on the relative fluctuations of S equal to the coefficient of variation of a habitat variable describing the heterogeneity among patches. Because heterogeneity across patches is inevitably present in natural ecosystems, we expect that the relative fluctuations of S always tend to a constant in the limit of large mean S or large patch area A, with contributions from community dynamics, inter-patches heterogeneity or both. We provide a theoretical framework for modelling these two contributions and we show that both can affect significantly the fluctuations of the SAR.

Evolving biodiversity patterns in changing river networks.

Biodiversity patterns are governed by landscape structure and dispersal strategies of residing organisms. Landscape, however, changes, and dispersal strategies evolve with it. It is unclear how these biological and geomorphological changes interplay to affect biodiversity patterns. Here we develop metacommunity models that allow for dispersal evolution and implement them in river networks with different structures, mimicking the geomorphological dynamics of fluvial landscape. For a given dispersal kernel, a more compact network structure, where local communities are closer to one another, results in biodiversity patterns characteristic of a more well-mixed environment. When dispersal evolution is present, however, organisms adopt more local dispersal strategies in a more compact network, counteracting the effects of the more well-mixed environment. The combined effects lead to biodiversity patterns different from when dispersal evolution is absent. These findings underscore the importance of taking the interplay between the evolution of dispersal, landscape, and biodiversity patterns into account when studying and managing biodiversity in changing landscape.

Near real-time forecasting for cholera decision making in Haiti after Hurricane Matthew.

Computational models of cholera transmission can provide objective insights into the course of an ongoing epidemic and aid decision making on allocation of health care resources. However, models are typically designed, calibrated and interpreted post-hoc. Here, we report the efforts of a team from academia, field research and humanitarian organizations to model in near real-time the Haitian cholera outbreak after Hurricane Matthew in October 2016, to assess risk and to quantitatively estimate the efficacy of a then ongoing vaccination campaign. A rainfall-driven, spatially-explicit meta-community model of cholera transmission was coupled to a data assimilation scheme for computing short-term projections of the epidemic in near real-time. The model was used to forecast cholera incidence for the months after the passage of the hurricane (October-December 2016) and to predict the impact of a planned oral cholera vaccination campaign. Our first projection, from October 29 to December 31, predicted the highest incidence in the departments of Grande Anse and Sud, accounting for about 45% of the total cases in Haiti. The projection included a second peak in cholera incidence in early December largely driven by heavy rainfall forecasts, confirming the urgency for rapid intervention. A second projection (from November 12 to December 31) used updated rainfall forecasts to estimate that 835 cases would be averted by vaccinations in Grande Anse (90% Prediction Interval [PI] 476-1284) and 995 in Sud (90% PI 508-2043). The experience gained by this modeling effort shows that state-of-the-art computational modeling and data-assimilation methods can produce informative near real-time projections of cholera incidence. Collaboration among modelers and field epidemiologists is indispensable to gain fast access to field data and to translate model results into operational recommendations for emergency management during an outbreak. Future efforts should thus draw together multi-disciplinary teams to ensure model outputs are appropriately based, interpreted and communicated.

Geomorphic controls on elevational gradients of species richness.

Elevational gradients of biodiversity have been widely investigated, and yet a clear interpretation of the biotic and abiotic factors that determine how species richness varies with elevation is still elusive. In mountainous landscapes, habitats at different elevations are characterized by different areal extent and connectivity properties, key drivers of biodiversity, as predicted by metacommunity theory. However, most previous studies directly correlated species richness to elevational gradients of potential drivers, thus neglecting the interplay between such gradients and the environmental matrix. Here, we investigate the role of geomorphology in shaping patterns of species richness. We develop a spatially explicit zero-sum metacommunity model where species have an elevation-dependent fitness and otherwise neutral traits. Results show that ecological dynamics over complex terrains lead to the null expectation of a hump-shaped elevational gradient of species richness, a pattern widely observed empirically. Local species richness is found to be related to the landscape elevational connectivity, as quantified by a newly proposed metric that applies tools of complex network theory to measure the closeness of a site to others with similar habitat. Our theoretical results suggest clear geomorphic controls on elevational gradients of species richness and support the use of the landscape elevational connectivity as a null model for the analysis of the distribution of biodiversity.