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Biogeographical studies have traditionally focused on readily visible organisms, but recent technological advances are enabling analyses of the large-scale distribution of microscopic organisms, whose biogeographical patterns have long been debated. Here we assessed the global structure of plankton geography and its relation to the biological, chemical, and physical context of the ocean (the 'seascape') by analyzing metagenomes of plankton communities sampled across oceans during the Tara Oceans expedition, in light of environmental data and ocean current transport. Using a consistent approach across organismal sizes that provides unprecedented resolution to measure changes in genomic composition between communities, we report a pan-ocean, size-dependent plankton biogeography overlying regional heterogeneity. We found robust evidence for a basin-scale impact of transport by ocean currents on plankton biogeography, and on a characteristic timescale of community dynamics going beyond simple seasonality or life history transitions of plankton., Competing Interests: DR, RW, TV, JL, PF, GR, NM, NH, GB, OD, TD, AF, SS, RN, CB, DE, FG, LG, KL, EM, JP, SR, SR, CD, SK, MP, SS, SP, JA, JB, CL, EP, PB, SS, FL, LK, CB, MS, EK, MM, IP, PP, PW, Cd, MR, DI, OJ No competing interests declared, (© 2022, Richter, Watteaux, Vannier et al.)

Understanding the conditions of feasibility and stability in ecological systems is a major challenge in theoretical ecology. The seminal work of May in 1972 and recent developments based on the theory of random matrices have shown the existence of emergent universal patterns of both stability and feasibility in ecological dynamics. However, only a few studies have investigated the role of delay coupled with population dynamics in the emergence of feasible and stable states. In this work, we study the effects of delay on generalized Loka-Volterra population dynamics of several interacting species in closed ecological environments. First, we investigate the relation between feasibility and stability of the modelled ecological community in the absence of delay and find a simple analytical relation when intra-species interactions are dominant. We then show how, by increasing the time delay, there is a transition in the stability phases of the population dynamics: from an equilibrium state to a stable non-point attractor phase. We calculate analytically the critical delay of that transition and show that it is in excellent agreement with numerical simulations. Finally, following a similar approach to characterizing stability in empirical studies, we investigate the coefficient of variation, which quantifies the magnitude of population fluctuations. We show that in the oscillatory regime induced by the delay, the variability at community level decreases for increasing diversity. This article is part of the theme issue 'Emergent phenomena in complex physical and socio-technical systems: from cells to societies'.

The critical brain hypothesis states that biological neuronal networks, because of their structural and functional architecture, work near phase transitions for optimal response to internal and external inputs. Criticality thus provides optimal function and behavioral capabilities. We test this hypothesis by examining the influence of brain injury (strokes) on the criticality of neural dynamics estimated at the level of single participants using directly measured individual structural connectomes and whole-brain models. Lesions engender a sub-critical state that recovers over time in parallel with behavior. The improvement of criticality is associated with the re-modeling of specific white-matter connections. We show that personalized whole-brain dynamical models poised at criticality track neural dynamics, alteration post-stroke, and behavior at the level of single participants., (© 2022. The Author(s).)

The critical brain hypothesis has emerged as an attractive framework to understand neuronal activity, but it is still widely debated. In this work, we analyze data from a multi-electrodes array in the rat's cortex and we find that power-law neuronal avalanches satisfying the crackling-noise relation coexist with spatial correlations that display typical features of critical systems. In order to shed a light on the underlying mechanisms at the origin of these signatures of criticality, we introduce a paradigmatic framework with a common stochastic modulation and pairwise linear interactions inferred from our data. We show that in such models power-law avalanches that satisfy the crackling-noise relation emerge as a consequence of the extrinsic modulation, whereas scale-free correlations are solely determined by internal interactions. Moreover, this disentangling is fully captured by the mutual information in the system. Finally, we show that analogous power-law avalanches are found in more realistic models of neural activity as well, suggesting that extrinsic modulation might be a broad mechanism for their generation., (© 2022. The Author(s).)

Molecular ecology uses molecular genetic data to answer traditional ecological questions in biogeography and biodiversity, among others. Several ecological principles, such as the niche hypothesis and the competitive exclusions , are based on the fact that species compete for resources. More in generally, it is now recognized that species interactions play a crucial role in determining the coexistence and abundance of species. However, experimentally controllable platforms, which allow us to study and measure competitions among species, are rare and difficult to implement. In this work, we suggest exploiting a Molecular Dynamics coarse-grained model to study interactions among single strands of DNA, representing individuals of different species, which compete for binding to other oligomers considered as resources. In particular, the well-established knowledge of DNA-DNA interactions at the nanoscale allows us to test the hypothesis that the maximum consecutive overlap between pairs of oligomers measure the species' competitive advantages. However, we suggest that a more complex structure also plays a role in the ability of the species to successfully bind to the target resource oligomer. We complement the simulations with experiments on populations of DNA strands which qualitatively confirm our hypotheses. These tools constitute a promising starting point for further developments concerning the study of controlled, DNA-based, artificial ecosystems.

The effectiveness of several biological and biotechnological processes relies on the remarkably selective pairing of nucleic acids in contexts of molecular complexity. Relevant examples are the on-target binding of primers in genomic PCR and the regulatory efficacy of microRNA via binding on the transcriptome. Here, we propose a statistical framework that enables us to describe and understand such selectivity by means of a model that is extremely cheap from a computational point of view. By re-parametrizing the hybridization thermodynamics on three classes of base pairing errors, we find a convenient way to obtain the free energy of pairwise interactions between nucleic acids. We thus evaluate the hybridization statistics of a given oligonucleotide within a large number of competitive sites that we assume to be random, and we compute the probability of on-target binding. We apply our strategy to PCR amplification and microRNA-based gene regulation, shedding new light on their selectivity. In particular, we show the relevance of the defectless pairing of 3' terminals imposed by the polymerase in PCR selection. We also evaluate the selectivity afforded by the microRNA seed region, thus quantifying the extra contributions given by mechanisms beyond pairing statistics.

Local coexistence of species in large ecosystems is traditionally explained within the broad framework of niche theory. However, its rationale hardly justifies rich biodiversity observed in nearly homogeneous environments. Here we consider a consumer-resource model in which a coarse-graining procedure accounts for a variety of ecological mechanisms and leads to effective spatial effects which favor species coexistence. Herein, we provide conditions for several species to live in an environment with very few resources. In fact, the model displays two different phases depending on whether the number of surviving species is larger or smaller than the number of resources. We obtain conditions whereby a species can successfully colonize a pool of coexisting species. Finally, we analytically compute the distribution of the population sizes of coexisting species. Numerical simulations as well as empirical distributions of population sizes support our analytical findings.

Since its first experimental signatures, the so called "critical brain hypothesis" has been extensively studied. Yet, its actual foundations remain elusive. According to a widely accepted teleological reasoning, the brain would be poised to a critical state to optimize the mapping of the noisy and ever changing real-world inputs, thus suggesting that primary sensory cortical areas should be critical. We investigated whether a single barrel column of the somatosensory cortex of the anesthetized rat displays a critical behavior. Neuronal avalanches were recorded across all cortical layers in terms of both multi-unit activities and population local field potentials, and their behavior during spontaneous activity compared to the one evoked by a controlled single whisker deflection. By applying a maximum likelihood statistical method based on timeseries undersampling to fit the avalanches distributions, we show that neuronal avalanches are power law distributed for both multi-unit activities and local field potentials during spontaneous activity, with exponents that are spread along a scaling line. Instead, after the tactile stimulus, activity switches to a transient across-layers synchronization mode that appears to dominate the cortical representation of the single sensory input., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2021 Mariani, Nicoletti, Bisio, Maschietto, Oboe, Leparulo, Suweis and Vassanelli.)

Big data require new techniques to handle the information they come with. Here we consider four datasets (email communication, Twitter posts, Wikipedia articles and Gutenberg books) and propose a novel statistical framework to predict global statistics from random samples. More precisely, we infer the number of senders, hashtags and words of the whole dataset and how their abundances (i.e. the popularity of a hashtag) change through scales from a small sample of sent emails per sender, posts per hashtag and word occurrences. Our approach is grounded on statistical ecology as we map inference of human activities into the unseen species problem in biodiversity. Our findings may have applications to resource management in emails, collective attention monitoring in Twitter and language learning process in word databases., Competing Interests: The authors have declared that no competing interests exist.

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., Competing Interests: The authors declare no competing interest., (Copyright © 2021 the Author(s). Published by PNAS.)

Microbial communities are ubiquitous and play crucial roles in many natural processes. Despite their importance for the environment, industry and human health, there are still many aspects of microbial community dynamics that we do not understand quantitatively. Recent experiments have shown that the structure and composition of microbial communities are intertwined with the metabolism of the species that inhabit them, suggesting that properties at the intracellular level such as the allocation of cellular proteomic resources must be taken into account when describing microbial communities with a population dynamics approach. In this work, we reconsider one of the theoretical frameworks most commonly used to model population dynamics in competitive ecosystems, MacArthur's consumer-resource model, in light of experimental evidence showing how proteome allocation affects microbial growth. This new framework allows us to describe community dynamics at an intermediate level of complexity between classical consumer-resource models and biochemical models of microbial metabolism, accounting for temporally-varying proteome allocation subject to constraints on growth and protein synthesis in the presence of multiple resources, while preserving analytical insight into the dynamics of the system. We first show with a simple experiment that proteome allocation needs to be accounted for to properly understand the dynamics of even the simplest microbial community, i.e. two bacterial strains competing for one common resource. Then, we study our consumer-proteome-resource model analytically and numerically to determine the conditions that allow multiple species to coexist in systems with arbitrary numbers of species and resources.

Deoxyribonucleic acid (DNA) hybridization is at the heart of countless biological and biotechnological processes. Its theoretical modeling played a crucial role, since it has enabled extracting the relevant thermodynamic parameters from systematic measurements of DNA melting curves. In this article, we propose a framework based on statistical physics to describe DNA hybridization and melting in an arbitrary mixture of DNA strands. In particular, we are able to analytically derive closed expressions of the system partition functions for any number N of strings and explicitly calculate them in two paradigmatic situations: (i) a system made of self-complementary sequences and (ii) a system comprising two mutually complementary sequences. We derive the melting curve in the thermodynamic limit (N→∞) of our description, which provides a full justification for the extra entropic contribution that in classic hybridization modeling was required to correctly describe within the same framework the melting of sequences either self-complementary or not. We thus provide a thorough study comprising limit cases and alternative approaches showing how our framework can give a comprehensive view of hybridization and melting phenomena.

Human cognitive abilities are limited resources. Today, in the age of cheap information-cheap to produce, to manipulate, to disseminate-this cognitive bottleneck translates into hypercompetition for rewarding outcomes among actors. These incentives push actors to mutualistically interact with specific memes, seeking the virality of their messages. In turn, memes' chances to persist and spread are subject to changes in the communication environment. In spite of all this complexity, here we show that the underlying architecture of empirical actor-meme information ecosystems evolves into recurring emergent patterns. We then propose an ecology-inspired modelling framework, bringing to light the precise mechanisms causing the observed flexible structural reorganisation. The model predicts-and the data confirm-that users' struggle for visibility induces a re-equilibration of the network's mesoscale towards self-similar nested arrangements. Our final microscale insights suggest that flexibility at the structural level is not mirrored at the dynamical one.

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., Competing Interests: The authors declare no competing interest., (Copyright © 2021 the Author(s). Published by PNAS.)

One of the outstanding problems in complexity science and engineering is the study of high-dimensional networked systems and of their susceptibility to transitions to undesired states as a result of changes in external drivers or in the structural properties. Because of the incredibly large number of parameters controlling the state of such complex systems and the heterogeneity of its components, the study of their dynamics is extremely difficult. Here we propose an analytical framework for collapsing complex N-dimensional networked systems into an S+1-dimensional manifold as a function of S effective control parameters with S << N. We test our approach on a variety of real-world complex problems showing how this new framework can approximate the system's response to changes and correctly identify the regions in the parameter space corresponding to the system's transitions. Our work offers an analytical method to evaluate optimal strategies in the design or management of networked systems., Competing Interests: The authors declare no competing interests., (© 2020 The Author(s).)

Characterizing species diversity and composition of bacteria hosted by biota is revolutionizing our understanding of the role of symbiotic interactions in ecosystems. Determining microbiomes diversity implies the assignment of individual reads to taxa by comparison to reference databases. Although computational methods aimed at identifying the microbe(s) taxa are available, it is well known that inferences using different methods can vary widely depending on various biases. In this study, we first apply and compare different bioinformatics methods based on 16S ribosomal RNA gene and shotgun sequencing to three mock communities of bacteria, of which the compositions are known. We show that none of these methods can infer both the true number of taxa and their abundances. We thus propose a novel approach, named Core-Kaiju, which combines the power of shotgun metagenomics data with a more focused marker gene classification method similar to 16S, but based on emergent statistics of core protein domain families. We thus test the proposed method on various mock communities and we show that Core-Kaiju reliably predicts both number of taxa and abundances. Finally, we apply our method on human gut samples, showing how Core-Kaiju may give more accurate ecological characterization and a fresh view on real microbiomes., (© The Author(s) 2020. Published by Oxford University Press on behalf of Nucleic Acids Research.)

Soil-salinization affects, to a different extent, more than one-third of terrestrial river basins (estimate based on the Food and Agriculture Organization Harmonized World Soil Database, 2012). Among these, many are endorheic and ephemeral systems already encompassing different degrees of aridity, land degradation, and vulnerability to climate change. The primary effect of salinization is to limit plant water uptake and evapotranspiration, thereby reducing available soil moisture and impairing soil fertility. In this, salinization resembles aridity and-similarly to aridity-may impose significant controls on hydrological partitioning and the strength of land-vegetation-atmosphere interactions at the catchment scale. However, the long-term impacts of salinization on the terrestrial water balance are still largely unquantified. Here, we introduce a modified Budyko's framework explicitly accounting for catchment-scale salinization and species-specific plant salt tolerance. The proposed framework is used to interpret the water-budget data of 237 Australian catchments-29% of which are already severely salt-affected-from the Australian Water Availability Project (AWAP). Our results provide theoretical and experimental evidence that salinization does influence the hydrological partitioning of salt-affected watersheds, imposing significant constraints on water availability and enhancing aridity. The same approach can be applied to estimate salinization level and vegetation salt tolerance at the basin scale, which would be difficult to assess through classical observational techniques. We also demonstrate that plant salt tolerance has a preeminent role in regulating the feedback of vegetation on the soil water budget of salt-affected basins., Competing Interests: The authors declare no competing interest.

Microbes are capable of physiologically adapting to diverse environmental conditions by differentially varying the rates at which they uptake different nutrients. In particular, microbes can switch hierarchically between different energy sources, consuming first those that ensure the highest growth rate. Experimentally, this can result in biphasic growth curves called "diauxic shifts" that typically arise when microbes are grown in media containing several nutrients. Despite these observations are well known in microbiology and molecular biology, the mathematical models generally used to describe the population dynamics of microbial communities do not account for dynamic metabolic adaptation, thus implicitly assuming that microbes cannot switch dynamically from one resource to another. Here, we introduce dynamic metabolic adaptation in the framework of consumer-resource models, which are commonly used to describe competitive microbial communities, allowing each species to temporally change its preferred energy source to maximize its own relative fitness. We show that dynamic metabolic adaptation enables the community to self-organize, allowing several species to coexist even in the presence of few resources, and to respond optimally to a time-dependent environment, thus showing that dynamic metabolic adaptation could be an important mechanism for maintaining high levels of diversity even in environments with few energy sources. We show that introducing dynamic metabolic strategies in consumer-resource models is necessary for reproducing experimental growth curves of the baker's yeast Saccharomyces cerevisiae growing in the presence of two carbon sources. Even though diauxic shifts emerge naturally from the model when two resources are qualitatively very different, the model predicts that the existence of such shifts is not a prerequisite for species coexistence in competitive communities., Competing Interests: The authors have declared that no competing interests exist.

The year 2017 saw the rise and fall of the crypto-currency market, followed by high variability in the price of all crypto-currencies. In this work, we study the abrupt transition in crypto-currency residuals, which is associated with the critical transition (the phenomenon of critical slowing down) or the stochastic transition phenomena. We find that, regardless of the specific crypto-currency or rolling window size, the autocorrelation always fluctuates around a high value, while the standard deviation increases monotonically. Therefore, while the autocorrelation does not display the signals of critical slowing down, the standard deviation can be used to anticipate critical or stochastic transitions. In particular, we have detected two sudden jumps in the standard deviation, in the second quarter of 2017 and at the beginning of 2018, which could have served as the early warning signals of two major price collapses that have happened in the following periods. We finally propose a mean-field phenomenological model for the price of crypto-currency to show how the use of the standard deviation of the residuals is a better leading indicator of the collapse in price than the time-series' autocorrelation. Our findings represent a first step towards a better diagnostic of the risk of critical transition in the price and/or volume of crypto-currencies., Competing Interests: We have no competing interests., (© 2020 The Authors.)

The evolutionary and ecological processes behind the origin of species are among the most fundamental problems in biology. In fact, many theoretical hypothesis on different type of speciation have been proposed. In particular, models of sympatric speciation leading to the formation of new species without geographical isolation, are based on the niche hypothesis: the diversification of the population is induced by the competition for a limited set of available resources. Interestingly, neutral models of evolution have shown that stochastic forces are sufficient to generate coexistence of different species. In this work, we put forward this dichotomy within the context of species formation, studying how neutral and niche forces contribute to sympatric speciation in a model ecosystem. In particular, we study the evolution of a population of individuals with asexual reproduction whose inherited characters or phenotypes are specified by both niche-based and neutral traits. We analyze the stationary state of the dynamics, and study the distribution of individuals in the whole phenotypic space. We show, both numerically and analytically, that there is a non-trivial coupling between neutral and niche forces induced by stochastic effects in the evolution of the population allowing the formation of clusters, that is, species in the phenotypic space. Remarkably, our framework can be generalized also to sexual reproduction or other type of population dynamics., (Copyright © 2019. Published by Elsevier Ltd.)

In our recent article [1] published in this journal we provide quantitative evidence to show that there are warnings and caveats in the way Gu and collaborators [2] define controllability of brain networks and measure the contribution of each of its nodes. The comment by Pasqualetti et al. [3] confirms the need to go beyond the methodology and approach presented in Gu et al.'s original work. In fact, they recognize that "the source of confusion is due to the fact that assessing controllability via numerical analysis typically leads to ill-conditioned problems, and thus often generates results that are difficult to interpret". This is indeed the first warning we discussed in [1]: our work was not meant to prove that brain networks are not controllable from one node, rather we wished to highlight that the one node controllability framework and all consequent results were not properly justified based on the methodology presented in Gu et al. [2]. We used in our work the same method of Gu et al. not because we believe it is the best methodology, but because we extensively investigated it with the aim of replicating, testing, and extending their results. The warning and caveats we have proposed are the results of this investigation. Indeed, on the basis of our controllability analyses of multiple human brain networks datasets, we concluded: "The λ min (W K ) are statistically compatible with zero and thus the associated controllability Gramian cannot be inverted 1 . These results show that it is not possible to infer one node controllability of the brain numerically". Hence both groups agree that one node controllability cannot be inferred numerically., (Copyright © 2019 Elsevier Inc. All rights reserved.)

Empirical evidences show that ecosystems with high biodiversity can persist in time even in the presence of few types of resources and are more stable than low biodiverse communities. This evidence is contrasted by the conventional mathematical modeling, which predicts that the presence of many species and/or cooperative interactions are detrimental for ecological stability and persistence. Here we propose a modelling framework for population dynamics, which also include indirect cooperative interactions mediated by other species (e.g. habitat modification). We show that in the large system size limit, any number of species can coexist and stability increases as the number of species grows, if mediated cooperation is present, even in presence of exploitative or harmful interactions (e.g. antibiotics). Our theoretical approach thus shows that appropriate models of mediated cooperation naturally lead to a solution of the long-standing question about complexity-stability paradox and on how highly biodiverse communities can coexist.

To measure, predict, and prevent social segregation, it is necessary to understand the factors that cause it. While in most available descriptions space plays an essential role, one outstanding question is whether and how this phenomenon is possible in a well-mixed social network. We define and solve a simple model of segregation on networks based on discrete convictions. In our model, space does not play a role, and individuals never change their conviction, but they may choose to connect socially to other individuals based on two criteria: sharing the same conviction and individual popularity (regardless of conviction). The tradeoff between these two moves defines a parameter, analogous to the "tolerance" parameter in classical models of spatial segregation. We show numerically and analytically that this parameter determines a true phase transition (somewhat reminiscent of phase separation in a binary mixture) between a well-mixed and a segregated state. Additionally, minority convictions segregate faster and inter-specific aversion alone may lead to a segregation threshold with similar properties. Together, our results highlight the general principle that a segregation transition is possible in absence of spatial degrees of freedom, provided that conviction-based rewiring occurs on the same time scale of popularity rewirings.

Understanding the relationship between large-scale structural and functional brain networks remains a crucial issue in modern neuroscience. Recently, there has been growing interest in investigating the role of homeostatic plasticity mechanisms, across different spatiotemporal scales, in regulating network activity and brain functioning against a wide range of environmental conditions and brain states (e.g., during learning, development, ageing, neurological diseases). In the present study, we investigate how the inclusion of homeostatic plasticity in a stochastic whole-brain model, implemented as a normalization of the incoming node's excitatory input, affects the macroscopic activity during rest and the formation of functional networks. Importantly, we address the structure-function relationship both at the group and individual-based levels. In this work, we show that normalization of the node's excitatory input improves the correspondence between simulated neural patterns of the model and various brain functional data. Indeed, we find that the best match is achieved when the model control parameter is in its critical value and that normalization minimizes both the variability of the critical points and neuronal activity patterns among subjects. Therefore, our results suggest that the inclusion of homeostatic principles lead to more realistic brain activity consistent with the hallmarks of criticality. Our theoretical framework open new perspectives in personalized brain modeling with potential applications to investigate the deviation from criticality due to structural lesions (e.g. stroke) or brain disorders.

This corrects the article DOI: 10.1038/ncomms14389.

The quantification of tropical tree biodiversity worldwide remains an open and challenging problem. More than two-fifths of the number of worldwide trees can be found either in tropical or in subtropical forests, but only ≈0.000067% of species identities are known. We introduce an analytical framework that provides robust and accurate estimates of species richness and abundances in biodiversity-rich ecosystems, as confirmed by tests performed on both in silico-generated and real forests. Our analysis shows that the approach outperforms other methods. In particular, we find that upscaling methods based on the log-series species distribution systematically overestimate the number of species and abundances of the rare species. We finally apply our new framework on 15 empirical tropical forest plots and quantify the minimum percentage cover that should be sampled to achieve a given average confidence interval in the upscaled estimate of biodiversity. Our theoretical framework confirms that the forests studied are comprised of a large number of rare or hyper-rare species. This is a signature of critical-like behavior of species-rich ecosystems and can provide a buffer against extinction.

The increasing volume of ecologically and biologically relevant data has revealed a wide collection of emergent patterns in living systems. Analysing different data sets, ranging from metabolic gene-regulatory to species interaction networks, we find that these networks are sparse, i.e. the percentage of the active interactions scales inversely proportional to the system size. To explain the origin of this puzzling common characteristic, we introduce the new concept of explorability: a measure of the ability of an interacting system to adapt to newly intervening changes. We show that sparsity is an emergent property resulting from optimising both explorability and dynamical robustness, i.e. the capacity of the system to remain stable after perturbations of the underlying dynamics. Networks with higher connectivities lead to an incremental difficulty to find better values for both the explorability and dynamical robustness, associated with the fine-tuning of the newly added interactions. A relevant characteristic of our solution is its scale invariance, i.e., it remains optimal when several communities are assembled together. Connectivity is also a key ingredient in determining ecosystem stability and our proposed solution contributes to solving May's celebrated complexity-stability paradox.

Recently, a theoretical framework aimed at separating the roles of dynamics and topology in multidimensional systems has been developed [Gao et al., Nature (London) 530, 307 (2016)10.1038/nature16948]. The validity of their method is assumed to hold depending on two main hypotheses: (i) The network determined by the the interaction between pairs of nodes has negligible degree correlations; (ii) the node activities are uniform across nodes on both the drift and the pairwise interaction functions. Moreover, the authors consider only positive (mutualistic) interactions. Here we show the conditions proposed by Gao and collaborators [Nature (London) 530, 307 (2016)10.1038/nature16948] are neither sufficient nor necessary to guarantee that their method works in general and validity of their results are not independent of the model chosen within the class of dynamics they considered. Indeed we find that a new condition poses effective limitations to their framework and we provide quantitative predictions of the quality of the one-dimensional collapse as a function of the properties of interaction networks and stable dynamics using results from random matrix theory. We also find that multidimensional reduction may work also for an interaction matrix with a mixture of positive and negative signs, opening up an application of the framework to food webs, neuronal networks, and social and economic interactions.

The role of species interactions in controlling the interplay between the stability of ecosystems and their biodiversity is still not well understood. The ability of ecological communities to recover after small perturbations of the species abundances (local asymptotic stability) has been well studied, whereas the likelihood of a community to persist when the conditions change (structural stability) has received much less attention. Our goal is to understand the effects of diversity, interaction strengths and ecological network structure on the volume of parameter space leading to feasible equilibria. We develop a geometrical framework to study the range of conditions necessary for feasible coexistence. We show that feasibility is determined by few quantities describing the interactions, yielding a nontrivial complexity-feasibility relationship. Analysing more than 100 empirical networks, we show that the range of coexistence conditions in mutualistic systems can be analytically predicted. Finally, we characterize the geometric shape of the feasibility domain, thereby identifying the direction of perturbations that are more likely to cause extinctions.

Ensuring food security requires food production and distribution systems function throughout disruptions. Understanding the factors that contribute to the global food system's ability to respond and adapt to such disruptions (i.e. resilience) is critical for understanding the long-term sustainability of human populations. Variable impacts of production shocks on food supply between countries indicate a need for national-scale resilience indicators that can provide global comparisons. However, methods for tracking changes in resilience have had limited application to food systems. We developed an indicator-based analysis of food systems resilience for the years 1992-2011. Our approach is based on three dimensions of resilience: socio-economic access to food in terms of income of the poorest quintile relative to food prices, biophysical capacity to intensify or extensify food production, and the magnitude and diversity of current domestic food production. The socio-economic indicator has large variability, but with low values concentrated in Africa and Asia. The biophysical capacity indicator is highest in Africa and Eastern Europe, in part because of high potential for extensification of cropland and for yield gap closure in cultivated areas. However, the biophysical capacity indicator has declined globally in recent years. The production diversity indicator has increased slightly, with a relatively even geographic distribution. Few countries had exclusively high or low values for all indicators. Collectively, these results are the basis for global comparisons of resilience between nations, and provide necessary context for developing generalizations about the resilience in the global food system.

Environmental fluctuations have important consequences in the organization of ecological communities, and understanding how such a variability influences the biodiversity of an ecosystem is a major question in ecology. In this paper, we analyze the case of two species competing for the resources within the framework of the neutral theory in the presence of environmental noise, devoting special attention on how such a variability modulates species fitness. The environment is dichotomous and stochastically alternates between periods favoring one of the species while disfavoring the other one, preserving neutrality on the long term. We study two different scenarios: in the first one species fitness varies linearly with the environment, and in the second one the effective fitness is re-scaled by the total fitness of the individuals competing for the same resource. We find that, in the former case environmental fluctuations always reduce the time of species coexistence, whereas such a time can be enhanced or reduced in the latter case, depending on the correlation time of the environment. This phenomenon can be understood as a direct consequence of Chesson's storage effect., (Copyright © 2016 Elsevier Ltd. All rights reserved.)

The easy access to large data sets has allowed for leveraging methodology in network physics and complexity science to disentangle patterns and processes directly from the data, leading to key insights in the behavior of systems. Here we use country specific food production data to study binary and weighted topological properties of the bipartite country-food production matrix. This country-food production matrix can be: 1) transformed into overlap matrices which embed information regarding shared production of products among countries, and or shared countries for individual products, 2) identify subsets of countries which produce similar commodities or subsets of commodities shared by a given country allowing for visualization of correlations in large networks, and 3) used to rank country fitness (the ability to produce a diverse array of products weighted on the type of food commodities) and food specialization (quantified on the number of countries producing a specific food product weighted on their fitness). Our results show that, on average, countries with high fitness produce both low and high specializion food commodities, whereas nations with low fitness tend to produce a small basket of diverse food products, typically comprised of low specializion food commodities., Competing Interests: The authors have declared that no competing interests exist.

In this work we study the likelihood of survival of single-species in the context of hostile and disordered environments. Population dynamics in this environment, as modeled by the Fisher equation, is characterized by negative average growth rate, except in some random spatially distributed patches that may support life. In particular, we are interested in the phase diagram of the survival probability and in the critical size problem, i.e., the minimum patch size required for surviving in the long-time dynamics. We propose a measure for the critical patch size as being proportional to the participation ratio of the eigenvector corresponding to the largest eigenvalue of the linearized Fisher dynamics. We obtain the (extinction-survival) phase diagram and the probability distribution function (PDF) of the critical patch sizes for two topologies, namely, the one-dimensional system and the fractal Peano basin. We show that both topologies share the same qualitative features, but the fractal topology requires higher spatial fluctuations to guarantee species survival. We perform a finite-size scaling and we obtain the associated scaling exponents. In addition, we show that the PDF of the critical patch sizes has an universal shape for the 1D case in terms of the model parameters (diffusion, growth rate, etc.). In contrast, the diffusion coefficient has a drastic effect on the PDF of the critical patch sizes of the fractal Peano basin, and it does not obey the same scaling law of the 1D case.

The relationships between the core-periphery architecture of the species interaction network and the mechanisms ensuring the stability in mutualistic ecological communities are still unclear. In particular, most studies have focused their attention on asymptotic resilience or persistence, neglecting how perturbations propagate through the system. Here we develop a theoretical framework to evaluate the relationship between the architecture of the interaction networks and the impact of perturbations by studying localization, a measure describing the ability of the perturbation to propagate through the network. We show that mutualistic ecological communities are localized, and localization reduces perturbation propagation and attenuates its impact on species abundance. Localization depends on the topology of the interaction networks, and it positively correlates with the variance of the weighted degree distribution, a signature of the network topological heterogeneity. Our results provide a different perspective on the interplay between the architecture of interaction networks in mutualistic communities and their stability.

Neutral dynamics, where taxa are assumed to be demographically equivalent and their abundance is governed solely by the stochasticity of the underlying birth-death process, has proved itself as an important minimal model that accounts for many empirical datasets in genetics and ecology. However, the restriction of the model to demographic [O√N)] noise yields relatively slow dynamics that appears to be in conflict with both short-term and long-term characteristics of the observed systems. Here we analyze two of these problems--age-size relationships and species extinction time--in the framework of a neutral theory with both demographic and environmental stochasticity. It turns out that environmentally induced variations of the demographic rates control the long-term dynamics and modify dramatically the predictions of the neutral theory with demographic noise only, yielding much better agreement with empirical data. We consider two prototypes of "zero mean" environmental noise, one which is balanced with regard to the arithmetic abundance, another balanced in the logarithmic (fitness) space, study their species lifetime statistics, and discuss their relevance to realistic models of community dynamics.

The escalating food demand by a growing and increasingly affluent global population is placing unprecedented pressure on the limited land and water resources of the planet, underpinning concerns over global food security and its sensitivity to shocks arising from environmental fluctuations, trade policies, and market volatility. Here, we use country-specific demographic records along with food production and trade data for the past 25 y to evaluate the stability and reactivity of the relationship between population dynamics and food availability. We develop a framework for the assessment of the resilience and the reactivity of the coupled population-food system and suggest that over the past two decades both its sensitivity to external perturbations and susceptibility to instability have increased.

Empirical evidence suggesting that living systems might operate in the vicinity of critical points, at the borderline between order and disorder, has proliferated in recent years, with examples ranging from spontaneous brain activity to flock dynamics. However, a well-founded theory for understanding how and why interacting living systems could dynamically tune themselves to be poised in the vicinity of a critical point is lacking. Here we use tools from statistical mechanics and information theory to show that complex adaptive or evolutionary systems can be much more efficient in coping with diverse heterogeneous environmental conditions when operating at criticality. Analytical as well as computational evolutionary and adaptive models vividly illustrate that a community of such systems dynamically self-tunes close to a critical state as the complexity of the environment increases while they remain noncritical for simple and predictable environments. A more robust convergence to criticality emerges in coevolutionary and coadaptive setups in which individuals aim to represent other agents in the community with fidelity, thereby creating a collective critical ensemble and providing the best possible tradeoff between accuracy and flexibility. Our approach provides a parsimonious and general mechanism for the emergence of critical-like behavior in living systems needing to cope with complex environments or trying to efficiently coordinate themselves as an ensemble.

A number of social-ecological systems exhibit complex behaviour associated with nonlinearities, bifurcations, and interaction with stochastic drivers. These systems are often prone to abrupt and unexpected instabilities and state shifts that emerge as a discontinuous response to gradual changes in environmental drivers. Predicting such behaviours is crucial to the prevention of or preparation for unwanted regime shifts. Recent research in ecology has investigated early warning signs that anticipate the divergence of univariate ecosystem dynamics from a stable attractor. To date, leading indicators of instability in systems with multiple interacting components have remained poorly investigated. This is a major limitation in the understanding of the dynamics of complex social-ecological networks. Here, we develop a theoretical framework to demonstrate that rising variance--measured, for example, by the maximum element of the covariance matrix of the network--is an effective leading indicator of network instability. We show that its reliability and robustness depend more on the sign of the interactions within the network than the network structure or noise intensity. Mutualistic, scale free and small world networks are less stable than their antagonistic or random counterparts but their instability is more reliably predicted by this leading indicator. These results provide new advances in multidimensional early warning analysis and offer a framework to evaluate the resilience of social-ecological networks.

Ecology, with a traditional focus on plants and animals, seeks to understand the mechanisms underlying structure and dynamics of communities. In microbial ecology, the focus is changing from planktonic communities to attached biofilms that dominate microbial life in numerous systems. Therefore, interest in the structure and function of biofilms is on the rise. Biofilms can form reproducible physical structures (i.e. architecture) at the millimetre-scale, which are central to their functioning. However, the spatial dynamics of the clusters conferring physical structure to biofilms remains often elusive. By experimenting with complex microbial communities forming biofilms in contrasting hydrodynamic microenvironments in stream mesocosms, we show that morphogenesis results in 'ripple-like' and 'star-like' architectures--as they have also been reported from monospecies bacterial biofilms, for instance. To explore the potential contribution of demographic processes to these architectures, we propose a size-structured population model to simulate the dynamics of biofilm growth and cluster size distribution. Our findings establish that basic physical and demographic processes are key forces that shape apparently universal biofilm architectures as they occur in diverse microbial but also in single-species bacterial biofilms., (© 2013 The Authors. Environmental Microbiology published by John Wiley & Sons Ltd and Society for Applied Microbiology.)

Mutualistic networks are formed when the interactions between two classes of species are mutually beneficial. They are important examples of cooperation shaped by evolution. Mutualism between animals and plants has a key role in the organization of ecological communities. Such networks in ecology have generally evolved a nested architecture independent of species composition and latitude; specialist species, with only few mutualistic links, tend to interact with a proper subset of the many mutualistic partners of any of the generalist species. Despite sustained efforts to explain observed network structure on the basis of community-level stability or persistence, such correlative studies have reached minimal consensus. Here we show that nested interaction networks could emerge as a consequence of an optimization principle aimed at maximizing the species abundance in mutualistic communities. Using analytical and numerical approaches, we show that because of the mutualistic interactions, an increase in abundance of a given species results in a corresponding increase in the total number of individuals in the community, and also an increase in the nestedness of the interaction matrix. Indeed, the species abundances and the nestedness of the interaction matrix are correlated by a factor that depends on the strength of the mutualistic interactions. Nestedness and the observed spontaneous emergence of generalist and specialist species occur for several dynamical implementations of the variational principle under stationary conditions. Optimized networks, although remaining stable, tend to be less resilient than their counterparts with randomly assigned interactions. In particular, we show analytically that the abundance of the rarest species is linked directly to the resilience of the community. Our work provides a unifying framework for studying the emergent structural and dynamical properties of ecological mutualistic networks.

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 on the basis of 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-term 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 (i) cooperative interactions among nations whereby water-rich countries maintain a tiny fraction of their food production available for export, (ii) changes in consumption patterns, and (iii) a positive feedback between demographic growth and technological innovations. We find that these strategies may indeed reduce the vulnerability of water-controlled societies.

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 midpoint (or any other intermediate) prescription. By introducing an inertial term in the GLE, we show that the Itô and Stratonovich prescriptions naturally arise depending on two time scales, 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, the features of which are tailored to the characters of the daily precipitation. A method is finally suggested to infer the most appropriate prescription from the data.

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 time spans 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 framework that accounts for the finiteness of the observational period exhibit power-law scaling limited by a cutoff 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 cutoff time scale 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.