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.

Controlling target brain regions by optimal selection of input nodes.

The network control theory framework holds great potential to inform neurostimulation experiments aimed at inducing desired activity states in the brain. However, the current applicability of the framework is limited by inappropriate modeling of brain dynamics, and an overly ambitious focus on whole-brain activity control. In this work, we leverage recent progress in linear modeling of brain dynamics (effective connectivity) and we exploit the concept of target controllability to focus on the control of a single region or a small subnetwork of nodes. We discuss when control may be possible with a reasonably low energy cost and few stimulation loci, and give general predictions on where to stimulate depending on the subset of regions one wishes to control. Importantly, using the robustly asymmetric effective connectome instead of the symmetric structural connectome (as in previous research), we highlight the fundamentally different roles in- and out-hubs have in the control problem, and the relevance of inhibitory connections. The large degree of inter-individual variation in the effective connectome implies that the control problem is best formulated at the individual level, but we discuss to what extent group results may still prove useful.

Delay effects on the stability of large ecosystems.

The common intuition among the ecologists of the midtwentieth century was that large ecosystems should be more stable than those with a smaller number of species. This view was challenged by Robert May, who found a stability bound for randomly assembled ecosystems; they become unstable for a sufficiently large number of species. In the present work, we show that May's bound greatly changes when the past population densities of a species affect its own current density. This is a common feature in real systems, where the effects of species' interactions may appear after a time lag rather than instantaneously. The local stability of these models with self-interaction is described by bounds, which we characterize in the parameter space. We find a critical delay curve that separates the region of stability from that of instability, and correspondingly, we identify a critical frequency curve that provides the characteristic frequencies of a system at the instability threshold. Finally, we calculate analytically the distributions of eigenvalues that generalize Wigner's as well as Girko's laws. Interestingly, we find that, for sufficiently large delays, the eigenvalues of a randomly coupled system are complex even when the interactions are symmetric.

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.

Pairing statistics and melting of random DNA oligomers: Finding your partner in superdiverse environments.

Understanding of the pairing statistics in solutions populated by a large number of distinct solute species with mutual interactions is a challenging topic, relevant in modeling the complexity of real biological systems. Here we describe, both experimentally and theoretically, the formation of duplexes in a solution of random-sequence DNA (rsDNA) oligomers of length L = 8, 12, 20 nucleotides. rsDNA solutions are formed by 4L distinct molecular species, leading to a variety of pairing motifs that depend on sequence complementarity and range from strongly bound, fully paired defectless helices to weakly interacting mismatched duplexes. Experiments and theory coherently combine revealing a hybridization statistics characterized by a prevalence of partially defected duplexes, with a distribution of type and number of pairing errors that depends on temperature. We find that despite the enormous multitude of inter-strand interactions, defectless duplexes are formed, involving a fraction up to 15% of the rsDNA chains at the lowest temperatures. Experiments and theory are limited here to equilibrium conditions.

River basin salinization as a form of aridity.

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.

Effect of delay on the emergent stability patterns in generalized Lotka-Volterra ecological dynamics.

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'.

Taxonomic classification method for metagenomics based on core protein families with Core-Kaiju.

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.

Needles in Haystacks: Understanding the Success of Selective Pairing of Nucleic Acids.

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.

OxDNA to Study Species Interactions.

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.

Effective Resource Competition Model for Species Coexistence.

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.

Dynamic metabolic adaptation can promote species coexistence in competitive microbial communities.

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.

Brain controllability: Not a slam dunk yet.

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 λmin(WK) are statistically compatible with zero and thus the associated controllability Gramian cannot be inverted1. 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.

Neutral and niche forces as drivers of species selection.

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.

Emergence of structural and dynamical properties of ecological mutualistic networks.

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.

Resilience and reactivity of global food security.

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.

Species coexistence in a neutral dynamics with environmental noise.

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.

Information-based fitness and the emergence of criticality in living systems.

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.

Water-controlled wealth of nations.

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.