1,721,006 research outputs found
Effects of noise on the critical points of Turing instability in complex ecosystems
No full text: Noise is ubiquitous in natural and artificial systems. In a noisy environment, the interactions among nodes may fluctuate randomly, leading to more complicated interactions. In this paper we focus on the effects of noise and network topology on the Turing pattern of ecological networks with activator-inhibitor structure, which may be interpreted as prey-predator interactions. Based on the stability theory of stochastic differential equations, a sufficient condition for the uniform state is derived. The analytical results indicate that noise is beneficial for the uniform state. When the ratio between the diffusion coefficients of the predator and prey increases, the ecosystems can exhibit a transition from a uniform stable state to a Turing pattern, while when the ratio decreases, the ecosystems transit from a Turing pattern to a uniform stable state. There are two crucial critical points in Turing patterns, forward and backward. We find that both forward and backward critical points increase as the noise intensity increases. This means that noise favors a stable homogeneous state compared to a state with a heterogeneous pattern, which is consistent with the analytical results. In addition, noise can weaken the hysteresis phenomenon and even eliminate it in some cases. Furthermore, we report that network topology plays an important role in modulating the uniform state of ecosystems, such as the size of prey-predator systems, the network connectivity, and the strength of interaction
Effect of delay on the emergent stability patterns in generalized Lotka-Volterra ecological dynamics
Full text linkUnderstanding 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'
Stochastic trade-offs and the emergence of diversification in E. coli evolution experiments
Full text linkLaboratory experiments with bacterial colonies under well-controlled conditions often lead to evolutionary diversification, where at least two ecotypes emerge from an initially monomorphic population. Empirical evidence suggests that such an “evolutionary branching” occurs stochastically, even under fixed and stable conditions. This stochasticity is characterized by (i) the occurrence of branching in a significant fraction, but not all, of the experimental settings, (ii) the emergence at widely varying times, and (iii) variable relative abundances of the resulting subpopulations across experiments. Theoretical approaches to understanding evolutionary branching under these conditions have been previously developed within the (deterministic) framework of “adaptive dynamics.” Here, we advance the understanding of the stochastic nature of evolutionary outcomes by introducing the concept of “stochastic trade-offs” as opposed to “hard” ones. The key idea is that the stochasticity of mutations occurs in a high-dimensional trait space and this translates into variability that is constrained to a flexible tradeoff curve in a lower-dimensional space. By incorporating this additional source of stochasticity, we are able to account for the observed empirical variability and make predictions regarding the likelihood of evolutionary branching under different experimental conditions. This approach effectively bridges the gap between theoretical predictions and empirical observations, providing insights into when and how evolutionary branching is more likely to occur in laboratory experiments
Zipf's and Taylor's laws
Full text linkZipf's law states that the frequency of an observation with a given value is inversely proportional to the square of that value; Taylor's law, instead, describes the scaling between fluctuations in the size of a population and its mean. Empirical evidence of the validity of these laws has been found in many and diverse domains. Despite the numerous models proposed to explain the presence of Zipf's law, there is no consensus on how it originates from a microscopic process of individual dynamics without fine-tuning. Here we show that Zipf's law and Taylor's law can emerge from a general class of stochastic processes at the individual level, which incorporate one of two features: environmental variability, i.e., fluctuations of parameters, or correlations, i.e., dependence between individuals. Under these assumptions, we show numerically and with theoretical arguments that the conditional variance of the population increments scales as the square of the population, and that the corresponding stationary distribution of the processes follows Zipf's law
Quantifying the Resilience of Coal Energy Supply in China Toward Carbon Neutrality
Full text linkFacing the challenge of achieving the goal of carbon neutrality, China is decoupling the currently close dependence of its economy on coal use. The energy supply and demand decarbonization has substantial influence on the resilience of the coal supply. However, a general understanding of the precise impact of energy decarbonization on the resilience of the coal energy supply is still lacking. Here, from the perspective of network science, we propose a theoretical framework to explore the resilience of the coal market of China. We show that the processes of increasing the connectivity and the competition between the coal enterprises, which are widely believed to improve the resilience of the coal market, can undermine the sustainability of the coal supply. Moreover, our results reveal that the policy of closing small-sized coal mines may not only reduce the safety accidents in the coal production but also improve the resilience of the coal market network. Using our model, we also suggest a few practical policies for minimizing the systemic risk of the coal energy supply
Emergent encoding of dispersal network topologies in spatial metapopulation models
Full text link: 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
Statistical mechanics of ecological systems: Neutral theory and beyond
Full text linkThe simplest theories often have much merit and many limitations, and, in this vein, the value of neutral theory (NT) of biodiversity has been the subject of much debate over the past 15 years. NT was proposed at the turn of the century by Stephen Hubbell to explain several patterns observed in the organization of ecosystems. Among ecologists, it had a polarizing effect: There were a few ecologists who were enthusiastic, and there were a larger number who firmly opposed it. Physicists and mathematicians, instead, welcomed the theory with excitement. Indeed, NT spawned several theoretical studies that attempted to explain empirical data and predicted trends of quantities that had not yet been studied. While there are a few reviews of NT oriented toward ecologists, the goal here is to review the quantitative aspects of NT and its extensions for physicists who are interested in learning what NT is, what its successes are, and what important problems remain unresolved. Furthermore, this review could also be of interest to theoretical ecologists because many potentially interesting results are buried in the vast NT literature. It is proposed to make these more accessible by extracting them and presenting them in a logical fashion. The focus of this review is broader than NT: new, more recent approaches for studying ecological systems and how one might introduce realistic non-neutral models are also discussed
Landscape and environmental heterogeneity support coexistence in competitive metacommunities
Full text linkMetapopulation models have been instrumental in quantifying the ecological impact of landscape structure on the survival of a focal species. However, extensions to multiple species with arbitrary dispersal networks often rely on phenomenological assumptions that inevitably limit their scope. Here, we propose a multilayer network model of competitive dispersing metacommunities to investigate how spatially structured environments impact species coexistence and ecosystem stability. We introduce the concept of landscape-mediated fitness, quantifying how fit a species is in a given environment in terms of colonization and extinction. We show that, when all environments are equivalent, one species excludes all the others—except the marginal case where species fitnesses are in exact trade-off. However, we prove that stable coexistence becomes possible in sufficiently heterogeneous environments by introducing spatial disorder in the model and solving it exactly in the mean-field limit. Crucially, coexistence is supported by the spontaneous localization of species through the emergence of ecological niches. We show that our results remain qualitatively valid in arbitrary dispersal networks, where topological features can improve species coexistence by buffering competition. Finally, we employ our model to study how correlated heterogeneity promotes spatial ecological patterns in realistic terrestrial and riverine landscapes. Our work provides a framework to understand how landscape structure enables coexistence in metacommunities by acting as the substrate for ecological interactions.ECH
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