Lagrange stability and ecological systems

This paper considers the ecological and mathematical relationships among various stability concepts. It is shown that diagonally dominant nonlinear systems have positive solutions for positive initial conditions. The boundedness of such positive solutions leads to a total systems concept of stability: Lagrange stability. This concept is discussed as a compatible method for determining the stability of ecosystems and their mathematical models. Stability in the sense of Lagrange is a total systems concept which does not directly address the problem of the stability of equilibria. A topological presentation is used to describe the Lagrange stability of nonlinear ecosystem compartment models. Finally, the concept of practical stability is developed and discussed with respect to maintaining the desired state of ecosystems in the presence of perturbations.     

The dimensionality of stability depends on disturbance type

Ecosystems respond in various ways to disturbances. Quantifying ecological stability therefore requires inspecting multiple stability properties, such as resistance, recovery, persistence and invariability. Correlations among these properties can reduce the dimensionality of stability, simplifying the study of environmental effects on ecosystems. A key question is how the kind of disturbance affects these correlations. We here investigated the effect of three disturbance types (random, species‐specific, local) applied at four intensity levels, on the dimensionality of stability at the population and community level. We used previously parameterized models that represent five natural communities, varying in species richness and the number of trophic levels. We found that disturbance type but not intensity affected the dimensionality of stability and only at the population level. The dimensionality of stability also varied greatly among species and communities. Therefore, studying stability cannot be simplified to using a single metric and multi‐dimensional assessments are still to be recommended.     

N‐dimensional hypervolumes to study stability of complex ecosystems

Although our knowledge on the stabilising role of biodiversity and on how it is affected by perturbations has greatly improved, we still lack a comprehensive view on ecosystem stability that is transversal to different habitats and perturbations. Hence, we propose a framework that takes advantage of the multiplicity of components of an ecosystem and their contribution to stability. Ecosystem components can range from species or functional groups, to different functional traits, or even the cover of different habitats in a landscape mosaic. We make use of n‐dimensional hypervolumes to define ecosystem states and assess how much they shift after environmental changes have occurred. We demonstrate the value of this framework with a study case on the effects of environmental change on Alpine ecosystems. Our results highlight the importance of a multidimensional approach when studying ecosystem stability and show that our framework is flexible enough to be applied to different types of ecosystem components, which can have important implications for the study of ecosystem stability and transient dynamics.     

Universal beta-diversity–functioning relationships are neither observed nor expected

Widespread evidence shows that local species richness (α-diversity) loss hampers the biomass production and stability of ecosystems. β-Diversity, namely the variation of species compositions among different ecological communities, represents another important biodiversity component, but studies on how it drives ecosystem functioning show mixed results. We argue that to better understand the importance of β-diversity we need to consider it across contexts. We focus on three scenarios that cause gradients in β-diversity: changes in (i) abiotic heterogeneity, (ii) habitat isolation, and (iii) species pool richness. We show that across these scenarios we should not expect universally positive relationships between β-diversity, production, and ecosystem stability. Nevertheless, predictable relationships between β-diversity and ecosystem functioning do exist in specific contexts, and can reconcile seemingly contrasting empirical relationships.     

Advancing our understanding of ecological stability

The concept of ecological stability occupies a prominent place in both fundamental and applied ecological research. We review decades of work on the topic and examine how our understanding has progressed. We show that our understanding of stability has remained fragmented and is limited largely to simple or simplified systems. There has been a profusion of metrics proposed to quantify stability, of which only a handful are used commonly. Furthermore, studies typically quantify one to two metrics of stability at a time and in response to a single perturbation, with some of the main environmental pressures of today being the least studied. We argue that we need to build on the existing consensus and strong theoretical foundation of the stability concept to better understand its multidimensionality and the interdependencies between metrics, levels of organisation and types of perturbations. Only by doing so can we make progress in the quantification of stability in theory and in practice, and eventually build a more comprehensive understanding of how ecosystems will respond to ongoing environmental change.     

Defining invasiveness and invasibility in ecological networks

The success of a biological invasion is context dependent, and yet two key concepts—the invasiveness of species and the invasibility of recipient ecosystems—are often defined and considered separately. We propose a framework that can elucidate the complex relationship between invasibility and invasiveness. It is based on trait-mediated interactions between species and depicts the response of an ecological network to the intrusion of an alien species, drawing on the concept of community saturation. Here, invasiveness of an introduced species with a particular trait is measured by its per capita population growth rate when the initial propagule pressure of the introduced species is very low. The invasibility of the recipient habitat or ecosystem is dependent on the structure of the resident ecological network and is defined as the total width of an opportunity niche in the trait space susceptible to invasion. Invasibility is thus a measure of network instability. We also correlate invasibility with the asymptotic stability of resident ecological network, measured by the leading eigenvalue of the interaction matrix that depicts trait-based interaction intensity multiplied by encounter rate (a pairwise product of propagule pressure of all members in a community). We further examine the relationship between invasibility and network architecture, including network connectance, nestedness and modularity. We exemplify this framework with a trait-based assembly model under perturbations in ways to emulate fluctuating resources and random trait composition in ecological networks. The maximum invasiveness of a potential invader (greatest intrinsic population growth rate) was found to be positively correlated with invasibility of the recipient ecological network. Additionally, ecosystems with high network modularity and high ecological stability tend to exhibit high invasibility. Where quantitative data are lacking we propose using a qualitative interaction matrix of the ecological network perceived by a potential invader so that the structural network stability and invasibility can be estimated from the literature or from expert opinion. This approach links network structure, invasiveness and invasibility in the context of trait-mediated interactions, such as the invasion of insects into mutualistic and antagonistic networks.     

Stability of complex food webs: resilience, resistance and the average interaction strength

In the face of stochastic climatic perturbations, the overall stability of an ecosystem will be determined by the balance between its resilience and its resistance, but their relative importance is still unknown. Using aquatic food web models we study ecosystem stability as a function of food web complexity. We measured three dynamical stability properties: resilience, resistance, and variability. Specifically, we evaluate how a decrease in the strength of predator-prey interactions with food web complexity, reflecting a decrease in predation efficiency with the number of prey per predator, affects the overall stability of the ecosystem. We find that in mass conservative ecosystems, a lower interaction strength slows down the mass cycling rate in the system and this increases its resistance to perturbations of the growth rate of primary producers. Furthermore, we show that the overall stability of the food webs is mostly given by their resistance, and not by their resilience. Resilience and resistance display opposite trends, although they are shown not to be simply opposite concepts but rather independent properties. The ecological implication is that weaker predator-prey interactions in closed ecosystems can stabilize food web dynamics by increasing its resistance to climatic perturbations.     

Measuring complexity to infer changes in the dynamics of ecological systems under stress

Despite advances in our mechanistic understanding of ecological processes, the inherent complexity of real-world ecosystems still limits our ability in predicting ecological dynamics especially in the face of on-going environmental stress. Developing a model is frequently challenged by structure uncertainty, unknown parameters, and limited data for exploring out-of-sample predictions. One way to address this challenge is to look for patterns in the data themselves in order to infer the underlying processes of an ecological system rather than to build system-specific models. For example, it has been recently suggested that statistical changes in ecological dynamics can be used to infer changes in the stability of ecosystems as they approach tipping points. For computer scientists such inference is similar to the notion of a Turing machine: a computational device that could execute a program (the process) to produce the observed data (the pattern). Here, we make use of such basic computational ideas introduced by Alan Turing to recognize changing patterns in ecological dynamics in ecosystems under stress. To do this, we use the concept of Kolmogorov algorithmic complexity that is a measure of randomness. In particular, we estimate an approximation to Kolmogorov complexity based on the Block Decomposition Method (BDM). We apply BDM to identify changes in complexity in simulated time-series and spatial datasets from ecosystems that experience different types of ecological transitions. We find that in all cases, K_BDM complexity decreased before all ecological transitions both in time-series and spatial datasets. These trends indicate that loss of stability in the ecological models we explored is characterized by loss of complexity and the emergence of a regular and computable underlying structure. Our results suggest that Kolmogorov complexity may serve as tool for revealing changes in the dynamics of ecosystems close to ecological transitions.     

An Exploratory Framework for the Empirical Measurement of Resilience

Deliberate progress towards the goal of long-term sustainability depends on understanding the dynamics of linked social and ecological systems. The concept of social-ecological resilience holds promise for interdisciplinary syntheses. Resilience is a multifaceted concept that as yet has not been directly operationalized, particularly in systems for which our ignorance is such that detailed, parameter-rich simulation models are difficult to develop. We present an exploratory framework as a step towards the operationalization of resilience for empirical studies. We equate resilience with the ability of a system to maintain its identity, where system identity is defined as a property of key components and relationships (networks) and their continuity through space and time. Innovation and memory are also fundamental to understanding identity and resilience. By parsing our systems into the elements that we subjectively consider essential to identity, we obtain a small set of specific focal variables that reflect changes in identity. By assessing the potential for changes in identity under specified drivers and perturbations, in combination with a scenario-based approach to considering alternative futures, we obtain a surrogate measure of the current resilience of our study system as the likelihood of a change in system identity under clearly specified conditions, assumptions, drivers and perturbations. Although the details of individual case studies differ, the concept of identity provides a level of generality that can be used to compare measure of resilience across cases. Our approach will also yield insights into the mechanisms of change and the potential consequences of different policy and management decisions, providing a level of decision support for each case study area.     

Marine Ecosystems as Complex Adaptive Systems: Emergent Patterns,Critical Transitions,and Public Goods

Complex adaptive systems provide a unified framework for explaining ecosystem phenomena. In the past 20 years, complex adaptive systems have been sharpened from an abstract concept into a series of tools that can be used to solve concrete problems. These advances have been led by the development of new techniques for coupling ecological and evolutionary dynamics, for integrating dynamics across multiple scales of organization, and for using data to infer the complex interactions among different components of ecological systems. Focusing on the development and usage of these new methods, we discuss how they have led to an improved understanding of three universal features of complex adaptive systems, emergent patterns; tipping points and critical phenomena; and cooperative behavior. We restrict our attention primarily to marine ecosystems, which provide numerous successful examples of the application of complex adaptive systems. Many of these are currently undergoing dramatic changes due to anthropogenic perturbations, and we take the opportunity to discuss how complex adaptive systems can be used to improve the management of public goods and to better preserve critical ecosystem services.     

The inherent multidimensionality of temporal variability: how common and rare species shape stability patterns

Empirical knowledge of diversity–stability relationships is mostly based on the analysis of temporal variability. Variability, however, often depends on external factors that act as disturbances, which makes comparisons across systems difficult to interpret. Here, we show how variability can reveal inherent stability properties of ecological communities. This requires that we abandon one‐dimensional representations, in which a single variability measurement is taken as a proxy for how stable a system is, and instead consider the whole set of variability values generated by all possible stochastic perturbations. Despite this complexity, in species‐rich systems, a generic pattern emerges from community assembly, relating variability to the abundance of perturbed species. Strikingly, the contrasting contributions of different species abundance classes to variability, driven by different types of perturbations, can lead to opposite diversity–stability patterns. We conclude that a multidimensional perspective on variability helps reveal the dynamical richness of ecological systems and the underlying meaning of their stability patterns.     

传粉昆虫下降背景下的授粉生态弹性: 内涵、机制和展望

全球传粉昆虫多样性正在下降, 如何保障农林生态系统传粉功能是当前研究的热点。理论上说, 传粉功能不仅与生态系统的传粉昆虫多样性相关, 还与生态系统的调节能力有关。近年来, 学者们逐渐认识到授粉生态弹性对传粉功能的影响。本文在回顾已有研究的基础之上, 总结传粉昆虫授粉生态弹性的内涵, 厘清授粉生态弹性与工程弹性、稳定性和抗性的异同。目前, 学者对授粉生态弹性形成机制开展广泛探讨, 提出功能冗余假说、密度补偿假说、响应多样性假说、连接周转假说和跨尺度弹性假说, 但这5个假说间的关系仍不清楚, 存在一词多义、词意混淆等现象。我们依次阐述功能冗余假说、密度补偿假说、响应多样性假说、连接周转假说和跨尺度弹性假说, 介绍不同假说中授粉生态弹性形成过程、研究热点和发展动态。通过解析授粉生态弹性的形成机制可知, 5个假说在内涵上存在紧密联系, 它们从不同空间尺度和研究对象下解释传粉昆虫授粉生态弹性的形成机制。未来授粉生态弹性研究将整合传粉昆虫群落动态和传粉功能动态的量化方法, 通过实验验证5个假说的合理性, 并揭示不同假说间的联系, 由此阐明授粉生态弹性的发生条件、形成阈值和动态规律。随着研究的深入, 授粉生态弹性理论有望用于指导农林生态系统传粉功能的经营管理。     

Understand ecosystem regime shifts by modelling ecosystem development using Boolean networks

Complex ecosystems are difficult to model and are still poorly understood. In spite of the long lasting efforts to predict them, we still lack a real integrated framework to grasp their behaviours. In this paper, the concept of ecosystem development is proposed to understand the sharp regime shifts they cumulate over the long term. To handle regime shifts, we develop an integrated model merging the physical, biological and social components and interactions (processes) of an ecosystem into a single graph representation. We then formalize sharp structural (topological) changes of the system with Boolean networks. We illustrate this theoretical approach borrowed from discrete model formalisms on some ecosystems assumed to be representative of most ecosystems: the eusocial (termite and ant) insect colonies and their associated interactions.Boolean networks, combined with rigorous production/rewriting rules and syntax, simulate the ecosystem's responses to strong perturbations. This deterministic and qualitative approach allows identifying fragile components, analysing ecosystem resilience to perturbations and to map out every lethal trajectory of the ecosystem. In our models, termite colonies appear to be almost six times less vulnerable to perturbations than ant colonies, and need (8%) more time steps to collapse. This robust result was partly due to the higher number of essential nodes in ant ecosystems, and partly due to interactions related to the ants' vertebrate predators. The rigorous and parsimonious abilities of such discrete models pave the way in reinterpreting and managing a wide range of ecosystems.     

景观生态恢复与重建是区域生态安全格局构建的关键途径

生态恢复与重建是跨尺度、多等级的问题,其主要表现层次应是生态系统（生物群落）、景观,甚至区域,而不能仅仅局限于生态系统。景观的恢复与重建是针对景观退化而言,景观退化从表现形式上可分为景观结构退化与景观功能退化。景观结构退化即景观破碎化,是指景观中各生态系统之间的各种功能联系断裂或连接度(connectivity)减少的现象;而鲜受重视的景观聚集（aggregation）在很多情况下同样具有造成景观退化的负面效应。景观功能退化是指与前一状态相比,由于景观异质性的改变导致景观的稳定性与服务功能等的衰退现象。景观恢复是指恢复原生生态系统间被人类活动终止或破坏的相互联系;景观生态建设应以景观单元空间结构的调整和重新构建为基本手段,包括调整原有的景观格局,引进新的景观组分等,以改善受胁或受损生态系统的功能,提高其基本生产力和稳定性,将人类活动对于景观演化的影响导入良性循环。二者的综合,统称为景观生态恢复与重建,是构建安全的区域生态格局的关键途径。其目标是建立一种由结构合理、功能高效、关系协调的模式生态系统（model ecosystem）组成的模式景观（model landscape）,以实现生态系统健康、生态格局安全和景观服务功能持续,以3S(RS,GPS,GIS)技术为支撑的GAP(ageographic approach to protect biological diversity)分析将为大尺度景观恢复的诊断、评价、规划提供重要的手段。景观中某些关键性点、位置或关系的破坏对整个生态安全具有毁灭性的后果,研究景观层次上的生态恢复模式及恢复技术、选择恢复的关键位置、构筑生态安全格局已成为景观生态学家关注的焦点。     

Diversity-dependent stability under mowing and nutrient addition: evidence from a 7-year grassland experiment

Anthropogenic perturbations may affect biodiversity and ecological stability as well as their relationships. However, diversity-stability patterns and associated mechanisms under human disturbances have rarely been explored. We conducted a 7-year field experiment examining the effects of mowing and nutrient addition on the diversity and temporal stability of herbaceous plant communities in a temperate steppe in northern China. Mowing increased population and community stability, whereas nutrient addition had the opposite effects. Stability exhibited positive relationships with species richness at population, functional group and community levels. Treatments did not alter these positive diversity-stability relationships, which were associated with the stabilising effect of species richness on component populations, species asynchrony and portfolio effects. Despite the difficulty of pinpointing causal mechanisms of diversity-stability patterns observed in nature, our results suggest that diversity may still be a useful predictor of the stability of ecosystems confronted with anthropogenic disturbances.     

Ecology,thermodynamics and H.T. Odum's conjectures

The central rôle of energy in all life processes has led to the development of numerous hypotheses, conjectures and theories on the relationships between thermodynamics and ecological processes. In this paper we examine the theoretical and empirical support for these developments, and in particular for the widely published set of thermodynamic conjectures developed by H.T. Odum, in which the maximum power principle is put forward as a generic feature of evolution in ecosystems. Although they are widely used, we argue that many of the ecological studies that have adopted the ideas encapsulated in Odum's work have done so without being aware of some of the fundamental problems underlying this approach. We discuss alternative ways in which a general available-work concept could be constructed for use as a numeraire in an energy-centered ecological theory or paradigm. In so doing, we examine what is meant by material accessibility and energy stocks and flows with respect to traditional food web and food chain theories, and relate these to results from the evolutionary dynamics of ecosystems. We conclude that the various forms and uses of energy bound up in essential ecosystem processes present a formidable obstacle to obtaining an operational definition of a general, aggregated available-work concept, a prerequisite for the systems approach of Odum and others. We also show that the prototypical derivations of the maximum power principle, and its interpretation, are contradicted on many scales both by empirical data and models, thereby invalidating the maximum power principle as a general principle of ecological evolution. The conclusions point to the fundamental problem of trying to describe ecosystems in a framework which has a one-dimensional currency.     

种间互作网络的结构、生态系统功能及稳定性机制研究

生态群落中不同物种间发生多样化的相互作用, 形成了复杂的种间互作网络。复杂生态网络的结构如何影响群落的生态系统功能及稳定性是群落生态学的核心问题之一。种间互作直接影响到物质和能量在生态系统不同组分之间的流动和循环以及群落构建过程, 使得网络结构与生态系统功能和群落稳定性密切相关。在群落及生态系统水平上开展种间互作网络研究将为群落的构建机制、生物多样性维持、生态系统稳定性、物种协同进化和性状分化等领域提供新的视野。当前生物多样性及生态系统功能受到全球变化的极大影响, 研究种间互作网络的拓扑结构、构建机制、稳定性和生态功能也可为生物多样性的保护和管理提供依据。该文从网络结构、构建机制、网络结构和稳定性关系、种间互作对生态系统功能的影响等4个方面综述当前种间网络研究进展, 并提出在今后的研究中利用机器学习和多层网络等来探究环境变化对种间互作网络结构和功能的影响, 并实现理论和实证研究的有效整合。     

Using Fluctuation Analysis to Establish Causal Relations between Cellular Events without Experimental Perturbation

Experimental perturbations are commonly used to establish causal relationships between the molecular components of a pathway and their cellular functions; however, this approach suffers inherent limitations. Especially in pathways with a significant level of nonlinearity and redundancy among components, such perturbations induce compensatory responses that obscure the actual function of the targeted component in the unperturbed pathway. A complementary approach uses constitutive fluctuations in component activities to identify the hierarchy of information flow through pathways. Here, we review the motivation for using perturbation-free approaches and highlight recent advances made in using perturbation-free fluctuation analysis as a means to establish causality among cellular events.     

稳定性同位素技术与Keeling曲线法在陆地生态系统碳/水交换研究中的应用

稳定性同位素技术和Keeling曲线法是现代生态学研究的重要手段和方法之一。稳定性同位素能够整合生态系统复杂的生物学、生态学和生物地球化学过程在时间和空间尺度上对环境变化的响应。Keeling曲线法是以生物过程前后物质平衡理论为基础,将CO₂或H₂O的同位素组成(δD、δ¹³C或δ¹⁸O)与其对应浓度测量结合起来,将生态系统净碳通量区分为光合固定和呼吸释放通量,或将整个生态系统水分蒸散区分为植物蒸腾和土壤蒸发。在全球尺度上,稳定性同位素技术、Keeling曲线法与全球尺度陆地生态系统模型相结合,还可区分陆地生态系统和海洋生态系统对全球碳通量的贡献以及不同植被类型(C₃或C₄)在全球CO₂同化量中所占的比例。然而,生态系统的异质性使得稳定性同位素技术和Keeling曲线法从冠层尺度外推到生态系统、区域或全球尺度时存在有一定程度的不确定性。此外,取样时间、地点的选取也会影响最终的研究结果。尽管如此,随着分析手段的不断精确和研究方法的日趋完善,稳定性同位素技术和Keeling曲线法与其它测量方法(如微气象法)的有机结合将成为未来陆地生态系统碳/水交换研究的重要手段和方法之一。