In theoretical studies, the most commonly used measure of ecological stability is resilience: ecosystems asymptotic rate of return to equilibrium after a pulse-perturbation -or shock. A complementary notion of growing popularity is reactivity: the strongest initial response to shocks. On the other hand, empirical stability is often quantified as the inverse of temporal variability, directly estimated on data, and reflecting ecosystems response to persistent and erratic environmental disturbances. It is unclear whether and how this empirical measure is related to resilience and reactivity. Here, we establish a connection by introducing two variability-based stability measures belonging to the theoretical realm of resilience and reactivity. We call them intrinsic, stochastic and deterministic invariability; respectively defined as the inverse of the strongest stationary response to white-noise and to single-frequency perturbations. We prove that they predict ecosystems worst response to broad classes of disturbances, including realistic models of environmental fluctuations. We show that they are intermediate measures between resilience and reactivity and that, although defined with respect to persistent perturbations, they can be related to the whole transient regime following a shock, making them more integrative notions than reactivity and resilience. We argue that invariability measures constitute a stepping stone, and discuss the challenges ahead to further unify theoretical and empirical approaches to stability. Copyright © 2015 Elsevier Ltd. All rights reserved.

To predict the ecological consequences of biodiversity loss, researchers have spent much time and effort quantifying how biological variation affects the magnitude and stability of ecological processes that underlie the functioning of ecosystems. Here we add to this work by looking at how biodiversity jointly impacts two aspects of ecosystem functioning at once: (1) the production of biomass at any single point in time (biomass/area or biomass/ volume), and (2) the stability of biomass production through time (the CV of changes in total community biomass through time). While it is often assumed that biodiversity simultaneously enhances both of these aspects of ecosystem functioning, the joint distribution of data describing how species richness regulates productivity and stability has yet to be quantified. Furthermore, analyses have yet to examine how diversity effects on production covary with diversity effects on stability. To overcome these two gaps, we reanalyzed the data from 34 experiments that have manipulated the richness of terrestrial plants or aquatic algae and measured how this aspect of biodiversity affects community biomass at multiple time points. Our reanalysis confirms that biodiversity does indeed simultaneously enhance both the production and stability of biomass in experimental systems, and this is broadly true for terrestrial and aquatic primary producers. However, the strength of diversity effects on biomass production is independent of diversity effects on temporal stability. The independence of effect sizes leads to two important conclusions. First, while it may be generally true that biodiversity enhances both productivity and stability, it is also true that the highest levels of productivity in a diverse community are not associated with the highest levels of stability. Thus, on average, diversity does not maximize the various aspects of ecosystem functioning we might wish to achieve in conservation and management. Second, knowing how biodiversity affects productivity gives no information about how diversity affects stability (or vice versa). Therefore, to predict the ecological changes that occur in ecosystems after extinction, we will need to develop separate mechanistic models for each independent aspect of ecosystem functioning.

As biodiversity is declining at an unprecedented rate, an important current scientific challenge is to understand and predict the consequences of biodiversity loss. Here, we develop a theory that predicts the temporal variability of community biomass from the properties of individual component species in monoculture. Our theory shows that biodiversity stabilises ecosystems through three main mechanisms: (1) asynchrony in species' responses to environmental fluctuations, (2) reduced demographic stochasticity due to overyielding in species mixtures and (3) reduced observation error (including spatial and sampling variability). Parameterised with empirical data from four long-term grassland biodiversity experiments, our prediction explained 22-75% of the observed variability, and captured much of the effect of species richness. Richness stabilised communities mainly by increasing community biomass and reducing the strength of demographic stochasticity. Our approach calls for a re-evaluation of the mechanisms explaining the effects of biodiversity on ecosystem stability.© 2013 Blackwell Publishing Ltd/CNRS.

Understanding the stability of ecological communities is a matter of increasing importance in the context of global environmental change. Yet it has proved to be a challenging task. Different metrics are used to assess the stability of ecological systems, and the choice of one metric over another may result in conflicting conclusions. Although each of the multitude of metrics is useful for answering a specific question about stability, the relationship among metrics is poorly understood. Such lack of understanding prevents scientists from developing a unified concept of stability. Instead, by investigating these relationships we can unveil how many dimensions of stability there are (i.e., in how many independent components stability metrics can be grouped), which should help build a more comprehensive concept of stability. Here we simultaneously measured 27 stability metrics frequently used in ecological studies. Our approach is based on dynamical simulations of multispecies trophic communities under different perturbation scenarios. Mapping the relationships between the metrics revealed that they can be lumped into 3 main groups of relatively independent stability components: early response to pulse, sensitivities to press, and distance to threshold. Selecting metrics from each of these groups allows a more accurate and comprehensive quantification of the overall stability of ecological communities. These results contribute to improving our understanding and assessment of stability in ecological communities.

Human actions challenge nature in many ways. Ecological responses are ineluctably complex, demanding measures that describe them succinctly. Collectively, these measures encapsulate the overall 'stability' of the system. Many international bodies, including the Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services, broadly aspire to maintain or enhance ecological stability. Such bodies frequently use terms pertaining to stability that lack clear definition. Consequently, we cannot measure them and so they disconnect from a large body of theoretical and empirical understanding. We assess the scientific and policy literature and show that this disconnect is one consequence of an inconsistent and one-dimensional approach that ecologists have taken to both disturbances and stability. This has led to confused communication of the nature of stability and the level of our insight into it. Disturbances and stability are multidimensional. Our understanding of them is not. We have a remarkably poor understanding of the impacts on stability of the characteristics that define many, perhaps all, of the most important elements of global change. We provide recommendations for theoreticians, empiricists and policymakers on how to better integrate the multidimensional nature of ecological stability into their research, policies and actions.© 2016 John Wiley & Sons Ltd/CNRS.

Ecological stability is touted as a complex and multifaceted concept, including components such as variability, resistance, resilience, persistence and robustness. Even though a complete appreciation of the effects of perturbations on ecosystems requires the simultaneous measurement of these multiple components of stability, most ecological research has focused on one or a few of those components analysed in isolation. Here, we present a new view of ecological stability that recognises explicitly the non-independence of components of stability. This provides an approach for simplifying the concept of stability. We illustrate the concept and approach using results from a field experiment, and show that the effective dimensionality of ecological stability is considerably lower than if the various components of stability were unrelated. However, strong perturbations can modify, and even decouple, relationships among individual components of stability. Thus, perturbations not only increase the dimensionality of stability but they can also alter the relationships among components of stability in different ways. Studies that focus on single forms of stability in isolation therefore risk underestimating significantly the potential of perturbations to destabilise ecosystems. In contrast, application of the multidimensional stability framework that we propose gives a far richer understanding of how communities respond to perturbations.© 2013 Blackwell Publishing Ltd/CNRS.

Biodiversity has been shown to increase the temporal stability of community and ecosystem attributes through multiple mechanisms, but these same mechanisms make less consistent predictions about the effects of richness on population stability. The overall effects of biodiversity on population and community stability will therefore depend on the dominant mechanisms that are likely to vary with the nature of biodiversity loss and the degree of environmental variability. We conducted a mesocosm experiment in which we generated a gradient in zooplankton species richness by directly manipulating dominant species and by allowing/preventing immigration from a metacommunity. The mesocosms were maintained under either constant or variable nutrient environments. Population, community, and ecosystem data were collected for five months. We found that zooplankton population and community stability is enhanced in species-rich communities in both constant and variable environments. Species richness increased primarily through the addition of species with low abundance. The communities that were connected to a metacommunity via immigration were the most diverse and the most stable, indicating the importance of both metacommunity dynamics and rare species for stability. We found little evidence for selection effects or overyielding as stabilizing forces. We did find support for asynchronous dynamics and statistical averaging, both of which predict destabilizing effects at the population level. We also found support for weak interactions, which predicts that both populations and communities will become more stable as richness increases. In order to understand the effects of biodiversity loss on stability, we will need to understand when different stabilizing mechanisms tend to operate but also how multiple mechanisms interact.

A rich body of knowledge links biodiversity to ecosystem functioning (BEF), but it is primarily focused on small scales. We review the current theory and identify six expectations for scale dependence in the BEF relationship: (1) a nonlinear change in the slope of the BEF relationship with spatial scale; (2) a scale-dependent relationship between ecosystem stability and spatial extent; (3) coexistence within and among sites will result in a positive BEF relationship at larger scales; (4) temporal autocorrelation in environmental variability affects species turnover and thus the change in BEF slope with scale; (5) connectivity in metacommunities generates nonlinear BEF and stability relationships by affecting population synchrony at local and regional scales; (6) spatial scaling in food web structure and diversity will generate scale dependence in ecosystem functioning. We suggest directions for synthesis that combine approaches in metaecosystem and metacommunity ecology and integrate cross-scale feedbacks. Tests of this theory may combine remote sensing with a generation of networked experiments that assess effects at multiple scales. We also show how anthropogenic land cover change may alter the scaling of the BEF relationship. New research on the role of scale in BEF will guide policy linking the goals of managing biodiversity and ecosystems.© 2020 The Authors. Ecology Letters published by CNRS and John Wiley & Sons Ltd.

 We present an inventory and analysis of discussions of ecological stability, considering 163 definitions of 70 different stability concepts. Our aim is to derive a strategy that can help to dispel the existing "confusion of tongues" on the subject of "stability" and prevent its future recurrence. The strategy consists of three questions that should be kept in mind when communicating about stability properties. These three questions should overcome the three main sources of confusion in terminology. Firstly, which stability properties are being addressed in the stability statement? Our analysis shows that the general term "stability" is so ambiguous as to be useless.It can be replaced by the stability properties "staying essentially unchanged" (constancy), "returning to the reference state (or dynamic) after a temporary disturbance" (resilience), and "persistence through time of an ecological system" (persistence). Second, to what ecological situation does the statement refer? An ecological situation is defined by a set of features that, taken as a whole, determine the domain of validity of a stability statement. The six most important features form the "ecological checklist", which serves to classify ecological situations and thereby provides a system of coordinates for communication. The six points are: variable of interest, level of description, reference state, disturbance, spatial scale and temporal scale. Thirdly, is the statement anchored in the situation in question, or is there unacceptable generalisation by inferring "stability" of the whole system from a certain stability property in a certain ecological ecological situation? This question separates the scientifically valuable content of a statement from the desire for general statements which is often projected through stability statements.

Understanding the factors governing ecological stability in variable environments is a central focus of ecology. Functional diversity can stabilize ecosystem function over time if one group of species compensates for an environmentally driven decline in another. Although intuitively appealing, evidence for this pattern is mixed. We hypothesized that diverse functional responses to rainfall will increase the stability of vegetation cover and biomass across rainfall conditions, but that this effect depends on land-use legacies that maintain functional diversity. We experimentally manipulated grazing in a California grassland to create land-use legacies of low and moderate grazing, across which we implemented rainout shelters and irrigation to create dry and wet conditions over 3 years. We found that the stability of the vegetation cover was greatly elevated and the stability of the biomass was slightly elevated across rainfall conditions in areas with histories of moderate grazing. Initial functional diversity-both in the seed bank and aboveground-was also greater in areas that had been moderately grazed. Rainfall conditions in conjunction with this grazing legacy led to different functional diversity patterns over time. Wet conditions led to rapid declines in functional diversity and a convergence on resource-acquisitive traits. In contrast, consecutively dry conditions maintained but did not increase functional diversity over time. As a result, grazing practices and environmental conditions that decrease functional diversity may be associated with lasting effects on the response of ecosystem functions to drought. Our results demonstrate that theorized relationships between diversity and stability are applicable and important in the context of working grazed landscapes.

Human-driven environmental changes may simultaneously affect the biodiversity, productivity, and stability of Earth's ecosystems, but there is no consensus on the causal relationships linking these variables. Data from 12 multiyear experiments that manipulate important anthropogenic drivers, including plant diversity, nitrogen, carbon dioxide, fire, herbivory, and water, show that each driver influences ecosystem productivity. However, the stability of ecosystem productivity is only changed by those drivers that alter biodiversity, with a given decrease in plant species numbers leading to a quantitatively similar decrease in ecosystem stability regardless of which driver caused the biodiversity loss. These results suggest that changes in biodiversity caused by drivers of environmental change may be a major factor determining how global environmental changes affect ecosystem stability. Copyright © 2015, American Association for the Advancement of Science.

Insurance effects of biodiversity can stabilize the functioning of multispecies ecosystems against environmental variability when differential species' responses lead to asynchronous population dynamics. When responses are not perfectly positively correlated, declines in some populations are compensated by increases in others, smoothing variability in ecosystem productivity. This variance reduction effect of biodiversity is analogous to the risk-spreading benefits of diverse investment portfolios in financial markets. We use data from the BIODEPTH network of grassland biodiversity experiments to perform a general test for stabilizing effects of plant diversity on the temporal variability of individual species, functional groups, and aggregate communities. We tested three potential mechanisms: reduction of temporal variability through population asynchrony; enhancement of long-term average performance through positive selection effects; and increases in the temporal mean due to overyielding. Our results support a stabilizing effect of diversity on the temporal variability of grassland aboveground annual net primary production through two mechanisms. Two-species communities with greater population asynchrony were more stable in their average production over time due to compensatory fluctuations. Overyielding also stabilized productivity by increasing levels of average biomass production relative to temporal variability. However, there was no evidence for a performance-enhancing effect on the temporal mean through positive selection effects. In combination with previous work, our results suggest that stabilizing effects of diversity on community productivity through population asynchrony and overyielding appear to be general in grassland ecosystems.

Effects of species diversity on population and community stability (or more precisely, the effects of species richness on temporal variability) have been studied for several decades, but there have been no large-scale tests in natural communities of predictions from theory. We used 91 data sets including plants, fish, small mammals, zooplankton, birds, and insects, to examine the relationship between species richness and temporal variability in populations and communities. Seventy-eight of 91 data sets showed a negative relationship between species richness and population variability; 46 of these relationships were statistically significant. Only five of the 13 positive richness-population variability relationships were statistically significant. Similarly, 51 of 91 data sets showed a negative relationship between species richness and community variability; of these, 26 were statistically significant. Seven of the 40 positive richness-community-variability relationships were statistically significant. We were able to test transferability (i.e., the predictive ability of models for sites that are spatially distinct from sites that were used to build the models) for 69 of 91 data sets; 35 and 31 data sets were transferable at the population and community levels, respectively. Only four were positive at the population level, and two at the community level. We conclude that there is compelling evidence of a negative relationship between species richness and temporal variability for about one-half of the ecological communities we examined. However, species richness explained relatively little of the variability in population or community abundances and resulted in small improvements in predictive ability.© 2018 by the Ecological Society of America.

Long-term variability in the abundance of populations depends on the sensitivity of species to environmental fluctuations and the amplification of environmental fluctuations by interactions among species. Although competitive interactions and species number may have diverse effects on variability measured at the individual species level, a combination of theoretical analyses shows that these factors have no effect on variability measured at the community level. Therefore, biodiversity may increase community stability by promoting diversity among species in their responses to environmental fluctuations, but increasing the number and strength of competitive interactions has little effect.

Understanding the mechanisms responsible for stability and persistence of ecosystems is one of the greatest challenges in ecology. Robert May showed that, contrary to intuition, complex randomly built ecosystems are less likely to be stable than simpler ones. Few attempts have been tried to test May's prediction empirically, and we still ignore what is the actual complexity-stability relationship in natural ecosystems. Here we perform a stability analysis of 116 quantitative food webs sampled worldwide. We find that classic descriptors of complexity (species richness, connectance and interaction strength) are not associated with stability in empirical food webs. Further analysis reveals that a correlation between the effects of predators on prey and those of prey on predators, combined with a high frequency of weak interactions, stabilize food web dynamics relative to the random expectation. We conclude that empirical food webs have several non-random properties contributing to the absence of a complexity-stability relationship.

Ecologists disagree on how diversity affects stability. At the heart of the controversy is the relationship between diversity and population stability, with conflicting findings from both theoretical and empirical studies. To help reconcile these results, we propose that this relationship may depend on trophic complexity, such that positive relations tend to emerge in multitrophic but not single-trophic communities. This hypothesis is based on the premise that stabilizing weak trophic interactions restrain population oscillations associated with strong trophic interactions in diverse multitrophic communities. We tested this hypothesis using simple freshwater bacterivorous protist communities differing in diversity with and without a predatory protist species. Coupling weak and strong trophic interactions reduced population temporal variability of the strong-interacting species, supporting the stabilizing role of weak interactions. In keeping with our hypothesis, predation altered the overall effect of diversity on population temporal stability and, in particular, caused a reversal of the diversity-stability relationship (negative without predators and positive with predators) for the strong-interacting species. A similar role of predation was also observed when examining the relationship between diversity and temporal stability of community biomass. Together, these findings demonstrated strong interactive effects of trophic interactions and diversity on temporal stability of population and community properties.

The question of how species diversity affects ecological stability has long interested ecologists and yet remains largely unresolved. Historically, attempts to answer this question have been hampered by the presence of multiple potentially confounding stability concepts, confusion over responses at different levels of ecological organization, discrepancy between theoretical predictions, and, particularly, the paucity of empirical studies. Here we used meta-analyses to synthesize results of empirical studies published primarily in the past 2 decades on the relationship between species diversity and temporal stability. We show that the overall effect of increasing diversity was positive for community-level temporal stability but neutral for population-level temporal stability. There were, however, striking differences in the diversity-stability relationship between single- and multitrophic systems, with diversity stabilizing both population and community dynamics in multitrophic but not single-trophic communities. These patterns were broadly equivalent across experimental and observational studies as well as across terrestrial and aquatic studies. We discuss possible mechanisms for population stability to increase with diversity in multitrophic systems and for diversity to influence community-level stability in general. Overall, our results indicate that diversity can affect temporal stability, but the effects may critically depend on trophic complexity.

Aim Global carbon cycle models do not incorporate the stabilizing effect of biodiversity on productivity despite this phenomenon has been widely described in several local scale manipulative experiments. The reason is a lack of evidence supporting the importance of biodiversity on spatial scales at which climate models are built. Here, we test the hypothesis that diversity enhances productivity stability at a large scale. Location South American dryland known as Caatinga (similar to 830,000 km(2)). Time period 2001-2010. Major taxa studied Woody plants. Methods We used the enhanced vegetation index of Caatinga vegetation remnants, from 2001 to 2010, to calculate vegetation productivity stability across years. We used occurrence records of 606 woody species from floristic surveys to derive species richness and phylogenetic diversity at similar to 5 km and similar to 55 km (0.5 degrees) resolution. Climate data were obtained from global databases. Results Plant phylogenetic diversity has a strong positive correlation with productivity stability even after controlling for several climatic variables, such as rainfall, temperature and cloudiness, at both resolutions. Species richness was not significant when climatic variables were included. Main conclusions This result expands by several orders of magnitude the spatial scale of the evidence that biodiversity strengths the resilience of key ecosystem functions. We highlight that, by incorporating plant phylogenetic diversity, regional and global climate models can generate more accurate predictions about future ecosystem functioning and services that are critical to humankind.

Research on the relationship between the architecture of ecological networks and community stability has mainly focused on one type of interaction at a time, making difficult any comparison between different network types. We used a theoretical approach to show that the network architecture favoring stability fundamentally differs between trophic and mutualistic networks. A highly connected and nested architecture promotes community stability in mutualistic networks, whereas the stability of trophic networks is enhanced in compartmented and weakly connected architectures. These theoretical predictions are supported by a meta-analysis on the architecture of a large series of real pollination (mutualistic) and herbivory (trophic) networks. We conclude that strong variations in the stability of architectural patterns constrain ecological networks toward different architectures, depending on the type of interaction.

A major ecosystem effect of biodiversity is to stabilise assemblages that perform particular functions. However, diversity-stability relationships (DSRs) are analysed using a variety of different population and community properties, most of which are adopted from theory that makes several restrictive assumptions that are unlikely to be reflected in nature. Here, we construct a simple synthesis and generalisation of previous theory for the DSR. We show that community stability is a product of two quantities: the synchrony of population fluctuations, and an average species-level population stability that is weighted by relative abundance. Weighted average population stability can be decomposed to consider effects of the mean-variance scaling of abundance, changes in mean abundance with diversity and differences in species' mean abundance in monoculture. Our framework makes explicit how unevenness in the abundances of species in real communities influences the DSR, which occurs both through effects on community synchrony, and effects on weighted average population variability. This theory provides a more robust framework for analysing the results of empirical studies of the DSR, and facilitates the integration of findings from real and model communities.© 2012 Blackwell Publishing Ltd/CNRS.

Although the impacts of the loss of biodiversity on ecosystem functioning are well established, the importance of the loss of biodiversity relative to other human-caused drivers of environmental change remains uncertain. Results of 11 experiments show that ecologically relevant decreases in grassland plant diversity influenced productivity at least as much as ecologically relevant changes in nitrogen, water, CO(2), herbivores, drought, or fire. Moreover, biodiversity became an increasingly dominant driver of ecosystem productivity through time, whereas effects of other factors either declined (nitrogen addition) or remained unchanged (all others). In particular, a change in plant diversity from four to 16 species caused as large an increase in productivity as addition of 54 kg · ha(-1) · y(-1) of fertilizer N, and was as influential as removing a dominant herbivore, a major natural drought, water addition, and fire suppression. A change in diversity from one to 16 species caused a greater biomass increase than 95 kg · ha(-1) · y(-1) of N or any other treatment. Our conclusions are based on >7,000 productivity measurements from 11 long-term experiments (mean length, ~ 13 y) conducted at a single site with species from a single regional species pool, thus controlling for many potentially confounding factors. Our results suggest that the loss of biodiversity may have at least as great an impact on ecosystem functioning as other anthropogenic drivers of environmental change, and that use of diverse mixtures of species may be as effective in increasing productivity of some biomass crops as fertilization and may better provide ecosystem services.

Theory relating species richness to ecosystem variability typically ignores the potential for environmental variability to promote species coexistence. Failure to account for fluctuation-dependent coexistence may explain deviations from the expected negative diversity-ecosystem variability relationship, and limits our ability to predict the consequences of increases in environmental variability. We use a consumer-resource model to explore how coexistence via the temporal storage effect and relative nonlinearity affects ecosystem variability. We show that a positive, rather than negative, diversity-ecosystem variability relationship is possible when ecosystem function is sampled across a natural gradient in environmental variability and diversity. We also show how fluctuation-dependent coexistence can buffer ecosystem functioning against increasing environmental variability by promoting species richness and portfolio effects. Our work provides a general explanation for variation in observed diversity-ecosystem variability relationships and highlights the importance of conserving regional species pools to help buffer ecosystems against predicted increases in environmental variability.© 2017 John Wiley & Sons Ltd/CNRS.

本文在简述生物多样性与生态系统稳定性研究动态的基础上,从生物多样性和稳定性的概念出发,指出忽视多样性和稳定性的生物组织层次可能是造成观点纷争的根源之一。特定生物组织层次的稳定性可能更多地与该层次的多样性特征相关。探讨多样性和稳定性的关系应从不同的生物组织层次上进行。扰动是生态系统多样性与稳定性关系悖论中的重要因子,如果根据扰动的性质,把生态系统（或其他组织层次）区分为受非正常外力干扰和受环境因子时间异质性波动干扰2类系统,稳定性的4个内涵可以理解为：对于受非正常外力干扰的系统而言,抵抗力和恢复力是稳定性适宜的测度指标；对于受环境因子时间异质性波动干扰的系统而言,利用持久性和变异性衡量系统的稳定性则更具实际意义。结合对群落和种群层次多样性与稳定性相关机制的初步讨论,本文认为: 在特定的前提下,多样性可以导致稳定性。

Temporal stability of ecosystem functioning increases the predictability and reliability of ecosystem services, and understanding the drivers of stability across spatial scales is important for land management and policy decisions. We used species-level abundance data from 62 plant communities across five continents to assess mechanisms of temporal stability across spatial scales. We assessed how asynchrony (i.e. different units responding dissimilarly through time) of species and local communities stabilised metacommunity ecosystem function. Asynchrony of species increased stability of local communities, and asynchrony among local communities enhanced metacommunity stability by a wide range of magnitudes (1-315%); this range was positively correlated with the size of the metacommunity. Additionally, asynchronous responses among local communities were linked with species' populations fluctuating asynchronously across space, perhaps stemming from physical and/or competitive differences among local communities. Accordingly, we suggest spatial heterogeneity should be a major focus for maintaining the stability of ecosystem services at larger spatial scales.© 2017 The Authors. Ecology Letters published by CNRS and John Wiley & Sons Ltd.

对自然生态系统的观察给人们以复杂的群落更稳定的直观印象, 但数学模型却得出了截然相反的结论。这一“悖论”使得复杂性-稳定性研究自20世纪70年代以来成为长期的热点。本文对这一领域的数学模型研究进行简要综述。首先对这一论题进行概念剖析, 然后将各类模型分为线性和非线性两大类, 前者即群落矩阵法, 后者包括相互作用矩阵法、复杂网络数值模拟法和食物网构件动力学法。它们分别基于不同的群落构建方法和稳定性判断标准, 探求各物种是如何相互作用并实现共存的。总体而言, 在随机构建的群落模型中, 多样性和连接度的增长不利于系统稳定; 而在更接近真实自然群落的模型中, 相互作用方式、网络拓扑结构、相互作用强度分布等方面的机制提供了稳定效应, 按此组织的生态网络可达到很高的复杂度。然而, 复杂性-稳定性的研究还远未结束, 当前的模型仍不足以反映自然群落中的复杂相互作用, 稳定性的概念也有待拓展。对这一议题的深入研究在生态学理论和生态系统管理实践方面都具有重大价值。

Although the effect of biodiversity on ecosystem functioning has become a major focus in ecology, its significance in a fluctuating environment is still poorly understood. According to the insurance hypothesis, biodiversity insures ecosystems against declines in their functioning because many species provide greater guarantees that some will maintain functioning even if others fail. Here we examine this hypothesis theoretically. We develop a general stochastic dynamic model to assess the effects of species richness on the expected temporal mean and variance of ecosystem processes such as productivity, based on individual species' productivity responses to environmental fluctuations. Our model shows two major insurance effects of species richness on ecosystem productivity: (i) a buffering effect, i.e., a reduction in the temporal variance of productivity, and (ii) a performance-enhancing effect, i.e., an increase in the temporal mean of productivity. The strength of these insurance effects is determined by three factors: (i) the way ecosystem productivity is determined by individual species responses to environmental fluctuations, (ii) the degree of asynchronicity of these responses, and (iii) the detailed form of these responses. In particular, the greater the variance of the species responses, the lower the species richness at which the temporal mean of the ecosystem process saturates and the ecosystem becomes redundant. These results provide a strong theoretical foundation for the insurance hypothesis, which proves to be a fundamental principle for understanding the long-term effects of biodiversity on ecosystem processes.