Interaction strengths in balanced carbon cycles and the absence of a relation between ecosystem complexity and stability

Seasonal Shifts in Trophic Interaction Strength Drive Stability of Natural Food Webs

It remains challenging to understand why natural food webs are remarkably stable despite highly variable environmental factors and population densities. We investigated the dynamics in the structure and stability of Lake Constance's pelagic food web using 7 years of high-frequency observations of biomasses and production, leading to 59 seasonally resolved quantitative food web descriptions. We assessed the dynamics in asymptotic food web stability through maximum loop weight, which revealed underlying stability mechanisms. Maximum loop weight showed a recurrent seasonal pattern with a consistently high stability despite pronounced dynamics in biomasses, fluxes and productivity. This stability resulted from seasonal rewiring of the food web, driven by energetic constraints within loops and their embedding into food web structure. The stabilising restructuring emerged from counter-acting effects of metabolic activity and competitiveness/susceptibility to predation within a diverse grazer community on loop weight. This underscores the role of functional diversity in promoting food web stability.

Five fundamental ways in which complex food webs may spiral out of control

Theory suggests that increasingly long, negative feedback loops of many interacting species may destabilize food webs as complexity increases. Less attention has, however, been paid to the specific ways in which these 'delayed negative feedbacks' may affect the response of complex ecosystems to global environmental change. Here, we describe five fundamental ways in which these feedbacks might pave the way for abrupt, large-scale transitions and species losses. By combining topological and bioenergetic models, we then proceed by showing that the likelihood of such transitions increases with the number of interacting species and/or when the combined effects of stabilizing network patterns approach the minimum required for stable coexistence. Our findings thus shift the question from the classical question of what makes complex, unaltered ecosystems stable to whether the effects of, known and unknown, stabilizing food-web patterns are sufficient to prevent abrupt, large-scale transitions under global environmental change.

Competitive hierarchies in bryozoan assemblages mitigate network instability by keeping short and long feedback loops weak

Competitive hierarchies in diverse ecological communities have long been thought to lead to instability and prevent coexistence. However, system stability has never been tested, and the relation between hierarchy and instability has never been explained in complex competition networks parameterised with data from direct observation. Here we test model stability of 30 multispecies bryozoan assemblages, using estimates of energy loss from observed interference competition to parameterise both the inter- and intraspecific interactions in the competition networks. We find that all competition networks are unstable. However, instability is mitigated considerably by asymmetries in the energy loss rates brought about by hierarchies of strong and weak competitors. This asymmetric organisation results in asymmetries in the interaction strengths, which reduces instability by keeping the weight of short (positive) and longer (positive and negative) feedback loops low. Our results support the idea that interference competition leads to instability and exclusion but demonstrate that this is not because of, but despite, competitive hierarchy.

Invasive Spartina alterniflora habitat forms high energy fluxes but low food web stability compared to adjacent native vegetated habitats

Invasive Spartina spp. mostly colonizes a bare tidal flat and then establishes a new vegetated habitat, where it promotes the productivity of local ecosystems. However, it was unclear whether the invasive habitat could well exhibit ecosystem functioning, e.g. how its high productivity propagates throughout the food web and whether it thereby develops a high food web stability relative to native vegetated habitats. By developing quantitative food webs for a long-established invasive Spartina alterniflora habitat and adjacent native salt marsh (Suaeda salsa) and seagrass (Zostera japonica) habitats in China's Yellow River Delta, we investigated the distributions of energy fluxes, assessed the stability of food webs, and investigated the net trophic effects between trophic groups by combining all direct and indirect trophic interactions. Results showed that the total energy flux in the invasive S. alterniflora habitat was comparable to that in the Z. japonica habitat, whereas 4.5 times higher than that in the S. salsa habitat. While, the invasive habitat had the lowest trophic transfer efficiencies. Food web stability in the invasive habitat was about 3 and 40 times lower than that in the S. salsa and Z. japonica habitats, respectively. Additionally, there were strong net effects caused by intermediate invertebrate species in the invasive habitat rather than by fish species in both native habitats. This study revealed the contradiction between the promotion of energy fluxes and the decrease of food web stability resulting from the invasion of S. alterniflora, which provides new insights into the community-based management of plant invasions.

Coexistence in diverse communities with higher-order interactions

A central assumption in most ecological models is that the interactions in a community operate only between pairs of species. However, two species may interactively affect the growth of a focal species. Although interactions among three or more species, called higher-order interactions, have the potential to modify our theoretical understanding of coexistence, ecologists lack clear expectations for how these interactions shape community structure. Here we analytically predict and numerically confirm how the variability and strength of higher-order interactions affect species coexistence. We found that as higher-order interaction strengths became more variable across species, fewer species could coexist, echoing the behavior of pairwise models. If interspecific higher-order interactions became too harmful relative to self-regulation, coexistence in diverse communities was destabilized, but coexistence was also lost when these interactions were too weak and mutualistic higher-order effects became prevalent. This behavior depended on the functional form of the interactions as the destabilizing effects of the mutualistic higher-order interactions were ameliorated when their strength saturated with species' densities. Last, we showed that more species-rich communities structured by higher-order interactions lose species more readily than their species-poor counterparts, generalizing classic results for community stability. Our work provides needed theoretical expectations for how higher-order interactions impact species coexistence in diverse communities.

Network analysis suggests changes in food web stability produced by bottom trawl fishery in Patagonia

Demersal fisheries are one of the top anthropic stressors in marine environments. In the long term, some species are more vulnerable to fishery impacts than others, which can lead to permanent changes on the food web. The trophic relationships between predator and prey constitute the food web and it represents a network of the energy channels in an ecosystem. In turn, the network structure influences ecosystem diversity and stability. The first aim of this study was to describe for the first time the food web of the San Jorge Gulf (Patagonia Argentina) with high resolution, i.e. to the species level when information is available. The San Jorge Gulf was subject to intense fisheries thus our second aim is to analyse the food web structure with and without fishery to evaluate if the bottom-trawl industrial fishery altered the network structure and stability. We used several network metrics like: mean trophic level, omnivory, modularity and quasi-sign stability. We included these metrics because they are related to stability and can be evaluated using predator diets that can weight the links between predators and prey. The network presented 165 species organized in almost five trophic levels. The inclusion of a fishery node adds 69 new trophic links. All weighted and unweighted metrics showed differences between the two networks, reflecting a decrease in stability when fishery was included in the system. Thus, our results suggested a probable change of state of the system. The observed changes in species abundances since the fishery was established, could represent the state change predicted by network analysis. Our results suggests that changes in the stability of food webs can be used to evaluate the impacts of human activity on ecosystems.

Reconstruction of Ecological Transitions in a Temperate Shallow Lake of the Middle Yangtze River Basin in the Last Century

Exogenous drivers may cause a gradual and reversible change in a lake equilibrium, or they may force it over a threshold to a persistent alternative stable state, described as a regime shift in the ecosystem. In the mid-and-lower Yangtze River Basin (MLYB), major environmental problems in shallow lakes have been eutrophication and abrupt algal blooms under anthropogenic disturbances for the recent century. Much value is therefore placed on understanding the changes in shallow-lake ecosystems that characteristically precede changes in the state of the lake. Here, we describe a case study of the paleolimnological signature in diatom assemblages of various types of regime shifts caused by historically documented anthropogenic drivers in a temperate shallow lake: Taibai Lake. We evaluate the effectiveness of paleolimnological data as a surrogate for long-term monitoring. Algorithms using sequential t and F statistics detected breakpoints in the time series of diatom assemblages, in 1994–1996, 1974–1977, 1952–1956, and 1931–1934, respectively. The regression statistics suggest that the hydrodynamic–ecosystem and aquacultural–ecosystem relationships fit better in the breakpoint regression model, and the relationship between nutrient loading and ecosystem state suits the linear model. Feedback loops help reconstruct dynamic changes in Taibai influenced by major stressors. Our study exemplifies the value of system approaches to identifying regime shifts and their possible causes in shallow lakes from paleolimnological records. The case study of Taibai set an example of reconstructing the ecological regime shifts in shallow lakes in the MLYB and understanding the state changes in lake ecosystems, which will benefit effective lake management.

Master stability functions for metacommunities with two types of habitats

Current questions in ecology revolve around instabilities in the dynamics on spatial networks and particularly the effect of node heterogeneity. We extend the master stability function formalism to inhomogeneous biregular networks having two types of spatial nodes. Notably, this class of systems also allows the investigation of certain types of dynamics on higher-order networks. Combined with the generalized modeling approach to study the linear stability of steady states, this is a powerful tool to numerically asses the stability of large ensembles of systems. We analyze the stability of ecological metacommunities with two distinct types of habitats analytically and numerically in order to identify several sets of conditions under which the dynamics can become stabilized by dispersal. Our analytical approach allows general insights into stabilizing and destabilizing effects in metapopulations. Specifically, we identify self-regulation and negative feedback loops between source and sink populations as stabilizing mechanisms and we show that maladaptive dispersal may be stable under certain conditions.

The long-term changes in food web structure and ecosystem functioning of a shallow lake: Implications for the lake management

The food web structure (FWS) and ecosystem functioning (EF) of lakes worldwide are impacted by multiple disturbances. The historical evolution of the FWS and EF are not well understood due to the lack of sufficient long-term records of biotic variations. This study reconstructed the food web models in the 1950s, 1980s, 1990s, 2000s, and 2010s for Baiyangdian Lake (BYDL), the largest shallow lake in northern China, using the Linear Inverse Modeling (LIM) and investigated EF in different periods. Our results confirmed that the FWS and EF of BYDL have undergone significant changes. The biomass of phytoplankton continuously increased, and the primary productivity of phytoplankton began to replace the primary productivity of submerged macrophytes in the 2000s and became the largest energy flow in the food web. Changes in the energy flow of primary producers are transmitted to high-trophic functional groups, which affects the diet composition of fish. Based on the ecological network analysis indices and food web stability indicators, it was concluded that after a turning point in the 1990s, the ecosystem showed initial stability and then gradually became unstable. Water level fluctuations and nutrient enrichment may be the key driving factors for changes in ecosystem state. Therefore, to maintain a good state of the ecosystem, we recommend implementing comprehensive management measures of hydrological management, nutrient-loading reduction, and biomanipulation. Furthermore, this study extended LIM to lake ecosystems, which may provide a new method for lake ecological environment management.

For flux's sake: General considerations for energy-flux calculations in ecological communities

Global change alters ecological communities with consequences for ecosystem processes. Such processes and functions are a central aspect of ecological research and vital to understanding and mitigating the consequences of global change, but also those of other drivers of change in organism communities. In this context, the concept of energy flux through trophic networks integrates food-web theory and biodiversity-ecosystem functioning theory and connects biodiversity to multitrophic ecosystem functioning. As such, the energy-flux approach is a strikingly effective tool to answer central questions in ecology and global-change research. This might seem straight forward, given that the theoretical background and software to efficiently calculate energy flux are readily available. However, the implementation of such calculations is not always straight forward, especially for those who are new to the topic and not familiar with concepts central to this line of research, such as food-web theory or metabolic theory. To facilitate wider use of energy flux in ecological research, we thus provide a guide to adopting energy-flux calculations for people new to the method, struggling with its implementation, or simply looking for background reading, important resources, and standard solutions to the problems everyone faces when starting to quantify energy fluxes for their community data. First, we introduce energy flux and its use in community and ecosystem ecology. Then, we provide a comprehensive explanation of the single steps towards calculating energy flux for community data. Finally, we discuss remaining challenges and exciting research frontiers for future energy-flux research.

Energetic constraints imposed on trophic interaction strengths enhance resilience in empirical and model food webs

Food web stability and resilience are at the heart of understanding the structure and functioning of ecosystems. Previous studies show that models of empirical food webs are substantially more stable than random ones, due to a few strong interactions embedded in a majority of weak interactions. Analyses of trophic interaction loops show that in empirical food webs the patterns of the interaction strengths prevent the occurrence of destabilizing heavy loops and thereby enhances resilience. Yet, it is still unexplored which biological mechanisms cause these patterns that enhance food web resilience. We quantified food web resilience using the real part of the maximum eigenvalue of the Jacobian matrix of the food web from a seagrass bed in the Yellow River Delta (YRD) wetland, that could be parametrized by the empirical data of the food web. We found that the empirically based Jacobian matrix of the YRD food web indicated a much higher resilience than random matrices with the same element values but arranged in random ways. Investigating the trophic interaction loops revealed that the high resilience was due to a negative correlation between the negative and positive interaction strengths (per capita top-down and bottom-up effects, respectively) within positive feedback loops with three species. The negative correlation showed that when the negative interaction strengths were strong the positive was weak, and vice versa. Our invented reformulation of loop weight in terms of biomasses and specific production rates showed that energetic properties of the trophic groups in the loop and mass-balance constraints, for example, the food uptake has to balance all losses, created the negative correlation between the interaction strengths. This result could be generalized using a dynamic intraguild predation model, which delivered the same pattern for a wide range of model parameters. Our results shed light on how energetic constraints at the trophic group and food web level create a pattern of interaction strengths within trophic interaction loops that enhances food web resilience.

Foreseeing the future of mutualistic communities beyond collapse

Changing conditions may lead to sudden shifts in the state of ecosystems when critical thresholds are passed. Some well-studied drivers of such transitions lead to predictable outcomes such as a turbid lake or a degraded landscape. Many ecosystems are, however, complex systems of many interacting species. While detecting upcoming transitions in such systems is challenging, predicting what comes after a critical transition is terra incognita altogether. The problem is that complex ecosystems may shift to many different, alternative states. Whether an impending transition has minor, positive or catastrophic effects is thus unclear. Some systems may, however, behave more predictably than others. The dynamics of mutualistic communities can be expected to be relatively simple, because delayed negative feedbacks leading to oscillatory or other complex dynamics are weak. Here, we address the question of whether this relative simplicity allows us to foresee a community's future state. As a case study, we use a model of a bipartite mutualistic network and show that a network's post-transition state is indicated by the way in which a system recovers from minor disturbances. Similar results obtained with a unipartite model of facilitation suggest that our results are of relevance to a wide range of mutualistic systems.

Subsurface biogeochemistry is a missing link between ecology and hydrology in dam-impacted river corridors

Global investment in hydropower is rapidly increasing, fueled by a need to manage water availability and by incentives promoting renewable energy sources. This expansion poses unrecognized risks to the world's vulnerable freshwater ecosystems. While many hydropower impacts have been investigated, dam-induced alterations to subsurface processes influence river corridor ecosystem health in ways that remain poorly understood. We advocate for a better understanding of dam impacts on subsurface biogeochemical activity, its connection to hydrology, and follow-on trophic cascades within the broader river corridor. We delineate an integrated view of hydropower impacts in which dam-induced changes to surface water flow regimes generate changes in surface-subsurface hydrologic exchange flows (HEFs) that subsequently (1) regulate resource availability for benthic microorganisms at the base of aquatic food webs and (2) impose kinetic constraints on biogeochemical reactions and organismal growth across a range of trophic levels. These HEF-driven effects on river corridor food webs, as mediated by subsurface biogeochemistry, are a key knowledge gap in our assessment of hydropower sustainability and putatively combine with other, more well-known dam impacts to result in significant changes to river corridor health. We suggest targeted laboratory and field-based studies to link hydrobiogeochemical models used to predict heat transport, biogeochemical rates, and hydrologic flow with ecological models that incorporate biomass changes in specific categories of organisms. Doing so will enable predictions of feedbacks among hydrology, temperature, biogeochemical rates, organismal abundances, and resource transfer across trophic levels. This understanding of dam impacts on subsurface hydrobiogeochemistry and its connection to the broader aquatic food web is fundamental to enabling mechanism-based decision making for sustainable hydropower operations.

The feasibility of equilibria in large ecosystems: A primary but neglected concept in the complexity-stability debate

The consensus that complexity begets stability in ecosystems was challenged in the seventies, a result recently extended to ecologically-inspired networks. The approaches assume the existence of a feasible equilibrium, i.e. with positive abundances. However, this key assumption has not been tested. We provide analytical results complemented by simulations which show that equilibrium feasibility vanishes in species rich systems. This result leaves us in the uncomfortable situation in which the existence of a feasible equilibrium assumed in local stability criteria is far from granted. We extend our analyses by changing interaction structure and intensity, and find that feasibility and stability is warranted irrespective of species richness with weak interactions. Interestingly, we find that the dynamical behaviour of ecologically inspired architectures is very different and richer than that of unstructured systems. Our results suggest that a general understanding of ecosystem dynamics requires focusing on the interplay between interaction strength and network architecture.

Energy Flux: The Link between Multitrophic Biodiversity and Ecosystem Functioning

Relating biodiversity to ecosystem functioning in natural communities has become a paramount challenge as links between trophic complexity and multiple ecosystem functions become increasingly apparent. Yet, there is still no generalised approach to address such complexity in biodiversity-ecosystem functioning (BEF) studies. Energy flux dynamics in ecological networks provide the theoretical underpinning of multitrophic BEF relationships. Accordingly, we propose the quantification of energy fluxes in food webs as a powerful, universal tool for understanding ecosystem functioning in multitrophic systems spanning different ecological scales. Although the concept of energy flux in food webs is not novel, its application to BEF research remains virtually untapped, providing a framework to foster new discoveries into the determinants of ecosystem functioning in complex systems.

Conditions for Eltonian Pyramids in Lotka-Volterra Food Chains

In ecological communities consumers (excluding parasites and parasitoids) are in general larger and less numerous than their resource. This results in a well-known observation known as 'Eltonian pyramids' or the 'pyramid of numbers', and metabolic arguments suggest that this pattern is independent of the number of trophic levels in a system. At the same time, Lotka-Volterra (LV) consumer-resource models are a frequently used tool to study many questions in community ecology, but their capacity to produce Eltonian pyramids has not been formally analysed. Here, I address this knowledge gap by investigating if and when LV food chain models give rise to Eltonian pyramids. I show that Eltonian pyramids are difficult to reproduce without density-dependent mortality in the consumers, unless biologically plausible relationships between mortality rate and interaction strength are taken into account.

Degree heterogeneity and stability of ecological networks

A classic measure of ecological stability describes the tendency of a community to return to equilibrium after small perturbations. While many advances show how the network architecture of these communities severely constrains such tendencies, one of the most fundamental properties of network structure, i.e. degree heterogeneity-the variability of the number of links associated with each species, deserves further study. Here we show that the effects of degree heterogeneity on stability vary with different types of interspecific interactions. Degree heterogeneity consistently destabilizes ecological networks with both competitive and mutualistic interactions, while its effects on networks of predator-prey interactions such as food webs depend on prey contiguity, i.e. the extent to which the species consume an unbroken sequence of prey in community niche space. Increasing degree heterogeneity tends to stabilize food webs except those with the highest prey contiguity. These findings help explain why food webs are highly but not completely interval and, more broadly, deepen our understanding of the stability of complex ecological networks.

Microbial control of soil organic matter mineralization responses to labile carbon in subarctic climate change treatments

Half the global soil carbon (C) is held in high-latitude systems. Climate change will expose these to warming and a shift towards plant communities with more labile C input. Labile C can also increase the rate of loss of native soil organic matter (SOM); a phenomenon termed 'priming'. We investigated how warming (+1.1 °C over ambient using open top chambers) and litter addition (90 g m^-2  yr^-1 ) treatments in the subarctic influenced the susceptibility of SOM mineralization to priming, and its microbial underpinnings. Labile C appeared to inhibit the mineralization of C from SOM by up to 60% within hours. In contrast, the mineralization of N from SOM was stimulated by up to 300%. These responses occurred rapidly and were unrelated to microbial successional dynamics, suggesting catabolic responses. Considered separately, the labile C inhibited C mineralization is compatible with previously reported findings termed 'preferential substrate utilization' or 'negative apparent priming', while the stimulated N mineralization responses echo recent reports of 'real priming' of SOM mineralization. However, C and N mineralization responses derived from the same SOM source must be interpreted together: This suggested that the microbial SOM-use decreased in magnitude and shifted to components richer in N. This finding highlights that only considering SOM in terms of C may be simplistic, and will not capture all changes in SOM decomposition. The selective mining for N increased in climate change treatments with higher fungal dominance. In conclusion, labile C appeared to trigger catabolic responses of the resident microbial community that shifted the SOM mining to N-rich components; an effect that increased with higher fungal dominance. Extrapolating from these findings, the predicted shrub expansion in the subarctic could result in an altered microbial use of SOM, selectively mining it for N-rich components, and leading to a reduced total SOM-use.

Beyond connectedness: why pairwise metrics cannot capture community stability

The connectedness of species in a trophic web has long been a key structural characteristic for both theoreticians and empiricists in their understanding of community stability. In the past decades, there has been a shift from focussing on determining the number of interactions to taking into account their relative strengths. The question is: How do the strengths of the interactions determine the stability of a community? Recently, a metric has been proposed which compares the stability of observed communities in terms of the strength of three‐ and two‐link feedback loops (cycles of interaction strengths). However, it has also been suggested that we do not need to go beyond the pairwise structure of interactions to capture stability. Here, we directly compare the performance of the feedback and pairwise metrics. Using observed food‐web structures, we show that the pairwise metric does not work as a comparator of stability and is many orders of magnitude away from the actual stability values. We argue that metrics based on pairwise‐strength information cannot capture the complex organization of strong and weak links in a community, which is essential for system stability.

No complexity-stability relationship in empirical ecosystems

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.

A long-standing ecological hypothesis is that complexity should decrease stability in food webs. Here, Jacquet and colleagues analyse over 100 real-world food webs and show that complexity does not decrease stability, but that a high frequency of weak species interactions stabilizes complex food webs.

How Structured Is the Entangled Bank? The Surprisingly Simple Organization of Multiplex Ecological Networks Leads to Increased Persistence and Resilience

Species are linked to each other by a myriad of positive and negative interactions. This complex spectrum of interactions constitutes a network of links that mediates ecological communities' response to perturbations, such as exploitation and climate change. In the last decades, there have been great advances in the study of intricate ecological networks. We have, nonetheless, lacked both the data and the tools to more rigorously understand the patterning of multiple interaction types between species (i.e., "multiplex networks"), as well as their consequences for community dynamics. Using network statistical modeling applied to a comprehensive ecological network, which includes trophic and diverse non-trophic links, we provide a first glimpse at what the full "entangled bank" of species looks like. The community exhibits clear multidimensional structure, which is taxonomically coherent and broadly predictable from species traits. Moreover, dynamic simulations suggest that this non-random patterning of how diverse non-trophic interactions map onto the food web could allow for higher species persistence and higher total biomass than expected by chance and tends to promote a higher robustness to extinctions.

Bounds on Transient Instability for Complex Ecosystems

Stability is a desirable property of complex ecosystems. If a community of interacting species is at a stable equilibrium point then it is able to withstand small perturbations to component species' abundances without suffering adverse effects. In ecology, the Jacobian matrix evaluated at an equilibrium point is known as the community matrix, which describes the population dynamics of interacting species. A system's asymptotic short- and long-term behaviour can be determined from eigenvalues derived from the community matrix. Here we use results from the theory of pseudospectra to describe intermediate, transient dynamics. We first recover the established result that the transition from stable to unstable dynamics includes a region of 'transient instability', where the effect of a small perturbation to species' abundances-to the population vector-is amplified before ultimately decaying. Then we show that the shift from stability to transient instability can be affected by uncertainty in, or small changes to, entries in the community matrix, and determine lower and upper bounds to the maximum amplitude of perturbations to the population vector. Of five different types of community matrix, we find that amplification is least severe when predator-prey interactions dominate. This analysis is relevant to other systems whose dynamics can be expressed in terms of the Jacobian matrix.

Stability and feedback levels in food web models

Neutel & Thorne (Ecology Letters, 17:651-661, June 2014) provide an approximation for the leading eigenvalue of a food web community matrix involving coefficients of its characteristic polynomial. Though valuably incorporating three-way species interactions, two critical problems emerge when one considers the dimensions of the system, calling the approach's accuracy and precision into question.