Self-regulation and the stability of large ecological networks

Exploring sustainable scenarios for the brown algae fishery in the intertidal zone along the central Chilean coast (Maule region)

This work presents the outcomes from five semi-quantitative loop models of different levels of complexity, built to explore and quantify the stability and resilience (used as proxies for sustainability) of the ecological and eco-social systems where intensive artisanal fishing activity of the algae Durvillaea incurvata (Di) and Lessonia spicata (Ls) is occurring in central Chile (Maule Region). The average values for Routh-Hurwitz local stability criterion 1 (Fs) and for Levins' criterion (Fn) showed that the model systems achieved the desired stability and resilience only when both algae exhibit asymmetric level of abundance (avoiding symmetric competition). Furthermore, both species should exhibit self-negative feedback, that is, their abundances should fluctuate between k/2 and maximum abundance (according to logistic growth). The latter results imply that both algae were the most sensitive to perturbations, regardless of their level of complexity, which limits exploitation strategies and emphasizes the need for integrated management. The substrate (S) also emerged as sensitive in the system. When fishers (F) and demand (D) are dominated by self-negative feedback, the average values of local stability (Fs) and resilience (Fn) were higher than when F and D exhibited self-positive feedback. Therefore, to ensure a sustainable exploitation of both algae, it would be necessary to: maintain the asymmetry of abundance (regardless of which of the two dominates), monitor the quality of the coastal rocky substrate to ensure the colonization of new plants, particularly L. spicata and D. incurvata, and design and implement policies that promote control over the activity of fishers and demand.

When Do Trait-Based Higher Order Interactions and Individual Variation Promote Robust Species Coexistence?

Models on the effects of individual variation often focus on pairwise interactions, but communities could harbor both pairwise and higher order interactions (HOIs). Theoretical studies on HOIs, where a third species modulates pairwise species competition, tend to assign them at random, even though they could be mediated and structured by one-dimensional traits. Here, we consider two different classes of models of both pairwise and higher order trait-mediated interactions: competition alleviated by increasing trait distance, and hierarchical competition where species higher in the hierarchy exert more competition on those lower and vice versa. Combining these models with evolutionary dynamics based on quantitative genetics, we compare their impact on species diversity, community pattern, and robustness of coexistence. Regardless of individual variation, trait-mediated HOIs generally do not promote and often hinder species coexistence, but there are some notable exceptions to this. We present an analytical argument to make sense of these results and argue that while the effects of trait-based HOIs on diversity may appear confusing on the surface, we can understand what outcome to expect in any given scenario by looking at the shape of the effective interaction kernel that arises from the joint action of pairwise and HOI terms. In addition, we find that (i) communities structured by competitive trait hierarchies are highly vulnerable to external perturbations, regardless of HOIs, and (ii) trait-based HOIs with distance-dependent competition create the most robust communities, with minimal impact from individual variation, and (iii) both individual variation and HOIs consistently lead to a more even distribution of species traits than would occur by chance. These findings suggest that trait-mediated HOIs foster coexistence only under special conditions, raising the question of whether HOIs must involve multiple traits to positively affect coexistence in competitive communities.

Synthetic Ecosystems: From the Test Tube to the Biosphere

The study of ecosystems, both natural and artificial, has historically been mediated by population dynamics theories. In this framework, quantifying population numbers and related variables (associated with metabolism or biological-environmental interactions) plays a central role in measuring and predicting system-level properties. As we move toward advanced technological engineering of cells and organisms, the possibility of bioengineering ecosystems (from the gut microbiome to wildlands) opens several questions that will require quantitative models to find answers. Here, we present a comprehensive survey of quantitative modeling approaches for managing three kinds of synthetic ecosystems, sharing the presence of engineered strains. These include test tube examples of ecosystems hosting a relatively low number of interacting species, mesoscale closed ecosystems (or ecospheres), and macro-scale, engineered ecosystems. The potential outcomes of synthetic ecosystem designs and their limits will be relevant to different disciplines, including biomedical engineering, astrobiology, space exploration and fighting climate change impacts on endangered ecosystems. We propose a space of possible ecosystems that captures this broad range of scenarios and a tentative roadmap for open problems and further exploration.

Ecosystem stability relies on diversity difference between trophic levels

The stability of ecological communities has a profound impact on humans, ranging from individual health influenced by the microbiome to ecosystem services provided by fisheries. A long-standing goal of ecology is the elucidation of the interplay between biodiversity and ecosystem stability, with some ecologists warning of instability due to loss of species diversity while others arguing that greater diversity will instead lead to instability. Here, by considering a minimal two-level ecosystem with multiple predator and prey species, we show that stability does not depend on absolute diversity but rather on diversity differences between levels. We found that increasing diversity in either level first destabilizes but then stabilizes the community (i.e., a reentrant stability transition). We therefore find that it is the diversity difference between levels that is the key to stability, with the least stable communities having similar diversities in different levels. An analytical stability criterion is derived, demonstrating quantitatively that the critical diversity difference is determined by the correlation between how one level affects another and how it is affected in turn. Our stability criterion also applies to consumer-resource models with other forms of interaction such as cross-feeding. Finally, we show that stability depends on diversity differences in ecosystems with three trophic levels. Our finding of a nonmonotonic dependence of stability on diversity provides a natural explanation for the variety of diversity-stability relationships reported in the literature, and emphasizes the significance of level structure in predicting complex community behaviors.

Complexity-stability relationships in competitive disordered dynamical systems

Robert May famously used random matrix theory to predict that large, complex systems cannot admit stable fixed points. However, this general conclusion is not always supported by empirical observation: from cells to biomes, biological systems are large, complex, and often stable. In this paper, we revisit May's argument in light of recent developments in both ecology and random matrix theory. We focus on competitive systems, and, using a nonlinear generalization of the competitive Lotka-Volterra model, we show that there are, in fact, two kinds of complexity-stability relationships in disordered dynamical systems: if self-interactions grow faster with density than cross-interactions, complexity is destabilizing; but if cross-interactions grow faster than self-interactions, complexity is stabilizing.

Stability of Ecological Systems: A Theoretical Review

The stability of ecological systems is a fundamental concept in ecology, which offers profound insights into species coexistence, biodiversity, and community persistence. In this article, we provide a systematic and comprehensive review on the theoretical frameworks for analyzing the stability of ecological systems. Notably, we survey various stability notions, including linear stability, sign stability, diagonal stability, D-stability, total stability, sector stability, and structural stability. For each of these stability notions, we examine necessary or sufficient conditions for achieving such stability and demonstrate the intricate interplay of these conditions on the network structures of ecological systems. We further discuss the stability of ecological systems with higher-order interactions.

Reviving collapsed plant-pollinator networks from a single species

Mutualistic ecological networks can suddenly transition to undesirable states due to small changes in environmental conditions. Recovering from such a collapse can be difficult as restoring the original environmental conditions may be infeasible. Additionally, such networks can also exhibit a phenomenon known as hysteresis, whereby the system could exhibit multiple states under the same environmental conditions, implying that ecological networks may not recover. Here, we attempted to revive collapsed mutualistic networks to a high-functioning state from a single species, using concepts from signal propagation theory and an eco-evolutionary model based on network structures of 115 empirical plant-pollinator networks. We found that restoring the environmental conditions rarely aided in recovery of collapsed networks, but a positive relationship between recovering pollinator density and network nestedness emerged, which was qualitatively supported by empirical plant-pollinator restoration data. In contrast, network resurrection from a collapsed state in undesirable environmental conditions where restoration has minimal impacts could be readily achieved by perturbing a single species or a few species that control the response of the dynamical networks. Additionally, nestedness in networks and a moderate amount of trait variation could aid in the revival of networks even in undesirable environmental conditions. Our work suggests that focus should be applied to a few species whose dynamics could be steered to resurrect entire networks from a collapsed state and that network architecture could play a crucial role in reviving collapsed plant-pollinator networks.

DyMMM-LEAPS: An ML-based framework for modulating evenness and stability in synthetic microbial communities

There have been a growing number of computational strategies to aid in the design of synthetic microbial consortia. A framework to identify regions in parametric space to maximize two essential properties, evenness and stability, is critical. In this study, we introduce DyMMM-LEAPS (dynamic multispecies metabolic modeling-locating evenness and stability in large parametric space), an extension of the DyMMM framework. Our method explores the large parametric space of genetic circuits in synthetic microbial communities to identify regions of evenness and stability. Due to the high computational costs of exhaustive sampling, we utilize adaptive sampling and surrogate modeling to reduce the number of simulations required to map the vast space. Our framework predicts engineering targets and computes their operating ranges to maximize the probability of the engineered community to have high evenness and stability. We demonstrate our approach by simulating five cocultures and one three-strain culture with different social interactions (cooperation, competition, and predation) employing quorum-sensing-based genetic circuits. In addition to guiding circuit tuning, our pipeline gives an opportunity for a detailed analysis of pockets of evenness and stability for the circuit under investigation, which can further help dissect the relationship between the two properties. DyMMM-LEAPS is easily customizable and can be expanded to a larger community with more complex interactions.

Stability, resilience and eco-evolutionary feedbacks of mutualistic networks to rising temperature

Ecological networks comprising of mutualistic interactions can suddenly transition to undesirable states, such as collapse, due to small changes in environmental conditions such as a rise in local environmental temperature. However, little is known about the capacity of such interaction networks to adapt to a rise in temperature and the occurrence of critical transitions. Here, combining quantitative genetics and mutualistic dynamics in an eco-evolutionary framework, we evaluated the stability and resilience of mutualistic networks to critical transitions as environmental temperature increases. Specifically, we modelled the dynamics of an optimum trait that determined the tolerance of species to local environmental temperature as well as to species interaction. We then evaluated the impact of individual trait variation and evolutionary dynamics on the stability of feasible equilibria, the occurrence of threshold temperatures at which community collapses, and the abruptness of such community collapses. We found that mutualistic network architecture, that is the size of the community and the arrangement of species interactions, interacted with evolutionary dynamics to impact the onset of network collapses. Some networks had more capacity to track the rise in temperatures than others and thereby increased the threshold temperature at which the networks collapsed. However, such a result was modulated by the amount of heritable trait variation species exhibited, with high trait variation in the mean optimum phenotypic trait increasing the environmental temperature at which networks collapsed. Furthermore, trait variation not only increased the onset of temperatures at which networks collapsed but also increased the local stability of feasible equilibria. Our study argued that mutualistic network architecture interacts with species evolutionary dynamics and increases the capacity of networks to adapt to changes in temperature and thereby delayed the occurrence of community collapses.

Interconnection between density-regulation and stability in competitive ecological network

In natural ecosystems, species can be characterized by the nonlinear density-dependent self-regulation of their growth profile. Species of many taxa show a substantial density-dependent reduction for low population size. Nevertheless, many show the opposite trend; density regulation is minimal for small populations and increases significantly when the population size is near the carrying capacity. The theta-logistic growth equation can portray the intraspecific density regulation in the growth profile, theta being the density regulation parameter. In this study, we examine the role of these different growth profiles on the stability of a competitive ecological community with the help of a mathematical model of competitive species interactions. This manuscript deals with the random matrix theory to understand the stability of the classical theta-logistic models of competitive interactions. Our results suggest that having more species with strong density dependence, which self-regulate at low densities, leads to more stable communities. With this, stability also depends on the complexity of the ecological network. Species network connectance (link density) shows a consistent trend of increasing stability, whereas community size (species richness) shows a context-dependent effect. We also interpret our results from the aspect of two different life history strategies: r and K-selection. Our results show that the stability of a competitive network increases with the fraction of r-selected species in the community. Our result is robust, irrespective of different network architectures.

Eigenvalue spectra of finely structured random matrices

Random matrix theory allows for the deduction of stability criteria for complex systems using only a summary knowledge of the statistics of the interactions between components. As such, results like the well-known elliptical law are applicable in a myriad of different contexts. However, it is often assumed that all components of the complex system in question are statistically equivalent, which is unrealistic in many applications. Here we introduce the concept of a finely structured random matrix. These are random matrices with element-specific statistics, which can be used to model systems in which the individual components are statistically distinct. By supposing that the degree of "fine structure" in the matrix is small, we arrive at a succinct "modified" elliptical law. We demonstrate the direct applicability of our results to the niche and cascade models in theoretical ecology, as well as a model of a neural network, and a directed network with arbitrary degree distribution. The simple closed form of our central results allow us to draw broad qualitative conclusions about the effect of fine structure on stability.

Local intraspecific aggregation in phytoplankton model communities: spatial scales of occurrence and implications for coexistence

The coexistence of multiple phytoplankton species despite their reliance on similar resources is often explained with mean-field models assuming mixed populations. In reality, observations of phytoplankton indicate spatial aggregation at all scales, including at the scale of a few individuals. Local spatial aggregation can hinder competitive exclusion since individuals then interact mostly with other individuals of their own species, rather than competitors from different species. To evaluate how microscale spatial aggregation might explain phytoplankton diversity maintenance, an individual-based, multispecies representation of cells in a hydrodynamic environment is required. We formulate a three-dimensional and multispecies individual-based model of phytoplankton population dynamics at the Kolmogorov scale. The model is studied through both simulations and the derivation of spatial moment equations, in connection with point process theory. The spatial moment equations show a good match between theory and simulations. We parameterized the model based on phytoplankters' ecological and physical characteristics, for both large and small phytoplankton. Defining a zone of potential interactions as the overlap between nutrient depletion volumes, we show that local species composition-within the range of possible interactions-depends on the size class of phytoplankton. In small phytoplankton, individuals remain in mostly monospecific clusters. Spatial structure therefore favours intra- over inter-specific interactions for small phytoplankton, contributing to coexistence. Large phytoplankton cell neighbourhoods appear more mixed. Although some small-scale self-organizing spatial structure remains and could influence coexistence mechanisms, other factors may need to be explored to explain diversity maintenance in large phytoplankton.

Both local stability and dispersal contribute to metacommunity sensitivity to asynchronous habitat availability

The stability of isolated communities depends on the complexity of their foodwebs. However, it remains unclear how local stability interacts with dispersal in multitrophic metacommunities to shape biodiversity patterns. This lack of understanding is deeper in the more realistic frame of landscapes that exhibit non-trivial and time-varying structures. Therefore, in this study, we aim to evaluate the influence of local stabilizing factors versus dispersal in determining the sensitivity of metacommunity biodiversity to increasing asynchrony of site availability. Additionally, we assess the role of foodweb complexity and landscape structure as modulating factors. To accomplish our goals we developed a model based on random matrices for local communities, which are linked by stochastic dispersal over explicit dynamic landscapes. We ran numerical simulations and computed the effect sizes of foodweb temperature, self-limitation, dispersal ability, and all pairwise combinations, on the sensitivity of biodiversity to landscape asynchrony. In our experiments we explored gradients of species richness, foodweb connectance, number of sites, and landscape modularity. Our results showed that asynchrony among site availability periods reduced α -diversity and increased β -diversity. Asynchrony increased γ -diversity at high dispersal rates. Both local and regional stabilizing factors determined the sensitivity of metacommunities to landscape asynchrony. Local factors were more influential in landscapes with fewer sites and lower modularity, as well as in metacommunities composed of complex foodwebs. This research offers insights into the dynamics of metacommunities in dynamic landscapes, providing valuable knowledge about the interplay between local and regional factors in shaping ecological stability and species persistence.

Diversity begets stability: Sublinear growth and competitive coexistence across ecosystems

The worldwide loss of species diversity brings urgency to understanding how diverse ecosystems maintain stability. Whereas early ecological ideas and classic observations suggested that stability increases with diversity, ecological theory makes the opposite prediction, leading to the long-standing "diversity-stability debate." Here, we show that this puzzle can be resolved if growth scales as a sublinear power law with biomass (exponent <1), exhibiting a form of population self-regulation analogous to models of individual ontogeny. We show that competitive interactions among populations with sublinear growth do not lead to exclusion, as occurs with logistic growth, but instead promote stability at higher diversity. Our model realigns theory with classic observations and predicts large-scale macroecological patterns. However, it makes an unsettling prediction: Biodiversity loss may accelerate the destabilization of ecosystems.

Reactivity of complex communities can be more important than stability

Understanding stability-whether a community will eventually return to its original state after a perturbation-is a major focus in the study of various complex systems, particularly complex ecosystems. Here, we challenge this focus, showing that short-term dynamics can be a better predictor of outcomes for complex ecosystems. Using random matrix theory, we study how complex ecosystems behave immediately after small perturbations. Our analyses show that many communities are expected to be 'reactive', whereby some perturbations will be amplified initially and generate a response that is directly opposite to that predicted by typical stability measures. In particular, we find reactivity is prevalent for complex communities of mixed interactions and for structured communities, which are both expected to be common in nature. Finally, we show that reactivity can be a better predictor of extinction risk than stability, particularly when communities face frequent perturbations, as is increasingly common. Our results suggest that, alongside stability, reactivity is a fundamental measure for assessing ecosystem health.

Time delays modulate the stability of complex ecosystems

What drives the stability, or instability, of complex ecosystems? This question sits at the heart of community ecology and has motivated a large body of theoretical work exploring how community properties shape ecosystem dynamics. However, the overwhelming majority of current theory assumes that species interactions are instantaneous, meaning that changes in the abundance of one species will lead to immediate changes in the abundances of its partners. In practice, time delays in how species respond to one another are widespread across ecological contexts, yet the impact of these delays on ecosystems remains unclear. Here we derive a new body of theory to comprehensively study the impact of time delays on ecological stability. We find that time delays are important for ecosystem stability. Large delays are typically destabilizing but, surprisingly, short delays can substantially increase community stability. Moreover, in stark contrast to delay-free systems, delays dictate that communities with more abundant species can be less stable than ones with less abundant species. Finally, we show that delays fundamentally shift how species interactions impact ecosystem stability, with communities of mixed interaction types becoming the most stable class of ecosystem. Our work demonstrates that time delays can be critical for the stability of complex ecosystems.

Changes in vertical and horizontal diversities mediated by the size structure of introduced fish collectively shape food-web stability

Species introductions can alter local food-web structure by changing the vertical or horizontal diversity within communities, largely driven by their body size distributions. Increasing vertical and horizontal diversities is predicted to have opposing effects on stability. However, their interactive effects remain largely overlooked. We investigated the independent and collective effects of vertical and horizontal diversities on food-web stability in alpine lakes stocked with variable body size distributions of introduced fish species. Introduced predators destabilize food-webs by increasing vertical diversity through food chain lengthening. Alternatively, increasing horizontal diversity results in more stable food-web topologies. A non-linear interaction between vertical and horizontal diversities suggests that increasing vertical diversity is most destabilizing when horizontal diversity is low. Our findings suggest that the size structure of introduced predators drives their impacts on stability by modifying the structure of food-webs, and highlights the interactive effects of vertical and horizontal diversities on stability.

Mean species responses predict effects of environmental change on coexistence

Environmental change research is plagued by the curse of dimensionality: the number of communities at risk and the number of environmental drivers are both large. This raises the pressing question if a general understanding of ecological effects is achievable. Here, we show evidence that this is indeed possible. Using theoretical and simulation-based evidence for bi- and tritrophic communities, we show that environmental change effects on coexistence are proportional to mean species responses and depend on how trophic levels on average interact prior to environmental change. We then benchmark our findings using relevant cases of environmental change, showing that means of temperature optima and of species sensitivities to pollution predict concomitant effects on coexistence. Finally, we demonstrate how to apply our theory to the analysis of field data, finding support for effects of land use change on coexistence in natural invertebrate communities.

Revisiting Nature's "Unifying Patterns": A Biological Appraisal

Effective bioinspiration requires dialogue between designers and biologists, and this dialogue must be rooted in a shared scientific understanding of living systems. To support learning from "nature's overarching design lessons" the Biomimicry Institute has produced ten "Unifying Patterns of Nature". These patterns have been developed to engage with those interested in finding biologically inspired solutions to human challenges. Yet, although well-intentioned and appealing, they are likely to dishearten biologists. The aim of this paper is to identify why and propose alternative principles based on evolutionary theory.

Stable diverse food webs become more common when interactions are more biologically constrained

Ecologists have long sought to understand how diversity and structure mediate the stability of whole ecosystems. For high-diversity food webs, the interactions between species are typically represented using matrices with randomly chosen interaction strengths. Unfortunately, this procedure tends to produce ecological systems with no underlying equilibrium solution, and so ecological inferences from this approach may be biased by nonbiological outcomes. Using recent computationally efficient methodological advances from metabolic networks, we employ for the first time an inverse approach to diversity-stability research. We compare classical random interaction matrices of realistic food web topology (hereafter the classical model) to feasible, biologically constrained, webs produced using the inverse approach. We show that an energetically constrained feasible model yields a far higher proportion of stable high-diversity webs than the classical random matrix approach. When we examine the energetically constrained interaction strength distributions of these matrix models, we find that although these diverse webs have consistent negative self-regulation, they do not require strong self-regulation to persist. These energetically constrained diverse webs instead show an increasing preponderance of weak interactions that are known to increase local stability. Further examination shows that some of these weak interactions naturally appear to arise in the model food webs from a constraint-generated realistic generalist-specialist trade-off, whereby generalist predators have weaker interactions than more specialized species. Additionally, the inverse technique we present here has enormous promise for understanding the role of the biological structure behind stable high-diversity webs and for linking empirical data to the theory.

Evolutionary implications of host genetic control for engineering beneficial microbiomes

Engineering new functions in the microbiome requires understanding how host genetic control and microbe-microbe interactions shape the microbiome. One key genetic mechanism underlying host control is the immune system. The immune system can promote stability in the composition of the microbiome by reshaping the ecological dynamics of its members, but the degree of stability will depend on the interplay between ecological context, immune system development, and higher-order microbe-microbe interactions. The eco-evolutionary interplay affecting composition and stability should inform the strategies used to engineer new functions in the microbiome. We conclude with recent methodological developments that provide an important path forward for both engineering new functionality in the microbiome and broadly understanding how ecological interactions shape evolutionary processes in complex biological systems.

Feasibility and stability in large Lotka Volterra systems with interaction structure

Complex system stability can be studied via linear stability analysis using random matrix theory (RMT) or via feasibility (requiring positive equilibrium abundances). Both approaches highlight the importance of interaction structure. Here we show, analytically and numerically, how RMT and feasibility approaches can be complementary. In generalized Lotka-Volterra (GLV) models with random interaction matrices, feasibility increases when predator-prey interactions increase; increasing competition/mutualism has the opposite effect. These changes have crucial impact on the stability of the GLV model.

Non-random interactions within and across guilds shape the potential to coexist in multi-trophic ecological communities

Theory posits that the persistence of species in ecological communities is shaped by their interactions within and across trophic guilds. However, we lack empirical evaluations of how the structure, strength and sign of biotic interactions drive the potential to coexist in diverse multi-trophic communities. Here, we model community feasibility domains, a theoretically informed measure of multi-species coexistence probability, from grassland communities comprising more than 45 species on average from three trophic guilds (plants, pollinators and herbivores). Contrary to our hypothesis, increasing community complexity, measured either as the number of guilds or community richness, did not decrease community feasibility. Rather, we observed that high degrees of species self-regulation and niche partitioning allow for maintaining larger levels of community feasibility and higher species persistence in more diverse communities. Our results show that biotic interactions within and across guilds are not random in nature and both structures significantly contribute to maintaining multi-trophic diversity.

Generalized Lotka-Volterra model with hierarchical interactions

In the analysis of complex ecosystems it is common to use random interaction coefficients, which are often assumed to be such that all species are statistically equivalent. In this work we relax this assumption by imposing hierarchical interspecies interactions. These are incorporated into a generalized Lotka-Volterra dynamical system. In a hierarchical community species benefit more, on average, from interactions with species further below them in the hierarchy than from interactions with those above. Using dynamic mean-field theory, we demonstrate that a strong hierarchical structure is stabilizing, but that it reduces the number of species in the surviving community, as well as their abundances. Additionally, we show that increased heterogeneity in the variances of the interaction coefficients across positions in the hierarchy is destabilizing. We also comment on the structure of the surviving community and demonstrate that the abundance and probability of survival of a species are dependent on its position in the hierarchy.

Eigenvalue spectra and stability of directed complex networks

Quantifying the eigenvalue spectra of large random matrices allows one to understand the factors that contribute to the stability of dynamical systems with many interacting components. This work explores the effect that the interaction network between components has on the eigenvalue spectrum. We build on previous results, which usually only take into account the mean degree of the network, by allowing for nontrivial network degree heterogeneity. We derive closed-form expressions for the eigenvalue spectrum of the adjacency matrix of a general weighted and directed network. Using these results, which are valid for any large well-connected complex network, we then derive compact formulas for the corrections (due to nonzero network heterogeneity) to well-known results in random matrix theory. Specifically, we derive modified versions of the Wigner semicircle law, the Girko circle law, and the elliptic law and any outlier eigenvalues. We also derive a surprisingly neat analytical expression for the eigenvalue density of a directed Barabási-Albert network. We are thus able to deduce that network heterogeneity is mostly a destabilizing influence in complex dynamical systems.

The coordination of green-brown food webs and their disruption by anthropogenic nutrient inputs

Aim

Our goal was to quantify nitrogen flows and stocks in green-brown food webs in different ecosystems, how they differ across ecosystems and how they respond to nutrient enrichment.

Location

Global.

Time period

Contemporary.

Major taxa studied

Plants, phytoplankton, macroalgae, invertebrates, vertebrates and zooplankton.

Methods

Data from >500 studies were combined to estimate nitrogen stocks and fluxes in green-brown food webs in forests, grasslands, brackish environments, seagrass meadows, lakes and oceans. We compared the stocks, fluxes and metabolic rates of different functional groups within each food web. We also used these estimates to build a dynamical model to test the response of the ecosystems to nutrient enrichment.

Results

We found surprising symmetries between the green and brown channels across ecosystems, in their stocks, fluxes and consumption coefficients and mortality rates. We also found that nitrogen enrichment, either organic or inorganic, can disrupt this balance between the green and brown channels.

Main conclusions

Linking green and brown food webs reveals a previously hidden symmetry between herbivory and detritivory, which appears to be a widespread property of natural ecosystems but can be disrupted by anthropogenic nitrogen additions.

Pathways to the density-dependent expression of cannibalism, and consequences for regulated population dynamics

Cannibalism, once viewed as a rare or aberrant behavior, is now recognized to be widespread and to contribute broadly to the self-regulation of many populations. Cannibalism can produce endogenous negative feedback on population growth because it is expressed as a conditional behavior, responding to the deteriorating ecological conditions that flow, directly or indirectly, from increasing densities of conspecifics. Thus, cannibalism emerges as a strongly density-dependent source of mortality. In this synthesis, we review recent research that has revealed a rich diversity of pathways through which rising density elicits increased cannibalism, including both factors that (a) elevate the rate of dangerous encounters between conspecifics and (b) enhance the likelihood that such encounters will lead to successful cannibalistic attacks. These pathways include both features of the autecology of cannibal populations and features of interactions with other species, including food resources and pathogens. Using mathematical models, we explore the consequences of including density-dependent cannibal attack rates on population dynamics. The conditional expression of cannibalism generally enhances stability and population regulation in single-species models but also may increase opportunities for alternative states and prey population escape from control by cannibalistic predators.

Intermediate Levels of Predation and Nutrient Enrichment Enhance the Activity of Ibuprofen-Degrading Bacteria

Water is the most indispensable natural resource; yet, organic pollution of freshwater sources is widespread. In recent years, there has been increasing concern over the vast array of emerging organic contaminants (EOCs) in the effluent of wastewater treatment plants (WWTPs). Several of these EOCs are degraded within the pore space of riverbeds by active microbial consortia. However, the mechanisms behind this ecosystem service are largely unknown. Here, we report how phosphate concentration and predator-prey interactions drive the capacity of bacteria to process a model EOC (ibuprofen). The presence of phosphate had a significant positive effect on the population growth rate of an ibuprofen-degrading strain. Thus, when phosphate was present, ibuprofen removal efficiency increased. Moreover, low and medium levels of predation, by a ciliated protozoan, stimulated bacterial population growth. This unimodal effect of predation was lost under high phosphate concentration, resulting in the flattening of the relationships between predator density and population growth of ibuprofen degraders. Our results suggest that moderate nutrient and predation levels promote the growth rate of bacterial degraders and, consequently, the self-purifying capability of the system. These findings enhance our understanding of the mechanisms by which riverbed communities drive the processing of EOCs.

The geometry of evolved community matrix spectra

Random matrix theory has been applied to food web stability for decades, implying elliptical eigenvalue spectra and that large food webs should be unstable. Here we allow feasible food webs to self-assemble within an evolutionary process, using simple Lotka–Volterra equations and several elementary interaction types. We show that, as complex food webs evolve under \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${10^5}$$\end{document}105 invasion attempts, the community matrix spectra become bi-modal, rather than falling onto elliptical geometries. Our results raise questions as to the applicability of random matrix theory to the analysis of food web steady states.

Synchrony and Stability in Trophic Metacommunities: When Top Predators Navigate in a Heterogeneous World

Ecosystem stability strongly depends on spatial aspects since localized perturbations spread across an entire region through species dispersal. Assessing the synchrony of the response of connected populations is fundamental to understand stability at different scales because if populations fluctuate asynchronously, the risk of their simultaneous extinction is low, thus reducing the species' regional extinction risk. Here, we consider a metacommunity model consisting of two food chains connected by dispersal and we review the various mechanisms governing the transmission of small perturbations affecting populations in the vicinity of equilibrium. First, we describe how perturbations propagate vertically (i.e., within food chains through trophic interactions) and horizontally (i.e., between food chains through dispersal) in metacommunities. Then, we discuss the mechanisms susceptible to alter synchrony patterns such as density-depend dispersal or spatial heterogeneity. Density-dependent dispersal, which is the influence of prey or predator abundance on dispersal, has a major impact because the species with the highest coefficient of variation of biomass governs the dispersal rate of the dispersing species and determines the synchrony of its populations, thus bypassing the classic vertical transmission of perturbations. Spatial heterogeneity, which is a disparity between patches of the attack rate of predators on prey in our model, alters the vertical transmission of perturbations in each patch, thus making synchrony dependent on which patch is perturbed. Finally, by combining our understanding of the impact of each of these mechanisms on synchrony, we are able to full explain the response of realistic metacommunities such as the model developed by Rooney et al. (2006). By disentangling the main mechanisms governing synchrony, our metacommunity model provides a broad insight into the consequences of spacial aspects on food web stability.

Community structure determines the predictability of population collapse

Early warning signals (EWS) are phenomenological tools that have been proposed as predictors of the collapse of biological systems. Although a growing body of work has shown the utility of EWS based on either statistics derived from abundance data or shifts in phenotypic traits such as body size, so far this work has largely focused on single species populations.

However, to predict reliably the future state of ecological systems, which inherently could consist of multiple species, understanding how reliable such signals are in a community context is critical.

Here, reconciling quantitative trait evolution and Lotka–Volterra equations, which allow us to track both abundance and mean traits, we simulate the collapse of populations embedded in mutualistic and multi‐trophic predator–prey communities. Using these simulations and warning signals derived from both population‐ and community‐level data, we showed the utility of abundance‐based EWS, as well as metrics derived from stability‐landscape theory (e.g. width and depth of the basin of attraction), were fundamentally linked. Thus, the depth and width of such stability‐landscape curves could be used to identify which species should exhibit the strongest EWS of collapse.

The probability a species displays both trait and abundance‐based EWS was dependent on its position in a community, with some species able to act as indicator species. In addition, our results also demonstrated that in general trait‐based EWS were less reliable in comparison with abundance‐based EWS in forecasting species collapses in our simulated communities. Furthermore, community‐level abundance‐based EWS were fairly reliable in comparison with their species‐level counterparts in forecasting species‐level collapses.

Our study suggests a holistic framework that combines abundance‐based EWS and metrics derived from stability‐landscape theory that may help in forecasting species loss in a community context.

Exploring coexistence mechanisms in a three-species assemblage

Interactions among species are essential in shaping ecological communities, although it is not always clear under what conditions they can persist when the number of species involved is higher than two. Here we describe a three-species assemblage involving the seagrass Cymodocea nodosa, the pen shell Pinna nobilis and the herbivore sea urchin Paracentrotus lividus, and we explore the mechanisms allowing its persistence through field observations and manipulative experiments. The abundance of pen shells was higher in seagrass beds than in bare sand, suggesting a recruitment facilitation. The presence of sea urchins, almost exclusively attached or around pen shells, indicated habitat facilitation for sea urchins, which overgrazed the meadow around the pen shells forming seagrass-free halos. Our results suggest that this system persists thanks to: (i) the behavioral reluctance of sea urchins to move far from pen shells, making their impact on seagrass strictly local, (ii) the sparse distribution of pen shells and (iii) the plant's resistance mechanisms to herbivory. Unpacking these mechanisms allows a better understanding of how ecological communities are assembled.

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.

Eigenvalues of Random Matrices with Generalized Correlations: A Path Integral Approach

Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical systems. In this Letter, we study the eigenvalue spectrum of an ensemble of random matrices with correlations between any pair of elements. To this end, we introduce an analytical method that maps the resolvent of the random matrix onto the response functions of a linear dynamical system. The response functions are then evaluated using a path integral formalism, enabling us to make deductions about the eigenvalue spectrum. Our central result is a simple, closed-form expression for the leading eigenvalue of a large random matrix with generalized correlations. This formula demonstrates that correlations between matrix elements that are not diagonally opposite, which are often neglected, can have a significant impact on stability.

Predator interference and complexity-stability in food webs

It is predicted that ecological communities will become unstable with increasing species numbers and subsequent interspecific interactions; however, this is contrary to how natural ecosystems with diverse species respond to changes in species numbers. This contradiction has steered ecologists toward exploring what underlying processes allow complex communities to stabilize even through varying pressures. In this study, a food web model is used to show an overlooked role of interference among multiple predator species in solving this complexity–stability problem. Predator interference in large communities weakens species interactions due to a reduction in consumption rates by prey-sharing species in the presence of predators in response to territorial and aggressive behavior, thereby playing a key stabilizing role in communities. Especially when interspecific interference is strong and a community has diverse species and dense species interactions, stabilization is likely to work and creates a positive complexity–stability relationship within a community. The clear positive effect of complexity on community stability is not reflected by/intraspecific interference, emphasizing the key role of interspecific interference among multiple predator species in maintaining larger systems.

Beware of oysters. Rapid advance of non-native species in tropical Pacific islands

Non-indigenous species can become a problem for the ecosystem health, especially when their distribution grows to the detriment of native species. In this moment, they can become invasive species. In marine ecosystems, the maritime transport is the principal gate and corridor for the movement of alien species. The genetic identification, using barcoding tools, of different oyster species in ports of the remote French Polynesia islands and atolls, showed a significant increase of exotic versus native oyster species between 2011 and 2018. This supports the spread of exotic species with the maritime traffic as the main cause. Moreover, the 11% of inaccurate identification at species level obtained in this study shows the need to complete the genetic databases.

Reinterpreting the relationship between number of species and number of links connects community structure and stability

For 50 years, ecologists have examined how the number of interactions (links) scales with the number of species in ecological networks. Here, we show that the way the number of links varies when species are sequentially removed from a community is fully defined by a single parameter identifiable from empirical data. We mathematically demonstrate that this parameter is network-specific and connects local stability and robustness, establishing a formal connection between community structure and two prime stability concepts. Importantly, this connection highlights a local stability-robustness trade-off, which is stronger in mutualistic than in trophic networks. Analysis of 435 empirical networks confirmed these results. We finally show how our network-specific approach relates to the classical across-network approach found in literature. Taken together, our results elucidate one of the intricate relationships between network structure and stability in community networks.

Understanding the emergence of contingent and deterministic exclusion in multispecies communities

Competitive exclusion can be classified as deterministic or as historically contingent. While competitive exclusion is common in nature, it has remained unclear when multispecies communities formed by more than two species should be dominated by deterministic or contingent exclusion. Here, we take a fully parameterised model of an empirical competitive system between invasive annual and native perennial plant species to explain both the emergence and sources of competitive exclusion in multispecies communities. Using a structural approach to understand the range of parameters promoting deterministic and contingent exclusions, we then find heuristic theoretical support for the following three general conclusions. First, we find that the life-history of perennial species increases the probability of observing contingent exclusion by increasing their effective intrinsic growth rates. Second, we find that the probability of observing contingent exclusion increases with weaker intraspecific competition, and not with the level of hierarchical competition. Third, we find a shift from contingent exclusion to deterministic exclusion with increasing numbers of competing species. Our work provides a heuristic framework to increase our understanding about the predictability of species persistence within multispecies communities.

Dynamic population stage structure due to juvenile-adult asymmetry stabilizes complex ecological communities

Natural ecological communities are diverse, complex, and often surprisingly stable, but the mechanisms underlying their stability remain a theoretical enigma. Interactions such as competition and predation presumably structure communities, yet theory predicts that complex communities are stable only when species growth rates are mostly limited by intraspecific self-regulation rather than by interactions with resources, competitors, and predators. Current theory, however, considers only the network topology of population-level interactions between species and ignores within-population differences, such as between juvenile and adult individuals. Here, using model simulations and analysis, I show that including commonly observed differences in vulnerability to predation and foraging efficiency between juvenile and adult individuals results in up to 10 times larger, more complex communities than observed in simulations without population stage structure. These diverse communities are stable or fluctuate with limited amplitude, although in the model only a single basal species is self-regulated, and the population-level interaction network is highly connected. Analysis of the species interaction matrix predicts the simulated communities to be unstable but for the interaction with the population-structure subsystem, which completely cancels out these instabilities through dynamic changes in population stage structure. Common differences between juveniles and adults and fluctuations in their relative abundance may hence have a decisive influence on the stability of complex natural communities and their vulnerability when environmental conditions change. To explain community persistence, it may not be sufficient to consider only the network of interactions between the constituting species.

A modified niche model for generating food webs with stage-structured consumers: The stabilizing effects of life-history stages on complex food webs

Almost all organisms grow in size during their lifetime and switch diets, trophic positions, and interacting partners as they grow. Such ontogenetic development introduces life-history stages and flows of biomass between the stages through growth and reproduction. However, current research on complex food webs rarely considers life-history stages. The few previously proposed methods do not take full advantage of the existing food web structural models that can produce realistic food web topologies.We extended the niche model developed by Williams and Martinez (Nature, 2000, 404, 180-183) to generate food webs that included trophic species with a life-history stage structure. Our method aggregated trophic species based on niche overlap to form a life-history structured population; therefore, it largely preserved the topological structure of food webs generated by the niche model. We applied the theory of allometric predator-prey body mass ratio and parameterized an allometric bioenergetic model augmented with biomass flow between stages via growth and reproduction to study the effects of a stage structure on the stability of food webs.When life-history stages were linked via growth and reproduction, more food webs persisted, and persisting food webs tended to retain more trophic species. Topological differences between persisting linked and unlinked food webs were small to modest. The slopes of biomass spectra were lower, and weak interaction links were more prevalent in the linked food webs than the unlinked ones, suggesting that a life-history stage structure promotes characteristics that can enhance stability of complex food webs.Our results suggest a positive relationship between the complexity and stability of complex food webs. A life-history stage structure in food webs may play important roles in dynamics of and diversity in food webs.

Automated design of synthetic microbial communities

Microbial species rarely exist in isolation. In naturally occurring microbial systems there is strong evidence for a positive relationship between species diversity and productivity of communities. The pervasiveness of these communities in nature highlights possible advantages for genetically engineered strains to exist in cocultures as well. Building synthetic microbial communities allows us to create distributed systems that mitigate issues often found in engineering a monoculture, especially as functional complexity increases. Here, we demonstrate a methodology for designing robust synthetic communities that include competition for nutrients, and use quorum sensing to control amensal bacteriocin interactions in a chemostat environment. We computationally explore all two- and three- strain systems, using Bayesian methods to perform model selection, and identify the most robust candidates for producing stable steady state communities. Our findings highlight important interaction motifs that provide stability, and identify requirements for selecting genetic parts and further tuning the community composition.

Merging dynamical and structural indicators to measure resilience in multispecies systems

Resilience is broadly understood as the ability of an ecological system to resist and recover from perturbations acting on species abundances and on the system's structure. However, one of the main problems in assessing resilience is to understand the extent to which measures of recovery and resistance provide complementary information about a system. While recovery from abundance perturbations has a strong tradition under the analysis of dynamical stability, it is unclear whether this same formalism can be used to measure resistance to structural perturbations (e.g. perturbations to model parameters). Here, we provide a framework grounded on dynamical and structural stability in Lotka-Volterra systems to link recovery from small perturbations on species abundances (i.e. dynamical indicators) with resistance to parameter perturbations of any magnitude (i.e. structural indicators). We use theoretical and experimental multispecies systems to show that the faster the recovery from abundance perturbations, the higher the resistance to parameter perturbations. We first use theoretical systems to show that the return rate along the slowest direction after a small random abundance perturbation (what we call full recovery) is negatively correlated with the largest random parameter perturbation that a system can withstand before losing any species (what we call full resistance). We also show that the return rate along the second fastest direction after a small random abundance perturbation (what we call partial recovery) is negatively correlated with the largest random parameter perturbation that a system can withstand before at most one species survives (what we call partial resistance). Then, we use a dataset of experimental microbial systems to confirm our theoretical expectations and to demonstrate that full and partial components of resilience are complementary. Our findings reveal that we can obtain the same level of information about resilience by measuring either a dynamical (i.e. recovery) or a structural (i.e. resistance) indicator. Irrespective of the chosen indicator (dynamical or structural), our results show that we can obtain additional information by separating the indicator into its full and partial components. We believe these results can motivate new theoretical approaches and empirical analyses to increase our understanding about risk in ecological systems.

Thermal mismatches in biological rates determine trophic control and biomass distribution under warming

Temperature has numerous effects on the structure and dynamics of ecological communities. Yet, there is no general trend or consensus on the magnitude and directions of these effects. To fill this gap, we propose a mechanistic framework based on key biological rates that predicts how temperature influences biomass distribution and trophic control in food webs. We show that these predictions arise from thermal mismatches between biological rates and across trophic levels. We couple our theory with experimental data for a wide range of species and find that warming should lead to top-heavier terrestrial food chains and stronger top-down control in aquatic environments. We then derive predictions for the effects of temperature on herbivory and validate them with data on stream grazers. Our study provides a mechanistic explanation of thermal effects on consumer-resource systems which is crucial to better understand the biogeography and the consequences of global warming on trophic dynamics.

Stability of ecosystems enhanced by species-interaction constraints

Ecosystem stability is a central question both in theoretical and applied biology. Dynamical systems theory can be used to analyze how growth rates, carrying capacities, and patterns of species interactions affect the stability of an ecosystem. The response to increasing complexity has been extensively studied and the general conclusion is that there is a limit. While there is a complexity limit to stability at which global destabilisation occurs, the collapse rarely happens suddenly if a system is fully viable (no species is extinct). In fact, when complexity is successively increased, we find that the generic response is to go through multiple single-species extinctions before a global collapse. In this paper we demonstrate this finding via both numerical simulations and elaborations of theoretical predictions. We explore more biological interaction patterns, and, perhaps most importantly, we show that constrained interaction structures-a constant row sum in the interaction matrix-prevent extinctions from occurring. This makes an ecosystem more robust in terms of allowed complexity, but it also means singles-species extinctions do not precede or signal collapse-a drastically different behavior compared to the generic and commonly assumed case. We further argue that this constrained interaction structure-limiting the total interactions for each species-is biologically plausible.

Dispersal-induced instability in complex ecosystems

In his seminal work in the 1970s, Robert May suggested that there is an upper limit to the number of species that can be sustained in stable equilibrium by an ecosystem. This deduction was at odds with both intuition and the observed complexity of many natural ecosystems. The so-called stability-diversity debate ensued, and the discussion about the factors contributing to ecosystem stability or instability continues to this day. We show in this work that dispersal can be a destabilising influence. To do this, we combine ideas from Alan Turing's work on pattern formation with May's random-matrix approach. We demonstrate how a stable equilibrium in a complex ecosystem with trophic structure can become unstable with the introduction of dispersal in space, and we discuss the factors which contribute to this effect. Our work highlights that adding more details to the model of May can give rise to more ways for an ecosystem to become unstable. Making May's simple model more realistic is therefore unlikely to entirely remove the upper bound on complexity.

Behaviour moderates the impacts of food-web structure on species coexistence

How species coexistence (mathematical 'feasibility') in food webs emerges from species' trophic interactions remains a long-standing open question. Here we investigate how structure (network topology and body-size structure) and behaviour (foraging strategy and spatial dimensionality of interactions) interactively affect feasibility in food webs. Metabolically-constrained modelling of food-web dynamics based on whole-organism consumption revealed that feasibility is promoted in systems dominated by large-eat-small foraging (consumers eating smaller resources) whenever (1) many top consumers are present, (2) grazing or sit-and-wait foraging strategies are common, and (3) species engage in two-dimensional interactions. Congruently, the first two conditions were associated with dominance of large-eat-small foraging in 74 well-resolved (primarily aquatic) real-world food webs. Our findings provide a new, mechanistic understanding of how behavioural properties can modulate the effects of structural properties on species coexistence in food webs, and suggest that 'being feasible' constrains the spectra of behavioural and structural properties seen in natural food webs.