How collectively integrated are ecological communities?

Beyond abiotic conditions, do population dynamics mostly depend on a species' direct predators, preys and conspecifics? Or can indirect feedback that ripples across the whole community be equally important? Determining where ecological communities sit on the spectrum between these two characterizations requires a metric able to capture the difference between them. Here we show that the spectral radius of a community's interaction matrix provides such a metric, thus a measure of ecological collectivity, which is accessible from imperfect knowledge of biotic interactions and related to observable signatures. This measure of collectivity integrates existing approaches to complexity, interaction structure and indirect interactions. Our work thus provides an original perspective on the question of to what degree communities are more than loose collections of species or simple interaction motifs and explains when pragmatic reductionist approaches ought to suffice or fail when applied to ecological communities.

A taxonomy of multiple stable states in complex ecological communities.

Natural systems are built from multiple interconnected units, making their dynamics, functioning and fragility notoriously hard to predict. A fragility scenario of particular relevance concerns so-called regime shifts: abrupt transitions from healthy to degraded ecosystem states. An explanation for these shifts is that they arise as transitions between alternative stable states, a process that is well-understood in few-species models. However, how multistability upscales with system complexity remains a debated question. Here, we identify that four different multistability regimes generically emerge in models of species-rich communities and other archetypical complex biological systems assuming random interactions. Across the studied models, each regime consistently emerges under a specific interaction scheme and leaves a distinct set of fingerprints in terms of the number of observed states, their species richness and their response to perturbations. Our results help clarify the conditions and types of multistability that can be expected to occur in complex ecological communities.

How biotic interactions structure species' responses to perturbations.

Predicting how ecological communities will respond to disturbances is notoriously challenging, especially given the variability in species' responses within the same community. Focusing solely on aggregate responses may obscure extinction risks for certain species owing to compensatory effects, emphasizing the need to understand the drivers of the response variability at the species level. Yet, these drivers remain poorly understood. Here, we reveal that despite the typical complexity of biotic interaction networks, species' responses follow a discernible pattern. Specifically, we demonstrate that the species whose population abundances are most reduced by biotic interactions-which are not always the rarest species-are those that exhibit the strongest responses to disturbances. This insight enables us to pinpoint sensitive species within communities without requiring precise information about biotic interactions. Our novel approach introduces avenues for future research aimed at identifying sensitive species and elucidating their impacts on entire communities.

Rapid evolution generates synergism between multiple stressors: Linking theory and an evolution experiment.

Global change encompasses many co-occurring anthropogenic stressors. Understanding the interactions between these multiple stressors, whether they be additive, antagonistic or synergistic, is critical for ecosystem managers when prioritizing which stressors to mitigate in the face of global change. While such interactions between stressors appear prevalent, it remains unclear if and how these interactions change over time, as the majority of multiple-stressor studies rarely span multiple generations of study organisms. Although meta-analyses have reported some intriguing temporal trends in stressor interactions, for example that synergism may take time to emerge, the mechanistic basis for such observations is unknown. In this study, by analysing data from an evolution experiment with the rotifer Brachionus calyciflorus (~35 generations and 31,320 observations), we show that adaptation to multiple stressors shifts stressor interactions towards synergism. We show that trade-offs, where populations cannot optimally perform multiple tasks (i.e. adapting to multiple stressors), generate this bias towards synergism. We also show that removal of stressors from evolved populations does not necessarily increase fitness and that there is variation in the evolutionary trajectories of populations that experienced the same stressor regimes. Our results highlight outstanding questions at the interface between evolution and global change biology, and illustrate the importance of considering rapid adaptation when managing or restoring ecosystems subjected to multiple stressors under global change.

Can biomass distribution across trophic levels predict trophic cascades?

The biomass distribution across trophic levels (biomass pyramid) and cascading responses to perturbations (trophic cascades) are archetypal representatives of the interconnected set of static and dynamical properties of food chains. A vast literature has explored their respective ecological drivers, sometimes generating correlations between them. Here we instead reveal a fundamental connection: both pyramids and cascades reflect the dynamical sensitivity of the food chain to changes in species intrinsic rates. We deduce a direct relationship between cascades and pyramids, modulated by what we call trophic dissipation - a synthetic concept that encodes the contribution of top-down propagation of consumer losses in the biomass pyramid. Predictable across-ecosystem patterns emerge when systems are in similar regimes of trophic dissipation. Data from 31 aquatic mesocosm experiments demonstrate how our approach can reveal the causal mechanisms linking trophic cascades and biomass distributions, thus providing a road map to deduce reliable predictions from empirical patterns.

General statistical scaling laws for stability in ecological systems.

Ecological stability refers to a family of concepts used to describe how systems of interacting species vary through time and respond to disturbances. Because observed ecological stability depends on sampling scales and environmental context, it is notoriously difficult to compare measurements across sites and systems. Here, we apply stochastic dynamical systems theory to derive general statistical scaling relationships across time, space, and ecological level of organisation for three fundamental stability aspects: resilience, resistance, and invariance. These relationships can be calibrated using random or representative samples measured at individual scales, and projected to predict average stability at other scales across a wide range of contexts. Moreover deviations between observed vs. extrapolated scaling relationships can reveal information about unobserved heterogeneity across time, space, or species. We anticipate that these methods will be useful for cross-study synthesis of stability data, extrapolating measurements to unobserved scales, and identifying underlying causes and consequences of heterogeneity.

Generic assembly patterns in complex ecological communities.

The study of ecological communities often involves detailed simulations of complex networks. However, our empirical knowledge of these networks is typically incomplete and the space of simulation models and parameters is vast, leaving room for uncertainty in theoretical predictions. Here we show that a large fraction of this space of possibilities exhibits generic behaviors that are robust to modeling choices. We consider a wide array of model features, including interaction types and community structures, known to generate different dynamics for a few species. We combine these features in large simulated communities, and show that equilibrium diversity, functioning, and stability can be predicted analytically using a random model parameterized by a few statistical properties of the community. We give an ecological interpretation of this "disordered" limit where structure fails to emerge from complexity. We also demonstrate that some well-studied interaction patterns remain relevant in large ecosystems, but their impact can be encapsulated in a minimal number of additional parameters. Our approach provides a powerful framework for predicting the outcomes of ecosystem assembly and quantifying the added value of more detailed models and measurements.

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

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

The three regimes of spatial recovery.

An enduring challenge for ecology is identifying the drivers of ecosystem and population stability. In a spatially explicit context, key features to consider are landscape spatial structure, local interactions, and dispersal. Substantial work has been done on each of these features as a driver of stability, but little is known on the interplay between them. Missing has been a more integrative approach, able to map and identify different dynamical regimes, predicting a system's response to perturbations. Here we first consider a simple scenario, i.e., the recovery of a homogeneous metapopulation from a single localized pulse disturbance. The analysis of this scenario reveals three fundamental recovery regimes: Isolated Regime when dispersal is not significant, Rescue Regime when dispersal mediates recovery, and Mixing Regime when perturbations spread throughout the system. Despite its simplicity, our approach leads to remarkably general predictions. These include the qualitatively different outcomes of various scenarios of habitat fragmentation, the surprising benefits of local extinctions on population persistence at the transition between regimes, and the productivity shifts of metacommunities in a changing environment. This study thus provides context to known results and insight into future directions of research.

Power laws in species' biotic interaction networks can be inferred from co-occurrence data.

Inferring biotic interactions from species co-occurrence patterns has long intrigued ecologists. Yet recent research revealed that co-occurrences may not reliably represent pairwise biotic interactions. We propose that examining network-level co-occurrence patterns can provide valuable insights into community structure and assembly. Analysing ten bipartite networks of empirically sampled biotic interactions and associated species spatial distribution, we find that approximately 20% of co-occurrences correspond to actual interactions. Moreover, the degree distribution shifts from exponential in co-occurrence networks to power laws in networks of biotic interactions. This shift results from a strong interplay between species' biotic (their interacting partners) and abiotic (their environmental requirements) niches, and is accurately predicted by considering co-occurrence frequencies. Our work offers a mechanistic understanding of the assembly of ecological communities and suggests simple ways to infer fundamental biotic interaction network characteristics from co-occurrence data.

How strongly does diet variation explain variation in isotope values of animal consumers?

Analysis of stable isotopes in consumers is used commonly to study their ecological and/or environmental niche. There is, however, considerable debate regarding how isotopic values relate to diet and how other sources of variation confound this link, which can undermine the utility. From the analysis of a simple, but general, model of isotopic incorporation in consumer organisms, we examine the relationship between isotopic variance among individuals, and diet variability within a consumer population. We show that variance in consumer isotope values is directly proportional to variation in diet (through Simpson indices), to the number of isotopically distinct food sources in the diet, and to the baseline variation within and among the isotope values of the food sources. Additionally, when considering temporal diet variation within a consumer we identify the interplay between diet turnover rates and tissue turnover rates that controls the sensitivity of stable isotopes to detect diet variation. Our work demonstrates that variation in the stable isotope values of consumers reflect variation in their diet. This relationship, however, can be confounded with other factors to the extent that they may mask the signal coming from diet. We show how simple quantitative corrections can recover a direct 1:1 correlation in some situations, and in others we can adjust our interpretation in light of the new understanding arising from our models. Our framework provides guidance for the design and analysis of empirical studies where the goal is to infer niche width from stable isotope data.

Universal scaling of robustness of ecosystem services to species loss.

Ensuring reliable supply of services from nature is key to the sustainable development and well-being of human societies. Varied and frequently complex relationships between biodiversity and ecosystem services have, however, frustrated our capacity to quantify and predict the vulnerability of those services to species extinctions. Here, we use a qualitative Boolean modelling framework to identify universal drivers of the robustness of ecosystem service supply to species loss. These drivers comprise simple features of the networks that link species to the functions they perform that, in turn, underpin a service. Together, they define what we call network fragility. Using data from >250 real ecological networks representing services such as pollination and seed-dispersal, we demonstrate that network fragility predicts remarkably well the robustness of empirical ecosystem services. We then show how to quantify contributions of individual species to ecosystem service robustness, enabling quantification of how vulnerability scales from species to services. Our findings provide general insights into the way species, functional traits, and the links between them together determine the vulnerability of ecosystem service supply to biodiversity loss.

The Impact of Spatial and Temporal Dimensions of Disturbances on Ecosystem Stability.

Ecosystems constantly face disturbances which vary in their spatial and temporal features, yet little is known on how these features affect ecosystem recovery and persistence, i.e., ecosystem stability. We address this issue by considering three ecosystem models with different local dynamics, and ask how their stability properties depend on the spatial and temporal properties of disturbances. We measure the spatial dimension of disturbances by their spatial extent while controlling for their overall strength, and their temporal dimension by the average frequency of random disturbance events. Our models show that the return to equilibrium following a disturbance depends strongly on the disturbance's extent, due to rescue effects mediated by dispersal. We then reveal a direct relation between the temporal variability caused by repeated disturbances and the recovery from an isolated disturbance event. Although this could suggest a trivial dependency of ecosystem response on disturbance frequency, we find that this is true only up to a frequency threshold, which depends on both the disturbance spatial features and the ecosystem dynamics. Beyond this threshold the response changes qualitatively, displaying spatial clusters of disturbed regions, causing an increase in variability, and even a system-wide collapse for ecosystems with alternative stable states. Thus, spanning the spatial dimension of disturbances is a way to probe the underlying dynamics of an ecosystem. Furthermore, considering spatial and temporal dimensions of disturbances in conjunction is necessary to predict ecosystem responses with dramatic ecological consequences, such as regime shifts or population extinction.

An invariability-area relationship sheds new light on the spatial scaling of ecological stability.

The spatial scaling of stability is key to understanding ecological sustainability across scales and the sensitivity of ecosystems to habitat destruction. Here we propose the invariability-area relationship (IAR) as a novel approach to investigate the spatial scaling of stability. The shape and slope of IAR are largely determined by patterns of spatial synchrony across scales. When synchrony decays exponentially with distance, IARs exhibit three phases, characterized by steeper increases in invariability at both small and large scales. Such triphasic IARs are observed for primary productivity from plot to continental scales. When synchrony decays as a power law with distance, IARs are quasilinear on a log-log scale. Such quasilinear IARs are observed for North American bird biomass at both species and community levels. The IAR provides a quantitative tool to predict the effects of habitat loss on population and ecosystem stability and to detect regime shifts in spatial ecological systems, which are goals of relevance to conservation and policy.

Unifying dynamical and structural stability of equilibria.

We exhibit a fundamental relationship between measures of dynamical and structural stability of linear dynamical systems-e.g. linearized models in the vicinity of equilibria. We show that dynamical stability, quantified via the response to external perturbations (i.e. perturbation of dynamical variables), coincides with the minimal internal perturbation (i.e. perturbations of interactions between variables) able to render the system unstable. First, by reformulating a result of control theory, we explain that harmonic external perturbations reflect the spectral sensitivity of the Jacobian matrix at the equilibrium, with respect to constant changes of its coefficients. However, for this equivalence to hold, imaginary changes of the Jacobian's coefficients have to be allowed. The connection with dynamical stability is thus lost for real dynamical systems. We show that this issue can be avoided, thus recovering the fundamental link between dynamical and structural stability, by considering stochastic noise as external and internal perturbations. More precisely, we demonstrate that a linear system's response to white-noise perturbations directly reflects the intensity of internal white-noise disturbance that it can accommodate before becoming stochastically unstable.