How ecosystems recover from pulse perturbations: A theory of short- to long-term responses

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.

Restoring ecological complexity in a changing environment

As land use leaves massive tracts of land vacant for recovery, restoration must undergo a substantial shift to incorporate a complexity perspective beyond the traditional community, biodiversity or functional views. With an interaction-function perspective, we may be able to achieve ecosystems with better chances to adapt to current environmental changes and, especially, to climate change. We explore combined approaches that include still unused and underexplored techniques that will soon go mainstream and produce massive amounts of information to address the complexity gap. As we understand how complexity reassembles after the end of agriculture, we will be able to design actions to restore or enhance it at unprecedented spatial scales while increasing its adaptability to environmental changes.

Marine protected areas are a useful tool to protect coral reef fishes but not representative to conserve their functional role

Anthropogenic actions have direct and indirect impacts on natural systems, leading to significant alterations in marine ecosystems worldwide. One of the most notable problems is species loss, as the disappearance of species from an area can compromise ecological functions. This is at the core of a severe biodiversity crisis. To address and reverse these processes, marine protected areas (MPAs) have been utilized as a crucial tool to mitigate species loss, increase biomass, and serve as a fisheries management tool. However, there is a lack of information assessing MPAs from the perspective of their contribution to maintaining ecological functions. In recent decades, functional diversity (FD) indices have been widely used to assess ecosystem functioning. In this paper, we conducted an assessment using a global database of reef fish abundance to analyze the effect of No-Take Zones (NTZ) on the FD and "true" diversity (TD) indices of tropical reef fish assemblages in seven tropical biogeographic regions. We found a significant protective effect for some indices, although these responses were dependent on the bioregion. At the bioregional level, NTZs included lower numbers of species and functional entities than open access areas. Consequently, the functional richness protected within these zones partially represented the functional diversity in each biogeographic province. However, smaller-scale functional diversity indices responded to NTZ protection depending on the bioregion. Therefore, these results reinforce that the assessed NTZs are responsive to the protection of functional diversity, although they are not sufficient for safeguarding ecosystem functions in tropical reefs. This highlights the importance of expanding the number of protection entities worldwide with management strategies focused on coral reef fish functionality, as well as effective local/regional assessments. Thus, a new paradigm is necessary in the planning and creation of MPAs to safeguard ecosystem functions, with a priority given to the protection of ecosystem functions and habitats.

Natural recovery of corals after severe disturbance

Ecosystem recovery from human-induced disturbances, whether through natural processes or restoration, is occurring worldwide. Yet, recovery dynamics, and their implications for broader ecosystem management, remain unclear. We explored recovery dynamics using coral reefs as a case study. We tracked the fate of 809 individual coral recruits that settled after a severe bleaching event at Lizard Island, Great Barrier Reef. Recruited Acropora corals, first detected in 2020, grew to coral cover levels that were equivalent to global average coral cover within just 2 years. Furthermore, we found that just 11.5 Acropora recruits per square meter were sufficient to reach this cover within 2 years. However, wave exposure, growth form and colony density had a marked effect on recovery rates. Our results underscore the importance of considering natural recovery in management and restoration and highlight how lessons learnt from reef recovery can inform our understanding of recovery dynamics in high-diversity climate-disturbed 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.

Spatial heterogeneity of biomass turnover has contrasting effects on synchrony and stability in trophic metacommunities

Spatial heterogeneity is a fundamental feature of ecosystems, and ecologists have identified it as a factor promoting the stability of population dynamics. In particular, differences in interaction strengths and resource supply between patches generate an asymmetry of biomass turnover with a fast and a slow patch coupled by a mobile predator. Here, we demonstrate that asymmetry leads to opposite stability patterns in metacommunities receiving localized perturbations depending on the characteristics of the perturbed patch. Perturbing prey in the fast patch synchronizes the dynamics of prey biomass between the two patches and destabilizes predator dynamics by increasing the predator's temporal variability. Conversely, perturbing prey in the slow patch decreases the synchrony of the prey's dynamics and stabilizes predator dynamics. Our results have implications for conservation ecology and suggest reinforcing protection policies in fast patches to dampen the effects of perturbations and promote the stability of population dynamics at the regional scale.

Structural asymmetry in biotic interactions as a tool to understand and predict ecological persistence

A universal feature of ecological systems is that species do not interact with others with the same sign and strength. Yet, the consequences of this asymmetry in biotic interactions for the short- and long-term persistence of individual species and entire communities remains unclear. Here, we develop a set of metrics to evaluate how asymmetric interactions among species translate to asymmetries in their individual vulnerability to extinction under changing environmental conditions. These metrics, which solve previous limitations of how to independently quantify the size from the shape of the so-called feasibility domain, provide rigorous advances to understand simultaneously why some species and communities present more opportunities to persist than others. We further demonstrate that our shape-related metrics are useful to predict short-term changes in species' relative abundances during 7 years in a Mediterranean grassland. Our approach is designed to be applied to any ecological system regardless of the number of species and type of interactions. With it, we show that is possible to obtain both mechanistic and predictive information on ecological persistence for individual species and entire communities, paving the way for a stronger integration of theoretical and empirical research.

No sensitivity to functional forms in the Rosenzweig-MacArthur model with strong environmental stochasticity

The classic Rosenzweig-MacArthur predator-prey model has been shown to exhibit, like other coupled nonlinear ordinary differential equations (ODEs) from ecology, worrying sensitivity to model structure. This sensitivity manifests as markedly different community dynamics arising from saturating functional responses with nearly identical shapes but different mathematical expressions. Using a stochastic differential equation (SDE) version of the Rosenzweig-MacArthur model with the three functional responses considered by Fussmann & Blasius (2005), I show that such sensitivity seems to be solely a property of ODEs or stochastic systems with weak noise. SDEs with strong environmental noise have by contrast very similar fluctuations patterns, irrespective of the mathematical formula used. Although eigenvalues of linearized predator-prey models have been used as an argument for structural sensitivity, they can also be an argument against structural sensitivity. While the sign of the eigenvalues' real part is sensitive to model structure, its magnitude and the presence of imaginary parts are not, which suggests noise-driven oscillations for a broad range of carrying capacities. I then discuss multiple other ways to evaluate structural sensitivity in a stochastic setting, for predator-prey or other ecological systems.

Equilibrium and surviving species in a large Lotka-Volterra system of differential equations

Lotka-Volterra (LV) equations play a key role in the mathematical modeling of various ecological, biological and chemical systems. When the number of species (or, depending on the viewpoint, chemical components) becomes large, basic but fundamental questions such as computing the number of surviving species still lack theoretical answers. In this paper, we consider a large system of LV equations where the interactions between the various species are a realization of a random matrix. We provide conditions to have a unique equilibrium and present a heuristics to compute the number of surviving species. This heuristics combines arguments from Random Matrix Theory, mathematical optimization (LCP), and standard extreme value theory. Numerical simulations, together with an empirical study where the strength of interactions evolves with time, illustrate the accuracy and scope of the results.

Multimodal distribution of transient time of predator extinction in a three-species food chain

The transient dynamics capture the time history in the behavior of a system before reaching an attractor. This paper deals with the statistics of transient dynamics in a classic tri-trophic food chain with bistability. The species of the food chain model either coexist or undergo a partial extinction with predator death after a transient time depending upon the initial population density. The distribution of transient time to predator extinction shows interesting patterns of inhomogeneity and anisotropy in the basin of the predator-free state. More precisely, the distribution shows a multimodal character when the initial points are located near a basin boundary and a unimodal character when chosen from a location far away from the boundary. The distribution is also anisotropic because the number of modes depends on the direction of the local of initial points. We define two new metrics, viz., homogeneity index and local isotropic index, to characterize the distinctive features of the distribution. We explain the origin of such multimodal distributions and try to present their ecological implications.

Ranking species based on sensitivity to perturbations under non-equilibrium community dynamics

Managing ecological communities requires fast detection of species that are sensitive to perturbations. Yet, the focus on recovery to equilibrium has prevented us from assessing species responses to perturbations when abundances fluctuate over time. Here, we introduce two data-driven approaches (expected sensitivity and eigenvector rankings) based on the time-varying Jacobian matrix to rank species over time according to their sensitivity to perturbations on abundances. Using several population dynamics models, we demonstrate that we can infer these rankings from time-series data to predict the order of species sensitivities. We find that the most sensitive species are not always the ones with the most rapidly changing or lowest abundance, which are typical criteria used to monitor populations. Finally, using two empirical time series, we show that sensitive species tend to be harder to forecast. Our results suggest that incorporating information on species interactions can improve how we manage communities out of equilibrium.

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.

Spatial and Ecological Scaling of Stability in Spatial Community Networks

There are many scales at which to quantify stability in spatial and ecological networks. Local-scale analyses focus on specific nodes of the spatial network, while regional-scale analyses consider the whole network. Similarly, species- and community-level analyses either account for single species or for the whole community. Furthermore, stability itself can be defined in multiple ways, including resistance (the inverse of the relative displacement caused by a perturbation), initial resilience (the rate of return after a perturbation), and invariability (the inverse of the relative amplitude of the population fluctuations). Here, we analyze the scale-dependence of these stability properties. More specifically, we ask how spatial scale (local vs. regional) and ecological scale (species vs. community) influence these stability properties. We find that regional initial resilience is the weighted arithmetic mean of the local initial resiliences. The regional resistance is the harmonic mean of local resistances, which makes regional resistance particularly vulnerable to nodes with low stability, unlike regional initial resilience. Analogous results hold for the relationship between community- and species-level initial resilience and resistance. Both resistance and initial resilience are “scale-free” properties: regional and community values are simply the biomass-weighted means of the local and species values, respectively. Thus, one can easily estimate both stability metrics of whole networks from partial sampling. In contrast, invariability generally is greater at the regional and community-level than at the local and species-level, respectively. Hence, estimating the invariability of spatial or ecological networks from measurements at the local or species level is more complicated, requiring an unbiased estimate of the network (i.e., region or community) size. In conclusion, we find that scaling of stability depends on the metric considered, and we present a reliable framework to estimate these metrics.

Well-mixed Lotka-Volterra model with random strongly competitive interactions

The random Lotka-Volterra model is widely used to describe the dynamical and thermodynamic features of ecological communities. In this work, we consider random symmetric interactions between species and analyze the strongly competitive interaction case. We investigate different scalings for the distribution of the interactions with the number of species and try to bridge the gap with previous works. Our results show two different behaviors for the mean abundance at zero and finite temperature, respectively, with a continuous crossover between the two. We confirm and extend previous results obtained for weak interactions: at zero temperature, even in the strong competitive interaction limit, the system is in a multiple-equilibria phase, whereas at finite temperature only a unique stable equilibrium can exist. Finally, we establish the qualitative phase diagrams and compare the species abundance distributions in the two cases.

Dynamical systems on large networks with predator-prey interactions are stable and exhibit oscillations

We analyze the stability of linear dynamical systems defined on sparse, random graphs with predator-prey, competitive, and mutualistic interactions. These systems are aimed at modeling the stability of fixed points in large systems defined on complex networks, such as ecosystems consisting of a large number of species that interact through a food web. We develop an exact theory for the spectral distribution and the leading eigenvalue of the corresponding sparse Jacobian matrices. This theory reveals that the nature of local interactions has a strong influence on a system's stability. We show that, in general, linear dynamical systems defined on random graphs with a prescribed degree distribution of unbounded support are unstable if they are large enough, implying a tradeoff between stability and diversity. Remarkably, in contrast to the generic case, antagonistic systems that contain only interactions of the predator-prey type can be stable in the infinite size limit. This feature for antagonistic systems is accompanied by a peculiar oscillatory behavior of the dynamical response of the system after a perturbation, when the mean degree of the graph is small enough. Moreover, for antagonistic systems we also find that there exist a dynamical phase transition and critical mean degree above which the response becomes nonoscillatory.

Effect of Organic Farming and Agricultural Abandonment on Beneficial Arthropod Communities Associated with Olive Groves in Western Spain: Implications for Bactrocera oleae Management

Agricultural abandonment and intensification are among the main land-use changes in Europe. Along with these processes, different proposals have been developed to counteract the negative effects derived from agricultural intensification, including organic management. In this context, we aimed to determine how organic management and farmland abandonment affect Bactrocera oleae and its main groups of natural enemies: hymenopteran parasitoids, spiders, ants, carabids, and staphylinids. Between May and October 2018, four samplings were carried out in nine olive groves (three under organic management, three under traditional management, and three abandoned) in a rural area on the border between Spain and Portugal (Salamanca, Western Spain). Our results suggested differences between the natural enemy community composition of abandoned and organic groves, with slightly higher levels of richness and abundance in abandoned groves. We found no differences between organic and traditional groves. The managed olive groves sustained a different natural enemy community but were similarly rich and diverse compared with the more complex abandoned groves, with the latter not acting as a reservoir of B. oleae in our study area. Both systems may provide complementary habitats; however, further abandonment could cause a reduction in heterogeneity at the landscape scale and, consequently, a biodiversity loss.

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.

Mitigating long transient time in deterministic systems by resetting

How long does a trajectory take to reach a stable equilibrium point in the basin of attraction of a dynamical system? This is a question of quite general interest and has stimulated a lot of activities in dynamical and stochastic systems where the metric of this estimation is often known as the transient or first passage time. In nonlinear systems, one often experiences long transients due to their underlying dynamics. We apply resetting or restart, an emerging concept in statistical physics and stochastic process, to mitigate the detrimental effects of prolonged transients in deterministic dynamical systems. We show that resetting the intrinsic dynamics intermittently to a spatial control line that passes through the equilibrium point can dramatically expedite its completion, resulting in a huge reduction in mean transient time and fluctuations around it. Moreover, our study reveals the emergence of an optimal restart time that globally minimizes the mean transient time. We corroborate the results with detailed numerical studies on two canonical setups in deterministic dynamical systems, namely, the Stuart-Landau oscillator and the Lorenz system. The key features-expedition of transient time-are found to be very generic under different resetting strategies. Our analysis opens up a door to control the mean and fluctuations in transient time by unifying the original dynamics with an external stochastic or periodic timer and poses open questions on the optimal way to harness transients in dynamical systems.

Abnormal Food Timing Promotes Alcohol-Associated Dysbiosis and Colon Carcinogenesis Pathways

Background: Alcohol consumption is an established risk factor for colorectal cancer (CRC). Identifying cofactor(s) that modulate the effect of alcohol on colon inflammation and carcinogenesis could help risk stratification for CRC. Disruption of circadian rhythm by light/dark shift promotes alcohol-induced colonic inflammation and cancer. More recently, we found that abnormal food timing causes circadian rhythm disruption and promotes alcohol associated colon carcinogenesis. In this study, we examined the interaction of wrong-time feeding (WTF) and alcohol on CRC-related pathways, in relation to changes in microbial community structure. Methods: Polyposis mice (TS4Cre ×cAPC Δ468) underwent four conditions: alcohol or water and feeding during the light (wrong-time fed/WTF) or during the dark (right-time fed). Colonic cecum mucosal gene expression was analyzed by RNA-seq. Microbiota 16S ribosomal RNA sequencing analysis was used to examine colonic feces. Modeling was used to estimate the extent of the gene expression changes that could be related to the changes in the colonic microbial composition. Results: The circadian rhythm pathway was the most altered pathway by the WTF treatment, indicating that WTF is disruptive to the colonic circadian rhythm. Pathway analysis revealed interaction of WTF with alcohol in dysregulating pathways related to colon carcinogenesis. Similarly, the interaction of alcohol and WTF was detected at multiple parameters of the colonic microbiota including α and β diversity, as well as the community structure. Our modeling revealed that almost a third of total gene alterations induced by our treatments could be related to alterations in the abundance of the microbial taxa. Conclusion: These data support the promoting effect of abnormal food timing alcohol-associated CRC-related pathways in the colon and suggest colon dysbiosis as a targetable mechanism.

Minimal fatal shocks in multistable complex networks

Multistability is a common phenomenon which naturally occurs in complex networks. Often one of the coexisting stable states can be identified as being the desired one for a particular application. We present here a global approach to identify the minimal perturbation which will instantaneously kick the system out of the basin of attraction of its desired state and hence induce a critical or fatal transition we call shock-tipping. The corresponding Minimal Fatal Shock is a vector whose length can be used as a global stability measure and whose direction in state space allows us to draw conclusions on weaknesses of the network corresponding to critical network motifs. We demonstrate this approach in plant-pollinator networks and the power grid of Great Britain. In both system classes, tree-like substructures appear to be the most vulnerable with respect to the minimal shock perturbation.

The stability of mutualism

Positive interactions are observed at high frequencies in nearly all living systems, ranging from human and animal societies down to the scale of microbial organisms. However, historically, detailed ecological studies of mutualism have been relatively unrepresented. Moreover, while ecologists have long portrayed competition as a stabilizing process, mutualism is often deemed destabilizing. Recently, several key modelling studies have applied random matrix methods, and have further corroborated the instability of mutualism. Here, I reassess these findings by factoring in species densities into the “community matrix,” a practice which has almost always been ignored in random matrix analyses. With this modification, mutualistic interactions are found to boost equilibrium population densities and stabilize communities by increasing their resilience. By taking into account transient dynamics after a strong population perturbation, it is found that mutualists have the ability to pull up communities by their bootstraps when species are dangerously depressed in numbers.

Mutualism is typically portrayed as a destabilizing process in community ecology. Here, via a random matrix model that considers species density, the author shows that mutualistic interactions can, in fact, enhance population density at equilibrium and increase community resilience to perturbation.

Informing management decisions for ecological networks, using dynamic models calibrated to noisy time-series data

Well-intentioned environmental management can backfire, causing unforeseen damage. To avoid this, managers and ecologists seek accurate predictions of the ecosystem-wide impacts of interventions, given small and imprecise datasets, which is an incredibly difficult task. We generated and analysed thousands of ecosystem population time series to investigate whether fitted models can aid decision-makers to select interventions. Using these time-series data (sparse and noisy datasets drawn from deterministic Lotka-Volterra systems with two to nine species, of known network structure), dynamic model forecasts of whether a species' future population will be positively or negatively affected by rapid eradication of another species were correct > 70% of the time. Although 70% correct classifications is only slightly better than an uninformative prediction (50%), this classification accuracy can be feasibly improved by increasing monitoring accuracy and frequency. Our findings suggest that models may not need to produce well-constrained predictions before they can inform decisions that improve environmental outcomes.

Unveiling dimensions of stability in complex ecological networks

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

Measuring resilience is essential if we are to understand it

"Sustainability", "resilience", and other terms group under the heading of "stability." Their ubiquity speaks to a vital need to characterise changes in complex social and environmental systems. In a bewildering array of terms, practical measurements are essential to permit comparisons and so untangle underlying relationships.

A potential role for rare species in ecosystem dynamics

The ecological importance of common species for many ecosystem processes and functions is unquestionably due to their high abundance. Yet, the importance of rare species is much less understood. Here we take a theoretical approach, exposing dynamical models of ecological networks to small perturbations, to explore the dynamical importance of rare and common species. We find that both species types contribute to the recovery of communities following generic perturbations (i.e. perturbations affecting all species). Yet, when perturbations are selective (i.e. affects only one species), perturbations to rare species have the most pronounced effect on community stability. We show that this is due to the strong indirect effects induced by perturbations to rare species. Because indirect effects typically set in at longer timescales, our results indicate that the importance of rare species may be easily overlooked and thus underrated. Hence, our study provides a potential ecological motive for the management and protection of rare species.

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.

Pyramids and cascades: a synthesis of food chain functioning and stability

Food chain theory is one of the cornerstones of ecology, providing many of its basic predictions, such as biomass pyramids, trophic cascades and predator-prey oscillations. Yet, ninety years into this theory, the conditions under which these patterns may occur and persist in nature remain subject to debate. Rather than address each pattern in isolation, we propose that they must be understood together, calling for synthesis in a fragmented landscape of theoretical and empirical results. As a first step, we propose a minimal theory that combines the long-standing energetic and dynamical approaches of food chains. We chart theoretical predictions on a concise map, where two main regimes emerge: across various functioning and stability metrics, one regime is characterised by pyramidal patterns and the other by cascade patterns. The axes of this map combine key physiological and ecological variables, such as metabolic rates and self-regulation. A quantitative comparison with data sheds light on conflicting theoretical predictions and empirical puzzles, from size spectra to causes of trophic cascade strength. We conclude that drawing systematic connections between various existing approaches to food chains, and between their predictions on functioning and stability, is a crucial step in confronting this theory to real ecosystems.

Qualitative and quantitative responses to press perturbations in ecological networks

Predicting the sign of press perturbation responses in ecological networks is challenging, due to the poor knowledge of the strength of the direct interactions among the species, and to the entangled coexistence of direct and indirect effects. We show in this paper that, for a class of networks that includes mutualistic and monotone networks, the sign of press perturbation responses can be qualitatively determined based only on the sign pattern of the community matrix, without any knowledge of parameter values. For other classes of networks, we show that a semi-qualitative approach yields sufficient conditions for community matrices with a given sign pattern to exhibit mutualistic responses to press perturbations; quantitative conditions can be provided as well for community matrices that are eventually nonnegative. We also present a computational test that can be applied to any class of networks so as to check whether the sign of the responses to press perturbations is constant in spite of parameter variations.