Delayed loss of stability of periodic travelling waves: Insights from the analysis of essential spectra

Periodic travelling waves (PTW) are a common solution type of partial differential equations. Such models exhibit multistability of PTWs, typically visualised through the Busse balloon, and parameter changes typically lead to a cascade of wavelength changes through the Busse balloon. In the past, the stability boundaries of the Busse balloon have been used to predict such wavelength changes. Here, motivated by anecdotal evidence from previous work, we provide compelling evidence that the Busse balloon provides insufficient information to predict wavelength changes due to a delayed loss of stability phenomenon. Using two different reaction-advection-diffusion systems, we relate the delay that occurs between the crossing of a stability boundary in the Busse balloon and the occurrence of a wavelength change to features of the essential spectrum of the destabilised PTW. This leads to a predictive framework that can estimate the order of magnitude of such a time delay, which provides a novel "early warning sign" for pattern destabilisation. We illustrate the implementation of the predictive framework to predict under what conditions a wavelength change of a PTW occurs.

Signature of climate dynamics on hydrological drought dynamics: A qualitative analysis

Understanding the complexity of climate dynamics is of paramount importance, because climate variability and change significantly affect water cycles and ecosystems. However, recurrent hydrological droughts that have been observed every 10 years on the two primary tributaries of the Congo River (the Ubangui and Kasaï Rivers) since the advent of the 1969 drought lack a plausible explanation for variability or climate change. This study proposes a plausible explanation for recurring hydrological droughts. Given the low rate of human activity and vegetation cover evolution in the Congo Watershed, we propose that climate dynamics play a crucial role in hydrological drought dynamics. By applying the Bayesian approach to a gridded precipitation database, we obtained posterior probability maps for each annual time step during our observational period (1940-2020). This provided a spatiotemporal representation of the areas affected by climatic disturbances, unlike previous studies that were limited to a spatial representation of the temporal location of the disturbances. Our qualitative analysis of the maximum intensity of the climate disturbance signal (CPS) revealed an average cycle of 10 years and eight months of signal migration. However, we observed that every 10 years since the advent of the drought during 1969, the hydrological drought occurrence dates coincided with CPS migration dates. This highlights the influence of this cycle on the hydrological drought dynamics. Nevertheless, because of the monthly scale involved in the propagation time from meteorological to hydrological drought, the error in this cycle was considered to be the propagation time of disturbances. Therefore, we recommend that future research should focus on estimating this time to test this hypothesis. This study underscores the significance of the cyclic dynamics of lengthy transient processes in understanding hydrological drought dynamics.

Metabolic Trade-Offs Can Reverse the Resource-Diversity Relationship

AbstractFor species that partition resources, the classic expectation is that increasing resource diversity allows for increased species diversity. On the other hand, for neutral species, such as those competing equally for a single resource, diversity reflects a balance between the rate of introduction of novelty (e.g., by immigration or speciation) and the rate of extinction. Recent models of microbial metabolism have identified scenarios where metabolic trade-offs among species partitioning multiple resources can produce emergent neutral-like dynamics. In this hybrid scenario, one might expect that both resource diversity and immigration will act to boost species diversity. We show, however, that the reverse may be true: when metabolic trade-offs hold and population sizes are sufficiently large, increasing resource diversity can act to reduce species diversity, sometimes drastically. This reversal is explained by a generic transition between neutral- and niche-like dynamics, driven by the diversity of resources. The inverted resource-diversity relationship that results may be a signature of consumer-resource systems with strong metabolic trade-offs.

Rapid predator-prey balance shift follows critical-population-density transmission between cod (Gadus morhua) and capelin (Mallotus villosus)

Sensing limitations have impeded knowledge about how individual predator-prey interactions build to organized multi-species group behaviour across an ecosystem. Population densities of overlapping interacting oceanic fish predator and prey species, however, can be instantaneously distinguished and quantified from roughly the elemental individual to spatial scales spanning thousands of square kilometres by wide-area multispectral underwater-acoustic sensing, as shown here. This enables fundamental mechanisms behind large-scale ordered predator-prey interactions to be investigated. Critical population densities that transition random individual behaviour to ordered group behaviour are found to rapidly propagate to form vast adversarial prey and predator shoals of capelin and surrounding cod in the Barents Sea Arctic ecosystem for these keystone species. This leads to a sudden major shift in predator-prey balance. Only a small change in local behaviour triggers the shift due to an unstable equilibrium. Such unstable equilibria and associated balance shifts at predation hotspots are often overlooked as blind spots in present ocean ecosystem monitoring and assessment due to use of highly undersampled spatio-temporal sampling methods.

Marine reserves can buffer against environmental fluctuations for overexploited but not sustainably harvested fisheries

Globally, decision-makers are seeking management levers that can mitigate the negative effects of climate change on ecosystems that have already been transformed from their natural state by the effects of fishing. An important question is whether marine reserves can provide buffering (i.e., population-level resilience) against climate disturbances to fished populations. Here, we examine one aspect of this question, by asking whether marine reserves can reduce the variability in either overall biomass or in fishery yield, in the face of environmental variability. This could happen because greater reproduction of longer-lived, larger fish inside reserves could supplement recruitment to the fished portion of the population. We addressed this question using age-structured population models, assuming a system where some proportion of the coastline is protected in marine reserves (0%-30%), and the remainder is fished (at a range of possible harvest rates). We modeled populations with sedentary adults and dispersal via a larval pool. Since recent extreme climate events (e.g., marine heatwaves) have reduced juvenile survival for some fish species, we assumed that environmental variability affected the survival of the first age class in our model. We viewed population variability as a question of buffering, measured as the proportion of time a simulated population spent below a target reference point, with the idea that marine reserves could prevent the population from reaching low levels in the face of fishing and environmental variability. We found that fisheries with more area in marine reserves always had less variability in biomass. However, adding marine reserves only reduced variability in fisheries yield when the fished part of the population was being harvested at a rate exceeding the maximum sustainable yield. This new result on reducing variability is in line with previous findings that the "spillover" effects of marine reserve benefits to fishery yields only accrue when the fishery outside reserve boundaries is being overharvested.

A mathematical framework for the statistical interpretation of biological growth models

Biological entities are inherently dynamic. As such, various ecological disciplines use mathematical models to describe temporal evolution. Typically, growth curves are modelled as sigmoids, with the evolution modelled by ordinary differential equations. Among the various sigmoid models, the logistic, Gompertz and Richards equations are well-established and widely used for the purpose of fitting growth data in the fields of biology and ecology. The present paper puts forth a mathematical framework for the statistical analysis of population growth models. The analysis is based on a mathematical model of the population-environment relationship, the theoretical foundations of which are discussed in detail. By applying this theory, stochastic evolutionary equations are obtained, for which the logistic, Gompertz, Richards and Birch equations represent a limiting case. To substantiate the models of population growth dynamics, the results of numerical simulations are presented. It is demonstrated that a variety of population growth models can be addressed in a comparable manner. It is suggested that the discussed mathematical framework for statistical interpretation of the joint population-environment evolution represents a promising avenue for further research.

How combined pairwise and higher-order interactions shape transient dynamics

Understanding how species interactions shape biodiversity is a core challenge in ecology. While much focus has been on long-term stability, there is rising interest in transient dynamics-the short-lived periods when ecosystems respond to disturbances and adjust toward stability. These transitions are crucial for predicting ecosystem reactions and guiding effective conservation. Our study introduces a model that uses convex combinations to blend pairwise and higher-order interactions (HOIs), offering a more realistic view of natural ecosystems. We find that pairwise interactions slow the journey to stability, while HOIs speed it up. Employing global stability analysis and numerical simulations, we establish that as the proportion of HOIs increases, mean transient times exhibit a significant reduction, thereby underscoring the essential role of HOIs in enhancing biodiversity stabilization. Our results reveal a robust correlation between the most negative real part of the eigenvalues of the Jacobian matrix associated with the linearized system at the coexistence equilibrium and the mean transient times. This indicates that a more negative leading eigenvalue correlates with accelerated convergence to stable coexistence abundances. This insight is vital for comprehending ecosystem resilience and recovery, emphasizing the key role of HOIs in promoting stabilization. Amid growing interest in transient dynamics and its implications for biodiversity and ecological stability, our study enhances the understanding of how species interactions affect both transient and long-term ecosystem behavior. By addressing a critical gap in ecological theory and offering a practical framework for ecosystem management, our work advances knowledge of transient dynamics, ultimately informing effective conservation strategies.

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.

Modeling tumors as complex ecosystems

Many cancers resist therapeutic intervention. This is fundamentally related to intratumor heterogeneity: multiple cell populations, each with different phenotypic signatures, coexist within a tumor and its metastases. Like species in an ecosystem, cancer populations are intertwined in a complex network of ecological interactions. Most mathematical models of tumor ecology, however, cannot account for such phenotypic diversity or predict its consequences. Here, we propose that the generalized Lotka-Volterra model (GLV), a standard tool to describe species-rich ecological communities, provides a suitable framework to model the ecology of heterogeneous tumors. We develop a GLV model of tumor growth and discuss how its emerging properties provide a new understanding of the disease. We discuss potential extensions of the model and their application to phenotypic plasticity, cancer-immune interactions, and metastatic growth. Our work outlines a set of questions and a road map for further research in cancer ecology.

Asymmetric Biotic Interactions Cannot Be Inferred Without Accounting for Priority Effects

Understanding biotic interactions is a crucial goal in community ecology and species distribution modelling, and large strides have been made towards improving multivariate computational methods with the aim of quantifying biotic interactions and improving predictions of species occurrence. Yet, while considerable attention has been given to computational approaches and the interpretation of these quantitative tools, the importance of sampling design to reveal these biotic interactions has received little consideration. This study explores the influential role of priority effects, that is, the order of habitat colonisation, in shaping our ability to detect biotic interactions. Using a simple set of simulations, we demonstrate that commonly used cross-sectional co-occurrence data alone cannot be used to make reliable inferences on asymmetric biotic interactions, even if they perform well in predicting the occurrence of species. We then show how sampling designs that consider priority effects can recover the asymmetric effects that are lost when priority effects are ignored. Based on these findings, we urge for caution when drawing inferences on biotic interactions from cross-sectional binary co-occurrence data, and provide guidance on sampling designs that may provide the necessary data to tackle this longstanding challenge.

Fairy circles and temporal periodic patterns in the delayed plant-sulfide feedback model

Incorporating the self-regulatory mechanism with time delay to a plant-sulfide feedback system for intertidal salt marshes, we proposed and studied a functional reaction-diffusion model. We analyzed the stability of the positive steady state of the system, and derived the sufficient conditions for the occurrence of Hopf bifurcations. By deriving the normal form on the center manifold, we obtained the formulas determining the properties of the Hopf bifurcations. Our analysis showed that there is a critical value of time delay. When the time delay is greater than the critical value, the system will show asymptotical temporal periodic patterns while the system will display asymptotical spatial homogeneous patterns when the time delay is smaller than the critical value. Our numerical study showed that there are transient fairy circles for any time delay while there are different types of fairy circles and rings in the system. Our results enhance the concept that transient fairy circle patterns in intertidal salt marshes can infer the underlying ecological mechanisms and provide a measure of ecological resilience when the self-regulatory mechanism with time delay is considered.

Ghost Channels and Ghost Cycles Guiding Long Transients in Dynamical Systems

Dynamical descriptions and modeling of natural systems have generally focused on fixed points, with saddles and saddle-based phase-space objects such as heteroclinic channels or cycles being central concepts behind the emergence of quasistable long transients. Reliable and robust transient dynamics observed for real, inherently noisy systems is, however, not met by saddle-based dynamics, as demonstrated here. Generalizing the notion of ghost states, we provide a complementary framework that does not rely on the precise knowledge or existence of (un)stable fixed points, but rather on slow directed flows organized by ghost sets in ghost channels and ghost cycles. Moreover, we show that the appearance of these novel objects is an emergent property of a broad class of models typically used for description of natural systems.

Quantifying the Resilience of Coal Energy Supply in China Toward Carbon Neutrality

Facing the challenge of achieving the goal of carbon neutrality, China is decoupling the currently close dependence of its economy on coal use. The energy supply and demand decarbonization has substantial influence on the resilience of the coal supply. However, a general understanding of the precise impact of energy decarbonization on the resilience of the coal energy supply is still lacking. Here, from the perspective of network science, we propose a theoretical framework to explore the resilience of the coal market of China. We show that the processes of increasing the connectivity and the competition between the coal enterprises, which are widely believed to improve the resilience of the coal market, can undermine the sustainability of the coal supply. Moreover, our results reveal that the policy of closing small-sized coal mines may not only reduce the safety accidents in the coal production but also improve the resilience of the coal market network. Using our model, we also suggest a few practical policies for minimizing the systemic risk of the coal energy supply.

Advanced stability analysis of a fractional delay differential system with stochastic phenomena using spectral collocation method

In recent years, there has been a growing interest in incorporating fractional calculus into stochastic delay systems due to its ability to model complex phenomena with uncertainties and memory effects. The fractional stochastic delay differential equations are conventional in modeling such complex dynamical systems around various applied fields. The present study addresses a novel spectral approach to demonstrate the stability behavior and numerical solution of the systems characterized by stochasticity along with fractional derivatives and time delay. By bridging the gap between fractional calculus, stochastic processes, and spectral analysis, this work contributes to the field of fractional dynamics and enriches the toolbox of analytical tools available for investigating the stability of systems with delays and uncertainties. To illustrate the practical implications and validate the theoretical findings of our approach, some numerical simulations are presented.

Rapid Evolution of Resistance and Tolerance Leads to Variable Host Recoveries following Disease-Induced Declines

AbstractRecoveries of populations that have suffered severe disease-induced declines are being observed across disparate taxa. Yet we lack theoretical understanding of the drivers and dynamics of recovery in host populations and communities impacted by infectious disease. Motivated by disease-induced declines and nascent recoveries in amphibians, we developed a model to ask the following question: How does the rapid evolution of different host defense strategies affect the transient recovery trajectories of hosts following pathogen invasion and disease-induced declines? We found that while host life history is predictably a major driver of variability in population recovery trajectories (including declines and recoveries), populations that use different host defense strategies (i.e., tolerance, avoidance resistance, and intensity-reduction resistance) experience notably different recoveries. In single-species host populations, populations evolving tolerance recovered on average four times slower than populations evolving resistance. Moreover, while populations using avoidance resistance strategies had the fastest potential recovery rates, these populations could get trapped in long transient states at low abundance prior to recovery. In contrast, the recovery of populations evolving intensity-reduction resistance strategies were more consistent across ecological contexts. Overall, host defense strategies strongly affect the transient dynamics of population recovery and may affect the ultimate fate of real populations recovering from disease-induced declines.

Using neural ordinary differential equations to predict complex ecological dynamics from population density data

Simple models have been used to describe ecological processes for over a century. However, the complexity of ecological systems makes simple models subject to modelling bias due to simplifying assumptions or unaccounted factors, limiting their predictive power. Neural ordinary differential equations (NODEs) have surged as a machine-learning algorithm that preserves the dynamic nature of the data (Chen et al. 2018 Adv. Neural Inf. Process. Syst.). Although preserving the dynamics in the data is an advantage, the question of how NODEs perform as a forecasting tool of ecological communities is unanswered. Here, we explore this question using simulated time series of competing species in a time-varying environment. We find that NODEs provide more precise forecasts than autoregressive integrated moving average (ARIMA) models. We also find that untuned NODEs have a similar forecasting accuracy to untuned long-short term memory neural networks and both are outperformed in accuracy and precision by empirical dynamical modelling . However, we also find NODEs generally outperform all other methods when evaluating with the interval score, which evaluates precision and accuracy in terms of prediction intervals rather than pointwise accuracy. We also discuss ways to improve the forecasting performance of NODEs. The power of a forecasting tool such as NODEs is that it can provide insights into population dynamics and should thus broaden the approaches to studying time series of ecological communities.

Analysis of long transients and detection of early warning signals of extinction in a class of predator-prey models exhibiting bistable behavior

In this paper, we develop a method of analyzing long transient dynamics in a class of predator-prey models with two species of predators competing explicitly for their common prey, where the prey evolves on a faster timescale than the predators. In a parameter regime near a singular zero-Hopf bifurcation of the coexistence equilibrium state, we assume that the system under study exhibits bistability between a periodic attractor that bifurcates from the singular Hopf point and another attractor, which could be a periodic attractor or a point attractor, such that the invariant manifolds of the coexistence equilibrium point play central roles in organizing the dynamics. To find whether a solution that starts in a vicinity of the coexistence equilibrium approaches the periodic attractor or the other attractor, we reduce the equations to a suitable normal form, and examine the basin boundary near the singular Hopf point. A key component of our study includes an analysis of the long transient dynamics, characterized by their rapid oscillations with a slow variation in amplitude, by applying a moving average technique. We obtain a set of necessary and sufficient conditions on the initial values of a solution near the coexistence equilibrium to determine whether it lies in the basin of attraction of the periodic attractor. As a result of our analysis, we devise a method of identifying early warning signals, significantly in advance, of a future crisis that could lead to extinction of one of the predators. The analysis is applied to the predator-prey model considered in Sadhu (Discrete Contin Dyn Syst B 26:5251-5279, 2021) and we find that our theory is in good agreement with the numerical simulations carried out for this model.

Transient social-ecological dynamics reveal signals of decoupling in a highly disturbed Anthropocene landscape

Understanding the transient dynamics of interlinked social-ecological systems (SES) is imperative for assessing sustainability in the Anthropocene. However, how to identify critical transitions in real-world SES remains a formidable challenge. In this study, we present an evolutionary framework to characterize these dynamics over an extended historical timeline. Our approach leverages multidecadal rates of change in socioeconomic data, paleoenvironmental, and cutting-edge sedimentary ancient DNA records from China's Yangtze River Delta, one of the most densely populated and intensively modified landscapes on Earth. Our analysis reveals two significant social-ecological transitions characterized by contrasting interactions and feedback spanning several centuries. Initially, the regional SES exhibited a loosely connected and ecologically sustainable regime. Nevertheless, starting in the 1950s, an increasingly interconnected regime emerged, ultimately resulting in the crossing of tipping points and an unprecedented acceleration in soil erosion, water eutrophication, and ecosystem degradation. Remarkably, the second transition occurring around the 2000s, featured a notable decoupling of socioeconomic development from ecoenvironmental degradation. This decoupling phenomenon signifies a more desirable reconfiguration of the regional SES, furnishing essential insights not only for the Yangtze River Basin but also for regions worldwide grappling with similar sustainability challenges. Our extensive multidecadal empirical investigation underscores the value of coevolutionary approaches in understanding and addressing social-ecological system dynamics.

Structural stability of invasion graphs for Lotka-Volterra systems

In this paper, we study in detail the structure of the global attractor for the Lotka-Volterra system with a Volterra-Lyapunov stable structural matrix. We consider the invasion graph as recently introduced in Hofbauer and Schreiber (J Math Biol 85:54, 2022) and prove that its edges represent all the heteroclinic connections between the equilibria of the system. We also study the stability of this structure with respect to the perturbation of the problem parameters. This allows us to introduce a definition of structural stability in ecology in coherence with the classical mathematical concept where there exists a detailed geometrical structure, robust under perturbation, that governs the transient and asymptotic dynamics.

Long-term recovery dynamics determined by the degree of the disturbance - Ten years tracking of aquatic macroinvertebrate recolonisation after an industrial disaster (Red Sludge Disaster, Hungary)

A ten-year-long examination of macroinvertebrate community recovery was conducted following a catastrophic spill of highly alkaline red sludge (pH >13) into lowland streams. Our primary objective was to compare recovery patterns after coarse- and fine-grain disturbances, focusing on two aspects: i) trend analysis to reveal long-term changes of six community parameters, and ii) variation analyses to assess parameter changes over time. We conducted statistical analysis on long-term data series of macroinvertebrates obtained from quantitative samples collected at four sections with varying degrees of disturbance along the impacted stream sections. We developed a comprehensive theoretical framework comprising a series of sequential phases: Ramp-up, Overshoot, and Oscillation Phases. i) A trend analysis revealed that disturbances show a gradual recovery pattern, while variance analyses showed an asymptotic convergence to an equilibrium. ii) Evaluating these trends across phases unveiled that the initial recovery phase exhibited a steep trajectory, lasting 4-9 months, irrespective of disturbance severity. Coarse-grain disturbances induced a remarkable Overshoot phenomenon across all community metrics. The more severe the disturbance, the greater the height and duration of the Overshoot. Our results suggest that the presence or absence of Overshoot can serve as an indicator for coarse-grain disturbances in the context of large and infrequent disturbances (LID). The entire recovery process lasts for 2.5-3 years irrespective of the severity of the LID. In conclusion, a minimum survey duration of two and half years is deemed imperative to capture the phases of recovery, and changes associated with LID are not expected to extend beyond the three-year threshold. The theoretical framework, including Overshoot parameters, may assist future studies in comparing recovery patterns of different LID types. Furthermore, our theoretical framework is likely to be applicable to other groups of organisms given a sufficiently long monitoring of recovery, influenced also by the length of reproductive cycles.

Parameter Sensitivity of Transient Community Dynamics

AbstractTransient dynamics have always intrigued ecologists, but current rapid environmental change (inducing transients even in previously undisturbed systems) has highlighted their importance more than ever. Here, I introduce a method for analyzing the sensitivity of transient ecological dynamics to parameter perturbations. The question the method answers is: how would the community dynamics have unfolded for some time horizon had the parameters been slightly different? I apply the method to three empirically parameterized models: competition between native forbs and exotic grasses in California, a host-parasitoid system, and an experimental chemostat predator-prey model. These applications showcase the ecological insights one can gain from models using transient sensitivity analysis. First, one can find parameters and their combinations whose perturbations disproportionately affect a system. Second, one can identify particular windows of time during which the predicted deviation from the unperturbed trajectories is especially large and utilize this information for management purposes. Third, there is an inverse relationship between transient and long-term sensitivities whenever the interacting populations are ecologically similar; paradoxically, the smaller the immediate response of the system, the more extreme its long-term response will be.

Understanding change in benthic marine systems

BACKGROUND

The unprecedented influence of human activities on natural ecosystems in the 21st century has resulted in increasingly frequent large-scale changes in ecological communities. This has heightened interest in understanding such changes and effective means to manage them. Accurate interpretation of state changes is challenging because of difficulties translating theory to empirical study, and most theory emphasizes systems near equilibrium, which may not be relevant in rapidly changing environments.

SCOPE

We review concepts of long-transient stages and phase shifts between stable community states, both smooth, continuous and discontinuous shifts, and the relationships among them. Three principal challenges emerge when applying these concepts. The first is how to interpret observed change in communities - distinguishing multiple stable states from long transients, or reversible shifts in the phase portrait of single attractor systems. The second is how to quantify the magnitudes of three sources of variability that cause switches between community states: (1) 'noise' in species' abundances, (2) 'wiggle' in system parameters and (3) trends in parameters that affect the topography of the basin of attraction. The third challenge is how variability of the system shapes evidence used to interpret community changes. We outline a novel approach using critical length scales to potentially address these challenges. These concepts are highlighted by a review of recent examples involving macroalgae as key players in marine benthic ecosystems.

CONCLUSIONS

Real-world examples show three or more stable configurations of ecological communities may exist for a given set of parameters, and transient stages may persist for long periods necessitating their respective consideration. The characteristic length scale (CLS) is a useful metric that uniquely identifies a community 'basin of attraction', enabling phase shifts to be distinguished from long transients. Variabilities of CLSs and time series data may likewise provide proactive management measures to mitigate phase shifts and loss of ecosystem services. Continued challenges remain in distinguishing continuous from discontinuous phase shifts because their respective dynamics lack unique signatures.

Unlocking ensemble ecosystem modelling for large and complex networks

The potential effects of conservation actions on threatened species can be predicted using ensemble ecosystem models by forecasting populations with and without intervention. These model ensembles commonly assume stable coexistence of species in the absence of available data. However, existing ensemble-generation methods become computationally inefficient as the size of the ecosystem network increases, preventing larger networks from being studied. We present a novel sequential Monte Carlo sampling approach for ensemble generation that is orders of magnitude faster than existing approaches. We demonstrate that the methods produce equivalent parameter inferences, model predictions, and tightly constrained parameter combinations using a novel sensitivity analysis method. For one case study, we demonstrate a speed-up from 108 days to 6 hours, while maintaining equivalent ensembles. Additionally, we demonstrate how to identify the parameter combinations that strongly drive feasibility and stability, drawing ecological insight from the ensembles. Now, for the first time, larger and more realistic networks can be practically simulated and analysed.

First Passage Times of Long Transient Dynamics in Ecology

Long transient dynamics in ecological models are characterized by extended periods in one state or regime before an eventual, and often abrupt, transition. One mechanism leading to long transient dynamics is the presence of ghost attractors, states where system dynamics slow down and the system lingers before eventually transitioning to the true attractor. This transition results solely from system dynamics rather than external factors. This paper investigates the dynamics of a classical herbivore-grazer model with the potential for ghost attractors or alternative stable states. We propose an intuitive threshold for first passage time analysis applicable to both bistable and ghost attractor regimes. By formulating the first passage time problem as a backward Kolmogorov equation, we examine how the mean first passage time changes as parameters are varied from the ghost attractor regime to the bistable one, through a saddle-node bifurcation. Our results reveal that the mean and variance of first passage times vary smoothly across the bifurcation threshold, eliminating the deterministic distinction between ghost attractors and bistable regimes. This work suggests that first passage time analysis can be an informative way to classify the length of a long transient. A better understanding of the duration of long transients may contribute to greater ecological understanding and more effective environmental management.

Taking the beat of the Arctic: are lemming population cycles changing due to winter climate?

Reports of fading vole and lemming population cycles and persisting low populations in some parts of the Arctic have raised concerns about the spread of these fundamental changes to tundra food web dynamics. By compiling 24 unique time series of lemming population fluctuations across the circumpolar region, we show that virtually all populations displayed alternating periods of cyclic/non-cyclic fluctuations over the past four decades. Cyclic patterns were detected 55% of the time (n = 649 years pooled across sites) with a median periodicity of 3.7 years, and non-cyclic periods were not more frequent in recent years. Overall, there was an indication for a negative effect of warm spells occurring during the snow onset period of the preceding year on lemming abundance. However, winter duration or early winter climatic conditions did not differ on average between cyclic and non-cyclic periods. Analysis of the time series shows that there is presently no Arctic-wide collapse of lemming cycles, even though cycles have been sporadic at most sites during the last decades. Although non-stationary dynamics appears a common feature of lemming populations also in the past, continued warming in early winter may decrease the frequency of periodic irruptions with negative consequences for tundra ecosystems.

Distinguishing Between Long-Transient and Asymptotic States in a Biological Aggregation Model

Aggregations are emergent features common to many biological systems. Mathematical models to understand their emergence are consequently widespread, with the aggregation-diffusion equation being a prime example. Here we study the aggregation-diffusion equation with linear diffusion in one spatial dimension. This equation is known to support solutions that involve both single and multiple aggregations. However, numerical evidence suggests that the latter, which we term 'multi-peaked solutions' may often be long-transient solutions rather than asymptotic steady states. We develop a novel technique for distinguishing between long transients and asymptotic steady states via an energy minimisation approach. The technique involves first approximating our study equation using a limiting process and a moment closure procedure. We then analyse local minimum energy states of this approximate system, hypothesising that these will correspond to asymptotic patterns in the aggregation-diffusion equation. Finally, we verify our hypotheses through numerical investigation, showing that our approximate analytic technique gives good predictions as to whether a state is asymptotic or transient. Overall, we find that almost all twin-peaked, and by extension multi-peaked, solutions are transient, except for some very special cases. We demonstrate numerically that these transients can be arbitrarily long-lived, depending on the parameters of the system.

Structured community transitions explain the switching capacity of microbial systems

Microbial systems appear to exhibit a relatively high switching capacity of moving back and forth among few dominant communities (taxon memberships). While this switching behavior has been mainly attributed to random environmental factors, it remains unclear the extent to which internal community dynamics affect the switching capacity of microbial systems. Here, we integrate ecological theory and empirical data to demonstrate that structured community transitions increase the dependency of future communities on the current taxon membership, enhancing the switching capacity of microbial systems. Following a structuralist approach, we propose that each community is feasible within a unique domain in environmental parameter space. Then, structured transitions between any two communities can happen with probability proportional to the size of their feasibility domains and inversely proportional to their distance in environmental parameter space-which can be treated as a special case of the gravity model. We detect two broad classes of systems with structured transitions: one class where switching capacity is high across a wide range of community sizes and another class where switching capacity is high only inside a narrow size range. We corroborate our theory using temporal data of gut and oral microbiota (belonging to class 1) as well as vaginal and ocean microbiota (belonging to class 2). These results reveal that the topology of feasibility domains in environmental parameter space is a relevant property to understand the changing behavior of microbial systems. This knowledge can be potentially used to understand the relevant community size at which internal dynamics can be operating in microbial systems.

Detecting shifts in nonlinear dynamics using Empirical Dynamic Modeling with Nested-Library Analysis

Abrupt changes in system states and dynamical behaviors are often observed in natural systems; such phenomena, named regime shifts, are explained as transitions between alternative steady states (more generally, attractors). Various methods have been proposed to detect regime shifts from time series data, but a generic detection method with theoretical linkage to underlying dynamics is lacking. Here, we provide a novel method named Nested-Library Analysis (NLA) to retrospectively detect regime shifts using empirical dynamic modeling (EDM) rooted in theory of attractor reconstruction. Specifically, NLA determines the time of regime shift as the cutting point at which sequential reduction of the library set (i.e., the time series data used to reconstruct the attractor for forecasting) optimizes the forecast skill of EDM. We illustrate this method on a chaotic model of which changing parameters present a critical transition. Our analysis shows that NLA detects the change point in the model system and outperforms existing approaches based on statistical characteristics. In addition, NLA empirically detected a real-world regime shift event revealing an abrupt change of Pacific Decadal Oscillation index around the mid-1970s. Importantly, our method can be easily generalized to various systems because NLA is equation-free and requires only a single time series.

Landscape quantifies the intermediate state and transition dynamics in ecological networks

Understanding the ecological mechanisms associated with the collapse and restoration is especially critical in promoting harmonious coexistence between humans and nature. So far, it remains challenging to elucidate the mechanisms of stochastic dynamical transitions for ecological systems. Using an example of plant-pollinator network, we quantified the energy landscape of ecological system. The landscape displays multiple attractors characterizing the high, low and intermediate abundance stable states. Interestingly, we detected the intermediate states under pollinator decline, and demonstrated the indispensable role of the intermediate state in state transitions. From the landscape, we define the barrier height (BH) as a global quantity to evaluate the transition feasibility. We propose that the BH can serve as a new early-warning signal (EWS) for upcoming catastrophic breakdown, which provides an earlier and more accurate warning signal than traditional metrics based on time series. Our results promote developing better management strategies to achieve environmental sustainability.

Deterministic and stochastic processes generating alternative states of microbiomes

The structure of microbiomes is often classified into discrete or semi-discrete types potentially differing in community-scale functional profiles. Elucidating the mechanisms that generate such "alternative states" of microbiome compositions has been one of the major challenges in ecology and microbiology. In a time-series analysis of experimental microbiomes, we here show that both deterministic and stochastic ecological processes drive divergence of alternative microbiome states. We introduced species-rich soil-derived microbiomes into eight types of culture media with 48 replicates, monitoring shifts in community compositions at six time points (8 media × 48 replicates × 6 time points = 2304 community samples). We then confirmed that microbial community structure diverged into a few state types in each of the eight medium conditions as predicted in the presence of both deterministic and stochastic community processes. In other words, microbiome structure was differentiated into a small number of reproducible compositions under the same environment. This fact indicates not only the presence of selective forces leading to specific equilibria of community-scale resource use but also the influence of demographic drift (fluctuations) on the microbiome assembly. A reference-genome-based analysis further suggested that the observed alternative states differed in ecosystem-level functions. These findings will help us examine how microbiome structure and functions can be controlled by changing the "stability landscapes" of ecological community compositions.

Interactions between temperature and nutrients determine the population dynamics of primary producers

Global change is rapidly and fundamentally altering many of the processes regulating the flux of energy throughout ecosystems, and although researchers now understand the effect of temperature on key rates (such as aquatic primary productivity), the theoretical foundation needed to generate forecasts of biomass dynamics and extinction risk remains underdeveloped. We develop new theory that describes the interconnected effects of nutrients and temperature on phytoplankton populations and show that the thermal response of equilibrium biomass (i.e. carrying capacity) always peaks at a lower temperature than for productivity (i.e. growth rate). This mismatch is driven by differences in the thermal responses of growth, death, and per-capita impact on the nutrient pool, making our results highly general and applicable to widely used population models beyond phytoplankton. We further show that non-equilibrium dynamics depend on the pace of environmental change relative to underlying vital rates and that populations respond to variable environments differently at high versus low temperatures due to thermal asymmetries.

Rate-induced tipping in complex high-dimensional ecological networks

In an ecosystem, environmental changes as a result of natural and human processes can cause some key parameters of the system to change with time. Depending on how fast such a parameter changes, a tipping point can occur. Existing works on rate-induced tipping, or R-tipping, offered a theoretical way to study this phenomenon but from a local dynamical point of view, revealing, e.g., the existence of a critical rate for some specific initial condition above which a tipping point will occur. As ecosystems are subject to constant disturbances and can drift away from their equilibrium point, it is necessary to study R-tipping from a global perspective in terms of the initial conditions in the entire relevant phase space region. In particular, we introduce the notion of the probability of R-tipping defined for initial conditions taken from the whole relevant phase space. Using a number of real-world, complex mutualistic networks as a paradigm, we find a scaling law between this probability and the rate of parameter change and provide a geometric theory to explain the law. The real-world implication is that even a slow parameter change can lead to a system collapse with catastrophic consequences. In fact, to mitigate the environmental changes by merely slowing down the parameter drift may not always be effective: Only when the rate of parameter change is reduced to practically zero would the tipping be avoided. Our global dynamics approach offers a more complete and physically meaningful way to understand the important phenomenon of R-tipping.

Hydrological disturbances enhance stochastic assembly processes and decrease network stability of algae communities in a highland floodplain system

Floodplains are hotspots for biodiversity research and conservation worldwide. Hydrological disturbances can profoundly influence the ecological processes and functions of floodplain systems by altering key biological groups such as algae communities. However, the impacts of flood disturbance on the assembly processes and co-occurrence patterns of algae communities in floodplain ecosystems are still unclear. To ascertain the response patterns of algae communities to flood disturbance, we characterized planktonic and benthic algae communities in 144 water and sediment samples collected from the Tibetan floodplain during non-flood and flood periods based on 23S ribosomal RNA gene sequencing. Results showed that planktonic algae exhibited higher diversity and greater compositional variations compared with benthic communities after flood disturbance. Flooding promoted algae community homogenization at horizontal (rivers vs. oxbow lakes) and vertical levels (water vs. sediment). Stochastic processes governed the assembly of distinct algae communities, and their ecological impacts were enhanced in response to flooding. In the non-flood period, dispersal limitation (81.78 %) was the primary ecological process driving algae community assembly. In the flood period, the relative contribution of ecological drift (72.91 %) to algae community assembly markedly increased, with dispersal limitation (22.61 %) being less important. Flooding reduced the interactions among algae taxa, resulting in lower network complexity and stability. Compared with the planktonic algae subnetworks, the benthic subnetworks showed greater stability in the face of flooding. Findings of this study broaden our understanding of how algae communities respond to hydrological disturbances from an ecological perspective and could be useful for the management of highland floodplain ecosystems.

Ninety years of change, from commercial extinction to recovery, range expansion and decline for Antarctic fur seals at South Georgia

With environmental change, understanding how species recover from overharvesting and maintain viable populations is central to ecosystem restoration. Here, we reconstruct 90 years of recovery trajectory of the Antarctic fur seal at South Georgia (S.W. Atlantic), a key indicator species in the krill-based food webs of the Southern Ocean. After being harvested to commercial extinction by 1907, this population rebounded and now constitutes the most abundant otariid in the World. However, its status remains uncertain due to insufficient and conflicting data, and anthropogenic pressures affecting Antarctic krill, an essential staple for millions of fur seals and other predators. Using integrated population models, we estimated simultaneously the long-term abundance for Bird Island, northwest South Georgia, epicentre of recovery of the species after sealing, and population adjustments for survey counts with spatiotemporal applicability. Applied to the latest comprehensive survey data, we estimated the population at South Georgia in 2007-2009 as 3,510,283 fur seals [95% CI: 3,140,548-3,919,604] (ca. 98% of global population), after 40 years of maximum growth and range expansion owing to an abundant krill supply. At Bird Island, after 50 years of exponential growth followed by 25 years of slow stable growth, the population collapsed in 2009 and has thereafter declined by -7.2% [-5.2, -9.1] per annum, to levels of the 1970s. For the instrumental record, this trajectory correlates with a time-varying relationship between coupled climate and sea surface temperature cycles associated with low regional krill availability, although the effects of increasing krill extraction by commercial fishing and natural competitors remain uncertain. Since 2015, fur seal longevity and recruitment have dropped, sexual maturation has retarded, and population growth is expected to remain mostly negative and highly variable. Our analysis documents the rise and fall of a key Southern Ocean predator over a century of profound environmental and ecosystem change.

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.

Local buffer mechanisms for population persistence

Assessing and predicting the persistence of populations is essential for the conservation and control of species. Here, we argue that local mechanisms require a better conceptual synthesis to facilitate a more holistic consideration along with regional mechanisms known from metapopulation theory. We summarise the evidence for local buffer mechanisms along with their capacities and emphasise the need to include multiple buffer mechanisms in studies of population persistence. We propose an accessible framework for local buffer mechanisms that distinguishes between damping (reducing fluctuations in population size) and repelling (reducing population declines) mechanisms. We highlight opportunities for empirical and modelling studies to investigate the interactions and capacities of buffer mechanisms to facilitate better ecological understanding in times of ecological upheaval.

Transient demographic dynamics of recovering fish populations shaped by past climate variability, harvest, and management

Large-scale commercial harvesting and climate-induced fluctuations in ocean properties shape the dynamics of marine populations as interdependent drivers at varied timescales. Persistent selective removals of larger, older members of a population can distort its demographic structure, eroding resilience to fluctuations in habitat conditions and thus amplifying volatility in transient dynamics. Many historically depleted marine fish stocks have begun showing signs of recovery in recent decades following the implementation of stricter management measures. But these interventions coincide with accelerated changes in the oceans triggered by increasingly warmer, more variable climates. Applying multilevel models to annual estimates of demographic metrics of 38 stocks comprising 11 species across seven northeast Atlantic ecoregions, this study explores how time-varying local and regional climates contributed to the transient dynamics of recovering populations exposed to variable fishing pressures moderated by management actions. Analyses reveal that progressive reductions in fishing pressure and shifting climate conditions discontinuously shaped rebuilding patterns of the stocks through restorations of maternal demographic structure (reversing age truncation) and reproductive capacity. As the survival rate and demographic structure of reproductive fish improved, transient growth became less sensitive to variability in recruitment and juvenile survival and more to that in adult survival. As the biomass of reproductive fish rose, recruitment success also became increasingly regulated by density-dependent processes involving higher numbers of older fish. When reductions in fishing pressure were insufficient or delayed, however, stocks became further depleted, with more eroded demographic structures. Although warmer local climates in spawning seasons promoted recruitment success in some ecoregions, changing climates in recent decades began adversely affecting reproductive performances overall, amplifying sensitivities to recruitment variability. These shared patterns underscore the value of demographic transients in developing robust strategies for managing marine resources. Such strategies could form the foundation for effective applications of adaptive measures resilient to future environmental change.

A two-galectin network establishes mesenchymal condensation phenotype in limb development

Previous work showed that Gal-1A and Gal-8, two proteins belonging to the galactoside-binding galectin family, are the earliest determinants of the patterning of the skeletal elements of embryonic chicken limbs, and further, that their experimentally determined interactions in the embryonic limb bud can be interpreted via a reaction-diffusion-adhesion (2GL: two galectin plus ligands) model. Here, we use an ordinary differential equation-based approach to analyze the intrinsic switching modality of the 2GL network and characterize the network behavior independent of the diffusive and adhesive arms of the patterning mechanism. We identify two states: where the concentrations of both the galectins are respectively, negligible, and very high. This bistable switch-like system arises via a saddle-node bifurcation from a monostable state. For the case of mass-action production terms, we provide an explicit Lyapunov function for the system, which shows that it has no periodic solutions. Our model therefore predicts that the galectin network may exist in low expression and high expression states separated in space or time, without any intermediate states. We test these predictions in experiments performed with high density cultures of chick limb mesenchymal cells and observe that cells inside precartilage protocondensations express Gal-1A at a much higher rate than those outside, for which it was negligible. The Gal-1A and -8-based patterning network is therefore sufficient to partition the mesenchymal cell population into two discrete cell states with different developmental (chondrogenic vs. non-chondrogenic) fates. When incorporated into an adhesion and diffusion-enabled framework this system can generate a spatially patterned limb skeleton.

The hidden order of Turing patterns in arid and semi-arid vegetation ecosystems

Vegetation Turing patterns play a critical role in the ecological functioning of arid and semi-arid ecosystems. However, the long-range spatial features of these patterns have been neglected compared to short-range features like patch shape and spatial wavelength. Drawing inspiration from hyperuniform structures in material science, we find that the arid and semi-arid vegetation Turing pattern exhibits long-range dispersion similar to hyperuniformity. As the degree of hyperuniformity of the vegetation Turing pattern increases, so does the water-use efficiency of the vegetation. This finding supports previous studies that suggest that Turing patterns represent a spatially optimized self-organization of ecosystems for water acquisition. The degree of hyperuniformity of Turing-type ecosystems exhibits significant critical slowing down near the tipping point, indicating that these ecosystems have non-negligible transient dynamical behavior. Reduced rainfall not only decreases the resilience of the steady state of the ecosystem but also slows down the rate of spatial optimization of water-use efficiency in long transient regimes. We propose that the degree of hyperuniformity indicates the spatial resilience of Turing-type ecosystems after strong, short-term disturbances. Spatially heterogeneous disturbances that reduce hyperuniformity lead to longer recovery times than spatially homogeneous disturbances that maintain hyperuniformity.

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.

Coral assemblages at higher latitudes favor short-term potential over long-term performance

The persistent exposure of coral assemblages to more variable abiotic regimes is assumed to augment their resilience to future climatic variability. Yet, while the determinants of coral population resilience across species remain unknown, we are unable to predict the winners and losers across reef ecosystems exposed to increasingly variable conditions. Using annual surveys of 3171 coral individuals across Australia and Japan (2016-2019), we explore spatial variation across the short- and long-term dynamics of competitive, stress-tolerant, and weedy assemblages to evaluate how abiotic variability mediates the structural composition of coral assemblages. We illustrate how, by promoting short-term potential over long-term performance, coral assemblages can reduce their vulnerability to stochastic environments. However, compared to stress-tolerant, and weedy assemblages, competitive coral taxa display a reduced capacity for elevating their short-term potential. Accordingly, future climatic shifts threaten the structural complexity of coral assemblages in variable environments, emulating the degradation expected across global tropical reefs.

Non-asymptotic transients away from steady states determine cellular responsiveness to dynamic spatial-temporal signals

Majority of the theory on cell polarization and the understanding of cellular sensing and responsiveness to localized chemical cues has been based on the idea that non-polarized and polarized cell states can be represented by stable asymptotic switching between them. The existing model classes that describe the dynamics of signaling networks underlying polarization are formulated within the framework of autonomous systems. However these models do not simultaneously capture both, robust maintenance of polarized state longer than the signal duration, and retained responsiveness to signals with complex spatial-temporal distribution. Based on recent experimental evidence for criticality organization of biochemical networks, we challenge the current concepts and demonstrate that non-asymptotic signaling dynamics arising at criticality uniquely ensures optimal responsiveness to changing chemoattractant fields. We provide a framework to characterize non-asymptotic dynamics of system's state trajectories through a non-autonomous treatment of the system, further emphasizing the importance of (long) transient dynamics, as well as the necessity to change the mathematical formalism when describing biological systems that operate in changing environments.

Rate and memory effects in bifurcation-induced tipping

A variation in the environment of a system, such as the temperature, the concentration of a chemical solution, or the appearance of a magnetic field, may lead to a drift in one of the parameters. If the parameter crosses a bifurcation point, the system can tip from one attractor to another (bifurcation-induced tipping). Typically, this stability exchange occurs at a parameter value beyond the bifurcation value. This is what we call, here, the shifted stability exchange. We perform a systematic study on how the shift is affected by the initial parameter value and its change rate. To that end, we present numerical simulations and partly analytical results for different types of bifurcations and different paradigmatic systems. We show that the nonautonomous dynamics can be split into two regimes. Depending on whether we exceed the numerical or experimental precision or not, the system may enter the nondeterministic or the deterministic regime. This is determined solely by the conditions of the drift. Finally, we deduce the scaling laws governing this phenomenon and we observe very similar behavior for different systems and different bifurcations in both regimes.

Epidemiological impacts of post-infection mortality

Infectious diseases may cause some long-term damage to their host, leading to elevated mortality even after recovery. Mortality due to complications from so-called 'long COVID' is a stark illustration of this potential, but the impacts of such post-infection mortality (PIM) on epidemic dynamics are not known. Using an epidemiological model that incorporates PIM, we examine the importance of this effect. We find that in contrast to mortality during infection, PIM can induce epidemic cycling. The effect is due to interference between elevated mortality and reinfection through the previously infected susceptible pool. In particular, robust immunity (via decreased susceptibility to reinfection) reduces the likelihood of cycling; on the other hand, disease-induced mortality can interact with weak PIM to generate periodicity. In the absence of PIM, we prove that the unique endemic equilibrium is stable and therefore our key result is that PIM is an overlooked phenomenon that is likely to be destabilizing. Overall, given potentially widespread effects, our findings highlight the importance of characterizing heterogeneity in susceptibility (via both PIM and robustness of host immunity) for accurate epidemiological predictions. In particular, for diseases without robust immunity, such as SARS-CoV-2, PIM may underlie complex epidemiological dynamics especially in the context of seasonal forcing.

Mutualisms in a warming world

Predicting the impacts of global warming on mutualisms poses a significant challenge given the functional and life history differences that usually exist among interacting species. However, this is a critical endeavour since virtually all species on Earth depend on other species for survival and/or reproduction. The field of thermal ecology can provide physiological and mechanistic insights, as well as quantitative tools, for addressing this challenge. Here, we develop a conceptual and quantitative framework that connects thermal physiology to species' traits, species' traits to interacting mutualists' traits and interacting traits to the mutualism. We first identify the functioning of reciprocal mutualism-relevant traits in diverse systems as the key temperature-dependent mechanisms driving the interaction. We then develop metrics that measure the thermal performance of interacting mutualists' traits and that approximate the thermal performance of the mutualism itself. This integrated approach allows us to additionally examine how warming might interact with resource/nutrient availability and affect mutualistic species' associations across space and time. We offer this framework as a synthesis of convergent and critical issues in mutualism science in a changing world, and as a baseline to which other ecological complexities and scales might be added.

Northern expansion is not compensating for southern declines in North American boreal forests

Climate change is expected to shift the boreal biome northward through expansion at the northern and contraction at the southern boundary respectively. However, biome-scale evidence of such a shift is rare. Here, we used remotely-sensed tree cover data to quantify temporal changes across the North American boreal biome from 2000 to 2019. We reveal a strong north-south asymmetry in tree cover change, coupled with a range shrinkage of tree cover distributions. We found no evidence for tree cover expansion in the northern biome, while tree cover increased markedly in the core of the biome range. By contrast, tree cover declined along the southern biome boundary, where losses were related largely to wildfires and timber logging. We show that these contrasting trends are structural indicators for a possible onset of a biome contraction which may lead to long-term carbon declines.

A framework for long-lasting, slowly varying transient dynamics

Much of the focus of applied dynamical systems is on asymptotic dynamics such as equilibria and periodic solutions. However, in many systems there are transient phenomena, such as temporary population collapses and the honeymoon period after the start of mass vaccination, that can last for a very long time and play an important role in ecological and epidemiological applications. In previous work we defined transient centers which are points in state space that give rise to arbitrarily long and arbitrarily slow transient dynamics. Here we present the mathematical properties of transient centers and provide further insight into these special points. We show that under certain conditions, the entire forward and backward trajectory of a transient center, as well as all its limit points must also be transient centers. We also derive conditions that can be used to verify which points are transient centers and whether those are reachable transient centers. Finally we present examples to demonstrate the utility of the theory, including applications to predatory-prey systems and disease transmission models, and show that the long transience noted in these models are generated by transient centers.

Recent exposure to environmental stochasticity does not determine the demographic resilience of natural populations

Escalating climatic and anthropogenic pressures expose ecosystems worldwide to increasingly stochastic environments. Yet, our ability to forecast the responses of natural populations to this increased environmental stochasticity is impeded by a limited understanding of how exposure to stochastic environments shapes demographic resilience. Here, we test the association between local environmental stochasticity and the resilience attributes (e.g. resistance, recovery) of 2242 natural populations across 369 animal and plant species. Contrary to the assumption that past exposure to frequent environmental shifts confers a greater ability to cope with current and future global change, we illustrate how recent environmental stochasticity regimes from the past 50 years do not predict the inherent resistance or recovery potential of natural populations. Instead, demographic resilience is strongly predicted by the phylogenetic relatedness among species, with survival and developmental investments shaping their responses to environmental stochasticity. Accordingly, our findings suggest that demographic resilience is a consequence of evolutionary processes and/or deep-time environmental regimes, rather than recent-past experiences.