Management implications of long transients in ecological systems

Ecosystem Knowledge Should Replace Coexistence and Stability Assumptions in Ecological Network Modelling

Quantitative population modelling is an invaluable tool for identifying the cascading effects of conservation on an ecosystem. When population data from monitoring programs is not available, deterministic ecosystem models have often been calibrated using the theoretical assumption that ecosystems have a stable, coexisting equilibrium. However, a growing body of literature suggests these theoretical assumptions are inappropriate for conservation contexts. Here, we develop an alternative for data-free population modelling that relies on expert-elicited knowledge of species populations. Our new Bayesian algorithm systematically removes model parameters that lead to impossible predictions, as defined by experts, without incurring excessive computational costs. We demonstrate our framework on an ordinary differential equation model by limiting predicted population sizes and their ability to change rapidly, utilising readily available knowledge from field observations and experts rather than relying on theoretical ecosystem properties. Our results show that using only coexistence and stability requirements can lead to unrealistic population dynamics, which can be avoided by switching to expert-derived information. We demonstrate how this change can dramatically impact population predictions, expected responses to management, conservation decision-making, and long-term ecosystem behaviour. Without data, we argue that field observations and expert knowledge are more trustworthy for representing ecosystems observed in nature, improving the precision and confidence in predictions.

Long-living transients in ecological models: Recent progress, new challenges, and open questions

Traditionally, mathematical models in ecology placed an emphasis on asymptotic, long-term dynamics. However, a large number of recent studies highlighted the importance of transient dynamics in ecological and eco-evolutionary systems, in particular 'long transients' that can last for hundreds of generations or even longer. Many models as well as empirical studies indicated that a system can function for a long time in a certain state or regime (a 'metastable regime') but later exhibits an abrupt transition to another regime not preceded by any parameter change (or following the change that occurred long before the transition). This scenario where tipping occurs without any apparent source of a regime shift is also referred to as 'metastability'. Despite considerable evidence of the presence of long transients in real-world systems as well as models, until recently research into long-living transients in ecology has remained in its infancy, largely lacking systematisation. Within the past decade, however, substantial progress has been made in creating a unifying theory of long transients in deterministic as well as stochastic systems. This has considerably accelerated further studies on long transients, in particular on those characterised by more complicated patterns and/or underlying mechanisms. The main goal of this review is to provide an overview of recent research on long transients and related regime shifts in models of ecological dynamics. We pay special attention to the role of environmental stochasticity, the effect of multiple timescales (slow-fast systems), transient spatial patterns, and relation between transients and spatial synchronisation. We also discuss current challenges and open questions in understanding transients with applications to ecosystems dynamics.

Stability of Ecological Systems: A Theoretical Review

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

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.

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.

Modeling the synergistic interplay between malaria dynamics and economic growth

The mosquito-borne disease (malaria) imposes significant challenges on human health, healthcare systems, and economic growth/productivity in many countries. This study develops and analyzes a model to understand the interplay between malaria dynamics, economic growth, and transient events. It uncovers varied effects of malaria and economic parameters on model outcomes, highlighting the interdependence of the reproduction number (R0) on both malaria and economic factors, and a reciprocal relationship where malaria diminishes economic productivity, while higher economic output is associated with reduced malaria prevalence. This emphasizes the intricate interplay between malaria dynamics and socio-economic factors. The study offers insights into malaria control and underscores the significance of optimizing external aid allocation, especially favoring an even distribution strategy, with the most significant reduction observed in an equal monthly distribution strategy compared to longer distribution intervals. Furthermore, the study shows that controlling malaria in high mosquito biting areas with limited aid, low technology, inadequate treatment, or low economic investment is challenging. The model exhibits a backward bifurcation implying that sustainability of control and mitigation measures is essential even when R0 is slightly less than one. Additionally, there is a parameter regime for which long transients are feasible. Long transients are critical for predicting the behavior of dynamic systems and identifying factors influencing transitions; they reveal reservoirs of infection, vital for disease control. Policy recommendations for effective malaria control from the study include prioritizing sustained control measures, optimizing external aid allocation, and reducing mosquito biting.

Modeling tumors as species-rich ecological communities

Many advanced cancers resist therapeutic intervention. This process is fundamentally related to intra-tumor heterogeneity: multiple cell populations, each with different mutational and phenotypic signatures, coexist within a tumor and its metastatic nodes. Like species in an ecosystem, many cancer cell populations are intertwined in a complex network of ecological interactions. Most mathematical models of tumor ecology, however, cannot account for such phenotypic diversity nor are able to predict its consequences. Here we propose that the Generalized Lotka-Volterra model (GLV), a standard tool to describe complex, species-rich ecological communities, provides a suitable framework to describe the ecology of heterogeneous tumors. We develop a GLV model of tumor growth and discuss how its emerging properties, such as outgrowth and multistability, provide a new understanding of the disease. Additionally, we discuss potential extensions of the model and their application to three active areas of cancer research, namely phenotypic plasticity, the cancer-immune interplay and the resistance of metastatic tumors to treatment. Our work outlines a set of questions and a tentative road map for further research in cancer ecology.

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.

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.

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.

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.

Impacts of Stressors on Riparian Health Indicators in the Upper and Lower Indus River Basins in Pakistan

Riparian zones along rivers and streams provide ecosystem services that may change over time as disturbances increase and deteriorate these buffer zones globally. The effect of stressors on ecosystem services along the rivers in underdeveloped countries is unclear, which impacts the environment directly in the form of riparian health indicators (RHIs). This study fills this gap and measures the impact of stressors on RHIs (parameters of habitat, plant cover, regeneration, exotics, and erosion) in the Indus River basin (IRB) in Pakistan. Data on 11 stressors and 27 RHIs were collected using a field-based approach in 269 transects in the upper and lower Indus basins (UIB and LIB) in 2020 and analyzed using multivariate statistical methods. The Kruskal-Wallis tests (p < 0.05) indicated that RHIs varied significantly under the influence of stressors in the UIB and LIB. However, their highest mean values were found in the UIB. Principal component analysis revealed the key RHIs and stressors, which explained 62.50% and 77.10% of the variance, respectively. The Pearson correlation showed that stressors had greater impacts on RHIs in LIB (with r ranging from -0.42 to 0.56). Our results also showed that stressors affected RHI indices with r ranging from -0.39 to 0.50 (on habitat), -0.36 to 0.46 (on plant cover), -0.34 to 0.35 (on regeneration), -0.34 to 0.56 (on erosion), and -0.42 to 0.23 (on exotics). Furthermore, it was confirmed by the agglomerative hierarchical cluster that indices and sub-indices of RHIs and stressors differ across the UIB and LIB. These findings may serve as guidance for managers of large rivers and ecosystem service providers to minimize the environmental impact of stressors in terms of RHIs.

Characterizing Long Transients in Consumer-Resource Systems With Group Defense and Discrete Reproductive Pulses

During recent years, the study of long transients has been expanded in ecological theory to account for shifts in long-term behavior of ecological systems. These long transients may lead to regime shifts between alternative states that resemble the dynamics of alternative stable states for a prolonged period of time. One dynamic that potentially leads to long transients is the group defense of a resource in a consumer-resource interaction. Furthermore, time lags in the population caused by discrete reproductive pulses have the potential to produce long transients, either independently or in conjunction to the transients caused by the group defense. In this work, we analyze the potential for long transients in a model for a consumer-resource system in which the resource exhibits group defense and reproduces in discrete reproductive pulses. This system exhibits crawl-by transients near the extinction and carrying capacity states of resource, and a transcritical bifurcation, under which a ghost limit cycle appears. We estimate the transient time of our system from these transients using perturbation theory. This work advances an understanding of how systems shift between alternate states and their duration of staying in a given regime and what ecological dynamics may lead to long transients.

Detecting hidden transient events in noisy nonlinear time-series

The information impulse function (IIF), running Variance, and local Hölder Exponent are three conceptually different time-series evaluation techniques. These techniques examine time-series for local changes in information content, statistical variation, and point-wise smoothness, respectively. Using simulated data emulating a randomly excited nonlinear dynamical system, this study interrogates the utility of each method to correctly differentiate a transient event from the background while simultaneously locating it in time. Computational experiments are designed and conducted to evaluate the efficacy of each technique by varying pulse size, time location, and noise level in time-series. Our findings reveal that, in most cases, the first instance of a transient event is more easily observed with the information-based approach of IIF than with the Variance and local Hölder Exponent methods. While our study highlights the unique strengths of each technique, the results suggest that very robust and reliable event detection for nonlinear systems producing noisy time-series data can be obtained by incorporating the IIF into the analysis.

Stabilizing microbial communities by looped mass transfer

Building and changing a microbiome at will and maintaining it over hundreds of generations has so far proven challenging. Despite best efforts, complex microbiomes appear to be susceptible to large stochastic fluctuations. Current capabilities to assemble and control stable complex microbiomes are limited. Here, we propose a looped mass transfer design that stabilizes microbiomes over long periods of time. Five local microbiomes were continuously grown in parallel for over 114 generations and connected by a loop to a regional pool. Mass transfer rates were altered and microbiome dynamics were monitored using quantitative high-throughput flow cytometry and taxonomic sequencing of whole communities and sorted subcommunities. Increased mass transfer rates reduced local and temporal variation in microbiome assembly, did not affect functions, and overcame stochasticity, with all microbiomes exhibiting high constancy and increasing resistance. Mass transfer synchronized the structures of the five local microbiomes and nestedness of certain cell types was eminent. Mass transfer increased cell number and thus decreased net growth rates μ′. Subsets of cells that did not show net growth μ′SCx were rescued by the regional pool R and thus remained part of the microbiome. The loop in mass transfer ensured the survival of cells that would otherwise go extinct, even if they did not grow in all local microbiomes or grew more slowly than the actual dilution rate D would allow. The rescue effect, known from metacommunity theory, was the main stabilizing mechanism leading to synchrony and survival of subcommunities, despite differences in cell physiological properties, including growth rates.

Managing biological invasions: the cost of inaction

Ecological and socioeconomic impacts from biological invasions are rapidly escalating worldwide. While effective management underpins impact mitigation, such actions are often delayed, insufficient or entirely absent. Presently, management delays emanate from a lack of monetary rationale to invest at early invasion stages, which precludes effective prevention and eradication. Here, we provide such rationale by developing a conceptual model to quantify the cost of inaction, i.e., the additional expenditure due to delayed management, under varying time delays and management efficiencies. Further, we apply the model to management and damage cost data from a relatively data-rich genus (Aedes mosquitoes). Our model demonstrates that rapid management interventions following invasion drastically minimise costs. We also identify key points in time that differentiate among scenarios of timely, delayed and severely delayed management intervention. Any management action during the severely delayed phase results in substantial losses $$( > 50\%$$ ( > 50 % of the potential maximum loss). For Aedes spp., we estimate that the existing management delay of 55 years led to an additional total cost of approximately $ 4.57 billion (14% of the maximum cost), compared to a scenario with management action only seven years prior (< 1% of the maximum cost). Moreover, we estimate that in the absence of management action, long-term losses would have accumulated to US$ 32.31 billion, or more than seven times the observed inaction cost. These results highlight the need for more timely management of invasive alien species—either pre-invasion, or as soon as possible after detection—by demonstrating how early investments rapidly reduce long-term economic impacts.

Kelp-forest dynamics controlled by substrate complexity

The factors that determine why ecosystems exhibit abrupt shifts in state are of paramount importance for management, conservation, and restoration efforts. Kelp forests are emblematic of such abruptly shifting ecosystems, transitioning from kelp-dominated to urchin-dominated states around the world with increasing frequency, yet the underlying processes and mechanisms that control their dynamics remain unclear. Here, we analyze four decades of data from biannual monitoring around San Nicolas Island, CA, to show that substrate complexity controls both the number of possible (alternative) states and the velocity with which shifts between states occur. The superposition of community dynamics with reconstructions of system stability landscapes reveals that shifts between alternative states at low-complexity sites reflect abrupt, high-velocity events initiated by pulse perturbations that rapidly propel species across dynamically unstable state-space. In contrast, high-complexity sites exhibit a single state of resilient kelp-urchin coexistence. Our analyses suggest that substrate complexity influences both top-down and bottom-up regulatory processes in kelp forests, highlight its influence on kelp-forest stability at both large (island-wide) and small (<10 m) spatial scales, and could be valuable for holistic kelp-forest management.

Impacts of riparian width and stream channel width on ecological networks in main waterways and tributaries

Riparian buffer width and stream channel width have different impacts on ecological networks (e.g., plant cover, regeneration, exotics, erosion, habitat, and stressors) and provide various ecosystem services. The protection of riparian zones of increasing widths for higher-order streams and connected tributaries alongside mega-reservoirs and around dams is of great global significance. However, it remains unclear which protection strategies are most effective for such zones. By applying a rapid field-based approach with 326 transects on an inundated area of 58,000 km² within the Three Gorges Dam Reservoir (TGDR) in China, we found that riparian buffer areas were influenced differently by broad-ranging widths. The riparian buffer width of 101.84 ± 72.64 m (mean ± standard deviation) had the greatest impact on the main waterway, whereas the stream channel width of 99.87 ± 97.10 m was most influential in tributaries. The correlation coefficient strengths among ecological and stress parameters (independently) were relatively greater in the main waterway riparian zones; the highest value was r = 0.930 using Pearson correlation (p < 0.05). In contrast, stress parameters revealed substantial and strong relationships with ecological parameters in tributaries, with the highest value being r = 0.551. Riparian width had the strongest influence on buffer vegetation scales, high-impact exotics, and bank stability. In comparison, channel width had the greatest effect on tree roots, dominant tree regeneration, and agricultural farming. These parameters showed distinctive responses in the shapes of indexing in higher-order streams and connected tributaries. These observations confirm the urgent need for research on regional-based extended riparian areas managed by the same administration strategies. Revised guidelines are needed to protect massive dam and reservoir ecosystems from further deterioration.

Effects of stochasticity on the length and behaviour of ecological transients

There is a growing recognition that ecological systems can spend extended periods of time far away from an asymptotic state, and that ecological understanding will therefore require a deeper appreciation for how long ecological transients arise. Recent work has defined classes of deterministic mechanisms that can lead to long transients. Given the ubiquity of stochasticity in ecological systems, a similar systematic treatment of transients that includes the influence of stochasticity is important. Stochasticity can of course promote the appearance of transient dynamics by preventing systems from settling permanently near their asymptotic state, but stochasticity also interacts with deterministic features to create qualitatively new dynamics. As such, stochasticity may shorten, extend or fundamentally change a system's transient dynamics. Here, we describe a general framework that is developing for understanding the range of possible outcomes when random processes impact the dynamics of ecological systems over realistic time scales. We emphasize that we can understand the ways in which stochasticity can either extend or reduce the lifetime of transients by studying the interactions between the stochastic and deterministic processes present, and we summarize both the current state of knowledge and avenues for future advances.