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A cellular automata model was developed and parameterized to test the effectiveness of application of biological control insects to water hyacinth (Pontederia crassipes), which is an invasive floating plant species in many parts of the world and outcompetes many submersed native aquatic species in southern Florida. In the model, P. crassipes was allowed to compete with Nuttall's waterweed (Elodea nuttallii). In the absence of biocontrol acting on the P. crassipes, E. nuttallii excluded P. crassipes at low concentrations of the limiting nutrient (nitrogen), and the reverse occurred at high nutrient concentrations. At intermediate values, alternative stable states could occur; either P. crassipes alone or a mixture of the two species. When the biocontrol agent, the weevil Neochetina eichhorniae, was applied in the model, there was initially a rapid reduction of the P. crassipes, however, over time a regular striped pattern of moving spatially alternating stripes of P. crassipes and E. nuttallii emerged. -This pattern of moving stripes emerged and persisted over thousands of days but could quickly transform into an irregular pattern at some apparently random time, when either external stochasticity (added adult weevils) or only the weak internal stochasticity of weevil movements occurred. The cause of the end of the long transient can be traced to a single slightly irregular pixel within the striped pattern. Model parameters were varied to study effects of plant growth rate, nutrient concentration and nutrient diffusion rate on the dynamics of the system. [ABSTRACT FROM AUTHOR]

The growing shortfall in wild seafood and expansion of aquaculture can involve ecological and economic feedback between wild and farmed fish populations such as disease transmission and market competition. Here, we investigate the resilience of bioeconomically interacting fisheries and aquaculture systems by developing and analyzing mathematical models that capture the ecological suppression of wild fish survival by aquaculture, the management of fisheries for maximum sustainable yield, and aquaculture growth via two regulatory scenarios: perfect competition or rent optimization. Stability analysis of the models indicates that coexistence of productive fisheries and aquaculture is stable if the ecological impacts of aquaculture on wild fish are held below a bioeconomic threshold. Otherwise, the dynamics involve regime shifts between alternative stable states of fishery dominance with little aquaculture versus aquaculture dominance with collapsed fisheries. These regime shifts are difficult to reverse due to hysteresis. Coexistence and alternative stable states occur in both regulatory scenarios, but resilience is higher under rent optimization than perfect competition. Our results indicate that bioeconomic feedback can have important consequences for the resilience of aquaculture-fishery systems. [ABSTRACT FROM AUTHOR]

Theory and empirical work suggest that coral reefs may exhibit alternative stable states of coral versus macroalgal dominance. However, it is unclear how dispersal of coral and macroalgae among reefs might impact this bistability and the resilience of the coral-dominated state. We develop a mathematical model to investigate how reef cover dynamics are affected by (1) coral and macroalgal dispersal between two reefs and (2) heterogeneous grazer abundances. We find that at low coral and macroalgal dispersal levels, a new type of stable state emerges with both coral and macroalgae present. Furthermore, we show that a reef abundant with coral and grazers can support a coral-dominated stable state in a second reef depauperate of grazers by dispersal of coral larvae. These results help explain previous empirical findings on reefs once thought to be incongruent with traditional coral-macroalgal alternative stable states theory—such as intermediate coral and macroalgal cover stable states and high coral-low grazing scenarios. Our findings indicate that changing dispersal levels (e.g., due to climate change, reef degradation) between reefs changes the possible stable states and the grazing rate at which the coral-dominated state is predicted to be stable. This work demonstrates the relevance of accounting for the level of dispersal among coral reefs or other bistable ecosystems when designing conservation management plans. [ABSTRACT FROM AUTHOR]

Critical slowing down-based early warning signals (EWSs) are well-known indicators that precede an approaching collapse in complex systems. To date, the majority of studies on the predictability of critical transitions consider systems perturbed with temporally uncorrelated noise. In contrast, here we study catastrophic and non-catastrophic transitions, and the performance of associated EWSs in systems perturbed with correlated noise. We find that elevated noise correlation can advance the occurrence of a catastrophic transition, and simultaneously progresses the system's recovery. However, noise correlation does not have a significant impact on the likelihood of non-catastrophic transitions. We show that depending upon the transition mechanism, the occurrence of weak to false signals increases with noise reddening. Imperfect data sampling, both spatial and temporal, further reduces the efficacy of EWSs. Spatially limited data has more impact on the efficacy of EWSs for negative noise correlation than that of positive. However, temporally imperfect data is more detrimental for positively correlated noise. Overall, our study suggests that performance of EWSs is critical to system-specific perturbations as well as data sampling. [ABSTRACT FROM AUTHOR]

Abrupt transitions leading to algal blooms are quite well known in aquatic ecosystems and have important implications for the environment. These ecosystem shifts have been largely attributed to nutrient dynamics and food web interactions. Contamination with heavy metals such as copper can modulate such ecological interactions which in turn may impact ecosystem functioning. Motivated by this, we explored the effect of copper enrichment on such regime shifts in planktonic systems. We integrated copper contamination to a minimal phytoplankton–zooplankton model which is known to demonstrate abrupt transitions between ecosystem states. Our results suggest that both the toxic and deficient concentration of copper in water bodies can lead to regime shift to an algal-dominated alternative stable state. Further, interaction with fish density can also lead to collapse of population cycles thus leading to algal domination in the intermediate copper ranges. Environmental stochasticity may result in state transition much prior to the tipping point and there is a significant loss in the bimodality on increasing intensity and redness of noise. Finally, the impending state shifts due to contamination cannot be predicted by the generic early warning indicators unless the transition is close enough. Overall the study provides fresh impetus to explore regime shifts in ecosystems under the influence of anthropogenic changes like chemical contamination. [ABSTRACT FROM AUTHOR]

Stochastic ecological dynamics result from both transient and asymptotic features of the underlying system, yet explanations for observed patterns often emphasize asymptotics. For example, an ecological state (e.g., a particular population size or community composition) that occurs frequently and/or persists for a meaningful duration might be assumed to be a stable equilibrium, even though transients can also persist for a long time and may recur. In this paper, we consider one particular pattern—a bimodal distribution of states as a system is observed through time—and consider alternative causes for this pattern. First, we consider the "asymptotic" explanation that each mode corresponds to a distinct stable state. Second, we consider that one mode might correspond to a long transient. We explore the dynamics that result from each of these causes in a classic bistable model, focusing particularly on the degree of environmental stochasticity needed to generate a bimodal distribution of states in each case. Our results highlight that observations of a system's dynamics do not provide enough information to determine the number and location of stable states. We conclude that a more serious and systematic consideration for the possible role of transients in driving observed dynamics will lead to stronger insights and understanding. [ABSTRACT FROM AUTHOR]

Dryland ecosystems are likely to respond discontinuously to gradual changes in environmental conditions. Direct facilitation between plants, whereby plants improve the local environmental conditions for others, has been shown to be a mechanism contributing to these discontinuous ecosystem transitions. Theoretical models describing dryland vegetation dynamics often consider a single plant species and one type of facilitation, namely direct facilitation. However, another type of facilitation–indirect facilitation–is widespread in dryland ecosystems as well; it is performed by plants protected against grazing, the nurses, when this protection extends to other plants growing in their neighbourhood that are deprived of such protection, the protegees. Little is known about the long-term effects of indirect facilitation on dryland dynamics. Here, we developed and analysed a theoretical model including two species–a nurse and a protegee–and indirect facilitation through grazing. We investigated the effects of indirect facilitation on species composition, species spatial clustering and the stability of dryland ecosystems. We showed that indirect facilitation through grazing enables the stable coexistence of the nurse and the protegee and allows the reversibility of the protegee extinction. Surprisingly, the strength of indirect facilitation affected neither the total nor the interspecific vegetation clustering. Our study highlights that spatially explicit grazing protection may affect species composition and the stability of dryland ecosystems and gives hints about how species interactions translate into spatial clustering. [ABSTRACT FROM AUTHOR]

In this article, we present a modern commentary on Ludwig, Jones, and Holling's classic paper, "Qualitative analysis of insect outbreak systems: the spruce budworm and forest," published in the Journal of Animal Ecology in 1978. In contrast to papers that become classics for advancing one big idea, Ludwig et al.'s contribution is striking for its breadth of impact. It has become a foundational reference in areas as disparate as insect ecology and management, alternative stable states, the effects of natural enemies, and the separation of time scales between fast- and slow-changing variables. Interestingly, the paper is not generally remembered as an attempt to bridge the divide between theoretical and empirical ecologists, as we will show, even though this is how the authors motivated their work. In this commentary, we examine the expected and unexpected ways Ludwig et al. (J Anim Ecol 47:315–332, 1978) have found a place in modern ecological thought. [ABSTRACT FROM AUTHOR]

Coral communities continue to be threatened by chronic and acute stressors and there is a pressing need to understand the mechanisms that maintain their persistence. In this work, we use a model of coral-macroalgae dynamics to explore the effects of different assumptions regarding grazing and coral recruitment seasonality in coral-algae systems. We find that the grazing functional form constrains the potential for alternative stable states and coexistence, highlighting the need to further elucidate herbivore dynamics on reef systems. We also show that coral recruitment from external sources facilitates coral persistence and recovery, both when recruitment is assumed to be constant over time, and when recruitment occurs seasonally. In systems with alternative stable states, the total number of larvae that reaches a patch is the primary driver that dictates whether a system with low coral cover can flip into the coral-dominated basin of attraction. However, in a limited parameter space, the duration and timing of this larval pulse can also determine whether coral can recover in a bistable system. These results highlight the multiple factors that influence whether a coral reef is likely to remain in its present state or not, especially as ocean conditions change. [ABSTRACT FROM AUTHOR]

Allee effects, or positive functional relationships between a population's density (or size) and its per unit abundance growth rate, are now considered to be a widespread if not common influence on the growth of ecological populations. Here we analyze how stochasticity and Allee effects combine to impact population persistence. We compare the deterministic and stochastic properties of four models: a logistic model (without Allee effects), and three versions of the original model of Allee effects proposed by Vito Volterra representing a weak Allee effect, a strong Allee effect, and a strong Allee effect with immigration. We employ the diffusion process approach for modeling single-species populations, and we focus on the properties of stationary distributions and of the mean first passage times. We show that stochasticity amplifies the risks arising from Allee effects, mainly by prolonging the amount of time a population spends at low abundance levels. Even weak Allee effects become consequential when the ubiquitous stochastic forces affecting natural populations are accounted for in population models. Although current concepts of ecological resilience are bound up in the properties of deterministic basins of attraction, a complete understanding of alternative stable states in ecological systems must include stochasticity. [ABSTRACT FROM AUTHOR]

Nutrient enrichment of native grasslands can promote invasion by exotic plant species, leading to reduced biodiversity and altered ecosystem function. Empirical evidence suggests that positive feedbacks may make such transitions difficult to reverse. We developed a mathematical model of grassland dynamics in which one group of species (native) is a better competitor for nitrogen (N) and another group (exotic) is a better competitor for light. We parameterized the model for a grassland community and reproduced observed transitions from a native- to an exotic-dominated state under N loading. Within known bounds of parameter values, both smooth and hysteretic transitions are plausible. The model also predicts that N loading alone is insufficient to achieve a transition to an exotic-dominated state on a timescale relevant to grassland management (a few decades), and that therefore some other disturbance (e.g., fire suppression or heaving grazing) must be present to accelerate it. The model predicts that to restore a grassland to a native-dominated state after N inputs have been reduced, fire and carbon supplements would be most effective. Further field research in N-enriched invaded grasslands is required to establish the strengths of positive feedbacks and, in turn, the consequences of anthropogenic modification of grasslands worldwide. [ABSTRACT FROM AUTHOR]

There is a long history in ecology of using mathematical models to identify deterministic processes that may lead to dramatic population dynamic patterns like boom-and-bust outbreaks. Stochasticity is also well-known to have a significant influence on the dynamics of many ecological systems, but this aspect has received far less attention. Here, we study a stochastic version of a classic bistable insect outbreak model to reveal the role of stochasticity in generating outbreak dynamics. We find that stochasticity has strong effects on the dynamics and that the stochastic system can behave in ways that are not easily anticipated by its deterministic counterpart. Both the intensity and autocorrelation of the stochastic environment are important. Stochasticity with higher intensity (variability) generally weakens bistability, causing the dynamics to spend more time at a single state rather than jumping between alternative stable states. Which state the population tends toward depends on the noise color. High-intensity white noise causes the insect population to spend more time at low density, potentially reducing the severity or frequency of outbreaks. However, red (positively autocorrelated) noise can make the population spend more time near the high density state, intensifying outbreaks. Under neither type of noise do early warning signals reliably predict impending outbreaks or population crashes. [ABSTRACT FROM AUTHOR]

The invasion of Nile perch into Lake Victoria is one of the iconic examples of the destructive effect of an introduced species on an ecosystem but no convincing explanation exists of why Nile perch only increased dramatically after a 25 year lag. Here, we consider this problem using a mathematical model that takes into account interactions between Nile perch and its cichlid prey. We examined competing hypotheses to explain Nile perch invasion and show that suppression of juvenile Nile perch by cichlids may cause the system to have two alternative stable states: one with only cichlids and one with coexistence of cichlids and Nile perch. Without cichlid predation on Nile perch, alternative stable states did not occur. Our analysis indicates that cichlid mortality, for example fishing mortality, may have induced the observed shift between the states. [ABSTRACT FROM AUTHOR]

Most work on generic early warning signals for critical transitions focuses on indicators of the phenomenon of critical slowing down that precedes a range of catastrophic bifurcation points. However, in highly stochastic environments, systems will tend to shift to alternative basins of attraction already far from such bifurcation points. In fact, strong perturbations (noise) may cause the system to 'flicker' between the basins of attraction of the system's alternative states. As a result, under such noisy conditions, critical slowing down is not relevant, and one would expect its related generic leading indicators to fail, signaling an impending transition. Here, we systematically explore how flickering may be detected and interpreted as a signal of an emerging alternative attractor. We show that-although the two mechanisms differ-flickering may often be reflected in rising variance, lag-1 autocorrelation and skewness in ways that resemble the effects of critical slowing down. In particular, we demonstrate how the probability distribution of a flickering system can be used to map potential alternative attractors and their resilience. Thus, while flickering systems differ in many ways from the classical image of critical transitions, changes in their dynamics may carry valuable information about upcoming major changes. [ABSTRACT FROM AUTHOR]

Various ecological and other complex dynamical systems may exhibit abrupt regime shifts or critical transitions, wherein they reorganize from one stable state to another over relatively short time scales. Because of potential losses to ecosystem services, forecasting such unexpected shifts would be valuable. Using mathematical models of regime shifts, ecologists have proposed various early warning signals of imminent shifts. However, their generality and applicability to real ecosystems remain unclear because these mathematical models are considered too simplistic. Here, we investigate the robustness of recently proposed early warning signals of regime shifts in two well-studied ecological models, but with the inclusion of time-delayed processes. We find that the average variance may either increase or decrease prior to a regime shift and, thus, may not be a robust leading indicator in time-delayed ecological systems. In contrast, changing average skewness, increasing autocorrelation at short time lags, and reddening power spectra of time series of the ecological state variable all show trends consistent with those of models with no time delays. Our results provide insights into the robustness of early warning signals of regime shifts in a broader class of ecological systems. [ABSTRACT FROM AUTHOR]

Ecosystem regime shifts are regarded as abrupt global transitions from one stable state to an alternative stable state, induced by slow environmental changes or by global disturbances. Spatially extended ecosystems, however, can also respond to local disturbances by the formation of small domains of the alternative state. Such a response can lead to gradual regime shifts involving front propagation and the coalescence of alternative-state domains. When one of the states is spatially patterned, a multitude of intermediate stable states appears, giving rise to step-like gradual shifts with extended pauses at these states. Using a minimal model, we study gradual state transitions and show that they precede abrupt transitions. We propose indicators to probe gradual regime shifts, and suggest that a combination of abrupt-shift indicators and gradual-shift indicators might be needed to unambiguously identify regime shifts. Our results are particularly relevant to desertification in drylands where transitions to bare soil take place from spotted vegetation, and the degradation process appears to involve step-like events of local vegetation mortality caused by repeated droughts. [ABSTRACT FROM AUTHOR]

There are many examples of ecological theory informing fishery management. Yet fisheries also provide tremendous opportunities to test ecological theory through large-scale, repeated, and well-documented perturbations of natural systems. Although treating fisheries as experiments presents several challenges, few comparable tests exist at the ecosystem scale. Experimental manipulations of fish populations in lakes have been widely used to develop and test ecological theory. Controlled manipulation of fish populations in open marine systems is rarely possible, but fisheries data provide a valuable substitute for such manipulations. To highlight the value of marine fisheries data, we review leading ecological theories that have been empirically tested using such data. For example, density dependence has been examined through meta-analysis of spawning stock and recruitment data to show that compensation (higher population growth) occurs commonly when populations are reduced to low levels, while depensation (the Allee effect) is rare. As populations decline, spatial changes typically involve populations contracting into high-density core habitats while abandoning less productive habitats. Fishing down predators may result in trophic cascades, possibly shifting entire ecosystems into alternate stable states, although alternate states can be maintained by both ecological processes and continued fishing pressure. Conversely, depleting low trophic level groups may affect central-place foragers, although these bottom-up effects rarely appear to impact fish-perhaps because many fish populations have been reduced to the point that they are no longer prey limited. Fisheries provide empirical tests for diversity-stability relations: catch data suggest that more diverse systems recover faster and provide more stable returns than less diverse systems. Fisheries have also provided examples of the tragedy of the commons, as well as counter-examples where common property resources have been managed successfully. We also address two barriers to use of fisheries data to answer ecological questions: differences in terminology for similar concepts and misuse of records of fishery landings (catch data) as a proxy for biomass trends. [ABSTRACT FROM AUTHOR]

Generic early-warning signals such as increased autocorrelation and variance have been demonstrated in time-series of systems with alternative stable states approaching a critical transition. However, lag times for the detection of such leading indicators are typically long. Here, we show that increased spatial correlation may serve as a more powerful early-warning signal in systems consisting of many coupled units. We first show why from the universal phenomenon of critical slowing down, spatial correlation should be expected to increase in the vicinity of bifurcations. Subsequently, we explore the applicability of this idea in spatially explicit ecosystem models that can have alternative attractors. The analysis reveals that as a control parameter slowly pushes the system towards the threshold, spatial correlation between neighboring cells tends to increase well before the transition. We show that such increase in spatial correlation represents a better early-warning signal than indicators derived from time-series provided that there is sufficient spatial heterogeneity and connectivity in the system. [ABSTRACT FROM AUTHOR]