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AbstractEven when environments deteriorate gradually, ecosystems may shift abruptly from one state to another. Such catastrophic shifts are difficult to predict and sometimes to reverse (so-called hysteresis). While well studied in simplified contexts, we lack a general understanding of how catastrophic shifts spread in realistically spatially structured landscapes. For different types of landscape structures, including typical terrestrial modular and riverine dendritic networks, we here investigate landscape-scale stability in metapopulations whose patches can locally exhibit catastrophic shifts. We find that such metapopulations usually exhibit large-scale catastrophic shifts and hysteresis and that the properties of these shifts depend strongly on the metapopulation spatial structure and on the population dispersal rate: an intermediate dispersal rate, a low average degree, or a riverine spatial structure can largely reduce hysteresis size. Our study suggests that large-scale restoration is easier with spatially clustered restoration efforts and in populations characterized by an intermediate dispersal rate.

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Anthropogenic activities are increasingly affecting ecosystems across the globe. Meanwhile, empirical and theoretical evidence suggest that natural systems can exhibit abrupt collapses in response to incremental increases in the stressors, sometimes with dramatic ecological and economic consequences. These catastrophic shifts are faster and larger than expected from the changes in the stressors and happen once a tipping point is crossed. The primary mechanisms that drive ecosystem responses to perturbations lie in their architecture of relationships, i.e. how species interact with each other and with the physical environment and the spatial structure of the environment. Nonetheless, existing theoretical work on catastrophic shifts has so far largely focused on relatively simple systems that have either few species and/or no spatial structure. This work has laid a critical foundation for understanding how abrupt responses to incremental stressors are possible, but it remains difficult to predict (let alone manage) where or when they are most likely to occur in more complex real-world settings. Here, we discuss how scaling up our investigations of catastrophic shifts from simple to more complex-species rich and spatially structured-systems could contribute to expanding our understanding of how nature works and improve our ability to anticipate the effects of global change on ecological systems. This article is part of the theme issue 'Ecological complexity and the biosphere: the next 30 years'.

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In many terrestrial, marine, and freshwater predator-prey communities, young predators can be vulnerable to attacks by large prey. Frequent prey counter-attacks may hinder the persistence of predators. Despite the commonness of such role reversals in nature, they have rarely been addressed in evolutionary modelling. To understand how role reversals affect ecological and evolutionary dynamics of a predator-prey community, we derived an ecological model from individual-level processes using ordinary differential equations. The model reveals complex ecological dynamics, with possible bistability between alternative coexistence states and an Allee effect for the predators. We find that when prey counter-attacks are frequent, cannibalism is necessary for predator persistence. Using numerical analysis, we also find that a sudden ecological shift from coexistence to predator extinction can occur through several catastrophic bifurcations, including 'saddle-node', 'homoclinic', and 'subcritical Hopf'. The analysis of single-species evolution reveals that predator selection towards increasing or decreasing cannibalism triggers a catastrophic shift towards an extinction state of the predators. Such an evolutionary extinction of the predators may also be caused by prey selection towards increasing foraging activity because it facilitates encounters with vulnerable, young predators. The analysis of predator-prey coevolution further demonstrates that predator's catastrophic extinction becomes an even more likely outcome than in single-species evolution. Our results suggest that when young predators are vulnerable to prey attacks, a sudden extinction of the predators may be more common than currently understood.

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Semiarid ecosystems are threatened by global warming due to longer dehydration times and increasing soil degradation. Mounting evidence indicates that, given the current trends, drylands are likely to expand and possibly experience catastrophic shifts from vegetated to desert states. Here, we explore a recent suggestion based on the concept of ecosystem terraformation, where a synthetic organism is used to counterbalance some of the nonlinear effects causing the presence of such tipping points. Using an explicit spatial model incorporating facilitation and considering a simplification of states found in semiarid ecosystems including vegetation, fertile and desert soil, we investigate how engineered microorganisms can shape the fate of these ecosystems. Specifically, two different, but complementary, terraformation strategies are proposed: Cooperation-based: C-terraformation; and Dispersion-based: D-terraformation. The first strategy involves the use of soil synthetic microorganisms to introduce cooperative loops (facilitation) with the vegetation. The second one involves the introduction of engineered microorganisms improving their dispersal capacity, thus facilitating the transition from desert to fertile soil. We show that small modifications enhancing cooperative loops can effectively modify the aridity level of the critical transition found at increasing soil degradation rates, also identifying a stronger protection against soil degradation by using the D-terraformation strategy. The same results are found in a mean-field model providing insights into the transitions and dynamics tied to these terraformation strategies. The potential consequences and extensions of these models are discussed.

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Ecosystems are complex systems, currently experiencing several threats associated with global warming, intensive exploitation and human-driven habitat degradation. Because of a general presence of multiple stable states, including states involving population extinction, and due to the intrinsic nonlinearities associated with feedback loops, collapse in ecosystems could occur in a catastrophic manner. It has been recently suggested that a potential path to prevent or modify the outcome of these transitions would involve designing synthetic organisms and synthetic ecological interactions that could push these endangered systems out of the critical boundaries. In this paper, we investigate the dynamics of the simplest mathematical models associated with four classes of ecological engineering designs, named Terraformation motifs (TMs). These TMs put in a nutshell different ecological strategies. In this context, some fundamental types of bifurcations pervade the systems' dynamics. Mutualistic interactions can enhance persistence of the systems by means of saddle-node bifurcations. The models without cooperative interactions show that ecosystems achieve restoration through transcritical bifurcations. Thus, our analysis of the models allows us to define the stability conditions and parameter domains where these TMs must work.

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Semiarid ecosystems (including arid, semiarid and dry-subhumid ecosystems) span more than 40% of extant habitats and contain a similar percentage of the human population. Theoretical models and palaeoclimatic data predict a grim future, with rapid shifts towards a desert state, with accelerated diversity losses and ecological collapses. These shifts are a consequence of the special nonlinearities resulting from ecological facilitation. Here, we investigate a simple model of semiarid ecosystems identifying the so-called ghost, which appears after a catastrophic transition from a vegetated to a desert state once a critical rate of soil degradation is overcome. The ghost involves a slowdown of transients towards the desert state, making the ecosystem seem stable even though vegetation extinction is inevitable. We use this model to show how to exploit the ecological ghosts to avoid collapse. Doing so involves the restoration of small fractions of desert areas with vegetation capable of maintaining a stable community once the catastrophic shift condition has been achieved. This intervention method is successfully tested under the presence of demographic stochastic fluctuations.

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Global and local bifurcations are extremely important since they govern the transitions between different qualitative regimes in dynamical systems. These transitions or tipping points, which are ubiquitous in nature, can be smooth or catastrophic. Smooth transitions involve a continuous change in the steady state of the system until the bifurcation value is crossed, giving place to a second-order phase transition. Catastrophic transitions involve a discontinuity of the steady state at the bifurcation value, giving place to first-order phase transitions. Examples of catastrophic shifts can be found in ecosystems, climate, economic or social systems. Here we report a new type of global bifurcation responsible for a catastrophic shift. This bifurcation, identified in a family of quasi-species equations and named as trans-heteroclinic bifurcation, involves an exchange of stability between two distant and heteroclinically connected fixed points. Since the two fixed points interchange the stability without colliding, a catastrophic shift takes place. We provide an exhaustive description of this new bifurcation, also detailing the structure of the replication-mutation matrix of the quasi-species equation giving place to this bifurcation. A perturbation analysis is provided around the bifurcation value. At this value the heteroclinic connection is replaced by a line of fixed points in the quasi-species model. But it is shown that, if the replication-mutation matrix satisfies suitable conditions, then, under a small perturbation, the exchange of heteroclinic connections is preserved, except on a tiny range around the bifurcation value whose size is of the order of magnitude of the perturbation. The results presented here can help to understand better novel mechanisms behind catastrophic shifts and contribute to a finer identification of such transitions in theoretical models in evolutionary biology and other dynamical systems.

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Predicting where state-changing thresholds lie can be inherently complex in ecosystems characterized by nonlinear dynamics. Unpacking the mechanisms underlying these transitions can help considerably reduce this unpredictability. We used empirical observations, field and laboratory experiments, and mathematical models to examine how differences in nutrient regimes mediate the capacity of macrophyte communities to sustain sea urchin grazing. In relatively nutrient-rich conditions, macrophyte systems were more resilient to grazing, shifting to barrens beyond 1 800 g m-2 (urchin biomass), more than twice the threshold of nutrient-poor conditions. The mechanisms driving these differences are linked to how nutrients mediate urchin foraging and algal growth: controlled experiments showed that low-nutrient regimes trigger compensatory feeding and reduce plant growth, mechanisms supported by our consumer-resource model. These mechanisms act together to halve macrophyte community resilience. Our study demonstrates that by mediating the underlying drivers, inherent conditions can strongly influence the buffer capacity of nonlinear systems.

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Large-scale regular vegetation patterns are common in nature, but their causes are disputed. Whereas recent theory focuses on scale-dependent feedbacks as a potentially universal mechanism, earlier studies suggest that many regular spatial patterns result from territorial interference competition between colonies of social-insect ecosystem engineers, leading to hexagonally overdispersed nest sites and associated vegetation. Evidence for this latter mechanism is scattered throughout decades of disparate literature and lacks a unified conceptual framework, fueling skepticism about its generality in debates over the origins of patterned landscapes. We review these mechanisms and debates, finding evidence that spotted and gapped vegetation patterns generated by ants, termites, and other subterranean animals are globally widespread, locally important for ecosystem functioning, and consistent with models of intraspecific territoriality. Because these and other mechanisms of regular-pattern formation are not mutually exclusive and can coexist and interact at different scales, the prevailing theoretical outlook on spatial self-organization in ecology must expand to incorporate the dynamic interplay of multiple processes.

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Abstract Dredging is a catastrophic disturbance that directly affects key biological processes in aquatic ecosystems, especially in those small and shallow. In the tropics, metabolic responses could still be enhanced by the high temperatures and solar incidence. Here, we assessed changes in the aquatic primary production along a small section of low-flow tropical downstream (Imboassica Stream, Brazil) after dredging. Our results suggested that these ecosystems may show catastrophic shifts between net heterotrophy and autotrophy in waters based on three short-term stages following the dredging: (I) a strongly heterotrophic net primary production -NPP- coupled to an intense respiration -R- likely supported by high resuspended organic sediments and nutrients from the bottom; (II) a strongly autotrophic NPP coupled to an intense gross primary production -GPP- favored by the high nutrient levels and low solar light attenuation from suspended solids or aquatic macrophytes; and (III) a NPP near to the equilibrium coupled to low GPP and R rates following, respectively, the shading by aquatic macrophytes and high particulate sedimentation. In conclusion, changes in aquatic primary production could be an important threshold for controlling drastic shifts in the organic matter cycling and the subsequent silting up of small tropical streams after dredging events.

Resumo Dragagem é um distúrbio catastrófico que afeta diretamente processos biológicos chave nos ecossistemas aquáticos, especialmente naqueles pequenos e rasos. Nos trópicos, as respostas metabólicas podem ser ainda mais intensificadas pelas altas temperaturas e incidência solar. No presente estudo, avaliamos mudanças na produção primária aquática ao longo de uma pequena seção de um riacho tropical após uma dragagem (riacho Imboassica, Brasil). Nossos resultados sugeriram que estes ecossistemas podem apresentar mudanças catastróficas desde heterotrofia à autotrofia líquida na água, baseadas em três etapas de curto prazo após a dragagem: (I) uma produção primária líquida -PPL- fortemente heterotrófica associada a uma intensa respiração -R-, provavelmente sustentada por sedimentos orgânicos e nutrientes advindos do fundo; (II) uma PPL fortemente autotrófica associada a uma intensa produção primária bruta -PPB- favorecida pelos elevados níveis de nutrientes e baixa atenuação da luz solar pelos sólidos em suspensão ou macrófitas aquáticas; e (III) uma PPL próxima ao equilíbrio associada às reduzidas taxas de PPB e R seguindo os sombreamento pelas macrófitas aquáticas e elevada sedimentação de particulados. Como conclusão, mudanças na produção primária aquática poderiam ser um importante limiar para controlar drásticas alterações na ciclagem da matéria orgânica e no subsequente assoreamento de pequenos riachos tropicais após eventos de dragagem.

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Transitions between regimes with radically different properties are ubiquitous in nature. Such transitions can occur either smoothly or in an abrupt and catastrophic fashion. Important examples of the latter can be found in ecology, climate sciences, and economics, to name a few, where regime shifts have catastrophic consequences that are mostly irreversible (e.g., desertification, coral reef collapses, and market crashes). Predicting and preventing these abrupt transitions remains a challenging and important task. Usually, simple deterministic equations are used to model and rationalize these complex situations. However, stochastic effects might have a profound effect. Here we use 1D and 2D spatially explicit models to show that intrinsic (demographic) stochasticity can alter deterministic predictions dramatically, especially in the presence of other realistic features such as limited mobility or spatial heterogeneity. In particular, these ingredients can alter the possibility of catastrophic shifts by giving rise to much smoother and easily reversible continuous ones. The ideas presented here can help further understand catastrophic shifts and contribute to the discussion about the possibility of preventing such shifts to minimize their disruptive ecological, economic, and societal consequences.

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