Early Warning Signals of Ecological Transitions: Methods for Spatial Patterns

A number of ecosystems can exhibit abrupt shifts between alternative stable states. Because of their important ecological and economic consequences, recent research has focused on devising early warning signals for anticipating such abrupt ecological transitions. In particular, theoretical studies show that changes in spatial characteristics of the system could provide early warnings of approaching transitions. However, the empirical validation of these indicators lag behind their theoretical developments. Here, we summarize a range of currently available spatial early warning signals, suggest potential null models to interpret their trends, and apply them to three simulated spatial data sets of systems undergoing an abrupt transition. In addition to providing a step-by-step methodology for applying these signals to spatial data sets, we propose a statistical toolbox that may be used to help detect approaching transitions in a wide range of spatial data. We hope that our methodology together with the computer codes will stimulate the application and testing of spatial early warning signals on real spatial data.

Interações competitivas entre Epizoanthus gabrieli Carlgreen, 1951 (Ordem Zoanthidea) e corais na Baía de Todos os Santos e suas implicações para a comunidade recifal.

Alguns recifes de coral da Baía de Todos os Santos passaram a ser dominado pelo zoantídeo Epizoanthus gabrieli em 2003. Fenômeno resultante da degradação dos recife de coral que atinge 20% desses ecossistemas e ameaça outros 35% no mundo. Apesar de sua importância, apenas a mudança na comunidade para o domínio de macroalgas foi suficientemente estudado. Assim, torna-se urgente estudos sobres alterações envolvendo a dominância de outros organismos. Estes fornecem subsídios para produção de modelos funcionais que podem ajudar na tomada de decisão para o manejo destes ecossistemas tanto na prevenção destas alterações quanto na recuperação de suas comunidades. Os objetivos deste trabalho são (i) verificar se este fenômeno constitui uma mudança de fase, a partir da redução da abundância de corais e persistência da alta cobertura de E. gabrieli por pelo menos cinco anos, (ii) avaliar os efeitos da competição entre este zoantídeo e corais adultos e recrutas com experimentos manipulativos e (iii) investigar os efeitos desta dominância na assembleia de peixes recifais. Os resultados confirmaram a existência de uma mudança de fase, sugerindo que a abundância de E. gabrieli aumentou em 2003 ou antes e que até 2007 houve uma redução da cobertura de coral, condição que se mantêm pelo menos até 2013. As três espécies de corais testadas mostram-se muito sensíveis ao contato com E. gabrieli, com necrose em 78% das colônias e ocupação do esqueleto dos corais em 35% dos casos em um período de 118 dias. Além disso, um modelo feito a partir dos dados de proporção de colônias de corais em contato com este zoantídeo e a cobertura de E. gabrieli sugere que quando o zoantídeo atinge 6% de cobertura, 50% das colônias de corais entram em contato com o mesmo. Estes dados são fortes evidências de que a redução da cobertura de coral observada entre 2003 e 2007 foi causada por competição entre estes organismos. Não foi observado efeito negativo no recrutamento do coral em substrato artificial livre em recifes dominados por E. gabrieli, nem nas proximidades das suas colônias. Isso sugere que uma suposta redução da cobertura deste zoantídeo deve ser acompanhada pelo aumento da taxa de recrutamento de corais e que a competição com a inibição do recrutamento não suporta um efeito de histerese. Foi constatado que esta mudança de fase reduz a riqueza de espécies de peixes recifais, apresentando dez espécies a menos que os recifes normais, e que favorecem os invertívoros moveis em detrimento dos carnívoros e invertívoros sésseis. Contudo não se observou diferença na abundância de peixes.

EXPERIMENTS ON AQUATIC ECOSYSTEM REGIME SHIFT IN ENCLOSURES NEAR LAKE DIANCHI, CHINA

To discover how a lake converts from a turbid state to clean state, and what drives this process, we constructed controlled enclosure ecosystems and used the ecological remediation method to force ecosystems to convert from the turbid state to the clean state. Our results show that the driving forces include temperature., macrophyte, silver carp and mussel, which form a combined force to drive the controlled ecosystem to switch. There is a threshold existing in treated enclosure ecosystem during the conversion from turbid to clean state. When TP <0.09 mg.L-1, Chl-a <0.036 mg.L-1, transparency >62 cm, TN <2.15 mg.L-1, CODMn <13.7 mg.L-1, tubidity <10, and the number of algal cells <10(6) cells.L-1, the treated ecosystem changes sharply from turbid to clean state. The conversion process can be divided into three phases: turbid state, clean-turbid transitional state as well as clean state, and described with the power function Y = a*X-b (where Y is water parameter, X is time, a and b are constants), which indicates that the shift in the enclosure ecosystem from turbid to clean state is discontinuous.

Predator–prey reversal: A possible mechanism for ecosystem hysteresis in the North Sea?

Removal of large predatory fishes from marine ecosystems has resulted in persistent ecosystem shifts, with collapsed predator populations and super-abundant prey populations. One explanation for these shifts is reversals of predator–prey roles that generate internal feedbacks in the ecosystems. Pelagic forage fish are often predators and competitors to the young life stages of their larger fish predators. I show that cod recruitment in the North Sea has been negatively related to the spawning-stock biomass of herring for the last 44 years. Herring, together with the abundance of Calanus finmarchicus, the major food for cod larvae, were the main predictors of cod recruitment. These predictors were of equivalent importance, worked additively, and explained different parts of the dynamics in cod recruitment. I suggest that intensive harvesting of cod has released herring from predator control, and that a large population of herring suppresses cod recruitment through predation on eggs and larvae. This feedback mechanism can promote alternative stable states and therefore cause hysteresis to occur under changing conditions; however, harvesting of herring might at present prevent a shift in the ecosystem to a herring-dominated state.

Mathematical modeling of colony formation in algal blooms: phenotypic plasticity in cyanobacteria

In this paper, we analyzed a mathematical model of algal-grazer dynamics, including the effect of colony formation, which is an example of phenotypic plasticity. The model consists of three variables, which correspond to the biomasses of unicellular algae, colonial algae, and herbivorous zooplankton. Among these organisms, colonial algae are the main components of algal blooms. This aquatic system has two stable attractors, which can be identified as a zooplankton-dominated (ZD) state and an algal-dominated (AD) state, respectively. Assuming that the handling time of zooplankton on colonial algae increases with the colonial algae biomass, we discovered that bistability can occur within the model system. The applicability of alternative stable states in algae-grazer dynamics as a framework for explaining the algal blooms in real lake ecosystems, thus, seems to depend on whether the assumption mentioned above is met in natural circumstances.

Lake restoration in terms of ecological resilience: a numerical study of biomanipulations under bistable conditions

An abstract version of the comprehensive aquatic simulation model (CASM) is found to exhibit bistability under intermediate loading of nutrient input, supporting the alternative-stable-states theory and field observations for shallow lakes. Our simulations of biomanipulations under the bistable conditions reveal that a reduction in the abundance of zooplanktivorous fish cannot switch the system from a turbid to a clear state. Rather, a direct reduction of phytoplankton and detritus was found to be most effective to make this switch in the present model. These results imply that multiple manipulations may be effective for practical restorations of lakes. We discuss the present results of biomanipulations in terms of ecological resilience in multivariable systems or natural systems.

Feedbacks between vegetation and disturbance processes promote long-term persistence of forest-grassland mosaics in south Brazil

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Catastrophic regime shift in water reservoirs and São Paulo water supply crisis

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Microwave absorption properties of permalloy nanodots in the vortex and quasi-uniform magnetization states

When the in-plane bias magnetic field acting on a flat circular magnetic dot is smaller than the saturation field, there are two stable competing magnetization configurations of the dot: the vortex and the quasi-uniform (C-state). We measured microwave absorption properties in an array of non-interacting permalloy dots in the frequency range 1-8 GHz when the in-plane bias magnetic field was varied in the region of the dot magnetization state bi-stability. We found that the microwave absorption properties in the vortex and quasi-uniform stable states are substantially different, so that switching between these states in a fixed bias field can be used for the development of reconfigurable microwave magnetic materials.

Multiple stable reference points in oyster populations: biological relationships for the eastern oyster (Crassostrea virginica) in Delaware Bay

Abstract—In the first of two companion papers, a 54-yr time series for the oyster population in the New Jersey waters of Delaware Bay was analyzed to develop biological relationships necessary to evaluate maximum sustainable yield (MSY) reference points and to consider how multiple stable points affect reference point-based management. The time series encompassed two regime shifts, one circa 1970 that ushered in a 15-yr period of high abundance, and a second in 1985 that ushered in a 20-yr period of low abundance. The intervening and succeeding periods have the attributes of alternate stable states. The biological relationships between abundance, recruitment, and mortality were unusual in four ways. First, the broodstock–recruitment relationship at low abundance may have been driven more by the provision of settlement sites for larvae by the adults than by fecundity. Second, the natural mortality rate was temporally unstable and bore a nonlinear relationship to abundance. Third, combined high abundance and low mortality, though likely requiring favorable environmental conditions, seemed also to be a self-reinforcing phenomenon. As a consequence, the abundance –mortality relationship exhibited both compensatory and depensatory components. Fourth, the geographic distribution of the stock was intertwined with abundance and mortality, such that interrelationships were functions both of spatial organization and inherent populatio

Multiple stable reference points in oyster populations: implications for reference point-based management

In the second of two companion articles, a 54-year time series for the oyster population in the New Jersey waters of Delaware Bay is analyzed to examine how the presence of multiple stable states affects reference-point–based management. Multiple stable states are described by four types of reference points. Type I is the carrying capacity for the stable state: each has associated with it a type-II reference point wherein surplus production reaches a local maximum. Type-II reference points are separated by an intermediate surplus production low (type III). Two stable states establish a type-IV reference point, a point-of-no-return that impedes recovery to the higher stable state. The type-II to type-III differential in surplus production is a measure of the difficulty of rebuilding the population and the sensitivity of the population to collapse at high abundance. Surplus production projections show that the abundances defining the four types of reference points are relatively stable over a wide range of uncertainties in recruitment and mortality rates. The surplus production values associated with type-II and type-III reference points are much more uncertain. Thus, biomass goals are more easily established than fishing mortality rates for oyster population

Precise calculations of the existence of multiple AMOC equilibria in coupled climate models Part I: equilibrium states

This study examines criteria for the existence of two stable states of the Atlantic Meridional Overturning Circulation (AMOC) using a combination of theory and simulations from a numerical coupled atmosphere–ocean climate model. By formulating a simple collection of state parameters and their relationships, the authors reconstruct the North Atlantic Deep Water (NADW) OFF state behavior under a varying external salt-flux forcing. This part (Part I) of the paper examines the steady-state solution, which gives insight into the mechanisms that sustain the NADW OFF state in this coupled model; Part II deals with the transient behavior predicted by the evolution equation. The nonlinear behavior of the Antarctic Intermediate Water (AAIW) reverse cell is critical to the OFF state. Higher Atlantic salinity leads both to a reduced AAIW reverse cell and to a greater vertical salinity gradient in the South Atlantic. The former tends to reduce Atlantic salt export to the Southern Ocean, while the latter tends to increases it. These competing effects produce a nonlinear response of Atlantic salinity and salt export to salt forcing, and the existence of maxima in these quantities. Thus the authors obtain a natural and accurate analytical saddle-node condition for the maximal surface salt flux for which a NADW OFF state exists. By contrast, the bistability indicator proposed by De Vries and Weber does not generally work in this model. It is applicable only when the effect of the AAIW reverse cell on the Atlantic salt budget is weak.

A general method for finding extremal states of Hamiltonian dynamical systems, with applications to perfect fluids

In addition to the Hamiltonian functional itself, non-canonical Hamiltonian dynamical systems generally possess integral invariants known as ‘Casimir functionals’. In the case of the Euler equations for a perfect fluid, the Casimir functionals correspond to the vortex topology, whose invariance derives from the particle-relabelling symmetry of the underlying Lagrangian equations of motion. In a recent paper, Vallis, Carnevale & Young (1989) have presented algorithms for finding steady states of the Euler equations that represent extrema of energy subject to given vortex topology, and are therefore stable. The purpose of this note is to point out a very general method for modifying any Hamiltonian dynamical system into an algorithm that is analogous to those of Vallis etal. in that it will systematically increase or decrease the energy of the system while preserving all of the Casimir invariants. By incorporating momentum into the extremization procedure, the algorithm is able to find steadily-translating as well as steady stable states. The method is applied to a variety of perfect-fluid systems, including Euler flow as well as compressible and incompressible stratified flow.

Challenges in the participatory assessment of sustainable management practices in dryland ecosystems under regime shifts

Regime shifts, defined as a radical and persistent reconfiguration of an ecosystem following a disturbance, have been acknowledged by scientists as a very important aspect of the dynamic of ecosystems. However, their consideration in land management planning remains marginal and limited to specific processes and systems. Current research focuses on mathematical modeling and statistical analysis of spatio-temporal data for specific environmental variables. These methods do not fulfill the needs of land managers, who are confronted with a multitude of processes and pressure types and require clear and simple strategies to prevent regime shift or to increase the resilience of their environment. The EU-FP7 CASCADE project is looking at regime shifts of dryland ecosystems in southern Europe and specifically focuses on rangeland and forest systems which are prone to various land degradation threats. One of the aims of the project is to evaluate the impact of different management practices on the dynamic of the environment in a participatory manner, including a multi-stakeholder evaluation of the state of the environment and of the management potential. To achieve this objective we have organized several stakeholder meetings and we have compiled a review of management practices using the WOCAT methodology, which enables merging scientific and land users knowledge. We highlight here the main challenges we have encountered in applying the notion of regime shift to real world socio-ecological systems and in translating related concepts such as tipping points, stable states, hysteresis and resilience to land managers, using concrete examples from CASCADE study sites. Secondly, we explore the advantages of including land users’ knowledge in the scientific understanding of regime shifts. Moreover, we discuss useful alternative concepts and lessons learnt that will allow us to build a participatory method for the assessment of resilient management practices in specific socio-ecological systems and to foster adaptive dryland management.

Self-Organization of n-Alkane Chains in Water: Length Dependent Crossover from Helix and Toroid to Molten Globule

We demonstrate a chain length dependent crossover in the structural properties of linear hydrocarbon (n-alkane) chains using detailed atomistic simulations in explicit water. We identify a number of exotic structures of the polymer chain through energy minimization of representative snapshots collected from molecular dynamics trajectory. While the collapsed state is ring-like (circular) for small chains (CnH2n+2; n <= 20) and spherical for very long ones (n = 100), we find the emergence of ordered helical structures at intermediate lengths (n similar to 40). We find different types of disordered helices and toroid-like structures at n = 60. We also report a sharp transition in the stability of the collapsed state as a function of the chain length through relevant free energy calculations. While the collapsed state is only marginally metastable for C20H42, a clear bistable free energy surface emerges only when the chain is about 30 monomers long. For n = 30, the polymer exhibits an intermittent oscillation between the collapsed and the coil structures, characteristic of two stable states separated by a small barrier.