Experimental demonstration of chaos in a microbial food web

Dynamic phenotypic clustering in noisy ecosystems

In natural ecosystems, hundreds of species typically share the same environment and are connected by a dense network of interactions such as predation or competition for resources. Much is known about how fixed ecological niches can determine species abundances in such systems, but far less attention has been paid to patterns of abundances in randomly varying environments. Here, we study this question in a simple model of competition between many species in a patchy ecosystem with randomly fluctuating environmental conditions. Paradoxically, we find that introducing noise can actually induce ordered patterns of abundance-fluctuations, leading to a distinct periodic variation in the correlations between species as a function of the phenotypic distance between them; here, difference in growth rate. This is further accompanied by the formation of discrete, dynamic clusters of abundant species along this otherwise continuous phenotypic axis. These ordered patterns depend on the collective behavior of many species; they disappear when only individual or pairs of species are considered in isolation. We show that they arise from a balance between the tendency of shared environmental noise to synchronize species abundances and the tendency for competition among species to make them fluctuate out of step. Our results demonstrate that in highly interconnected ecosystems, noise can act as an ordering force, dynamically generating ecological patterns even in environments lacking explicit niches.

Ecological consequences of global bifurcations in some food chain models

Food chain models of ordinary differential equations (ode's) are often used in ecology to gain insight in the dynamics of populations of species, and the interactions of these species with each other and their environment. One powerful analysis technique is bifurcation analysis, focusing on the changes in long-term (asymptotic) behaviour under parameter variation. For the detection of local bifurcations there exists standardised software, but until quite recently most software did not include any capabilities for the detection and continuation of global bifurcations. We focus here on the occurrence of global bifurcations in four food chain models, and discuss the implications of their occurrence. In two stoichiometric models (one piecewise continuous, one smooth) there exists a homoclinic bifurcation, that results in the disappearance of a limit cycle attractor. Instead, a stable positive equilibrium becomes the global attractor. The models are also capable of bistability. In two three-dimensional models a Shil'nikov homoclinic bifurcation functions as the organising centre of chaos, while tangencies of homoclinic cycle-to-cycle connections 'cut' the chaotic attractors, which is associated with boundary crises. In one model this leads to extinction of the top predator, while in the other model hysteresis occurs. The types of ecological events occurring because of a global bifurcation will be categorized. Global bifurcations are always catastrophic, leading to the disappearance or merging of attractors. However, there is no 1-on-1 coupling between global bifurcation type and the possible ecological consequences. This only emphasizes the importance of including global bifurcations in the analysis of food chain models.

Cycles, phase synchronization, and entrainment in single-species phytoplankton populations

Complex dynamics, such as population cycles, can arise when the individual members of a population become synchronized. However, it is an open question how readily and through which mechanisms synchronization-driven cycles can occur in unstructured microbial populations. In experimental chemostats we studied large populations (>10(9) cells) of unicellular phytoplankton that displayed regular, inducible and reproducible population oscillations. Measurements of cell size distributions revealed that progression through the mitotic cycle was synchronized with the population cycles. A mathematical model that accounts for both the cell cycle and population-level processes suggests that cycles occur because individual cells become synchronized by interacting with one another through their common nutrient pool. An external perturbation by direct manipulation of the nutrient availability resulted in phase resetting, unmasking intrinsic oscillations and producing a transient collective cycle as the individuals gradually drift apart. Our study indicates a strong connection between complex within-cell processes and population dynamics, where synchronized cell cycles of unicellular phytoplankton provide sufficient population structure to cause small-amplitude oscillations at the population level.

Coupled predator-prey oscillations in a chaotic food web

Coupling of several predator-prey oscillations can generate intriguing patterns of synchronization and chaos. Theory predicts that prey species will fluctuate in phase if predator-prey cycles are coupled through generalist predators, whereas they will fluctuate in anti-phase if predator-prey cycles are coupled through competition between prey species. Here, we investigate predator-prey oscillations in a long-term experiment with a marine plankton community. Wavelet analysis of the species fluctuations reveals two predator-prey cycles that fluctuate largely in anti-phase. The phase angles point at strong competition between the phytoplankton species, but relatively little prey overlap among the zooplankton species. This food web architecture is consistent with the size structure of the plankton community, and generates highly dynamic food webs. Continued alternations in species dominance enable coexistence of the prey species through a non-equilibrium 'killing-the-winner' mechanism, as the system shifts back and forth between the two predator-prey cycles in a chaotic fashion.

Intertwined interspecies relationships: approaches to untangle the microbial network

In nature, microorganisms live by interacting with each other. Microbiological studies that only consider pure cultures are not sufficient to adequately describe the natural behaviour of microbes. Several microbial interactions have been recognized to affect the growth or metabolism of others; e.g. syntrophic cometabolism, competition, production of inhibitors or activators, and predation. It is believed that third-party organisms easily affect the two-species relationships and these relationships form the basis of interspecies networks within microbial communities. A microbial network contributes to 'functional redundancy' or 'structural diversity' and the microbial communities effectively act as a multicellular organism. It is necessary to understand not only the physiological activity of members within microbial communities but also their roles to regulate the activity or population of others. To access the microbial network, we require (i) comprehensive determination of all possible interspecies relationships among microbes, (ii) knock-out experiments by which certain members can be removed or suppressed, and (iii) supplemental addition of microbes or activation of certain members. Microbial network studies have started using defined microbial communities, i.e. a mixed culture that is composed of three or four species. In order to expand these studies to microflora in nature, microbial ecology requires the help of mathematical biology.

Interannual variability in species composition explained as seasonally entrained chaos

The species composition of plankton, insect and annual plant communities may vary markedly from year to year. Such interannual variability is usually thought to be driven by year-to-year variation in weather conditions. Here we examine an alternative explanation. We studied the effects of regular seasonal forcing on a multi-species predator-prey model consisting of phytoplankton and zooplankton species. The model predicts that interannual variability in species composition can easily arise without interannual variability in external conditions. Seasonal forcing increased the probability of chaos in our model communities, but squeezed these irregular species dynamics within the seasonal cycle. As a result, the population dynamics had a peculiar character. Consistent with long-term time series of natural plankton communities, seasonal variation led to a distinct seasonal succession of species, yet the species composition varied from year to year in an irregular fashion. Our results suggest that interannual variability in species composition is an intrinsic property of multi-species communities in seasonal environments.

Chaotic expression dynamics implies pluripotency: when theory and experiment meet

Background

During normal development, cells undergo a unidirectional course of differentiation that progressively decreases the number of cell types they can potentially become. Pluripotent stem cells can differentiate into several types of cells, but terminally differentiated cells cannot differentiate any further. A fundamental problem in stem cell biology is the characterization of the difference in cellular states, e.g., gene expression profiles, between pluripotent stem cells and terminally differentiated cells.

Presentation of the hypothesis

To address the problem, we developed a dynamical systems model of cells with intracellular protein expression dynamics and interactions with each other. According to extensive simulations, cells with irregular (chaotic) oscillations in gene expression dynamics have the potential to differentiate into other cell types. During development, such complex oscillations are lost successively, leading to a loss of pluripotency. These simulation results, together with recent single-cell-level measurements in stem cells, led us to the following hypothesis regarding pluripotency: Chaotic oscillation in the expression of some genes leads to cell pluripotency and affords cellular state heterogeneity, which is supported by itinerancy over quasi-stable states. Differentiation stabilizes these states, leading to a loss of pluripotency.

Testing the hypothesis

To test the hypothesis, it is crucial to measure the time course of gene expression levels at the single-cell level by fluorescence microscopy and fluorescence-activated cell sorting (FACS) analysis. By analyzing the time series of single-cell-level expression data, one can distinguish whether the variation in protein expression level over time is due only to stochasticity in expression dynamics or originates from the chaotic dynamics inherent to cells, as our hypothesis predicts. By further analyzing the expression in differentiated cell types, one can examine whether the loss of pluripotency is accompanied by a loss of oscillation.

Implications of the hypothesis

Recovery of pluripotency from determined cells is a long-standing aspiration, from both scientific and clinical perspectives. Our hypothesis suggests a feasible route to recover the potential to differentiate, i.e., by increasing the variety of expressed genes to restore chaotic expression dynamics, as is consistent with the recent generation of induced pluripotent stem (iPS) cells.

Reviewers

This article was reviewed by David Krakauer, Jeroen van Zon (nominated by Rob de Boer), and Williams S. Hlavacek.

TRANSITIONS FROM STABLE EQUILIBRIA TO CHAOS, AND BACK, IN AN EXPERIMENTAL FOOD WEB

The question of whether deterministic chaos occurs in natural populations has been discussed since the 1970s following the discovery that simple population models can generate chaotic dynamics. Natural populations undergo a diverse mixture of deterministic and stochastic processes that define population dynamics. In most habitats populations are also exposed to changes in biotic and abiotic parameters. Models predict that shifts in ecological parameters may lead to a transition between deterministic chaos, stable equilibria, and limit cycles, yet clear examples from empirical studies are rare. However, such transitions should be considered when discussing the occurrence of chaos in nature because ecological time series are in general short and have large sampling intervals. Here we document short-term transitions in population dynamics to and from chaos in an experimental system. Manipulation of only one experimental parameter (chemostat dilution rate) in a multi-species food web of two bacteria and a bacterivorous ciliate showed that switching between different dynamic behaviors occured with surprising rapidity in the microbial populations. Thus, short periods of chaotic dynamics may easily be overlooked in field observations.

Differential and chaotic calcium signatures in the symbiosis signaling pathway of legumes

Understanding how the cell uses a limited set of proteins to transduce very different signals into specific cellular responses is a central goal of cell biology and signal transduction disciplines. Although multifunctionality in signal transduction is widespread, the mechanisms that allow differential modes of signaling in multifunctional signaling pathways are not well defined. In legume plants, a common symbiosis signaling pathway composed of at least seven proteins mediates infection by both mycorrhizal fungi and rhizobial bacteria. Here we show that the symbiosis signaling pathway in legumes differentially transduces both bacterial and fungal signals (inputs) to generate alternative calcium responses (outputs). We show that these differential calcium responses are dependent on the same proteins, DMI1 and DMI2, for their activation, indicating an inherent flexibility in this signaling pathway. By using Lyapunov and other mathematical analyses, we discovered that both bacterial-induced and fungal-induced calcium responses are chaotic in nature. Chaotic systems require minimal energy to produce a wide spectrum of outputs in response to marginally different inputs. The flexibility provided by chaotic systems is consistent with the need to transduce two different signals, one from rhizobial bacteria and one from mycorrhizal fungi, by using common components of a single signaling pathway.

A synthetic Escherichia coli predator-prey ecosystem

We have constructed a synthetic ecosystem consisting of two Escherichia coli populations, which communicate bi-directionally through quorum sensing and regulate each other's gene expression and survival via engineered gene circuits. Our synthetic ecosystem resembles canonical predator-prey systems in terms of logic and dynamics. The predator cells kill the prey by inducing expression of a killer protein in the prey, while the prey rescue the predators by eliciting expression of an antidote protein in the predator. Extinction, coexistence and oscillatory dynamics of the predator and prey populations are possible depending on the operating conditions as experimentally validated by long-term culturing of the system in microchemostats. A simple mathematical model is developed to capture these system dynamics. Coherent interplay between experiments and mathematical analysis enables exploration of the dynamics of interacting populations in a predictable manner.

Stochastic analysis of a pulse-type prey-predator model

A stochastic Lotka-Volterra model, a so-called pulse-type model, for the interaction between two species and their random natural environment is investigated. The effect of a random environment is modeled as random pulse trains in the birth rate of the prey and the death rate of the predator. The generalized cell mapping method is applied to calculate the probability distributions of the species populations at a state of statistical quasistationarity. The time evolution of the population densities is studied, and the probability of the near extinction time, from an initial state to a critical state, is obtained. The effects on the ecosystem behaviors of the prey self-competition term and of the pulse mean arrival rate are also discussed. Our results indicate that the proposed pulse-type model shows obviously distinguishable characteristics from a Gaussian-type model, and may confer a significant advantage for modeling the prey-predator system under discrete environmental fluctuations.

Mixing of supersaturated assemblages and the precipitous loss of species

Mechanisms influencing species richness are many. Recent theoretical research revealed additional mechanisms that involved neutral and lumpy coexistence and alternating assemblage states. These mechanisms can lead to conditions where the number of coexisting species is greater than the number of limiting resources, that is, species supersaturation. Our research focused on the role of disturbances (migration and pulsed through-flows) in supersaturated plankton systems. Our simulations employed 30 different supersaturated assemblages generated by using various ecological principals. Our findings indicated that immigration rates as low as 0.1% of total biomass per day generally led to regional homogenization of species and dramatic extinction events, with assemblages characteristic of lumpy coexistence being more resilient than those characteristic of neutral coexistence or alternating states. Generally, pulsed through-flows tended to offset, to some extent, the negative effects of migration. The precipitous loss of species with the onset of migration is observed in other systems as well, for example, cichlid fish communities of East Africa rift lakes and songbird assemblages from Indian Ocean islands. While many explanations have been offered to explain postimmigration extinctions in species-rich systems, another explanation might be that the assemblages in these systems are in a fragile state of supersaturated coexistence.

Functional responses of prokaryotes and viruses to grazer effects and nutrient additions in freshwater microcosms

For aquatic systems, there is little data on the interactions between viruses, prokaryotes, grazers and the availability of resources. We conducted a microcosm experiment using a size fractionation approach to manipulate grazers, with a purpose to examine the effects of inorganic and organic nutrients on viral and prokaryotic standing stocks and activities, and on prokaryotic community composition as assessed by fluorescent in situ hybridization (FISH) method. Experiments were performed during periods of severe phosphate (P)-limiting conditions in the oligotrophic Sep Reservoir (Massif Central, France). In the absence of nutrient addition, the presence of grazers in microcosms stimulated prokaryotic growth and viral proliferation, likely through nutrient and substrate enrichment. Addition of nutrients had a stronger effect on viral infection of prokaryotes than grazing. Addition of P led to the most pronounced increase in prokaryotic abundance, production and growth efficiency, thus providing direct evidence of P limitation of prokaryotes. Enhanced prokaryotic activity in P treatments also stimulated viral abundance and viral-induced lyses of prokaryotes. Changes in prokaryotic community composition due to nutrient additions were evident in the grazer-free samples. Prokaryotic populations hybridizing for the probes bacteria, beta-Proteobacteria and alpha-Proteobacteria responded to nutrient enrichment with significant increases in their relative abundances, whereas cells hybridizing for Archaea and Cytophaga-Flavobacterium (now known as Bacteroidetes) probes failed to show any functional response. Cells hybridizing for the latter cluster increased towards the end of incubation period in the control samples (that is, without nutrient additions) with grazers present, suggesting the development of grazing resistant forms. From our nutrient enrichment microcosm experiments, we conclude that the presence of grazers is a stimulating factor for prokaryotic growth and viral proliferation in the plankton, probably through nutrient regeneration process.

Estimating a predator-prey dynamical model with the parameter cascades method

Ordinary differential equations (ODEs) are widely used in ecology to describe the dynamical behavior of systems of interacting populations. However, systems of ODEs rarely provide quantitative solutions that are close to real field observations or experimental data because natural systems are subject to environmental and demographic noise and ecologists are often uncertain about the correct parameterization. In this article we introduce "parameter cascades" as an improved method to estimate ODE parameters such that the corresponding ODE solutions fit the real data well. This method is based on the modified penalized smoothing with the penalty defined by ODEs and a generalization of profiled estimation, which leads to fast estimation and good precision for ODE parameters from noisy data. This method is applied to a set of ODEs originally developed to describe an experimental predator-prey system that undergoes oscillatory dynamics. The new parameterization considerably improves the fit of the ODE model to the experimental data sets. At the same time, our method reveals that important structural assumptions that underlie the original ODE model are essentially correct. The mathematical formulations of the two nonlinear interaction terms (functional responses) that link the ODEs in the predator-prey model are validated by estimating the functional responses nonparametrically from the real data. We suggest two major applications of "parameter cascades" to ecological modeling: It can be used to estimate parameters when original data are noisy, missing, or when no reliable priori estimates are available; it can help to validate the structural soundness of the mathematical modeling approach.

Microbial community composition of the Danshui river estuary of Northern Taiwan and the practicality of the phylogenetic method in microbial barcoding

In this study, the microbial community in a mangrove ecosystem was surveyed and used to test the eligibility of 16S rDNA library and neighbor-joining method for the purpose of estimating microbial composition. Genetic diversity (pi) and four other diversity indices (Simpson's unbiased, Shannon-Wiener, Evenness, and Chao1 indices) were applied to estimate the adaptive lineages of microorganisms in the mangrove ecosystem. The results indicated that gamma-Proteobacteria is the most diverse taxon, while the most abundant family is Rhodobacteraceae (alpha-Proteobacteria), followed by Comamonadaceae (beta-Proteobacteria). This result may imply the existence of a graded distribution of microbial diversity across a spectrum of different salinities in the waterbody of this estuary ecosystem. Furthermore, at least 500-1,000 bps of the posterior portion of 16S rDNA is required as a marker to profile the microbial diversity in a microcosm of interest using phylogenetic methods, according to the results of our sliding window analyses for the measurements of pi, consistency index, and retention index.

Dispersal, density dependence, and population dynamics of a fungal microbe on leaf surfaces

Despite the ubiquity and importance of microbes in nature, little is known about their natural population dynamics, especially for those that occupy terrestrial habitats. Here we investigate the dynamics of the yeast-like fungus Aureobasidium pullulans (Ap) on apple leaves in an orchard. We asked three questions. (1) Is variation in fungal population density among leaves caused by variation in leaf carrying capacities and strong density-dependent population growth that maintains densities near carrying capacity? (2) Do resident populations have competitive advantages over immigrant cells? (3) Do Ap dynamics differ at different times during the growing season? To address these questions, we performed two experiments at different times in the growing season. Both experiments used a 2 x 2 factorial design: treatment 1 removed fungal cells from leaves to reveal density-dependent population growth, and treatment 2 inoculated leaves with an Ap strain engineered to express green fluorescent protein (GFP), which made it possible to track the fate of immigrant cells. The experiments showed that natural populations of Ap vary greatly in density due to sustained differences in carrying capacities among leaves. The maintenance of populations close to carrying capacities indicates strong density-dependent processes. Furthermore, resident populations are strongly competitive against immigrants, while immigrants have little impact on residents. Finally, statistical models showed high population growth rates of resident cells in one experiment but not in the other, suggesting that Ap experiences relatively "good" and "bad" periods for population growth. This picture of Ap dynamics conforms to commonly held, but rarely demonstrated, expectations of microbe dynamics in nature. It also highlights the importance of local processes, as opposed to immigration, in determining the abundance and dynamics of microbes on surfaces in terrestrial systems.

Preventing extinction and outbreaks in chaotic populations

Interactions in ecological communities are inherently nonlinear and can lead to complex population dynamics including irregular fluctuations induced by chaos. Chaotic population dynamics can exhibit violent oscillations with extremely small or large population abundances that might cause extinction and recurrent outbreaks, respectively. We present a simple method that can guide management efforts to prevent crashes, peaks, or any other undesirable state. At the same time, the irregularity of the dynamics can be preserved when chaos is desirable for the population. The control scheme is easy to implement because it relies on time series information only. The method is illustrated by two examples: control of crashes in the Ricker map and control of outbreaks in a stage-structured model of the flour beetle Tribolium. It turns out to be effective even with few available data and in the presence of noise, as is typical for ecological settings.

Pattern formation, outbreaks, and synchronization in food chains with two and three species

We study the dynamics of populations of predators and preys using a mean field approach and a spatial model. The mean field description assumes that the individuals are homogeneously mixed and interact with one another with equal probability, so that space can be ignored. In the spatial model, on the other hand, predators can prey only in a certain neighborhood of their spatial location. We show that the size of these predation neighborhoods has dramatic effects on the dynamics and on the organization of the species in space. In the case of a three species food chain, in particular, the populations of predators display a sequence of apparently irregular outbreaks when the predation neighborhood has intermediate values, as compared to the size of the available space. Nonetheless, further increasing their size makes the outbreaks disappear and the dynamics approach that of the mean field model. Our study of synchronization also shows that the periodic behavior displayed by the average populations in a spatially extended system may hide the existence of patches that oscillate out of phase in a highly coordinated fashion.

Effects of rapid prey evolution on predator-prey cycles

We study the qualitative properties of population cycles in a predator-prey system where genetic variability allows contemporary rapid evolution of the prey. Previous numerical studies have found that prey evolution in response to changing predation risk can have major quantitative and qualitative effects on predator-prey cycles, including: (1) large increases in cycle period, (2) changes in phase relations (so that predator and prey are cycling exactly out of phase, rather than the classical quarter-period phase lag), and (3) "cryptic" cycles in which total prey density remains nearly constant while predator density and prey traits cycle. Here we focus on a chemostat model motivated by our experimental system (Fussmann et al. in Science 290:1358-1360, 2000; Yoshida et al. in Proc roy Soc Lond B 424:303-306, 2003) with algae (prey) and rotifers (predators), in which the prey exhibit rapid evolution in their level of defense against predation. We show that the effects of rapid prey evolution are robust and general, and furthermore that they occur in a specific but biologically relevant region of parameter space: when traits that greatly reduce predation risk are relatively cheap (in terms of reductions in other fitness components), when there is coexistence between the two prey types and the predator, and when the interaction between predators and undefended prey alone would produce cycles. Because defense has been shown to be inexpensive, even cost-free, in a number of systems (Andersson et al. in Curr Opin Microbiol 2:489-493, 1999: Gagneux et al. in Science 312:1944-1946, 2006; Yoshida et al. in Proc Roy Soc Lond B 271:1947-1953, 2004), our discoveries may well be reproduced in other model systems, and in nature. Finally, some of our key results are extended to a general model in which functional forms for the predation rate and prey birth rate are not specified.

On the reproducibility of microcosm experiments - different community composition in parallel phototrophic biofilm microcosms

Phototrophic biofilms were cultivated simultaneously using the same inoculum in three identical flow-lane microcosms located in different laboratories. The growth rates of the biofilms were similar in the different microcosms, but denaturing gradient gel electrophoresis (DGGE) analysis of both 16S and 18S rRNA gene fragments showed that the communities developed differently in terms of species richness and community composition. One microcosm was dominated by Microcoleus and Phormidium species, the second microcosm was dominated by Synechocystis and Phormidium species, and the third microcosm was dominated by Microcoleus- and Planktothrix- affiliated species. No clear effect of light intensity on the cyanobacterial community composition was observed. In addition, DGGE profiles obtained from the cultivated biofilms showed a low resemblance with the profiles derived from the inoculum. These findings demonstrate that validation of reproducibility is essential for the use of microcosm systems in microbial ecology studies.

Eukaryotic community distribution and its relationship to water physicochemical parameters in an extreme acidic environment, Rio Tinto (southwestern Spain)

The correlation between water physicochemical parameters and eukaryotic benthic composition was examined in Río Tinto. Principal component analysis showed a high inverse relationship between pH and most of the heavy metals analyzed as well as Dunaliella sp., while Chlamydomonas sp. abundance was positively related. Zn, Cu, and Ni clustered together and showed a strong inverse correlation with the diversity coefficient and most of the species analyzed. These eukaryotic communities seem to be more influenced by the presence of heavy metals than by the pH.

Impact of local temperature increase on the early development of biofilm-associated ciliate communities

Indications of global climate change and associated unusual temperature fluctuations have become increasingly obvious over the past few decades. Consequently, the relevance of temperature increases for ecological communities and for whole ecosystems is one of the major challenges of current ecological research. One approach to investigating the effects of increasing temperatures on communities is the use of fast-growing microbial communities. Here we introduce a river bypass system in which we tested the effect of temperature increases (0, 2, 4, 6 degrees C above the long-term average) on both the colonization speed and the carrying capacity of biofilm-associated ciliate communities under different seasonal scenarios. We further investigated interactions of temperature and resource availability by cross-manipulations in order to test the hypothesis that temperature-mediated effects will be strongest in environments that are not resource-limited. Strong seasonal differences in both tested parameters occurred under natural conditions (no resource addition), and the effects of temperature increase at a given time were relatively low. However, increasing temperature can significantly accelerate the colonization speed and reduce the carrying capacity in particular seasons. These effects were strongest in winter. Simultaneous manipulation of temperature and of resource availability amplified the response to temperature increase, adumbrating strong interactive control of populations by temperature and resource availability. Our results show that the response of communities to local temperature increases strongly depends on the seasonal setting, the resource availability and the stage of succession (early colonization speed vs. carrying capacity).

Colored-noise-induced Hopf bifurcations in predator-prey communities

A broad class of (N+1) -species ratio-dependent predator-prey stochastic models, which consist of one predator population and N prey populations, is considered. The effect of a fluctuating environment on the carrying capacities of prey populations is taken into account as colored noise. In the framework of the mean-field theory, approximate self-consistency equations for prey-populations mean density and for predator-population density are derived (to the first order in the noise variance). In some cases, the mean field exhibits Hopf bifurcations as a function of noise correlation time. The corresponding transitions are found to be reentrant, e.g., the periodic orbit appears above a critical value of the noise correlation time, but disappears again at a higher value of the noise correlation time. The nonmonotonous dependence of the critical control parameter on the noise correlation time is found, and the conditions for the occurrence of Hopf bifurcations are presented. Our results provide a possible scenario for environmental-fluctuations-induced transitions between the oscillatory regime and equilibrium state of population sizes observed in nature.

Marine monitoring: Its shortcomings and mismatch with the EU Water Framework Directive's objectives

The main goal of the EU Water Framework Directive (WFD) is to achieve good ecological status across European surface waters by 2015 and as such, it offers the opportunity and thus the challenge to improve the protection of our coastal systems. It is the main example for Europe's increasing desire to conserve aquatic ecosystems. Ironically, since c. 1975 the increasing adoption of EU directives has been accompanied by a decreasing interest of, for example, the Dutch government to assess the quality of its coastal and marine ecosystems. The surveillance and monitoring started in NL in 1971 has declined since the 1980s resulting in a 35% reduction of sampling stations. Given this and interruptions the remaining data series is considered to be insufficient for purposes other than trend analysis and compliance. The Dutch marine managers have apparently chosen a minimal (cost-effective) approach despite the WFD implicitly requiring the incorporation of the system's 'ecological complexity' in indices used to evaluate the ecological status of highly variable systems such as transitional and coastal waters. These indices should include both the community structure and system functioning and to make this really cost-effective a new monitoring strategy is required with a tailor-made programme. Since the adoption of the WFD in 2000 and the launching of the European Marine Strategy in 2002 (and the recently proposed Marine Framework Directive) we suggest reviewing national monitoring programmes in order to integrate water quality monitoring and biological monitoring and change from 'station oriented monitoring' to 'basin or system oriented monitoring' in combination with specific 'cause-effect' studies for highly dynamic coastal systems. Progress will be made if the collected information is integrated and aggregated in valuable tools such as structure- and functioning-oriented computer simulation models and Decision Support Systems. The development of ecological indices integrating community structure and system functioning, such as in Ecological Network Analysis, are proposed to meet a cost-effective approach at the national level and full assessment of the ecosystem status at the EU level. The WFD offers the opportunity to re-consider and re-invest in environmental research and monitoring. Using examples from the Netherlands and, to a lesser extent, the United Kingdom, the present paper therefore reviews marine monitoring and marine environmental research in combination and in the light of such major policy initiatives such as the WFD.