TY - JOUR A1 - Huppert, Amit A1 - Blasius, Bernd A1 - Olinky, Ronen A1 - Stone, Lewi T1 - A Model for Seasonal Phytoplankton Blooms N2 - We analyse a generic bottom-up nutrient phytoplankton model to help understand the dynamics of seasonally recurring algae blooms. The deterministic model displays a wide spectrum of dynamical behaviours, from simple cyclical blooms which trigger annually, to irregular chaotic blooms in which both the time between outbreaks and their magnitudes are erratic. Unusually, despite the persistent seasonal forcing, it is extremely difficult to generate blooms that are both annually recurring and also chaotic or irregular (i.e. in amplitude) even though this characterizes many real time series. Instead the model has a tendency to `skip' with outbreaks often being suppressed from one year to the next. This behaviour is studied in detail and we develop an analytical expression to describe the model's flow in phase space, yielding insights into the mechanism of the bloom recurrence. We also discuss how modifications to the equations through the inclusion of appropriate functional forms can generate more realistic dynamics. Y1 - 2005 UR - http://www.agnld.uni-potsdam.de/~bernd/papers/jtb2.pdf ER - TY - JOUR A1 - Blasius, Bernd T1 - Anomalous phase synchronization in two asymmetrically coupled oscillators in the presence of noise N2 - We study the route to synchronization in two noisy, nonisochronous oscillators. Anomalous phase synchronization arises if both oscillators differ in their respective value of nonisochronicity and it is characterized by a strong detuning of the oscillator frequencies with the onset of coupling. Here we show that anomalous synchronization, both in limit-cycle or chaotic oscillators, can considerably be enlarged under the influence of asymmetrical coupling and noise. In these systems we describe a number of noise induced effects, such as an inversion of the natural frequency difference and coupling induced desynchronization of two identical oscillators. Our results can be explained in terms of a noisy particle in a tilted washboard potential Y1 - 2005 ER - TY - JOUR A1 - Belykh, Vladimir N. A1 - Osipov, Grigory V. A1 - Kuckländer, Nina A1 - Blasius, Bernd A1 - Kurths, Jürgen T1 - Automatic control of phase synchronization in coupled complex oscillators N2 - We present an automatic control method for phase locking of regular and chaotic non-identical oscillations, when all subsystems interact via feedback. This method is based on the well known principle of feedback control which takes place in nature and is successfully used in engineering. In contrast to unidirectional and bidirectional coupling, the approach presented here supposes the existence of a special controller, which allows to change the parameters of the controlled systems. First we discuss general principles of automatic phase synchronization (PS) for arbitrary coupled systems with a controller whose input is given by a special quadratic form of coordinates of the individual systems and its output is a result of the application of a linear differential operator. We demonstrate the effectiveness of our approach for controlled PS on several examples: (i) two coupled regular oscillators, (ii) coupled regular and chaotic oscillators, (iii) two coupled chaotic R"ossler oscillators, (iv) two coupled foodweb models, (v) coupled chaotic R"ossler and Lorenz oscillators, (vi) ensembles of locally coupled regular oscillators, (vii) ensembles of locally coupled chaotic oscillators, and (viii) ensembles of globally coupled chaotic oscillators. Y1 - 2005 UR - http://www.agnld.uni-potsdam.de/~bernd/papers/physica_D.pdf ER - TY - JOUR A1 - Blasius, Bernd A1 - Clodong, Sébastien T1 - Chaos in a periodically forced chemostat with algal mortality N2 - We study the possibility of chaotic dynamics in the externally driven Droop model. This model describes a phytoplankton population in a chemostat under periodic supply of nutrients. Previously it has been proven under very general assumptions that such systems are not able to exhibit chaotic dynamics. Here we show that the simple introduction of algal mortality may lead to chaotic oscillations of algal density in the forced chemostat. Our numerical simulations show that the existence of chaos is intimately related to plankton overshooting in the unforced model. We provide a simple measure, based on stability analysis, for estimating the amount of overshooting. These findings are not restricted to the Droop model but hold also for other chemostat models with mortality. Our results suggest periodically driven chemostats as a simple model system for the experimental verification of chaos in ecology. Y1 - 2004 ER - TY - JOUR A1 - Fussmann, Gregor F. A1 - Blasius, Bernd T1 - Community response to enrichment is highly sensitive to model structure N2 - Biologists use mathematical functions to model, understand, and predict nature. For most biological processes, however, the exact analytical form is not known. This is also true for one of the most basic life processes, the uptake of food or resources. We show that the use of a number of nearly indistinguishable functions, which can serve as phenomenological descriptors of resource uptake, may lead to alarmingly different dynamical behaviour in a simple community model. More specifically, we demonstrate that the degree of resource enrichment needed to destabilize the community dynamics depends critically on the mathematical nature of the uptake function. Y1 - 2005 UR - http://www.agnld.uni-potsdam.de/~bernd/papers/BiolLett1.pdf ER - TY - JOUR A1 - Massie, Thomas Michael A1 - Ryabov, Alexei A1 - Blasius, Bernd A1 - Weithoff, Guntram A1 - Gaedke, Ursula T1 - Complex transient dynamics of stage-structured populations in response to environmental changes JF - The American naturalist : a bi-monthly journal devoted to the advancement and correlation of the biological sciences N2 - Stage structures of populations can have a profound influence on their dynamics. However, not much is known about the transient dynamics that follow a disturbance in such systems. Here we combined chemostat experiments with dynamical modeling to study the response of the phytoplankton species Chlorella vulgaris to press perturbations. From an initially stable steady state, we altered either the concentration or dilution rate of a growth-limiting resource. This disturbance induced a complex transient response-characterized by the possible onset of oscillations-before population numbers relaxed to a new steady state. Thus, cell numbers could initially change in the opposite direction of the long-term change. We present quantitative indexes to characterize the transients and to show that the dynamic response is dependent on the degree of synchronization among life stages, which itself depends on the state of the population before perturbation. That is, we show how identical future steady states can be approached via different transients depending on the initial population structure. Our experimental results are supported by a size-structured model that accounts for interplay between cell-cycle and population-level processes and that includes resource-dependent variability in cell size. Our results should be relevant to other populations with a stage structure including organisms of higher order. KW - chemostat experiments KW - Chlorella vulgaris KW - environmental changes KW - population dynamics KW - stage structure KW - transient dynamics Y1 - 2013 U6 - https://doi.org/10.1086/670590 SN - 0003-0147 SN - 1537-5323 VL - 182 IS - 1 SP - 103 EP - 119 PB - Univ. of Chicago Press CY - Chicago ER - TY - JOUR A1 - Bragard, Jean A1 - Montbrio, Ernest A1 - Mendoza, C. A1 - Boccaletti, Stefano A1 - Blasius, Bernd T1 - Defect-enhanced anomaly in frequency synchronization of asymmetrically coupled spatially extended systems N2 - We analytically establish and numerically show that anomalous frequency synchronization occurs in a pair of asymmetrically coupled chaotic space extended oscillators. The transition to anomalous behaviors is crucially dependent on asymmetries in the coupling configuration, while the presence of phase defects has the effect of enhancing the anomaly in frequency synchronization with respect to the case of merely time chaotic oscillators. Y1 - 2005 UR - http://www.agnld.uni-potsdam.de/~bernd/papers/pre4.pdf ER - TY - JOUR A1 - Massie, Thomas Michael A1 - Weithoff, Guntram A1 - Kucklaender, Nina A1 - Gaedke, Ursula A1 - Blasius, Bernd T1 - Enhanced Moran effect by spatial variation in environmental autocorrelation JF - Nature Communications N2 - Spatial correlations in environmental stochasticity can synchronize populations over wide areas, a phenomenon known as the Moran effect. The Moran effect has been confirmed in field, laboratory and theoretical investigations. Little is known, however, about the Moran effect in a common ecological case, when environmental variation is temporally autocorrelated and this autocorrelation varies spatially. Here we perform chemostat experiments to investigate the temporal response of independent phytoplankton populations to autocorrelated stochastic forcing. In contrast to naive expectation, two populations without direct coupling can be more strongly correlated than their environmental forcing (enhanced Moran effect), if the stochastic variations differ in their autocorrelation. Our experimental findings are in agreement with numerical simulations and analytical calculations. The enhanced Moran effect is robust to changes in population dynamics, noise spectra and different measures of correlation-suggesting that noise-induced synchrony may play a larger role for population dynamics than previously thought. Y1 - 2015 U6 - https://doi.org/10.1038/ncomms6993 SN - 2041-1723 VL - 6 PB - Nature Publ. Group CY - London ER - TY - JOUR A1 - Gross, Thilo A1 - D'Lima, Carlos J. Dommar A1 - Blasius, Bernd T1 - Epidemic dynamics on an adaptive network N2 - Many real-world networks are characterized by adaptive changes in their topology depending on the state of their nodes. Here we study epidemic dynamics on an adaptive network, where the susceptibles are able to avoid contact with the infected by rewiring their network connections. This gives rise to assortative degree correlation, oscillations, hysteresis, and first order transitions. We propose a low-dimensional model to describe the system and present a full local bifurcation analysis. Our results indicate that the interplay between dynamics and topology can have important consequences for the spreading of infectious diseases and related applications Y1 - 2006 UR - http://prl.aps.org/ U6 - https://doi.org/10.1103/Physrevlett.96.208701 SN - 0031-9007 ER - TY - JOUR A1 - Dana, Syamal Kumar A1 - Blasius, Bernd A1 - Kurths, Jürgen T1 - Experimental evidence of anomalous phase synchronization in two diffusively coupled Chua oscillators N2 - We study the transition to phase synchronization in two diffusively coupled, nonidentical Chua oscillators. In the experiments, depending on the used parameterization, we observe several distinct routes to phase synchronization, including states of either in-phase, out-of-phase, or antiphase synchronization, which may be intersected by an intermediate desynchronization regime with large fluctuations of the frequency difference. Furthermore, we report the first experimental evidence of an anomalous transition to phase synchronization, which is characterized by an initial enlargement of the natural frequency difference with coupling strength. This results in a maximal frequency disorder at intermediate coupling levels, whereas usual phase synchronization via monotonic decrease in frequency difference sets in only for larger coupling values. All experimental results are supported by numerical simulations of two coupled Chua models Y1 - 2006 UR - http://ojps.aip.org/chaos/ U6 - https://doi.org/10.1063/1.2197168 SN - 1054-1500 ER - TY - JOUR A1 - Wichmann, Matthias A1 - Johst, Karin A1 - Schwager, Monika A1 - Jeltsch, Florian A1 - Blasius, Bernd T1 - Extinction risk, coloured noise and the scaling of variance N2 - The impact of temporally correlated fluctuating environments (coloured noise) on the extinction risk of populations has become a main focus in theoretical population ecology. In this study we particularly focus on the extinction risk in strongly autocorrelated environments. Here, in contrast to moderate autocorrelation, we found the extinction risk to be highly dependent on the process of noise generation, in particular on the method of variance scaling. Such variance scaling is commonly applied to avoid variance-driven biases when comparing the extinction risk for white and coloured noise. In this study we found an often-used scaling technique to lead to high variability in the resulting variances of different time series for strong auto-correlation eventually leading to deviations in the projected extinction risk. Therefore, we present an alternative method that always delivers the target variance, even in the case of strong temporal correlation. Furthermore, in contrast to the earlier method, our very intuitive method is not bound to auto-regressive processes but can be applied to all types of coloured noises. We recommend the method introduced here to be used when the target of interest is the effect of noise colour on extinction risk not obscured by any variance effects. Y1 - 2005 UR - http://www.agnld.uni-potsdam.de/~bernd/papers/tpb1.pdf ER - TY - JOUR A1 - Seebens, Hanno A1 - Essl, Franz A1 - Dawson, Wayne A1 - Fuentes, Nicol A1 - Moser, Dietmar A1 - Pergl, Jan A1 - Pysek, Petr A1 - van Kleunen, Mark A1 - Weber, Ewald A1 - Winter, Marten A1 - Blasius, Bernd T1 - Global trade will accelerate plant invasions in emerging economies under climate change JF - Global change biology N2 - Trade plays a key role in the spread of alien species and has arguably contributed to the recent enormous acceleration of biological invasions, thus homogenizing biotas worldwide. Combining data on 60-year trends of bilateral trade, as well as on biodiversity and climate, we modeled the global spread of plant species among 147 countries. The model results were compared with a recently compiled unique global data set on numbers of naturalized alien vascular plant species representing the most comprehensive collection of naturalized plant distributions currently available. The model identifies major source regions, introduction routes, and hot spots of plant invasions that agree well with observed naturalized plant numbers. In contrast to common knowledge, we show that the 'imperialist dogma,' stating that Europe has been a net exporter of naturalized plants since colonial times, does not hold for the past 60 years, when more naturalized plants were being imported to than exported from Europe. Our results highlight that the current distribution of naturalized plants is best predicted by socioeconomic activities 20 years ago. We took advantage of the observed time lag and used trade developments until recent times to predict naturalized plant trajectories for the next two decades. This shows that particularly strong increases in naturalized plant numbers are expected in the next 20 years for emerging economies in megadiverse regions. The interaction with predicted future climate change will increase invasions in northern temperate countries and reduce them in tropical and (sub) tropical regions, yet not by enough to cancel out the trade-related increase. KW - alien vascular plants KW - bioinvasion KW - climate warming KW - global spread KW - imperialist dogma KW - model KW - network of plant invasion Y1 - 2015 U6 - https://doi.org/10.1111/gcb.13021 SN - 1354-1013 SN - 1365-2486 VL - 21 IS - 11 SP - 4128 EP - 4140 PB - Wiley-Blackwell CY - Hoboken ER - TY - JOUR A1 - Pasternak, Zohar A1 - Blasius, Bernd A1 - Abelson, Avigdor T1 - Host location by larvae of a parasitic barnacle: larval chemotaxis and plume tracking in flow N2 - Numerous studies describe stimulation and/or enhancement of larval settlement by distance chemoreception in response to chemical factors emitted by conspecific adults, host and prey species and microbial films. However, active upstream tracking of odor plumes, needed in order to locate specific, spatially limited settlement sites, has thus far recieved little scientific attention. This study examines host location in flow and still water by larvae of the parasitic barnacle Heterosaccus dollfusi, which inhabits the brachyuran crab Charybdis longicollis. Experiments included analysis of larval motion patterns under four conditions: still water, in flow, in still water with waterborn host metabolites and in flow with host metabolites. Our results show that the H. dollfusi larvae are capable of actively and effectively locating their host in still water and in flow, using chemotaxis and rheotaxis and modifying their swimming pattern, direction, velocity, determination and turning rate to accommodate efficient navigation in changing environmental conditions. Y1 - 2004 UR - http://www.agnld.uni-potsdam.de/~bernd/papers/JPlankR1.pdf ER - TY - JOUR A1 - Pasternak, Zohar A1 - Blasius, Bernd A1 - Abelson, Avigdor A1 - Achituv, Yair T1 - Host-finding behaviour and navigation capabilities of symbiotic zooxanthellae N2 - Past studies have shown that the initiation of symbiosis between the Red-Sea soft coral Heteroxenia fuscescens and its symbiotic dinoflagellates occurs due to the chemical attraction of the motile algal cells to substances emanating from the coral polyps. However, the resulting swimming patterns of zooxanthellae have not been previously studied. This work examined algal swimming behaviour, host location and navigation capabilities under four conditions: (1) still water, (2) in still water with waterborne host attractants, (3) in flowing water, and (4) in flow with host attractants. Algae were capable of actively and effectively locating their host in still water as well as in flow. When in water containing host attractants, swimming became slower, motion patterns straighter and the direction of motion was mainly towards the host-even if this meant advancing upstream against flow velocities of up to 0.5 mm s(-1)supercript stop. Coral-algae encounter probability decreased the further downstream of the host algae were located, probably due to diffusion of the chemical signal. The results show how the chemoreceptive zooxanthellae modify their swimming pattern, direction, velocity, circuity and turning rate to accommodate efficient navigation in changing environmental conditions Y1 - 2006 UR - http://www.springerlink.com/content/100407 U6 - https://doi.org/10.1007/s00338-005-0085-2 ER - TY - JOUR A1 - Pasternak, Zohar A1 - Blasius, Bernd A1 - Abelson, Avigdor A1 - Achituv, Yair T1 - Host-location in flow by larvae of the symbiotic barnacle Savignium dentatum using odor-gated rheotaxis N2 - The detection and location of specific organisms in the aquatic environment, whether they are mates, prey or settlement sites, are two of the most important challenges facing aquatic animals. Large marine invertebrates such as a lobster have been found to locate specific organisms by navigating in the plume of chemicals emitted by the target. However, active plume tracking in flow by small organisms such as a marine larvae has recieved little scientific attention. Here, we present results from a study examining host location in flow by nauplius larvae of the barnacle Trevathana dentata, which inhabits the stony reef coral Cyphastrea chalcidicium.The experiments included analysis of larval motion in an annular flume under four conditions: (i) still water, (ii) in flow, (iii) in still water with waterborne host metabolites and (iv) in flow with host metabolites. Our results show that T. dentata nauplii are unable to locate their target organism in still water using chemotaxis, but are capable of efficient host location in flow using odour-gated rheotaxis. This technique may enable host location by earlier, less-developed larval stages. Y1 - 2004 UR - http://www.agnld.uni-potsdam.de/~bernd/papers/ProcRoySoc4.pdf ER - TY - JOUR A1 - Mittler, Udo A1 - Blasius, Bernd A1 - Gaedke, Ursula A1 - Ryabov, Alexey B. T1 - Length-volume relationship of lake phytoplankton JF - Limnology and Oceanography: Methods N2 - The shapes of phytoplankton units (unicellular organisms and colonies) are extremely diverse, and no unique relationship exists between their volume, V, and longest linear dimension, L. However, an approximate scaling between these parameters can be found because the shape variations within each size class are constrained by cell physiology, grazing pressure, and optimality of resource acquisition. To determine this scaling and to test for its seasonal and interannual variation under changing environmental conditions, we performed weighted regression analysis of time-dependent length-volume relations of the phytoplankton community in large deep Lake Constance from 1979 to 1999. We show that despite a large variability in species composition, the V(L) relationship can be approximated as a power law, V similar to L-alpha, with a scaling exponent alpha = 3 for small cells (L < 25 mu m) and alpha = 1.7 if the fitting is performed over the entire length range, including individual cells and colonies. The best description is provided by a transitional power function describing a regime change from a scaling exponent of 3 for small cells to an exponent of 0.4 in the range of large phytoplankton. Testing different weighted fitting approaches we show that remarkably the best prediction of the total community biovolume from measurements of L and cell density is obtained when the regression is weighted with the squares of species abundances. Our approach should also be applicable to other systems and allows converting phytoplankton length distributions (e.g., obtained with automatic monitoring such as flow cytometry) into distributions of biovolume and biovolume-related phytoplankton traits. Y1 - 2018 U6 - https://doi.org/10.1002/lom3.10296 SN - 1541-5856 VL - 17 IS - 1 SP - 58 EP - 68 PB - Wiley CY - Hoboken ER - TY - JOUR A1 - Blasius, Bernd A1 - Rudolf, Lars A1 - Weithoff, Guntram A1 - Gaedke, Ursula A1 - Fussmann, Gregor F. T1 - Long-term cyclic persistence in an experimental predator-prey system JF - Nature : the international weekly journal of science N2 - Predator-prey cycles rank among the most fundamental concepts in ecology, are predicted by the simplest ecological models and enable, theoretically, the indefinite persistence of predator and prey(1-4). However, it remains an open question for how long cyclic dynamics can be self-sustained in real communities. Field observations have been restricted to a few cycle periods(5-8) and experimental studies indicate that oscillations may be short-lived without external stabilizing factors(9-19). Here we performed microcosm experiments with a planktonic predator-prey system and repeatedly observed oscillatory time series of unprecedented length that persisted for up to around 50 cycles or approximately 300 predator generations. The dominant type of dynamics was characterized by regular, coherent oscillations with a nearly constant predator-prey phase difference. Despite constant experimental conditions, we also observed shorter episodes of irregular, non-coherent oscillations without any significant phase relationship. However, the predator-prey system showed a strong tendency to return to the dominant dynamical regime with a defined phase relationship. A mathematical model suggests that stochasticity is probably responsible for the reversible shift from coherent to non-coherent oscillations, a notion that was supported by experiments with external forcing by pulsed nutrient supply. Our findings empirically demonstrate the potential for infinite persistence of predator and prey populations in a cyclic dynamic regime that shows resilience in the presence of stochastic events. Y1 - 2019 U6 - https://doi.org/10.1038/s41586-019-1857-0 SN - 0028-0836 SN - 1476-4687 VL - 577 IS - 7789 SP - 226 EP - 230 PB - Nature Publ. Group CY - London ER - TY - JOUR A1 - Gross, Thilo A1 - Allhoff, Korinna Theresa A1 - Blasius, Bernd A1 - Brose, Ulrich A1 - Drossel, Barbara A1 - Fahimipour, Ashkaan K. A1 - Guill, Christian A1 - Yeakel, Justin D. A1 - Zeng, Fanqi T1 - Modern models of trophic meta-communities JF - Philosophical transactions of the Royal Society of London : B, Biological sciences N2 - Dispersal and foodweb dynamics have long been studied in separate models. However, over the past decades, it has become abundantly clear that there are intricate interactions between local dynamics and spatial patterns. Trophic meta-communities, i.e. meta-foodwebs, are very complex systems that exhibit complex and often counterintuitive dynamics. Over the past decade, a broad range of modelling approaches have been used to study these systems. In this paper, we review these approaches and the insights that they have revealed. We focus particularly on recent papers that study trophic interactions in spatially extensive settings and highlight the common themes that emerged in different models. There is overwhelming evidence that dispersal (and particularly intermediate levels of dispersal) benefits the maintenance of biodiversity in several different ways. Moreover, some insights have been gained into the effect of different habitat topologies, but these results also show that the exact relationships are much more complex than previously thought, highlighting the need for further research in this area. This article is part of the theme issue 'Integrative research perspectives on marine conservation'. KW - dispersal KW - meta-community KW - foodweb Y1 - 2020 U6 - https://doi.org/10.1098/rstb.2019.0455 SN - 0962-8436 SN - 1471-2970 VL - 375 IS - 1814 PB - Royal Society CY - London ER - TY - JOUR A1 - Toenjes, Ralf A1 - Blasius, Bernd T1 - Perturbation analysis of complete synchronization in networks of phase oscillators N2 - The behavior of weakly coupled self-sustained oscillators can often be well described by phase equations. Here we use the paradigm of Kuramoto phase oscillators which are coupled in a network to calculate first- and second-order corrections to the frequency of the fully synchronized state for nonidentical oscillators. The topology of the underlying coupling network is reflected in the eigenvalues and eigenvectors of the network Laplacian which influence the synchronization frequency in a particular way. They characterize the importance of nodes in a network and the relations between them. Expected values for the synchronization frequency are obtained for oscillators with quenched random frequencies on a class of scale-free random networks and for a Erdoumls-Reacutenyi random network. We briefly discuss an application of the perturbation theory in the second order to network structural analysis. Y1 - 2009 UR - http://pre.aps.org/ U6 - https://doi.org/10.1103/Physreve.80.026202 SN - 1539-3755 ER - TY - JOUR A1 - Toenjes, Ralf A1 - Blasius, Bernd T1 - Perturbation analysis of the Kuramoto phase-diffusion equation subject to quenched frequency disorder N2 - The Kuramoto phase-diffusion equation is a nonlinear partial differential equation which describes the spatiotemporal evolution of a phase variable in an oscillatory reaction-diffusion system. Synchronization manifests itself in a stationary phase gradient where all phases throughout a system evolve with the same velocity, the synchronization frequency. The formation of concentric waves can be explained by local impurities of higher frequency which can entrain their surroundings. Concentric waves in synchronization also occur in heterogeneous systems, where the local frequencies are distributed randomly. We present a perturbation analysis of the synchronization frequency where the perturbation is given by the heterogeneity of natural frequencies in the system. The nonlinearity in the form of dispersion leads to an overall acceleration of the oscillation for which the expected value can be calculated from the second-order perturbation terms. We apply the theory to simple topologies, like a line or sphere, and deduce the dependence of the synchronization frequency on the size and the dimension of the oscillatory medium. We show that our theory can be extended to include rotating waves in a medium with periodic boundary conditions. By changing a system parameter, the synchronized state may become quasidegenerate. We demonstrate how perturbation theory fails at such a critical point. Y1 - 2009 UR - http://pre.aps.org/ U6 - https://doi.org/10.1103/Physreve.79.016112 SN - 1539-3755 ER -