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 - 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 - Steuer, Ralf A1 - Gross, Thilo A1 - Selbig, Joachim A1 - Blasius, Bernd T1 - Structural kinetic modeling of metabolic networks JF - Proceedings of the National Academy of Sciences of the United States of America N2 - To develop and investigate detailed mathematical models of metabolic processes is one of the primary challenges in systems biology. However, despite considerable advance in the topological analysis of metabolic networks, kinetic modeling is still often severely hampered by inadequate knowledge of the enzyme-kinetic rate laws and their associated parameter values. Here we propose a method that aims to give a quantitative account of the dynamical capabilities of a metabolic system, without requiring any explicit information about the functional form of the rate equations. Our approach is based on constructing a local linear model at each point in parameter space, such that each element of the model is either directly experimentally accessible or amenable to a straightforward biochemical interpretation. This ensemble of local linear models, encompassing all possible explicit kinetic models, then allows for a statistical exploration of the comprehensive parameter space. The method is exemplified on two paradigmatic metabolic systems: the glycolytic pathway of yeast and a realistic-scale representation of the photosynthetic Calvin cycle. KW - systems biology KW - computational biochemistry KW - metabolomics KW - metabolic regulation KW - biological robustness Y1 - 2006 U6 - https://doi.org/10.1073/pnas.0600013103 SN - 0027-8424 SN - 1091-6490 VL - 103 IS - 32 SP - 11868 EP - 11873 PB - National Academy of Sciences CY - Washington 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 - 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 - 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 - 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 - 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 - Blasius, Bernd A1 - Toenjes, Ralf T1 - Zipf's Law in the popularity distribution of chess openings N2 - We perform a quantitative analysis of extensive chess databases and show that the frequencies of opening moves are distributed according to a power law with an exponent that increases linearly with the game depth, whereas the pooled distribution of all opening weights follows Zipf's law with universal exponent. We propose a simple stochastic process that is able to capture the observed playing statistics and show that the Zipf law arises from the self-similar nature of the game tree of chess. Thus, in the case of hierarchical fragmentation the scaling is truly universal and independent of a particular generating mechanism. Our findings are of relevance in general processes with composite decisions. Y1 - 2009 UR - http://prl.aps.org/ U6 - https://doi.org/10.1103/Physrevlett.103.218701 SN - 0031-9007 ER -