@article{WichmannJohstSchwageretal.2005, author = {Wichmann, Matthias and Johst, Karin and Schwager, Monika and Jeltsch, Florian and Blasius, Bernd}, title = {Extinction risk, coloured noise and the scaling of variance}, year = {2005}, abstract = {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.}, language = {en} } @article{ToenjesBlasius2009, author = {T{\"o}njes, Ralf and Blasius, Bernd}, title = {Perturbation analysis of the Kuramoto phase-diffusion equation subject to quenched frequency disorder}, issn = {1539-3755}, doi = {10.1103/Physreve.79.016112}, year = {2009}, abstract = {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.}, language = {en} } @article{ToenjesBlasius2009, author = {T{\"o}njes, Ralf and Blasius, Bernd}, title = {Perturbation analysis of complete synchronization in networks of phase oscillators}, issn = {1539-3755}, doi = {10.1103/Physreve.80.026202}, year = {2009}, abstract = {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.}, language = {en} } @article{SteuerGrossSelbigetal.2006, author = {Steuer, Ralf and Gross, Thilo and Selbig, Joachim and Blasius, Bernd}, title = {Structural kinetic modeling of metabolic networks}, series = {Proceedings of the National Academy of Sciences of the United States of America}, volume = {103}, journal = {Proceedings of the National Academy of Sciences of the United States of America}, number = {32}, publisher = {National Academy of Sciences}, address = {Washington}, issn = {0027-8424}, doi = {10.1073/pnas.0600013103}, pages = {11868 -- 11873}, year = {2006}, abstract = {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.}, language = {en} } @article{SeebensEsslDawsonetal.2015, author = {Seebens, Hanno and Essl, Franz and Dawson, Wayne and Fuentes, Nicol and Moser, Dietmar and Pergl, Jan and Pysek, Petr and van Kleunen, Mark and Weber, Ewald and Winter, Marten and Blasius, Bernd}, title = {Global trade will accelerate plant invasions in emerging economies under climate change}, series = {Global change biology}, volume = {21}, journal = {Global change biology}, number = {11}, publisher = {Wiley-Blackwell}, address = {Hoboken}, issn = {1354-1013}, doi = {10.1111/gcb.13021}, pages = {4128 -- 4140}, year = {2015}, abstract = {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.}, language = {en} } @article{PasternakBlasiusAbelsonetal.2006, author = {Pasternak, Zohar and Blasius, Bernd and Abelson, Avigdor and Achituv, Yair}, title = {Host-finding behaviour and navigation capabilities of symbiotic zooxanthellae}, doi = {10.1007/s00338-005-0085-2}, year = {2006}, abstract = {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}, language = {en} } @article{PasternakBlasiusAbelsonetal.2004, author = {Pasternak, Zohar and Blasius, Bernd and Abelson, Avigdor and Achituv, Yair}, title = {Host-location in flow by larvae of the symbiotic barnacle Savignium dentatum using odor-gated rheotaxis}, year = {2004}, abstract = {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.}, language = {en} } @article{PasternakBlasiusAbelson2004, author = {Pasternak, Zohar and Blasius, Bernd and Abelson, Avigdor}, title = {Host location by larvae of a parasitic barnacle: larval chemotaxis and plume tracking in flow}, year = {2004}, abstract = {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.}, language = {en} } @article{MontbrioKurthsBlasius2004, author = {Montbrio, Ernest and Kurths, J{\"u}rgen and Blasius, Bernd}, title = {Synchronization of two interacting populations of oscillators}, year = {2004}, abstract = {We analyze synchronization between two interacting populations of different phase oscillators. For the important case of asymmetric coupling functions, we find a much richer dynamical behavior compared to that of symmetrically coupled populations of identical oscillators. It includes three types of bistabilities, higher order entrainment and the existence of states with unusual stability properties. All possible routes to synchronization of the populations are presented and some stability boundaries are obtained analytically. The impact of these findings for neuroscience is discussed.}, language = {en} } @article{MittlerBlasiusGaedkeetal.2018, author = {Mittler, Udo and Blasius, Bernd and Gaedke, Ursula and Ryabov, Alexey B.}, title = {Length-volume relationship of lake phytoplankton}, series = {Limnology and Oceanography: Methods}, volume = {17}, journal = {Limnology and Oceanography: Methods}, number = {1}, publisher = {Wiley}, address = {Hoboken}, issn = {1541-5856}, doi = {10.1002/lom3.10296}, pages = {58 -- 68}, year = {2018}, abstract = {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.}, language = {en} }