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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
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.
Complex transient dynamics of stage-structured populations in response to environmental changes
(2013)
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.
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.
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.
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.
Host location by larvae of a parasitic barnacle: larval chemotaxis and plume tracking in flow
(2004)
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.
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