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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.
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.
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.
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.
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.
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.
We study the pattern formation in a lattice of locally coupled phase oscillators with quenched disorder. In the synchronized regime quasi regular concentric waves can arise which are induced by the disorder of the system. Maximal regularity is found at the edge of the synchronization regime. The emergence of the concentric waves is related to the symmetry breaking of the interaction function. An explanation of the numerically observed phenomena is given in a one- dimensional chain of coupled phase oscillators. Scaling properties, describing the target patterns are obtained.
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.
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.