The Weierstrassian movement patterns of snails (original) (raw)
Related papers
From Random Walk to Multifractal Random Walk in Zooplankton Swimming Behavior
2004
From random walk to multifractal random walk in zooplankton swimming behavior. Zoological Studies 43(2): 498-510. Herein, we investigate the statistical properties of the swimming behavior of two of the most common freshwater and marine zooplankters, the cladoceran, Daphnia pulex, and the copepod, Temora longicornis. Both species undergo a very structured type of trajectory, with successive moves displaying intermittent amplitudes. We present an original statistical procedure, derived from the fields of turbulence and anomalous diffusion and specifically devoted to the characterization of intermittent patterns. We then show that the swimming paths belong to multifractal random walks", characterized by a nonlinear moment scaling function for distance versus time. This clearly differs from the traditional Brownian and fractional Brownian walks expected or previously detected in animal behaviors. More specifically, we have identified differential behaviors in the horizontal and vertical planes. This suggests the existence of reminiscence of diel vertical migration as a predator-avoidance strategy or differential swimming behaviors related to mating, feeding, or predator-avoidance strategies. We also compare the structure of the swimming paths to the multifractal behavior of microscale phytoplankton distributions demonstrated in turbulent environments, and briefly discuss the potential causes of the observed differences between D. pulex and T. longicornis swimming behaviors.
Levy Walks Evolve Through Interaction Between Movement and Environmental Complexity
Science, 2011
Ecological theory predicts that animal movement is shaped by its efficiency of resource acquisition. Focusing solely on efficiency, however, ignores the fact that animal activity can affect resource availability and distribution. Here, we show that feedback between individual behavior and environmental complexity can explain movement strategies in mussels. Specifically, experiments show that mussels use a Lévy walk during the formation of spatially patterned beds, and models reveal that this Lévy movement accelerates pattern formation. The emergent patterning in mussel beds, in turn, improves individual fitness. These results suggest that Lévy walks evolved as a result of the selective advantage conferred by autonomously generated, emergent spatial patterns in mussel beds. Our results emphasize that an interaction between individual selection and habitat complexity shapes animal movement in natural systems.
Chaos and fractals in fish school motion
Chaos, Solitons & Fractals, 2001
The once abstract notions of fractal patterns and processes now appear naturally and inevitably in various chaotic dynamical systems. The examples range from Brownian motion [1±5] to the dynamics of social relations [6]. In this paper, after introducing a certain hybrid mathematical model of the plankton±®sh school interplay, we study the fractal properties of the model ®sh school walks. We show that the complex planktivorous ®sh school motion is dependent on the ®sh predation rate. A decrease in the rate is followed by a transition from low-persistent to high-persistent ®sh school walks, i.e., from a motion with frequent to a motion with few changes of direction. The low-persistent motion shows fractal properties for all time scales, whereas the high-persistent motion has pronounced multifractal properties for large-scale displacements.
2004
Active Brownian Particles are self-propelled particles that move in a dissipative medium subject to random forces, or "noise". Additionally, they can be confined by an external field and/or they can interact with one another. The external field may actually be an attractive marker, for example a light field (as in the experiment) or an energy potential or a chemical gradient (as in the theory). The potential energy can also be the result of interparticle attractive and/or repulsive forces summed over all particles (a mean field potential). Four, qualitatively different motions of the particles are possible: at small particle density their motions are approximately independent of one another subject only to the external field and the noise, which results in moving randomly through or performing rotational motions about a central point in space. At increasing densities interactions play an important role and individuals form a swarm performing several types of self-organized collective motion. We apply this model for the description of zooplankton Daphnia swarms. In the case of the zooplankton Daphnia (and probably many other aquatic animals that form similar motions as well) this vortex is hydrodynamical but motivated by the self-propelled motion of the individuals. Similar vortex-type motions have been observed for other creatures ranging in size from bacteria to flocks of birds and schools of fish. However, our experiment with Daphnia is unique in that all four motions can be observed in controlled laboratory conditions with the same animal. Moreover, the theory, presented in both continuous differential equation and random walk forms, offers a quantitative, physically based explanation of the four motions.
Theoretical analysis of rhythmical clustering in an intertidal gastropod
Ecological Modelling, 1989
As do many other molluscs inhabiting rocky shores, the intertidal snail Nerita textilis Gmelin exhibits very important stress-reducing behaviour, the collective homing lo sheltered locations of the cliff via inter-individual trail-following. The aggregated population of snails présents, in this species, a semilunar rhythm reaching maximum around neap tide and minimum after spring tide. This paper proposes a mathematical model of this behaviour, which takes into account ihe trail-following mechanism, the effect of cliff morphology and the semilunar rhythm. The results show the effects that différent population densities and tidal amplitudes have on the numbers of aggregated snails. They permit a discussion of the snails' response lo the environmental signal. The model reliability is also discussed, using field observations on a S omalian population of this species. Finally, the utihty of the model in the estimation of parameter values is considered.
Scientific Reports, 2013
Correlated random walks are the dominant conceptual framework for modelling and interpreting organism movement patterns. Recent years have witnessed a stream of high profile publications reporting that many organisms perform Lévy walks; movement patterns that seemingly stand apart from the correlated random walk paradigm because they are discrete and scale-free rather than continuous and scale-finite. Our new study of the movement patterns of Tenebriomolitor beetles in unchanging, featureless arenas provides the first empirical support for a remarkable and deep theoretical synthesis that unites correlated random walks and Lévy walks. It demonstrates that the two models are complementary rather than competing descriptions of movement pattern data and shows that correlated random walks are a part of the Lévy walk family. It follows from this that vast numbers of Lévy walkers could be hiding in plain sight.
As noted by Hao Bai-Lin in the preface to his admirable collection of in¯uential papers on nonlinear dynamics, the discovery of chaos in ecological dierence equations, as much as anything else, fertilized a¯owering of interest in this subject some twenty-®ve years ago. Perhaps not surprisingly, it was in the physical, as opposed to the biological, sciences that``chaos theory'', as it is often (and inaccurately!) referred to, really took hold. In ecology itself, the ubiquity of chaos and other non-linear phenomena in both discrete and continuous models was subsequently con®rmed 1 [1,3,4,9,27,34,46,57,70±72]. At the same time, convincing evidence for chaos in natural systems proved harder to come by . For example, in the case of pre-vaccination epidemics of measles in large, ®rst world cities, what was once judged [63] to be one of the more likely examples of real-world ecological chaos, is now the subject of divergent opinion .