Article

Modeling Vortex Swarming In Daphnia

ETH Zurich, Chair of Systems Design, Kreuzplatz 5, CH-8032 Zurich, Switzerland.
Bulletin of Mathematical Biology (Impact Factor: 1.39). 03/2007; 69(2):539-62. DOI: 10.1007/s11538-006-9135-3
Source: PubMed

ABSTRACT

Based on experimental observations in Daphnia, we introduce an agent-based model for the motion of single and swarms of animals. Each agent is described by a stochastic equation that also considers the conditions for active biological motion. An environmental potential further reflects local conditions for Daphnia, such as attraction to light sources. This model is sufficient to describe the observed cycling behavior of single Daphnia. To simulate vortex swarming of many Daphnia, i.e. the collective rotation of the swarm in one direction, we extend the model by considering avoidance of collisions. Two different ansatzes to model such a behavior are developed and compared. By means of computer simulations of a multi-agent system we show that local avoidance - as a special form of asymmetric repulsion between animals - leads to the emergence of a vortex swarm. The transition from uncorrelated rotation of single agents to the vortex swarming as a function of the swarm size is investigated. Eventually, some evidence of avoidance behavior in Daphnia is provided by comparing experimental and simulation results for two animals.

Download full-text

Full-text

Available from: Frank Schweitzer
  • Source
    • "Paper [24] deals with plasma kinetic theory to derive the corresponding hydrodynamic equation for the density of Daphnicle. An interesting agent-based stochastic model of vortex swarming in Daphnia has been proposed in [22]. A cell– based model has been considered in [35] and the effect of social interactions between cells has been described. "
    [Show abstract] [Hide abstract]
    ABSTRACT: The present paper deals with the modeling of formation and destruction of swarms using a nonlinear Boltzmann–like equation. We introduce a new model that contains parameters characterizing the attractiveness or repulsiveness of individuals. The model can represent both gregarious and solitarious behaviors. In the latter case we provide a mathematical analysis in the space homogeneous case. Moreover we identify relevant hydrodynamic limits on a formal way. We introduce some preliminary results in the case of gregarious behavior and we indicate open problems for further research. Finally , we provide numerical simulations to illustrate the ability of the model to represent formation or destruction of swarms.
    Full-text · Article · Jan 2014 · Kinetic and Related Models
  • Source
    • "The high concentration of nutrients attracts individuals and repulsive forces between individuals, as well as the turning behaviour towards high nutrient concentrations (see fi,2(t) above), cause the aggregation and circular motion of individuals in our simulations. Previous theoretical work has already demonstrated that self-propelled individuals readily form vortices around attractive potentials, even with minimal interactions between individuals [26], [31]. This result serves to illustrate that non-homogeneous nutrient distributions can affect the movement dynamics and we further discuss this below. "
    [Show abstract] [Hide abstract]
    ABSTRACT: Taking in sufficient quantities of nutrients is vital for all living beings and in doing so, individuals interact with the local resource environment. Here, we focus explicitly on the interactions between feeding individuals and the resource landscape. In particular, we are interested in the emergent movement dynamics resulting from these interactions. We present an individual-based simulation model for the movement of populations in a resource landscape that allows us to vary the strength of the interactions mentioned above. The key assumption and novelty of our model is that individuals can cause the release of additional nutrients, as well as consuming them. Our model produces clear predictions. For example, we expect more tortuous individual movement paths and higher levels of aggregation in populations occupying homogeneous environments where individual movement makes more nutrients available. We also show how observed movement dynamics could change when local nutrient sources are depleted or when the population density increases. Our predictions are testable and qualitatively reproduce the different feeding behaviours observed in filter-feeding ducks, for example. We suggest that considering two-way interactions between feeding individuals and resource landscapes could help to explain fine-scale movement dynamics.
    Full-text · Article · Oct 2013 · PLoS ONE
  • Source
    • "Swarms, also called herds, flocks, schools, clusters depending on whether they refer, respectively, to insects, mammals, birds, fish, bacteria and cells are often observed in nature. The typical examples are herds of sheep, flocks of birds or schools of fish (see References in [3] and [11] [19] [29] [30]). "
    [Show abstract] [Hide abstract]
    ABSTRACT: In the present paper the macroscopic limits of the kinetic model for inter-acting entities (individuals, organisms, cells) are studied. The kinetic model is one-dimensional and entities are characterized by their position and orientation (+/-) with swarming interaction controlled by the sensitivity parameter. The macroscopic limits of the model are considered for solutions close either to the diffusive (isotropic) or to the aligned (swarming) equilibrium states for various sensitivity parameters. In the former case the classical linear difusion equation results whereas in the latter a traveling wave solution does both in the zeroth (`Euler') and frst (`Navier-Stokes') order of approximation.
    Full-text · Article · Jul 2012 · Mathematical Models and Methods in Applied Sciences
Show more