Plankton predation rates in turbulence: A study of the limitations imposed on a predator with a non-spherical field of sensory perception

Hydrodynamic and biological constraints on group cohesion in plankton

The dynamics of plankton in the ocean are determined by biophysical interactions. Although physics and biotic behaviors are known to influence the observed patchiness of planktonic populations, it is still unclear how much, and if, group behavior contributes to this biophysical interaction. Here, we demonstrate how simple rules of behavior can enhance or inhibit active group cohesion in plankton in a turbulent environment. In this study, we used coral-reef fish larvae as a model to investigate the interaction between microscale turbulence and planktonic organisms. We synthesized available information on the swimming speeds and sizes of reef fish larvae, and developed a set of equations to investigate the effects of viscosity and turbulence on larvae dispersion. We then calculated the critical dispersion rates for three different swimming strategies - cruise, random-walk, and pause-travel - to determine which strategies could facilitate group cohesion during dispersal. Our results indicate that swimming strategies and migration to low-turbulence regions are the key to maintaining group cohesion, suggesting that many reef fish species have the potential to remain together, from hatching to settlement. In addition, larvae might change their swimming strategies to maintain group cohesion, depending on environmental conditions and/or their ontogenic stage. This study provides a better understanding of the hydrodynamic and biological constraints on group formation and cohesion in planktonic organisms, and reveals a wide range of conditions under which group formation may occur.

Transit times in turbulent flows

Statistics of the motion of passively convected point particles in turbulent flows are studied. The database used is obtained by direct numerical solution of the Navier-Stokes equation. We estimate the probability distribution of the transit times of such particles through reference volumes with given forms and sizes. A selected position within the reference volume is moving with the local flow velocity, thus determining the motion of the entire surface. The transit time is defined as the interval between entrance and exit times of surrounding particles convected through the volume by the turbulent motions. Spherical as well as hemispherical surfaces are studied. Scale sizes in the inertial as well as in the viscous subranges of the turbulence are considered. Simple, and seemingly universal, scaling laws are obtained for the probability density of the transit times in terms of the basic properties of the turbulent flow and the geometry. In the present formulation, the results of the analysis are relevant for chemical reactions, but also for understanding details of the feeding rate of micro-organisms in turbulent waters, for instance.

On the relationship between fractal dimension and encounters in three-dimensional trajectories

The encounter of individuals-prey, predators and mates-living in the surrounding environment is a fundamental process in the life of an organism. Along with the sensory abilities, this process will be regulated by the movement rules adopted by the individual. In this work we discuss the encounter-enhancement effect due to different natatorial modes by calculating the number of encounters realised by differently convoluted trajectories in two homogeneous distributions of particles. Using numerically generated trajectories representative of specific swimming behaviour, we demonstrate that high values of three-dimensional fractal dimension D(3D)(>1.9) are beneficial only at high concentration, whereas at low concentration less tortuous tracks (D(3D) approximately 1.5) are almost equally efficient. In the light of our results it is possible to better understand the behavioural adaptations evolved by individuals to thrive in their environment.