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

Quantitative comparison of 2D and 3D monitoring dimensions in fish behavior analysis

To improve the accuracy and efficiency of fish behavior assessment, this paper focuses on quantitatively exploring the variations and relationships between different monitoring dimensions. A systematic comparison was conducted between 3D and 2D behavioral factors using an infrared tracing system, during both day and night. Significant differences in swimming distance were observed among the different monitoring methods, as determined by two-way ANOVA and Tukey's test. A correction was applied to account for the disparities observed in 2D swimming distance, ensuring accurate measurements. These findings present a cost-effective and efficient approach for obtaining precise 3D distance data. Additionally, a kinematic factor called the "number of U-turns" was proposed to provide a more intuitive characterization of directional changes in fish swimming. Significant differences were observed between 2D and 3D data, with higher percentages of false U-turn counts and missing U-turn counts compared to correct counts in the 2D view. These findings suggest that reducing the monitoring dimension may impact the accurate estimation of swimming motion, potentially resulting in inaccurate outcomes. Finally, the statistical analyses of the non-linear properties of fractal dimension revealed significant differences among the various monitoring methods. This conclusion has practical implications for biologists and physicists, enabling them to improve the accuracy of behavioral phenotyping for organisms exhibiting 3D motion.

Homeostatic swimming of zooplankton upon crowding: the case of the copepod Centropages typicus

Crowding has a major impact on the dynamics of many material and biological systems, inducing effects as diverse as glassy dynamics and swarming. While this issue has been deeply investigated for a variety of living organisms, more research remains to be done on the effect of crowding on the behaviour of copepods, the most abundant metazoans on Earth. To this aim, we experimentally investigate the swimming behaviour, used as a dynamic proxy of animal adaptations, of males and females of the calanoid copepod Centropages typicus at different densities of individuals (10, 50 and 100 ind. l^-1) by performing three-dimensional single-organism tracking. We find that the C. typicus motion is surprisingly unaffected by crowding over the investigated density range. Indeed, the mean square displacements as a function of time always show a crossover from ballistic to Fickian regime, with poor variations of the diffusion constant on increasing the density. Close to the crossover, the displacement distributions display exponential tails with a nearly density-independent decay length. The trajectory fractal dimension, D_3D ≅ 1.5, and the recently proposed 'ecological temperature' also remain stable on increasing the individual density. This suggests that, at least over the range of animal densities used, crowding does not impact on the characteristics of C. typicus swimming motion, and that a homeostatic mechanism preserves the stability of its swimming performance.

Hydrocarbon contamination decreases mating success in a marine planktonic copepod

The mating behavior and the mating success of copepods rely on chemoreception to locate and track a sexual partner. However, the potential impact of the water-soluble fraction of hydrocarbons on these aspects of copepod reproduction has never been tested despite the widely acknowledged acute chemosensory abilities of copepods. I examined whether three concentrations of the water-soluble fraction of diesel oil (0.01%, 0.1% and 1%) impacts (i) the swimming behavior of both adult males and females of the widespread calanoid copepod Temora longcornis, and (ii) the ability of males to locate, track and mate with females. The three concentrations of the water-soluble fraction of diesel oil (WSF) significantly and non-significantly affect female and male swimming velocities, respectively. In contrast, both the complexity of male and female swimming paths significantly decreased with increasing WSF concentrations, hence suggesting a sex-specific sensitivity to WSF contaminated seawater. In addition, the three WSF concentrations impacted both T. longicornis mating behavior and mating success. Specifically, the ability of males to detect female pheromone trails, to accurately follow trails and to successfully track a female significantly decreased with increasing WSF concentrations. This led to a significant decrease in contact and capture rates from control to WSF contaminated seawater. These results indicate that hydrocarbon contamination of seawater decreases the ability of male copepods to detect and track a female, hence suggest an overall impact on population fitness and dynamics.

Random walk models in biology

Mathematical modelling of the movement of animals, micro-organisms and cells is of great relevance in the fields of biology, ecology and medicine. Movement models can take many different forms, but the most widely used are based on the extensions of simple random walk processes. In this review paper, our aim is twofold: to introduce the mathematics behind random walks in a straightforward manner and to explain how such models can be used to aid our understanding of biological processes. We introduce the mathematical theory behind the simple random walk and explain how this relates to Brownian motion and diffusive processes in general. We demonstrate how these simple models can be extended to include drift and waiting times or be used to calculate first passage times. We discuss biased random walks and show how hyperbolic models can be used to generate correlated random walks. We cover two main applications of the random walk model. Firstly, we review models and results relating to the movement, dispersal and population redistribution of animals and micro-organisms. This includes direct calculation of mean squared displacement, mean dispersal distance, tortuosity measures, as well as possible limitations of these model approaches. Secondly, oriented movement and chemotaxis models are reviewed. General hyperbolic models based on the linear transport equation are introduced and we show how a reinforced random walk can be used to model movement where the individual changes its environment. We discuss the applications of these models in the context of cell migration leading to blood vessel growth (angiogenesis). Finally, we discuss how the various random walk models and approaches are related and the connections that underpin many of the key processes involved.