Constructing a stochastic model of bumblebee flights from experimental data

Bat Motion can be Described by Leap Frogging

We present models of bat motion derived from radio-tracking data collected over 14 nights. The data presents an initial dispersal period and a return to roost period. Although a simple diffusion model fits the initial dispersal motion we show that simple convection cannot provide a description of the bats returning to their roost. By extending our model to include non-autonomous parameters, or a leap frogging form of motion, where bats on the exterior move back first, we find we are able to accurately capture the bat's motion. We discuss ways of distinguishing between the two movement descriptions and, finally, consider how the different motion descriptions would impact a bat's hunting strategy.

Analysis of aligning active local searchers orbiting around their common home position

We discuss effects of pairwise aligning interactions in an ensemble of central place foragers or of searchers that are connected to a common home. In a wider sense, we also consider self-moving entities that are attracted to a central place such as, for instance, the zooplankton Daphnia being attracted to a beam of light. Single foragers move with constant speed due to some propulsive mechanism. They explore at random loops the space around and return rhytmically to their home. In the ensemble, the direction of the velocity of a searcher is aligned to the motion of its neighbors. At first, we perform simulations of this ensemble and find a cooperative behavior of the entities. Above an overcritical interaction strength the trajectories of the searcher qualitatively changes and searchers start to move along circles around the home position. Thereby, all searchers rotate either clockwise or anticlockwise around the central home position as it was reported for the zooplankton Daphnia. At second, the computational findings are analytically explained by the formulation of transport equations outgoing from the nonlinear mean field Fokker-Planck equation of the considered situation. In the asymptotic stationary limit, we find expressions for the critical interaction strength, the mean radial and orbital velocities of the searchers and their velocity variances. We also obtain the marginal spatial and angular densities in the undercritical regime where the foragers behave like individuals as well as in the overcritical regime where they rotate collectively around the considered home. We additionally elaborate the overdamped Smoluchowski-limit for the ensemble.

The prevalence of olfactory- versus visual-signal encounter by searching bumblebees

While the phrase 'foraging bumblebee' brings to mind a bumbling bee flying flower to flower in a sunny meadow, foraging is a complicated series of behaviors such as: locating a floral patch; selecting a flower-type; learning handling skills for pollen and nectar extraction; determining when to move-on from a patch; learning within-patch paths (traplining); and learning efficient hive-to-patch routes (spatial navigation). Thus the term 'forager' encompasses multiple distinct behaviors that rely on different sensory modalities. Despite a robust literature on bumblebee foraging behavior, few studies are directly relevant to sensory-guided search; i.e. how workers locate novel patches. The first step in answering this question is to determine what sensory information is available to searching bumblebees. This manuscript presents a computational model that elucidates the relative frequency of visual and olfactory cues that are available to workers searching for floral resources under a range of ecologically relevant scenarios. Model results indicate that odor is the most common sensory cue encountered during search flights. When the likelihood of odor-plume contact is higher, odor-encounter is ubiquitous. While integrative (visual + olfactory) cues are common when foragers are searching for larger flowers (e.g. Echinacea), they become rare when foragers are searching for small flowers (e.g. Penstemon). Visual cues are only encountered in isolation when foragers are seeking large flowers with a low odor-plume contact probability. These results indicate that despite the multisensory nature of floral signals, different modalities may be encountered in isolation during search-behavior, as opposed to the reliably multimodal signals encountered during patch-exploitation or nectar/ pollen acquisition.

Fractional diffusion equation for an n-dimensional correlated Lévy walk

Lévy walks define a fundamental concept in random walk theory that allows one to model diffusive spreading faster than Brownian motion. They have many applications across different disciplines. However, so far the derivation of a diffusion equation for an n-dimensional correlated Lévy walk remained elusive. Starting from a fractional Klein-Kramers equation here we use a moment method combined with a Cattaneo approximation to derive a fractional diffusion equation for superdiffusive short-range auto-correlated Lévy walks in the large time limit, and we solve it. Our derivation discloses different dynamical mechanisms leading to correlated Lévy walk diffusion in terms of quantities that can be measured experimentally.