Spatiotemporal Dynamics of Bumblebees Foraging under Predation Risk

We analyze 3D flight paths of bumblebees searching for nectar in a laboratory experiment with and without predation risk from artificial spiders. For the flight velocities we find mixed probability distributions reflecting the access to the food sources while the threat posed by the spiders shows up only in the velocity correlations. The bumblebees thus adjust their flight patterns spatially to the environment and temporally to predation risk. Key information on response to environmental changes is contained in temporal correlation functions, as we explain by a simple emergent model.

Figure 1

Diagram of the foraging arena together with part of the flight trajectory of a single bumblebee. The bumblebees forage on a grid of artificial flowers on one wall of the box. While being on the landing platforms, the bumblebees have access to food supply. All flowers can be equipped with spider models and trapping mechanisms simulating predation attempts.

Figure 2

Estimated velocity distributions (main part) and quantile-quantile probability plot of a Gaussian mixture as the best fit (inset). Semilogarithmic plot of the normalized histogram of velocities $v_y$ parallel to the $y$ axis in Fig. 1 (black crosses) for a single bumblebee in the spider-free stage (1) together with a Gaussian mixture (red solid line), exponential (blue dotted line), power law (green dashed line), and Gaussian distribution (violet dotted line), fitted via maximum likelihood estimation. The inset shows quantiles of $v_y$ (in $\mathrm{m}/\mathrm{s}$) of a single bumblebee against quantiles of an estimated mixture of two Gaussians. An ideal match would yield a straight line. The red lines show 20 surrogate data sets of the same size.

Figure 3

Autocorrelation of the velocities at different experimental stages: without spiders (red triangles), under threat of predation (green circles), and under threat a day after the last encounter with the spiders (blue crosses). (a) In the $x$ direction perpendicular to the wall the velocities are anticorrelated for small times ($\approx 0.5\mathrm{s}$) due to short flights from one flower to a nearby flower back at the flower wall. Inset: The distribution of flight times $T_f$ for each stage shows a corresponding maximum for these short jumps. Under threat of predation (dotted line) long flights become more frequent. (b) The correlation of $v_y$ parallel to the wall shows the effect of the presence of spiders on the flight behavior of the bumblebees. The inset shows the resampled autocorrelation for the spider-free stage in the region where the correlation differs from the stages with spider models, which confirms that the positive autocorrelations are not a numerical artifact.