We statistically analyze experimental data of two types of systems
exhibiting biological motion and construct stochastic models
reproducing their dynamics. First, we study the experimentally
observed trajectories of single kidney cells crawling on
substrates. We find a superdiffusive increase of the mean squared
displacement, non-Gaussian probability distributions of the positions
and power-law decays of the velocity autocorrelations. These
experimental findings are reproduced from a fractional Klein-Kramers
equation generating anomalous diffusion [1]. We then 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 thus contained in the velocity autocorrelation functions, as is
reproduced from a generalized Langevin equation [2].