  This book chapter introduces to the problem to which extent search strategies
of foraging biological organisms can be identified by statistical data analysis
and mathematical modeling. A famous paradigm in this field is the Levy Flight
Hypothesis: It states that under certain mathematical conditions Levy flights,
which are a key concept in the theory of anomalous stochastic processes,
provide an optimal search strategy. This hypothesis may be understood
biologically as the claim that Levy flights represent an evolutionary adaptive
optimal search strategy for foraging organisms. Another interpretation,
however, is that Levy flights emerge from the interaction between a forager and
a given (scale-free) distribution of food sources. These hypotheses are
discussed controversially in the current literature. We give examples and
counterexamples of experimental data and their analyses supporting and
challenging them.
