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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.
A combined dynamics consisting of Brownian motion and Levy flights is exhibited by a variety of biological systems performing search processes. Assessing the search reliability of ever locating the target and the search efficiency of doing so economi
Inferring the processes underlying the emergence of observed patterns is a key challenge in theoretical ecology. Much effort has been made in the past decades to collect extensive and detailed information about the spatial distribution of tropical ra
We address the generic problem of random search for a point-like target on a line. Using the measures of search reliability and efficiency to quantify the random search quality, we compare Brownian search with Levy search based on long-tailed jump le
The pace and unpredictability of evolution are critically relevant in a variety of modern challenges: combating drug resistance in pathogens and cancer, understanding how species respond to environmental perturbations like climate change, and develop
Motivated by studies on the recurrent properties of animal and human mobility, we introduce a path-dependent random walk model with long range memory for which not only the mean square displacement (MSD) can be obtained exactly in the asymptotic limi