Anomalous Diffusion in Ecology

by Mirko Lukovic
Doctoral thesis
Date of Examination:2014-02-06
Date of issue:2015-01-14
Advisor:Prof. Dr. Theo Geisel
Referee:Prof. Dr. Marc Timme
Referee:Prof. Dr. Fred Wolf
Persistent Address: http://dx.doi.org/10.53846/goediss-4861

 

 

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Abstract

English

As measurement techniques improve and increasingly sophisticated analysis methods are more common, biology becomes subject to the wide range of treatments coming from physics. In this thesis, we consider a specific application of this trend, applying the theory of stochastic processes, and of anomalous diffusion processes in particular, to the field of ecology. In both experimental and theoretical ecology there is interest in the estimation of the geographic range over which a single or a group of animals forage in order to better plan habitat conservation. Since the motion of many foraging animals is approximately random, the average area of the convex hulls (minimum convex polygon) enclosing their trajectories can be used as a good estimate of the geographic range. Other applications include determining the spatial extent of an epidemic outbreak among animals and potentially, outside of biology, assessing the area affected by spreading contaminants. We use numerical methods and scaling considerations to determine the properties of convex hulls of super-diffusive processes such as Levy walks. Motivated by the ongoing debate regarding whether or not there exist animals that perform a Levy walk, we propose the use of convex hulls of the home range of animals as a robust and accurate method to discriminate between different types of foraging strategies. Furthermore, because there is growing evidence that human activity is drastically changing the foraging habits of animals, forcing them to adopt sub-diffusive search strategies, we discuss continuous time random walks and their role in ecology. We derive exact analytical expressions for the evolution of the average perimeter and area of the convex hull of this class of non-Markovian sub-diffusive processes.
Keywords: Anomalous diffusion; Movement Ecology; Levy Walk; Continuous Time Random Walk; Random Convex Hull; Home range estimation
 
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