|dc.description.abstracteng||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.||de