Statistical distributions and modelling of GPS-Telemetry elephant movement data including the effect of covariates.
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Abstract
In this thesis, I investigate the application of various statistical methods towards
analysing GPS tracking data collected using GPS collars placed on large mammals
in Kruger National Park, South Africa. Animal movement tracking is a rapidly
advancing area of ecological research and large amount of data is being collected,
with short sampling intervals between successive locations. A statistical challenge
is to determine appropriate methods that capture most properties of the data
is lacking despite the obvious importance of such information to understanding
animal movement. The aim of this study was to investigate appropriate alter-
native models and compare them with the existing approaches in the literature
for analysing GPS tracking data and establish appropriate statistical approaches
for interpreting large scale mega-herbivore movements patterns. The focus was
on which methods are the most appropriate for the linear metrics (step length
and movement speed) and circular metrics (turn angles) for these animals and
the comparison of the movement patterns across herds with covariate. A four
parameter family of stable distributions was found to better describe the animal
movement linear metrics as it captured both skewness and heavy tail properties of
the data. The stable model performed favourably better than normal, Student's t
and skewed Student's t models in an ARMA-GARCH modelling set-up. The
ex-
ibility of the stable distribution was further demonstrated in a regression model
and compared with the heavy tailed t regression model. We also explore the ap-
plication circular linear regression model in analysing animal turn angle data with
covariate. A regression model assuming Von Mises distributed turn angles was
shown to fit the data well and further areas of model development highlighted. A couple of methods for testing the uniformity hypothesis of turn angles are pre-
sented. Finally, we model the linear metrics assuming the error terms are stable
distributed and the turn angles assuming the error terms are von Mises distributed
are recommended for analysing animal movement data with covariate.
Description
Ph. D. University of KwaZulu-Natal, Pietermaritzburg 2015.
Keywords
Distribution (Probability theory), Global Positioning System., Animal navigation., Theses -- Statistics.