  With the influx of complex and detailed tracking data gathered from
electronic tracking devices, the analysis of animal movement data has recently
emerged as a cottage industry amongst biostatisticians. New approaches of ever
greater complexity are continue to be added to the literature. In this paper,
we review what we believe to be some of the most popular and most useful
classes of statistical models used to analyze individual animal movement data.
Specifically we consider discrete-time hidden Markov models, more general
state-space models and diffusion processes. We argue that these models should
be core components in the toolbox for quantitative researchers working on
stochastic modelling of individual animal movement. The paper concludes by
offering some general observations on the direction of statistical analysis of
animal movement. There is a trend in movement ecology toward what are arguably
overly-complex modelling approaches which are inaccessible to ecologists,
unwieldy with large data sets or not based in mainstream statistical practice.
Additionally, some analysis methods developed within the ecological community
ignore fundamental properties of movement data, potentially leading to
misleading conclusions about animal movement. Corresponding approaches, e.g.
based on L\'evy walk-type models, continue to be popular despite having been
largely discredited. We contend that there is a need for an appropriate balance
between the extremes of either being overly complex or being overly simplistic,
whereby the discipline relies on models of intermediate complexity that are
usable by general ecologists, but grounded in well-developed statistical
practice and efficient to fit to large data sets.
