Animal Movement - Mobility Data - page 282

not relevant to compute the displacement: {+ δ, + δ, − δ, − δ, − δ } is equivalent

to ,etc.

To be more realistic, let us consider a bidimensional space. In many cases it
appears that animal movements are characterized by a directional persistence,
in the sense that animals tend to persist along their previous direction. This is
evident in Path 1 (Figure 13.3 a) displaying the observed movement of a female
fallowdeer. The correlated randomwalk (CRW) is useful to represent directional
persistence. CRW is similar to URW except that directions are correlated. This
means that next steps are more or less oriented toward the same direction (e.g.,
to the north) so that turning angles are close to zero. The CRW represents a
standard model to describe animals' movement (Turchin 1998). For instance,
Paths2and3inFigure 13.3 are more sinuous than Paths 1 and 4.
In some respects CRW appears a more realistic model for the movement
of actual organisms that URW, however, there are some shortcomings in this
approach. First, movement appears more or less sinuous but the amount of
turning is similar (apart stochastic fluctuations) along the path. In the simple
case where the step length d is constant, the sinuosity S =

{− δ, − δ, − δ, + δ, + δ } or {− δ, + δ, − δ, + δ, − δ }

σ
√ d , where σ is the
standard deviation of the angular distribution. However, many animals exhibit
areas where sinuosity is high intermingled with areas where the path is straighter.
This behavior is called area-restricted search (ARS).
However, animal tactics can be more complex to increase search efficiency,
that is, the amount of resources encountered per unit time. The walker intensifies
its search (increases path sinuosity) in areas where the density of targets is likely
to be higher than on average (e.g., in a food patch) and perform more linear
paths while moving among patches. This is represented by Path 4 (Figure 13.3 ).
In fallow deer it is possible to show the presence of area-restricted search by
computing the autocorrelation function of move length or the cross-correlation
between angles and distance. Fallow deer present a positive cross-correlated
function so that large displacements are correlated to turning angles. These
mechanisms allow these animals to remain within a food patch and provide
behavioral mechanisms for ARS.
Semantic trajectories can be used to study the ecology of the species of
interest. In this study on fallow deer we recorded the foraging stations used
by the animals and later we determine the amount of vegetal biomass of each
station. According to optimal foraging theory the animal should leave in each
station a prescribed amount of vegetal biomass. This was indeed observed.
Several models may explain the presence of ARS in one animal's path. Here
we consider two basic, and hence potentially general, approaches to this problem.
The composite CRW (CCRW) derives directly from CRW theory by assuming
that an animal is able to vary its movement parameters ( α i and d i ) as a function
of some specific spatial parameter. The CCRW is also called adaptive CRW.