Title: Mean squared displacement and sinuosity of three-dimensional random search movements,
Abstract: Correlated random walks (CRW) have been used for a long time as a null model
for animal's random search movement in two dimensions (2D). An increasing
number of studies focus on animals' movement in three dimensions (3D), but the
key properties of CRW, such as the way the mean squared displacement is related
to the path length, are well known only in 1D and 2D. In this paper I derive
such properties for 3D CRW, in a consistent way with the expression of these
properties in 2D. This should allow 3D CRW to act as a null model when
analyzing actual 3D movements similarly to what is done in 2D