MODELLING FREE-RANGE CATTLE MOVEMENTS IN FORESTS USING MULTISTATE RANDOM WALKS

In this study multi-state random walk models were tested as general approach to analyse movement states in animal relocation data. For this purpose, GPS collars were fit to free-range cattle inhabiting Andean forests in Patagonia, Argentina. The results indicate that animal trajectories have re-visitation patterns in restricted areas of few kilometres and that a large part of behaviors occur at a time scale lower than six hours. Simple multi-state random walk models proved to be practical in modelling characteristics such as step and turning angles distribution in addition to emergent properties of animal trajectories such as temporal autocorrelation. Re-visitation patterns and the emergence of home-range, among other memory processes could be marked as possible limitations of these models. This work is the first description of free-range cattle movement inhabiting the andean-Patagonian forests in semi-feral conditions.

A note on the asymptotic properties of correlated random walks

We describe a simple relation between the asymptotic behavior of the variance and of the expected number of distinct sites visited during a correlated random walk. The relation is valid for multistate random walks with finite variance in dimensions 1 and 2. A similar relation, valid in all dimensions, exists between the asymptotic behavior of the variance and of the probability of return to the origin.

A note on the asymptotic properties of correlated random walks

We describe a simple relation between the asymptotic behavior of the variance and of the expected number of distinct sites visited during a correlated random walk. The relation is valid for multistate random walks with finite variance in dimensions 1 and 2. A similar relation, valid in all dimensions, exists between the asymptotic behavior of the variance and of the probability of return to the origin.