More on the meanderings of mangabeys: how to test whether bounded walks are random

Abstract

1.  Barrett & Lowen (1998) and Waser (1976) attempted to explain the net monthly and yearly displacements of Grey-Cheeked Mangabeys using observed short-term step lengths and assuming a random walk, with and without boundaries. This paper reanalyses their data.

2. Analytic approaches require the root-mean-square step length, not the mean. However, a more flexible approach to making and testing predictions is Monte-Carlo simulation. With a random walk long-term displacements have a large variance, so a single observation is unlikely to disprove this null hypothesis.

3. Restricting movement to a square lattice is a reasonable approximation even when rectangular boundaries are incorporated. Describing the boundary configuration accurately is more important.

4. The observed non-uniformity in turning angles should have been incorporated as it has a large effect on predicted net displacements, unless the arena is tightly constricted. Randomness of movement within a day can be distinguished from that between days. For Waser's population it makes sense to predict long-term displacements using only long-distance daily displacements.

5. There are better approaches to establish both whether boundaries exist and whether movements follow a random walk.