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More on the meanderings of mangabeys: how to test whether bounded walks are random
Author(s) -
Hutchinson J. M. C.
Publication year - 2000
Publication title -
functional ecology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.272
H-Index - 154
eISSN - 1365-2435
pISSN - 0269-8463
DOI - 10.1046/j.1365-2435.2000.00407.x
Subject(s) - random walk , randomness , statistical physics , boundary (topology) , bounded function , term (time) , mathematics , monte carlo method , random walker algorithm , population , statistics , mathematical analysis , physics , demography , quantum mechanics , sociology
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.