When Do Treatment Differences in Movement Behaviors Produce Observable Differences in Long‐Term Displacements?

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Movement behaviors are of central importance to the biology of many organisms, and there are many studies that examine the effects of experimental treatments on such movement parameters as the average direction and distance moved. However, thee are few studies that address explicitly the long—term consequences of treatment differences in movement parameters. Instead, it is often assumed that treatment differences in movement parameters will extend, over long periods of time, into treatment differences in long—term, net displacements from a point of origin. I use diffusion models to show that this assumption is not necessarily correct, thus indicating that treatment differences in movement behaviors should be interpreted with caution. In addition, for organisms whose long—term movements can be represented by simple diffusion, I provide formulae that allow calculation of whether treatment effects on movement parameters would be likely to produce treatment differences in long—term displacements. I illustrate these analyses with computer simulations and with data concerning the spread of clonal plants, and I use published values of the diffusion coefficient to help place my results in an ecological context.