7. Movements of individuals
7.1. Introduction and motivation

One of the assumptions of the travel time model described previously (equations (4.7) and (4.8)) is that the movements of individuals follow a Wiener drift process. A restrictive property of this process is that disjoint movement increments are independent, no matter how fine the time scale. Clearly this property is limiting in describing the movement of animals. In the short term, an animal moving at a particular velocity will likely continue at that velocity. In the longer term, however, independent increments may be realistic.

Analyzing group release travel time data, as I have done in previous chapters, cannot confirm the Wiener drift process assumption. With this type of data, information about individual movements is lost, and several different movement processes could produce similar arrival distributions. To overcome these limitations, I analyze the movements of juvenile salmonids observed in radio-tracking experiments. I compare these data to two models: the Wiener process and a model based on the Ornstein-Uhlenbeck process. This latter model has the following two properties: 1) In the short term, disjoint increments are correlated; and 2) as the time increment gets large, the process becomes indistinguishable from the Wiener process. In addition, the models are nested; as the correlation parameter in the O-U based model gets large, the behavior of the two models approaches each other.

In analyzing the radio-tracking data, I will address the following questions: 1) Is the distribution of movements consistent with the models, and if so, which model is more appropriate; and 2) is the correlation among movements important at the time scale of the data.