This paper presents methods to infer the rate of movement of fish that are marked, released, and subsequently captured. The information that is available is the location and date of the release and the recapture. In addition, the intensity of fishing effort (i.e. sampling) by location and time is known. The simplest approach is to make a frequency plot of the distance between each release and recapture. This is somewhat problematic, as recaptures 1) are biased by variable sampling between locations, and 2) do not consider the possibility of moving further than the maximum distance between any release and recapture point. An alternative approach presented here is to build an underlying model of movement, and then consider spatially variable sampling of marked fish moving according to this model. While this model-based approach requires assuming some description of movement, it has the advantage of being able to allow a much richer description of movement than is available with the frequency of distances approach. In addition, it also provides a way to generate a movement model that is parameterized, which includes uncertainty that can readily be integrated into a population simulation. If the goal of estimating movement distances and rates is to estimate mixing times for mark recapture studies, there are simpler approaches that might be useful. For instance, one alternative would be to ask how much time is required for the probability of recapture in a location to match the relative probability of catching an unmarked fish in that location. Clearly this may be related to the distance from the release point, but considering this distance and the time required, one could estimate the time required for mixing from any initial deployment scheme. Other issues surrounding the use of mark-recapture data for estimating movement patterns are considered.
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