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In all the models developed below, I start with a probability density function, f(x,t), of individuals through space and time. If the data are continuous in both time and space (e.g., radio-tracking data), then the model can be applied directly to the data in this form. Otherwise, the model needs to be modified to be consistent with the data. For instance, the model can be converted to a spatial distribution, f(x), of individuals at a particular point in time, or a temporal distribution, g(t), at a particular point in space. Also, the data are often discrete - for example the number of fish collected at a dam during a discrete time interval. The model can be converted into a discrete form by integrating. For example:
(3.1)
describes the probability of a fish occurring in the discrete spatial interval (x, x + 
x) at time t0. If a total of N organisms are observed, then
(3.2)
is the predicted number of individuals occurring in the ith interval. In this form, the 
's follow a multinomial distribution.
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Spatial and Temporal Models of Migrating Juvenile Salmon with Applications.
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