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The classic fisheries assumption is that catch divided by effort is proportional to the population size. This assumption allows the use of catch per unit of effort (or CPUE) as an index of abundance. But everyone know the relationship is variable. The “catchability coefficient”, q, may change systematically with changes in technology. Q may also vary from time to time at random in which case the variability can be considered to be process error.
Variability in fishing mortality is expressed by a log-normal multiplicitive error (exp(delta)). These errors express variability in the relationship of population size to catch per unit of effort.
In this application fishing effort is normalized to its mean so that q is an estimate of mean fishing mortality.
There are a number of time periods for which tags were recovered, but no fishing effort was reported. The mean (i.e... 1.0) was substituted in these cases.
The likelihood function is modified by adding a weight times sigma.