We assumed that the dynamics of the tagged population were identical to the untagged population. Denoting the number of tagged fish of age athat are alive in year t as , the number of tagged fish in the following year is:
,
where is the number of tagged fish of age areleased in year t and k is the rate of tag loss or mortality associated with tagging assumed to occur shortly after tagging. The expected number of recaptures Tt,a is then:
.
Here, ut,a is the mean of the rates for the fisheries in the three regions and is the reporting rate. Reporting rates of 0.9 were assumed for all years except 2003 and 2004 when (lower) values of 0.75 and 0.70 reflecting comments from the fishing industry.
, the number of tagged fish in the following year is:
,
is the number of tagged fish of age a 
.
is the reporting rate. Reporting rates of 0.9 were assumed for all years except 2003 and 2004 when (lower) values of 0.75 and 0.70 reflecting comments from the fishing industry.