The instantaneous rate of fishing mortality F denotes the force of the fishery on the stock. The F and abundance N determine the rate of catch:
The fishing mortality rate generally must be estimated from data, often including data on the fishing-effort rate E, a measure of the amount of fishing gear used per unit time. The theoretical relationship between the two is F — qE, where q, the 'catchability coefficient', is constant and specific to the gear, vessel, location, and possibly other factors. Much effort in fishery modeling is devoted to estimating q and standardizing E for a particular fishery.
Catch Ct over period t can be found by integrating catch rate (eqn ) with respect to time. Because Nt depends on M as well as F, the solution requires knowing the natural mortality rate. A formulation that does not require M explicitly (though it does implicitly) is
where F, is the (constant) fishing mortality rate during period t, and Nt the average population size in the same period.
For an age-structured population, eqn  is applied to each age class:
Given Ma, eqn  can be solved by integration to obtain catch at age over the year (or any time interval). The result is the Baranov catch equation, a cornerstone of fishery models:
Given annual catch at age Cat, annual total catch is simply the sum across ages, Ct = XaCa,t. The annual yield (catch in weight) is
where the Wa are the average weights at age during the period.
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