Legault and Ehrhardt: Correcting annual catches from seasonal fisheries for use in virtual population analysis 
283 
Assumed N(K+\) 
Figure 2 
Percent bias in corrected catch due to incorrect choice of N K+l for 3 different 
cases of when the catch occurs. In this example, the true N K+1 is 10,000, the 
observed catch is 5,000, and M is 0.3 annually. 
guess or from results of VPA, the corrected catch can 
be computed from the observed catch, the time se- 
quence of the accumulation of this observed catch, 
and the natural mortality rate. Each cell in the catch 
matrix can have its own timing pattern. For example, 
if two gears operate in the fishery during different 
times of the year and target different-size fish, the 
timing of the catch will be different among ages. The 
observed catch for each time interval (C-) is used to 
solve for the fishing mortality rate during the inter- 
val (F j ), given the population numbers at the start of 
the next interval (Af +1 ), the annual natural mortal- 
ity (M), and the length of the time interval (At-) (step 
2a of the algorithm). The fishing mortality rate can- 
not be solved for directly in the equation and thus a 
search routine or iterative solution must be em- 
ployed. A simple bisection algorithm will suffice, al- 
though quicker methods are available (see e.g. Press 
et. al., 1989). Once the fishing mortality rate for the 
time interval (F ) is estimated, the population size 
at the start of the time interval (Af ) can be computed 
directly with the equation in step 2b of the algorithm. 
Thus the natural and fishing mortality rates are as- 
sumed constant during each time interval, and the 
year should be split into time intervals accordingly. 
In most cases, monthly time steps should be suffi- 
cient unless the fishing season is extremely short and 
intense or the natural mortality rate is extremely 
high (or both situations occur). 
The algorithm progresses backwards in time, from 
31 December to 1 January, to minimize the propaga- 
tion of errors, in the same manner that virtual popu- 
lation analysis follows a cohort backwards in time 
(Pope, 1972). When all the time intervals are com- 
pleted, the corresponding annual fishing mortality 
rate (F A ) can be computed from the equation given 
in step 3 of the algorithm. The population size at the 
start of time interval K+l is equivalent to the popu- 
