292 
Fishery Bulletin 95(2), 1997 
Table 4 
Unweighted average percent bias in population numbers 
for the three scenarios when catch occurs and the three 
catch matrices input in VPA( summary of Tables 1, 2 and 3). 
Catch matrix 
January 
June and July 
December 
Observed 
23.4 
-2.1 
-22.5 
Corrected 
-2.7 
-2.2 
-1.7 
Recorrected 
0.1 
0.1 
0.1 
analyses, where a constant annual fishing mortality 
rate is assumed, will bias the population-size esti- 
mates. If the catch occurs at the beginning of the 
year, the population size will be overestimated, 
whereas catch late in the year will cause underesti- 
mation of the population size. The observed catches 
can be easily corrected to reflect the assumption of a 
constant fishing mortality rate and to eliminate bias 
through the algorithm presented in this paper. 
The determination of current stock health in rela- 
tion to a biological reference point will also be af- 
fected by the timing of the catch, especially spawn- 
ing potential ratios. If the catch is taken before 
spawning, a much lower spawning potential ratio will 
result in relation to the catch being taken after 
spawning (compare observed population numbers for 
June in Figures 5 and 6). Thus the timing of the catch 
must be incorporated into the prediction or reference 
point algorithms, whereas the population numbers 
at the start of the year can be derived from annual 
VPA’s or from other techniques when the constant F 
is assumed, if the corrected catch values are input. 
All the examples and discussion so far have been 
in terms of numbers of fish, but the quotas used by 
management are most often given in weight. The 
average weight at age for the catch and population 
has a confounding effect on the correction algorithm 
that can either reduce or increase the bias. The use 
of average weight of a fish at the midpoint of the 
year, combined with the assumption of a constant 
fishing mortality rate, can lead to highly biased quo- 
tas in relation to the true timing of the catch and the 
average weight at age of the fish at that time. A quota 
in weight, for fish caught early in the year, will cause 
more fish to be caught than the same quota filled 
late in the year when the fish have increased in 
weight. Thus particular attention must be paid to 
the growth of the fish during the year in relation to 
the timing of the catch in cases where management 
advice is based on weight data. 
Summary 
Use of observed catch values from seasonal fisheries 
directly in virtual population analysis or in other 
Acknowledgments 
This manuscript benefited greatly from comments 
provided by V. Restrepo, J. Powers, D. Sampson, and 
two anonymous reviewers. 
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