280 
Abstract .—The catch equation used 
in virtual population analysis (VPA), 
and most annual age-structured meth- 
ods, assumes a constant fishing mor- 
tality rate (F) throughout the year even 
though many, if not most, fisheries are 
seasonal. Breaking this assumption of 
a constant F creates a bias in the re- 
sulting population-size estimates when 
the observed catch is used as input in 
VPA. The bias can be reduced by chang- 
ing the time step in the analysis to 
quarters or months, as has been sug- 
gested in the past, but this change is 
not always easy or practical. This pa- 
per presents an alternative method for 
reducing the bias: correction of the 
catch values to meet the assumption of 
a constant fishing mortality rate. A 
simple algorithm is presented that gives 
the number of fish t hat would have been 
caught from a given population if the 
observed fishing mortality rate had been 
spread evenly throughout the year. An 
iterative process improves the required 
guess for the population size such that 
the bias is eliminated. 
Manuscript accepted 12 September 1996. 
Fishery Bulletin 95:280-292 (1997). 
Correcting annual catches from 
seasonal fisheries for use in 
virtual population analysis 
Christopher M. Legault 
Nelson M. Ehrhardt 
Division of Marine Biology and Fisheries 
Rosenstiel School of Marine and Atmospheric Science 
University of Miami 
4600 Rickenbacker Causeway, Miami, Florida 33149 
E-mail address: clegault@rsmas.miami.edu 
Many, if not most, fisheries operate 
during only part of the year. The 
seasonal nature of fisheries is 
caused by quota and regulatory 
limitations, weather conditions, and 
fish availability among other rea- 
sons. The catch equation used in 
virtual population analysis (VPA) 
and in other annual age-structured 
analyses, assumes that a constant 
fishing mortality rate is applied con- 
tinuously throughout the year. Un- 
der this assumption, a bias will be 
introduced into the analysis when 
the fishery is in fact seasonal. With 
the catch equation, the total catch is 
assumed to be distributed through- 
out the year, such that it follows the 
exponential decline of the popula- 
tion. The resulting total mortality 
rate inferred from the decline of the 
population with the catch equation 
is different from what actually oc- 
curred in the population. For ex- 
ample, given a total catch of 5,000 fish 
distributed unevenly during the first 
half ofthe year (Fig. 1, top panel), the 
population numbers at the end of the 
year would be negatively biased with 
the assumption inherent in the catch 
equation (Fig. 1, lower panel). 
This bias has been examined in 
the past and found to be at a low 
level for most situations; exceptions 
occur for heavily exploited fisheries 
that occur during either the first or 
last quarter of the year. The fact 
that seasonal catches cause the es- 
timated exploitation rate to be bi- 
ased was described by Youngs 
(1976). The impact of seasonal 
catches on population-size esti- 
mates from cohort analysis was ex- 
plored by Ulltang (1977), who rec- 
ommended using smaller time units 
than a year to overcome the errors. 
Sims (1982) used both analytic 
methods and simulation to demon- 
strate the effects of seasonal catches 
on cohort analysis, concluding that 
the relative errors in population- 
size estimates are not severe unless 
the natural mortality rate is large 
or the fishery is heavily exploited, 
or both. The traditional recommen- 
dation for seasonal fisheries is to 
change the time scale from year to 
quarter or month so that the fish- 
ing mortality rate will be approxi- 
mately constant within the time 
unit. The conversion from annual to 
monthly or to some other time step 
is not always simple, either in the 
coding of programs or in the collec- 
tion of data. For example, the cre- 
ation of adequate age-length keys 
for ageing the catch under monthly 
or even quarterly time steps could 
require prohibitively expensive 
sampling schemes and would be 
technically challenging. 
A more recent approach to deal 
with the problem of seasonal fish- 
eries is the generalization of the 
equations used in virtual population 
analysis. An attempt to remove the 
