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Fishery Bulletin 109(3) 
lucent zones in its otolith, the date when newly formed 
translucent zones typically become delineated from the 
otolith periphery, i.e., December-January (Laurenson 
et al., 1994), the date of capture of the fish, and the 
birth date, represented by the peak date of spawning, 
i.e., 1 December (Laurenson et al., 1993a). 
Gillnet selectivity and mortality 
Gillnet mesh selectivity values for C. macrocephalus, 
which were required to eliminate possible selection 
bias in research samples of age composition, were cal- 
culated for the composite gill net by using the method 
and model described by Kirkwood and Walker (1986). 
The function describing selectivity for fish of different 
lengths by gillnet panels with different mesh sizes is 
determined by fitting gamma distributions to the length 
compositions of fish caught in each of the range of differ- 
ent mesh sizes in the gill net. The means of the gamma 
distributions are assumed to have a linear relationship 
with mesh size. 
The probability distribution function of a variable x 
that has a gamma distribution is 
whereas those that were shorter than the MLL ex- 
perience no fishing mortality and are affected only by 
natural mortality. Thus, the age composition of the 
population within the estuary will reflect this pattern 
of fishing mortality. However, the age composition of the 
population was assumed to be influenced not only by 
natural and fishing mortality, but also by interannual 
variability in recruitment strength. Thus, the number of 
fish of age a and year class y in year t may be assumed 
to be represented by 
R, 
if a = a. 
ff exp 
-IZj 
if a > a 1 
( 1 ) 
where R y = the annual recruitment (to age aq) for year 
class y (where y=t—a ); 
a 1 = the first age present in the age-composition 
data; and 
Z a -M+F a = the total mortality experienced by fish of 
age a. 
{ x“exp(-x/ /?)/ r(a + l) }//3“ +1 , 
where a and j3 are the parameters of this distribution. 
The mode of the distribution is at x=a/5, and the vari- 
ance is (a+l)/3 2 . Kirkwood and Walker (1986) define 0 1 
as the constant of proportionality between the modal 
length and mesh size m, i.e., a/3=0 1 m, and assume that 
the variance of the distribution is constant over the 
different mesh sizes, denoting this by 0 2 . By relating 
this variance to the equation for the variance of the 
gamma distribution, Kirkwood and Walker (1986) 
advise that 
/) = -0.5 j 0 1 m-(0 1 2 m 2 + 40 2 )° 5 }. 
The fishing mortality of fish of this age is zero if the 
length of fish at the midpoint of the ages in the age 
class is less than the MLL, otherwise F a =F, the fishing 
mortality of fully vulnerable fish. The above equation 
for a>a 1 may be rewritten as 
N a.,,i = fl,exp[-M (a-a, )]exp 
7=“ 1 
( 2 ) 
where S a = the selectivity of the fishing gear used in 
commercial fishing and it is assumed that 
S a - 0 if the length of fish at the midpoint 
of the ages in the age class is less than the 
MLL, otherwise S a =l. 
The fishing-induced mortality (F) of fully vulnerable 
fish was estimated by using the age composition data 
derived from gillnet sampling in 1988 and 1989 and in 
2006, 2007, and 2008. The model used for this analysis, 
which is described in detail below, was based on the 
relative abundance model described by Deriso et al. 
(1985). Because mature males of C. macrocephalus 
excavate burrows before the spawning period and 
protect their small juveniles within those burrows, 
the data used to estimate F were restricted to those 
collected in late summer (February) and autumn (May) 
to eliminate the possible effects of such behavior on 
the age composition of this population. For this model 
a constant known level of natural mortality (M) is 
assumed, i.e., the value for the estimate calculated 
from the maximum age recorded for C. macrocephalus 
by employing Hoenig’s (1983) equation for natural fish 
mortality. 
It was assumed that fish longer than the minimum 
legal length (MLL) for retention (i.e., 430 mm TL) are 
fully exposed to a constant level of fishing mortality, 
Denoting the expected count of fish of age a caught 
from year class y in year t by c a y t , we may express this as 
where I t is a factor that represents a combination of the 
catchability of the fully vulnerable fish and the fishing 
effort used to collect the research sample in year t, i.e., 
the sampling intensity in that year, and S* is the selec- 
tivity of the research fishing gear used for collecting the 
age composition data. 
Thus, 
lo gA.^ ^^g e I t +\og e Sl + ^g e R y -M(a-a 1 )-F^S j , 
j=(h 
where the summation term is set to zero if a=a 1 . 
The cumulative sum of the age-dependent selectivities 
of the commercial fishing gear to which the stock was 
exposed before age a, i.e., from age a x to age a-1, may 
be written as 
