60 
Fishery Bulletin 107(1) 
delineated from the otolith periphery, and on an appro- 
priate birth date for A. gouldii (see Results). The von 
Bertalanffy growth equation, used for describing the 
growth of A. gouldii, is 
L t = lJi - exp^ f_ * 0 ^ | , 
where L t = the length (mm TL) at age t (years); 
- the mean asymptotic length (mm) predicted 
by the equation; 
k = the growth coefficient (per year); and 
t 0 = the hypothetical age (years) at which fish 
would have zero length. 
The observed lengths at age of fish were assumed to 
be normally distributed about the predicted lengths 
at age for each sex, and to have a common standard 
deviation. 
The probability that fish j was of sex s was denoted 
by P S j, where pi = 1 -p n j and where p n j = 1 if the fish 
possessed testes, p n - = 0 if the fish possessed ovaries 
and pj = the value calculated with the logistic equa- 
tion presented in the next section if the fish had been 
eviscerated and sex could not therefore be determined. 
The value of the normal probability density function, 
for fish j of sex s, <pj, was calculated as 
Von Bertalanffy growth curves were fitted to the lengths 
at age of A. gouldii in the cases of 1) all fish irrespec- 
tive of their sex; 2) females and males that had been 
sexed on the basis of an examination of their gonads; 
and 3) those fish that were a mixture of green and blue 
among the individuals used for constructing the growth 
curves for each sex in 2 (the above growth curves were 
fitted by using nonlinear regression in the Statistical 
Package for the Social Sciences, SPSS (vers. 11.0, SPSS 
Inc., Chicago, IL); and 4) von Bertalanffy growth curves 
for each sex were next fitted to the combination of the 
lengths at age of sexed and unsexed individuals, taking 
into account the probability that, from its total length 
and color, an unsexed fish would be a male or a female. 
For each unsexed fish, the expected length, If- , was 
first calculated as 
* = 1 / {^2n: sd 2 \exp -f(L J .-L s 7 ) 2 ]/(2sd 
where L = the observed length at age; 
Lj = the predicted length at age; 
s d = the standard deviation; and 
ji = the constant pi. 
The log-likelihood, A, determined as X log '(X p A I, was 
maximized by using Solver in Microsoft Excel to esti- 
mate the parameters U x , U, tf Q , L™, k m , t diverge , and sd. 
Approximate 95% bootstrap confidence limits of the 
parameters were calculated as the 2.5 and 97.5 percen- 
tiles of the parameter estimates obtained by fitting the 
model to 1000 resampled data sets. 
Reproductive biology 
L -(l - eX P ( f j “ *0 )]) ^ 8 = f °r tj < ^ge 
L'” ( 1 - exp [-/A m ( tj - 1 ) ]) if s = m and tj > t dlverge 
where s 
h 
l diverge 
L f and L™ 
M and k m 
d 0 and t'g 
sex (s = f for a female and m for a male); 
the age of fish j; 
the age at which it was assumed that 
female and male growth curves began to 
diverge; 
the mean asymptotic lengths for females 
and males, respectively; 
the growth coefficients for females and 
males, respectively; and 
the hypothetical ages at which, assuming 
growth in accordance with the above von 
Bertalanffy growth equations, females 
and males, respectively, would have zero 
length. 
Note that, if L diverae is the expected length of the females 
at age tdiverge’ then 
C = 4 - (u k' (log, [l - (l 4iw / Zi)]+ 
(l/t")log,[l-(L diw /L;)], 
where log e = the natural logarithm. 
The gonadosomatic index (GSI) of each female with a 
length > the TL 50 at maturity (see Results ) was calcu- 
lated as 
GSI = (W 1 /W)x 100, 
where W 1 - wet gonad weight; and 
W = wet body weight. 
The criteria of Moore et al. (2007), adapted from Laev- 
astu (1965), was used to allocate each gonad to one of the 
following maturity stages, I = virgin; II = immature or 
resting; III = developing; IV = maturing; V = prespawn- 
ing; VI = spawning; VII = spent; and VIII = recovering 
or spent. Note that the TL 50 at maturity was used as the 
cut off for determining the GSI of individuals because, 
outside the spawning period, it was not possible macro- 
scopically to distinguish the gonads of virgins (stage I) 
from those of fish that had matured but were in a resting 
state (stage II). 
Gonads from a large subsample of females and males 
in each month were placed in Bouin’s fixative for 24 to 
48 hr — the duration depending on the size of the gonad. 
They were then dehydrated in a series of increasing 
concentrations of ethanol and their mid-regions were 
embedded in paraffin wax and cut into 6-pm transverse 
sections, which were stained with Mallory’s trichrome. 
The histological characteristics of the ovaries in that 
large subsample (see Coulson et al., 2005) were used to 
