Coulson et at: Biological features of Achoerodus gouldii 
61 
validate the macroscopic staging. Note that comparisons 
of transverse sections through the anterior, middle, 
and posterior regions of the gonads of 10 A. gouldii 
over a wide size range demonstrated that the charac- 
teristics of those gonads remained similar throughout 
their length. 
The length at which 50% of female A. gouldii attained 
maturity (TL 50 ) was determined by fitting a logistic 
curve to the probability that, during the spawning pe- 
riod, a female fish at a specific length would possess 
gonads at one of stages III to VIII. As such fish were 
potentially destined to become mature or had reached 
maturity during that period (see Results), they are, for 
convenience, referred to as mature in the present study. 
The logistic equation used for this analysis was 
P = l/{n-exp[-log e (l9)(TL-TL 50 )/(TL 95 -TL 50 )]}, 
where P = proportion mature; 
TL = total length in mm; and 
TL 50 and TL 95 = the total lengths in mm at which 50% 
and 95% of fish were mature, respec- 
tively. 
The logistic equation was fitted by using Markovian 
chain Monte Carlo simulation in WinBUGS (vers. 1.4.3, 
MRC Biostatistics Unit, Cambridge, U.K.) from 500,000 
iterations, discarding the first 1000 iterations as the 
initial burn in set and using a thinning interval of 100 
iterations. After assessment in WinBUGS that con- 
vergence was likely to have been achieved, the point 
estimates of the parameters of the logistic equation and 
their 95% confidence intervals, and of the probabilities 
of fish being mature at a range of specified lengths, were 
determined as the medians and the 2.5 and 97.5 percen- 
tiles of the estimates produced by WinBUGS. 
Because the six fish with gonads containing both 
testicular and ovarian tissue all had lengths that lay 
within the range where the prevalence of females was 
decreasing and that of males was increasing, they were 
considered likely to be changing from female to male. 
Because the testicular tissue in those fish was more ma- 
ture than the ovarian material, the data for these fish 
were combined with those for male A. gouldii for deter- 
mining the length and age at which A. gouldii change 
sex. WinBUGS was then used as above to estimate the 
TL 50 and TL 95 for change in both sex and color, i.e., 
from green to blue (from female to male). 
Logistic regression analysis was employed to relate 
the probability, p m -, that fish j was a male to its length 
L ■ and color C- (green=0, blue = l). p™ was determined 
as 
[l + exp {-a-fcLj-fifij)] , 
where a, and /3 2 are constants. 
The probability that fish y possessed female gonads, pL 
was determined as pf- =1- p m -. The Akaike information 
criterion (AIC) (Burnham and Anderson, 2002) was 
used to determine which of the models, based solely on 
either length (/3 2 = 0) or color ( /3 X = 0 ) , provided the better 
predictions. The AIC is determined by the following 
equation: 
AIC = -2A + 2 K, 
where A = the log-likelihood; and 
K = number of parameters. 
The model with the lowest AIC value was selected as 
the better of the two models. The likelihood-ratio test 
(Cerrato, 1990) was then used to determine whether the 
model that contained both length and color significantly 
improved the prediction that a fish was a male. 
Recruitment variability, mortality, 
and spawning potential ratio 
The number of fish in each year class in each of three 
successive annual periods was determined. Because 
1 August coincides with the birth date designated for 
A. gouldii, these estimates of numbers encompassed 
each of the three successive 12-month periods between 
1 August and the following 31 July in the years 2004 
to 2007. 
Total mortality, Z, for A. gouldii was estimated from 
the age compositions of samples of fish collected during 
the above three successive 12 -month periods (years) by 
using catch curve analysis and then relative abundance 
analysis (see below). We used data obtained from the 
commercial gillnet fisheries and assumed knife-edge 
recruitment into the fishery at 15 years, i.e., we re- 
stricted data to those for the descending limbs of the 
catch curves (Ricker, 1975). 
Initially, an estimate of Z was calculated by using 
catch curve analysis, where recruitment was assumed 
to be constant. For a fish stock that experiences a con- 
stant level of Z from the age of full recruitment, a = t c 
years, the estimated proportion, P a t , of fish at age a 
in year t is 
Kt = { R t- a exp[-(a - t c )Z]} / ^ R t -j e*p[-( J - t c ) . Z] 
J =t c 
where A 
j 
Rt-a 
R 
H 
the maximum observed age; 
an index of age, where t e —j — A', 
the number of fish of year class t — a that 
recruited at age t c years to the fully vulner- 
able portion of the fish stock in year t-a+t c , 
and which, in year t, are of age a years; 
and 
the number of fish of year class t - j that 
recruited at age t c years to the fully vulner- 
able portion of the fish stock in year t-j+t c , 
and which, in year t, are of age j years. 
