Chuwen et al.: Changes in the catch rates and length and age at maturity of Cnidoglanis macrocephalus 
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C— 1 
j=a i 
for a>a x and K = 0, and we may express this model as 
l °S e c a , y , t = log/, + log A + log,ff v -M(a-a 1 )-FK a . 
If we assume that M, S* a , and S a are known, then the 
observed counts of fish within the various age classes 
for each sampling year may be considered to be random 
variates drawn from Poisson distributions, the means of 
which may be calculated with the above equation. Thus, 
with R software (R Development Core Team, 2008), 
Poisson regression analysis was used to fit the above 
model to the age-composition data for C. macrocephalus 
collected in each period and thereby to obtain estimates 
(and standard errors) of both the relative year class 
strengths and the fishing mortality reflected in those 
data. Because the sampling intensity employed in the 
different years was constant, it was removed from the 
model. Profiles of the residual deviances versus fishing 
mortality were constructed for each period by fitting the 
model to a set of fixed values of F over a wide range and 
by recording the resulting estimate of residual deviance 
for each value of F. Approximate 95% CLs for F were then 
selected as those values less than and greater than the 
maximum likelihood estimate of F and which produced 
residual deviances different from that at the maximum 
likelihood estimate by a value equal to # 005 ® ie., 3.84. 
Length and age at maturity 
The gonads of each fish were identified macroscopically 
as either ovaries or testes, or as indeterminate in the 
case of juvenile fish with very small gonads. On the basis 
of their macroscopic characteristics and the scheme of 
Laevastu (1965), the gonads of each fish were allocated 
to one of the following eight stages of gonadal develop- 
ment: I-II=immature or resting adult; III=developing; 
IV=maturing; V=prespawning; Vl^spawning; VII=spent; 
and VIII=recovering spent. 
Because gonads at stages I and II could not be dis- 
tinguished morphologically, we could not use the mac- 
roscopic appearance of gonads to differentiate between 
virgin fish and fish that may have already spawned. 
However, the trends exhibited by the prevalences of 
the different gonad stages of fish caught in sequential 
months before and during the spawning period indi- 
cated that the gonads of the larger fish, e.g., greater 
than the length at which 95% of fish are mature (L 95 ), 
would almost invariably have been destined to progress 
through to stage VIII if the fish had survived. This 
point is substantiated by the fact that the maturity 
ogives, derived by using gonads at stage III or higher 
during the spawning period as the indicator that a 
fish will become or has reached maturity during that 
period, have asymptotes of 100% (see Results section). 
In other words, during the spawning period, the gonads 
of any fish remaining in the stage I— II category are 
virgin gonads, i.e., stage I. Fish that possessed gonads 
at stages III— VIII during the spawning period were 
classified as mature. 
In each season, the gonads of up to 20 females, covering 
a wide range of lengths and the full suite of gonadal 
stages observed in that season, were retained and 
prepared for histological examination. For this purpose, 
a portion of the mid-region of one ovarian lobe was 
placed in Bouin’s fixative for -48 hours and dehydrated 
in a series of increasing concentrations of ethanol. The 
ovarian portions were then embedded in paraffin wax, 
cut transversely into 6 mm sections and stained with 
Mallory’s trichrome. The stages in oocyte development 
in each ovarian section were then determined by 
examination with a Leica MZ7.5 dissecting microscope 
(Leica Microsystems, Wetzlar, Germany) to validate 
that each ovary had been assigned to the appropriate 
stage on the basis of its macroscopic appearance. 
The lengths (L 50 and L 95 ) and ages (A 50 and A 95 ) at 
maturity were estimated for the females of C. macro- 
cephalus in Wilson Inlet during 2005-08 and, with the 
raw data of Laurenson et al. (1993a), also for 1987-89. 
In the case of fish lengths, logistic regression analysis 
was used to fit curves to the probabilities that female 
fish at each length during that year’s spawning period 
would possess gonads at one of stages III— VIII and were 
thus mature or destined to become mature during that 
spawning period. The logistic equation describing the 
probability of an individual possessing mature gonads, 
P, at length, L, was 
P = [l + exp(-log p (19)(L- L 50 )/(L 95 -L 50 ))] \ 
where the parameters L 50 and L 95 are the total lengths 
at which 50 and 95% of the individuals, respectively, 
would be expected to possess gonads at stages III— VIII . 
On the basis of its length, the likelihood of the jth 
fish possessing or not possessing gonads at stages III— 
VIII was calculated as Pj or 1 - P jy respectively. Setting 
Xj - 0 if the jth fish did not possess gonads at such a 
stage and setting X = 1 if it did possess such gonads, 
the overall log-likelihood. A, was calculated as 
X{^log e P,+(l-X.)log e [(l-P 7 )]}. 
j 
The logistic equation was fitted by maximizing this 
log-likelihood with SOLVER in Excel (Microsoft Corp., 
Redmond, WA). The data were randomly resampled and 
analyzed to create 1000 sets of bootstrap estimates of the 
parameters of the logistic equation and the probabilities 
of females and males being mature for each of a range 
of specified lengths. The 95% CLs of the probability of 
maturity at each specified length were taken as the 
2.5 and 97.5 percentiles of the corresponding predicted 
values resulting from this resampling analysis. The 
medians of the bootstrap estimates were used as the 
point estimates of each parameter and of the probabil- 
ity of maturity at each specified length. The A 50 for the 
females of C. macrocephalus at maturity were estimated 
