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Fishery Bulletin 109(3) 
by the same procedure outlined above, but by substitut- 
ing ages for lengths. 
The logistic regressions describing the lengths and 
ages at maturity for female C. macrocephalus during 
2005-08 and 1987-89 were compared by using a like- 
lihood-ratio test (Cerrato, 1990). The log-likelihood, A, 
which, ignoring constants, was calculated with SOLVER 
in Excel as 
where n - sample size; and 
ss = the sum of squared residuals between the 
observed and expected lengths and ages at 
maturity. 
The value of a test statistic, G, was then calculated as 
twice the difference between the log-likelihoods obtained 
by fitting a common curve for both periods and that 
obtained by fitting a separate curve for each period. The 
hypothesis that the lengths and ages at maturity in the 
two periods could be described by a single curve was 
rejected at the a= 0.05 level of significance if G>x 2 a (q), 
where q is the difference between the numbers of param- 
eters in the two approaches. 
Growth 
Von Bertalanffy growth curves were fitted to the lengths 
at age of C. macrocephalus at the date of capture for 
both 1987-89 and 2005-08. The von Bertalanffy growth 
equation for describing growth is L t -LJ^ 1— g (_ *(t-o))) ? 
where L t is the length (mm TL) at age t (years), L x is the 
asymptotic length (mm TL) predicted by the equation, 
k is the growth coefficient (per year) and t 0 is the hypo- 
thetical age (years) at which fish have zero length. The 
parameters for the von Bertalanffy growth equation and 
their 95% CLs were estimated from the lengths at age 
of fish at the date of capture by employing the nonlinear 
regression routine in SPSS (IBM Corp., Somers, NY). 
The von Bertalanffy growth equations for females 
and males were compared using the likelihood-ratio 
test described above. The same likelihood-ratio test was 
used to compare the growth of C. macrocephalus during 
the current study (2005-08) with that derived for 1987- 
89 from the raw data collected by Laurenson et al. 
(1994). Because the likelihood-ratio test identifies very 
small differences in growth as statistically significant 
for large sample sizes, emphasis was placed on the level 
of difference in growth that was likely to be of biological 
significance. Such differences were considered to exist 
when any of the predicted lengths at integer ages >1 
year in the range of the dominant ages within the data, 
i.e., 1 to 4 years, differed by >5% of the mean of the two 
asymptotic lengths (see Results section). 
Maturation reaction norms 
Probabilistic reaction norms for length and age at matu- 
ration (Heino et al., 2002a; Barot et al., 2004) were 
determined for each period. For this purpose, logistic 
regression analysis was employed to relate the prob- 
ability that a fish was mature to its length and age, i.e., 
P = {l + exp[-(« + /lL + yA)]} 
The logistic regression equations for the two periods 
were compared by using the likelihood-ratio test. The 
probability of a fish maturing at age A was then cal- 
culated as 
m(A,L) = [P(A,L)- P(A-l,L-AL)\/[l- P{A-1,L-AL)\, 
assuming that, if a fish was of length L at age A, then, 
from the von Bertalanffy curve fitted to the data for 
the period, 
L-AL - Lexp(^)-L oo [exp(A)-l]. 
Note that, in this equation, L is not assumed to be the 
expected length at age, but represents the length of an 
individual fish. By setting m (A, L) and solving the equa- 
tion, the value of L may be estimated for any specified 
value of A to determine those lengths and ages at which 
the probability of fish maturing was 50% and conditional 
on the fish being alive at those ages. The contours rep- 
resented by these midpoints of the reaction norms for 
the two periods were plotted and overlaid by the von 
Bertalanffy growth curves for those periods. 
Water temperatures 
Because water temperatures can influence maturation 
or growth (or both) and thus maturation reaction norms 
(Neuheimer and Taggart, 2007, 2010), the possibility 
that temperature was greater during either 1987-89 
or 2006-08 was explored. Although there were no daily 
recordings of water temperature for Wilson Inlet during 
the two periods, such data are available for air tempera- 
ture at Albany in the vicinity of Wilson Inlet (Australian 
Bureau of Meteorology: http://www.bom.gov.au/climate/ 
data/, accessed November 2010). One-sample /-tests 
with SPSS software were used to examine whether, for 
both the minimum and maximum temperatures, the 
mean of the pairwise differences between the average 
monthly air temperatures in corresponding months 
over each of the 120 consecutive months of 1980-1989 
and 1998-2007 was significantly different from zero. 
These periods encompassed all or the vast majority 
of the thermal history of fish caught during the two 
sampling periods. 
Results 
Length and age compositions and catch rates 
Although C. macrocephalus caught with research gill 
nets at the same sites in Wilson Inlet during 1987-89 
and 2005-08 covered a similar length range, i.e., -160 
