696 
Fishery Bulletin 95(4), 1 997 
Ages, to the nearest whole year, were assigned 
solely on the basis of number of visible annuli for 
fish collected from mid-July through December. Fish 
collected 1 January through mid-July had one year 
added to their age if the marginal increment was 
estimated to be >80% of the previous annual incre- 
ment. Ages from samples collected by Johnson et al. 
(1983) were adjusted similarly with their marginal 
increment data. This adjustment was necessary be- 
cause an annulus typically forms during the spring 
(Beaumariage, 1973; Johnson et al., 1983) but is of- 
ten difficult to distinguish until later in the summer. 
Von Bertalanffy growth equations were fitted to 
quarterly observed lengths-at-age by using Mar- 
quardt’s nonlinear regression procedure (SAS Insti- 
tute, Inc., 1988). Annual ages were converted to quar- 
terly ages by adding 0.25 to the age if the fish was 
collected during April-June, 0.50 if collected during 
July— September, and 0.75 if collected during Octo- 
ber-December. Quarterly ages were used to minimize 
the variance about the sizes-at-age because obsex’ved 
annual sizes-at-age, especially for young ( 1-2 yr old ) 
fish that are growing faster than older fish, can vary 
considerably depending on month of capture. 
For the 1986-92 data, we tested for differences in 
von Bertalanffy equations between sexes within re- 
gions and among regions within a sex, i.e. we com- 
pared fitted growth curves, using an F-statistic de- 
rived from the multivariate Hotelling’s T 2 ( Bernard, 
1981; Vaughan and Helser, 1990). Estimates of the 
parameters L x , K, and t Q are often correlated, mak- 
ing univariate statistical tests inappropriate for com- 
paring differences between like parameters from two 
groups of fish (Bernard, 1981). To analyze the 1977- 
78 growth data, we simply examined plots of the von 
Bertalanffy curves and their 95% confidence limits. 
We did not use Hotelling’s T 2 to test the 1986-92 data 
for interannual differences, the 1977-78 data for any 
growth differences, or to compare the 1977-78 and 
1986-92 data, primarily because size and age distri- 
butions of the samples varied considerably among 
regions (and to some extent between sexes) and sec- 
ondarily because the sample size was sometimes 
quite small. Von Bertalanffy parameter estimates, 
which are used as data for the Hotelling’s T 2 test, 
would certainly be influenced by sample size and age 
distributions; if the two groups being tested had dis- 
similar distributions, then a significant difference 
might not be biologically meaningful. 
Bernard (1981) noted that one of the assumptions 
for Hotelling’s T 2 is that the two sets of estimates 
being compared have a common variance structure. 
However, citing Ito and Schull (1964), “if the vari- 
ance-covariance matrices are unequal, the probabil- 
ity of a Type I error and correspondingly the power 
of the T 2 deviate from tabulated values with the same 
degrees of freedom. However, when both N x and N 2 
are equal, different variance-covariance matrices do 
not effect the error level or the power of the test.” To 
run each test with equal sample sizes so we could 
avoid the problems just mentioned, we randomly 
sampled from the larger group a number of observa- 
tions equal to the sample size of the smaller group, 
then used parameter estimates derived from that 
sample in the test. However, all growth curves shown 
in the figures in the present study were based on the 
full number of available observations. 
Results 
We aged 14,213 king mackerel — 12,180 collected 
during 1986-92, 2,033 from 1977-78. The numbers 
of females and males aged from 1986-92 were 3,407 
and 2,083 from the Atlantic, 2,753 and 1,285 from 
the eastern Gulf, and 1,662 and 990 from the west- 
ern Gulf. From the 1977-78 collections, the numbers 
of females and males aged were 323 and 128 from 
the Atlantic, 1,011 and 343 from the eastern Gulf, 
and 188 and 40 from the western Gulf (Table 1). The 
geographical distribution of the 1986-92 samples 
varied annually, and although fish were collected off 
every coastal state from Virginia to Texas and in 
Veracruz, Campeche, and in Yucatan, Mexico, the 
greatest proportion were collected in North Carolina 
in the Atlantic region, northwest Florida in the east- 
ern Gulf, and south Texas in the western Gulf (Table 
1). Most fish collected in 1977-78 came from North 
Carolina, northwest Florida, and Louisiana (Table 1). 
Size and age distributions 
Size distributions of aged fish were similar among 
regions during 1986-92, although females tended to 
predominate at larger sizes (Fig. 1). In contrast, in 
1977-78, size distributions differed markedly, among 
both regions and sexes (Fig. 1). Males do not grow as 
large as females, and this difference was reflected in 
their narrower size distributions (Fig. 1; Table 2). 
Annual size distributions of aged fish, 1986-92, 
showed similar ranges each year but some variation 
in modal sizes (Table 2). The maximum sizes of fe- 
males aged from 1986-92 were 152 (age 18 [yr]), 158 
(age 18), and 147 (age 11) cm for the Atlantic, east- 
ern Gulf, and western Gulf; sizes of males ranged to 
121 (age 20), 127 (age 16), and 117 (age 13) cm for 
those same regions. Maximum sizes of 1977-78 
samples were slightly smaller than those from 1986- 
92 in 5 out of 6 region and sex combinations, most 
likely because the older data had much smaller 
