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Fishery Bulletin 109(4) 
calculated measurements (residuals) were employed to 
identify regional characteristics. According to the null 
hypothesis, 50% of the measurements for otoliths from 
a region should fall above the regression line and 50% 
below it if there is no regional bias for otolith perimeter 
or weight. We tested that hypothesis using the following 
equation expressed as a percentage: 
n 
where Z ; = 1 if the observed measurement is greater 
than the calculated value from the regres- 
sion line (otherwise scored as 0); and 
n = the total number in the sample set. 
We termed the results “perimeter-weight profiles,” or 
PWPs. 
PWPs reported this way correlated well with residu- 
als expressed as plus or minus values in mm or mg. The 
correlation coefficients determined by comparing PWP 
(%) vs. average residuals (mm or mg) for 61 sample sets 
from San Diego collected monthly for over five years 
were the following: perimeter based on area, 0.876; 
perimeter based on length, 0.889; and weight based on 
length, 0.920. PWPs provide an advantage for categoriz- 
ing the data on residuals, particularly when there is a 
wide spread of values and when the average residuals 
fall near zero. 
Statistical significance of the three PWP calculations 
between geographic areas was determined by three-way 
chi-square tests and by using likelihood-ratio tests (or 
log linear model) with G 2 statistics (log-linear analy- 
sis, http://faculty.vassar.edu/lowry/abc.html, accessed 
September 2010). For the ABC chi-square matrix, we 
used pairs of values (i.e., 2x2x2): A=two locations; 
B=the number of otoliths above and the number below 
the regression line that describes the model otolith for 
each kind of measurement; and C=two kinds of mea- 
surements (PWP perimeter derived from the otolith 
area and PWP weight derived from the otolith length). 
Significance values (P) were determined from the G 2 
statistic for AB(C) that represented the AB interaction 
when the AC and BC interactions were removed. It can 
be obtained by constructing a separate AB table for 
each level of C, calculating a separate G 2 measure for 
each AB table, and then summing the results. 
Comparisons between northern and southern Cali- 
fornia sardine otoliths were conducted several ways. A 
GLM with logistic link was used to examine the pos- 
sible differences between PWP for perimeter based on 
area (P/A), perimeter based on length (P/L), and weight 
based on length (W/L) for regions 3 and 4 (Monterey 
and San Diego, location effect) using cohorts collected 
in 2006 and 2007 (year effect): 
g(PWP) = P 0 + /IjXj + P 2 x 2 + P a x 1 x 2 , ( 2 ) 
where g(PWP) is a logistic link function of the population 
proportion for each of the three equations (P/A), (P/L), 
and (W/L); and 
g(PWP) = log (PWP / (1- PWP)), (3) 
where x 1 and x 2 are categorical variables: x x =0 for 2006 
and 1 for 2007, and x 2 =0 for Monterey and 1 for San 
Diego. The last term (/3 3 ) is the interaction term. When 
the coefficient j3 3 was significant, the GLM was per- 
formed to test the location effect for each year with x 2 
as the only independent variable. 
Because the multiyear data collected from Monterey 
area included more than one age, the GLM was also 
used to test age and year effect on otoliths sampled 
during 2006-07 by using the same methods described 
for Equations 2 and 3. The only difference between 
these two GLM applications was that here x 2 is the age 
category: x 2 =0 for age-0 fish and 1 for age 1-2 fish. The 
coefficient /3 2 was applied to measure the age effect, 
whereas in the previous GLM, x 2 was the indicator for 
the location. 
Results 
Coast-wide survey 
PCA and MANOVA When otoliths of all ages and from 
all regions were compared, most measurements were 
highly correlated (coefficients>0.90, /r=2309 otoliths; 
data not shown). Length, perimeter, and area had the 
highest correlation coefficients (0.98-0.99). Otolith 
weight strongly correlated with length, perimeter, and 
area (0.94-0.98), and fish standard length similarly 
correlated with those four otolith features (0.95-0.97). 
When correlations were conducted for each of the seven 
areas, no regional patterns were detected (data not 
shown). 
For the PCA of age-1 otoliths with all eleven mea- 
surements, the otolith dimensions (except C-C’) had 
nearly equivalent PCI coefficients (data not shown). 
When only the four most important dimensions were 
compared by PCA (area, length, perimeter, and weight), 
PCI explained 86% of the variance and the coefficients 
were similar (Table 2). PCI was the only component 
with an eigenvalue >1. These samples represented ag- 
gregated collections by region for all dates and provided 
one otolith per pair. When PCA was conducted with 
both otoliths per pair, the results were nearly identical 
(results not shown). 
MANOVA on these four variables based on the cor- 
relation matrix indicated otolith sizes were not the 
same for all regions despite the selection of a single age 
class (0.73-1.30 mg, nearly a two-fold difference within 
the class). MANOVA results showed that all regions 
were not the same, and each of the six tested regional 
contrasts were significantly different (P<0.05) (Table 
3). In three of the six regional contrasts, perimeter, or 
perimeter and weight together, contributed the most to 
the differences. Length was generally the least influen- 
tial factor for any of these contrasts. 
Although differences between widely spaced collection 
areas might be expected (contrasts 1, 3, and 4), the rea- 
