638 



Fishery Bulletin 97(3), 1999 



adult and 16 juvenile squid were calculated from a 

 mean of three separate counts made by one reader. 



Statistical analyses 



Paired-sample f-tests indicated no significant differ- 

 ence between left and right statolith total length mea- 

 sures (^=0.67, df=101, P=0.50, n^l02), or adult statolith 

 weight measures it^OAT, df=79, P=0.64, n=80), but 

 wherever possible, the left statolith was used for analy- 

 ses. For the purpose of this study, statolith "size" refers 

 to the length of each statolith dimension, whereas 

 "shape" indicates that all statolith dimensions have 

 been combined to describe overall statolith structure. 



Rates of growth calculated from size-at-age data 

 were not significantly different between adult males 

 and females (Table 1). A size comparison of males 

 and females, adjusted for age, found no significant 

 difference in size between the sexes (Table 2). Indi- 

 viduals were therefore classified as either juveniles 

 or adults, with no distinction made between adult 

 sexes. This classification avoided over-complicating 

 analyses and also provided a larger adult sample size. 



Principal components analysis (PCA) was per- 

 formed on statolith dimensions with the covariance 

 matrix of transformed (logj^) data, allowing complete 

 descriptions of statolith shape for all dimensions si- 

 multaneously. The magnitude of coefficients in the 



first eigenvector varies because of changing statolith 

 proportions and relative growth patterns. These co- 

 efficients indicate the nature of allometric growth 

 for each variable (dimension) (Jolicoeur, 1963). The 

 coefficients for each variable in the first eigenvector 

 describe the relative growth rates of all the compo- 

 nents simultaneously (Shea, 1985). Variables with 

 coefficient scores on the first principal component 

 vector equal to the mean coefficient (( l/p)" ■^, where p 

 is the number of variables in the analysis) are iso- 

 metric. Positive and negative allometry is indicated 

 by values greater than and less than the mean coef- 

 ficient, respectively (Jolicoeur, 1963). 



The resampling technique jack-knifing provided 

 means and standard errors (SE) of each coefficient 

 (Marcus. 1990). The probability that the mean coef- 

 ficient was significantly different from the hypoth- 

 esized value (Marcus, 1990) is 



\mean coefficient - hypothesized coefficient^ 

 > T X SE X mean coefficient 



(1) 



where T = the number of standard errors for which 

 the probability statement is made. 



In this case T = AAl provides a probability of 0.05. 

 Simply, the difference between the mean coefficient 

 and the hypothesized coefficient is greater than a 

 critical difference (T x SE x calculated coefficient) 

 with a probability <\IT ^. 



Results 



Statolith size relationships 



The smallest statolith total length (648 nm) was ob- 

 served in the youngest specimen ( 17 days old). The 

 largest adult statolith total length (2167 ^m) was 

 observed in a 162-day-old mature female, although 



