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Fishery Bulletin 94(2), 1996 



ear regression model was given by Equation 5, 

 whereas for the multiplicative error structure, the 

 nonlinear regression model was 



2, = hx(Y(t i ))+ae i , 



(9) 



where z = \n(y i ) was the log-transformed size of the 

 i th squid in the data set. 



We estimated parameters of the Schnute growth 

 model for several subsets of the length-at-age and 

 weight-at-age data to assess the adequacy of the ad- 

 ditive and multiplicative error structures. The good- 

 ness of fit of the additive and the multiplicative er- 

 ror structures was compared by testing whether the 

 residuals of estimated growth curves were normally 

 or lognormally distributed with the Shapiro-Wilk test 

 (Shapiro and Wilk, 1965). In particular, parameters 

 for case I of the growth model were estimated for the 

 set of pooled-sex samples (n=353) by using the addi- 

 tive and the multiplicative error structures. The set 

 was then partitioned into immature squid of inde- 

 terminate sex («=76), female (n = 131), and male 

 (n=146) samples, and parameters for case I were es- 

 timated. We also partitioned the set into samples 

 with hatching dates from June to October (« = 145) 

 and from November to May in =208), and parameters 

 for case I were estimated. Last, female and male 

 samples were partitioned into samples with hatch- 

 ing dates from June to October (^=61 and n M =76) 

 and from November to May (« F =70 and n M =70), and 

 parameters of case I were estimated. Overall, growth 

 curves for case I were estimated for each of 10 sub- 

 sets of the length-at-age and weight-at-age data. 



We then estimated parameters for cases II, III, and 

 IV of the Schnute growth model for each of the 10 

 subsets of size-at-age data using the best error struc- 

 ture. For each subset of size-at-age data, the esti- 

 mated growth curves were compared on the basis of 

 two criteria. First, an estimated growth curve was 

 rejected if at least one of its parameters was not sig- 

 nificantly different from at the 5% level of signifi- 

 cance. Second, if more than one growth curve had 

 significant parameters, an analysis of variance of the 

 residual sum of squares (RSS) for full and reduced 

 parameter cases was used to select the best fit on 

 the basis of the variance ratio described by Schnute 

 ( 1981; see also Bigelow 1994). A comparison between 

 cases II and IV tested whether the hypothesis a=0 

 was acceptable, and a comparison between cases III 

 and IV tested whether the hypothesis that /3=0 was 

 acceptable. Cases II and III were compared on the 

 basis of the lowest RSS. For each of the 10 subsets of 

 data, one growth curve was selected as the best rela- 

 tionship between length at age and weight at age. 



Results 



Month of hatching 



Long-finned squid hatched during all months of the 

 year (Table 2). The fact that some samples hatched 

 during December- April indicated thatL. pealei were 

 successfully reproducing during the winter. Given 

 this, our data show that L. pealei from the north- 

 west Atlantic have the capacity to spawn through- 

 out the year. 



The frequency distribution of hatch month of L. 

 pealei samples grouped by collection season (Fig. 3) 

 indicated that several microcohorts were present 

 within seasonal collections. For the winter collections 

 ( Fig. 3 A ), most squid were hatched during June— Sep- 

 tember. Considerable variability in squid size was 

 apparent in the length-frequency distribution (ML 

 ranged from 6.3 to 44.0 cm [u=19.3, cr=ll.l|). Most 

 squid in the spring collections (Fig. 3B) were hatched 

 during August-November. Again, considerable vari- 

 ability in squid size was apparent (ML ranged from 

 1.8 to 40.8 cm [u=16.6, o=9.0|>. For the summer col- 

 lections (Fig. 3C), most of the squid were hatched 

 during December-March, with the exception of 17 

 juvenile squid of indeterminate sex from the 17 July 

 1991 Rhode Island Department of Environmental 

 Management survey that hatched during May. In 

 comparison to the winter and spring collections, there 

 was less variability in squid size within the summer 

 collections (ML ranged from 1.3 to 16.3 cm |u=5.0, 

 <7=3. 5]). Most of the squid in the fall collections 

 (Fig. 3D) were hatched during March-May and ML 



