420 



Fishery Bulletin 93(2), 1995 



tionship (Eq. lb), the use of such a model may be 

 inappropriate for the study offish larvae. 



Materials and methods 



Ichthyoplankton samples were obtained during two 

 surveys of Conception Bay (47°45'N, 53°00'W), New- 

 foundland, Canada. Cruises were held during the 

 periods from 27 June 1990 to 15 July 1990 and from 

 25 September 1990 to 30 September 1990. Sampling 

 was conducted during daylight hours (0700-1900) 

 with a 4-m 2 Tucker trawl equipped with panels of 

 1,000-, 570-, and 333-|am mesh nitex. At each sta- 

 tion, a single oblique tow of approximately 15 min- 

 utes was made at 2 knots ( 1 m-s _1 ). The net was low- 

 ered to 40 m at a rate of approximately 0.25 m-s -1 

 and retrieved at 0.064 m-s -1 . After the net was 

 washed, samples were preserved in 2% buffered form- 

 aldehyde. Within three to six months after collection, 

 ichthyoplankton were sorted and identified to spe- 

 cies or to the lowest taxonomic level possible (Atlan- 

 tic Reference Centre, Huntsman Marine Science 

 Centre, St. Andrews, New Brunswick, Canada). 

 Sorted specimens were stored in 95% ethanol for 

 approximately three years. Sixteen species were used 

 in this analysis. For each species, 20 to 80 larvae were 

 measured and weighted, depending on abundance, gen- 

 eral condition, and the range of sizes available. 



Larvae were measured to the nearest 0.1 mm by 

 using an image analysis system mounted on a Wild 

 M3C dissecting microscope that was equipped with 

 an S-type mount fitted with a 0.5x objective. Each 

 larva was placed on a preweighted aluminium sheet 

 and dried in an oven at 65°Celsius. After 24 hours, 

 larvae were transferred to a desiccator for no less 

 than 1 hour and no more than 3 hours. Each larva 

 was weighted to the nearest 0. 1 ug by using a Cahn- 

 31 microbalance. 



Length-weight relationships of log 10 -transformed 

 data were evaluated by using two models. In the first 

 instance, a general allometric model of the form 



log W = a' + b log L + £ , 



(3) 



where W and L are weight and length, a' is equal to 

 log(a ) from Equation lb, b is the exponent in Equa- 

 tion 1, and e is error, was fit by using a general lin- 

 ear algorithm (procedure GLM, SAS, 1988). In the 

 second case, a model of the form 



logW = a" + b"(logL) c '"+£, 



(4) 



where W and L are weight and length, respectively, 

 and a", b", and c" are constants, and e is error, was 



fit by using a nonlinear iterative least squares algo- 

 rithm (procedure NLIN, SAS, 1988). When the value 

 of c" is not significantly different from 1, Equation 4 

 reduces to the general allometric model (Eq. 3). Equa- 

 tion 3 is a well-recognized and general functional 

 form used in the estimation of length-weight rela- 

 tionships (Ricker, 1975; Zweifel and Lasker, 1976; 

 Cone, 1989). Equation 4 is not a common form (e.g. a 

 Gompertz model; Laird et al., 1968; Zweifel and 

 Lasker, 1976) but represents a first-order increase 

 in complexity over the general allometric model (Eq. 

 3). I chose not to use the more complex Gompertz 

 length-weight model, which has been used in other 

 studies (e.g. McGurk, 1987) for two reasons. First, a 

 Gompertz model is best suited for data that cover 

 the entire range of sizes for a developmental stage. 

 Such data were not available from the surveys con- 

 ducted as part of this study. Second, preliminary 

 analysis revealed that Equation 4 is numerically 

 more stable than the Gompertz model for the data 

 used in this study. 



To establish whether there was a significant de- 

 parture from loglinearity (Eq. 3), a second order poly- 

 nomial was fit to the residuals (Y = a + bX + cX 2 , 

 where Y are the residuals and X is the log-trans- 

 formed length). If the second order coefficient (c) is 

 not significantly different from 0, then there is no 

 departure from loglinearity and all other terms will 

 also not differ from 0. 



Results 



Despite the wide variation in the range of informa- 

 tion available for each species considered in this 

 analysis (Table 1), the relationship between length 

 and weight appears to be strong in all instances (Fig. 

 1 ). Analysis with the general linear allometric model 

 (Eq. 3) shows a very highly significant fit for all spe- 

 cies (Table 1). Evidence of a nonlinearity in the allo- 

 metric relationship between length and weight is 

 apparent in an analysis of the residuals from the 

 general allometric model (Eq. 3). In 10 of 16 species, 

 the second-order polynomial fit to the residuals in 

 relation to log-transformed length was significant 

 (Table 2). 



The value of c" (Eq. 4) was significantly different 

 from 1 for 11 of the 16 species used in this study 

 (Table 3). In the case of Ammodytes sp., the value of 

 c" indicates an asymptotic relationship. An exponen- 

 tial length-weight relationship of the log-transformed 

 data is indicated in the 10 other species with values 

 of c" significantly different from 1. Fitting Equation 

 4 to the data resulted in a decrease in residual sum 

 of squares in 14 of the 16 species which averaged 



