NOTE Pepin: An analysis of the length-weight relationship of larval fish 



421 



19% (range: 2-47%). In the cases of Lumpenus sp. 

 and Sebastes sp., the use of Equation 4 resulted in 

 an increase in the residual sum of squares of 15% 

 and 8%, respectively. 



Although lengths and weights were not corrected 

 for shrinkage, Hay's (1984) and Johnston and 

 Mathias' (1993) studies show that proportional 

 weight loss due to preservation is greater than 

 shrinkage in length and is proportionally greater as 

 size of larvae decreases. If correction factors had been 

 available, the net result would have been to increase 

 the departure from log-linearity. 



Discussion 



Despite the apparently strong fit to the general allo- 

 metric relationship between length and weight of 

 larval fish, this analysis clearly shows a consistent 

 nonlinear pattern in the log-transformed data. Al- 

 though the curvature appears subtle, incorrect as- 

 sumptions about model form may cause bias in the 

 prediction of weights from lengths as well as in the 

 interpretation of size-related variations in the physi- 

 cal condition of fish larvae. The significance of such 

 inaccuracies may be minor for some aspects of the 



early life history (e.g. range of weights based on a 

 mean functional relationship [Houde, 1989]) but may 

 become more important in the calculation of meta- 

 bolic processes (e.g. Checkley, 1984; Ki0rboe, 1989; 

 Giguere et al., 1989). Furthermore, the interpreta- 

 tion of gross measures of condition could also be in- 

 fluenced by the nonlinear nature of the length-weight 

 relationship of larval fish. For example, calculation 

 of Fulton's K, an index of condition, relies on the as- 

 sumption that the general length-weight relationship 

 of organisms follows a linear logarithmic function, 

 specifically an isometric one (i.e. b=3). Increases or 

 decreases in this coefficient are believed to be related 

 to variations in condition. Not only is the general 

 isometric assumption violated in 11 of 16 species 

 (Table 1), but also that of linearity (Table 3). The sig- 

 nificance of a departure from an isometric relationship 

 in the interpretation of measures of condition relative 

 to changes in body shape has been discussed in gen- 

 eral terms by Cone ( 1989) and in relation to larval fish 

 by Laurence (1978). As Ricker (1975) points out, 

 Fulton's K can be used only to contrast individuals of 

 approximately the same length. However, this is only 

 true if the logarithmic length-weight relationship is lin- 

 ear and may not be appropriate when there is a signifi- 

 cant departure from linearity, as shown in this study. 



