PAULY: ESTIMATING FOOD CONSUMPTION OF FISH POPULATIONS 



is derived from the results of experiments conducted 

 with dab (Limanda limanda) by Pandian (1970, figs. 

 5, 6) 4 in which the type of food, M (0 = herring meat, 

 1 = cod meat), and sex, S (0 = o% 1 = 9), and the 

 temperature, T(in °C) were reported in addition to 

 the weight, W (in g and log 10 units). 



This model permits exact tests on the effects of 

 each factor (Table 3), and permits adjusting param- 

 eter values (W^, (1) so that they relate to conditions 

 resembling those occurring in nature. 



Then, W m is estimated— at least in principle— 

 from 



4 A table listing all values extracted from figures 5 and 6 in Pan- 

 dian (1970) is included in the document mentioned in footnote 1, 

 and will be supplied on request by me. 



Table 3. — Details of a Type I multiple regression to quan- 

 tify the effects of some factors on the food conversion 

 efficiency of dab (Limanda limanda) (see text footnote 3). 



W„ = antilog 10 (1/0) (a + b x V x + b 2 V 2 . . . b n V n ). 



(28) 



This equation implies that there is, for every com- 

 bination of V x , V 2 , ... V n values, a corresponding 

 value of W^. This is reasonable, as it confirms that 

 W M is environmentally controlled (Taylor 1958; 

 Pauly 1981, 1984b). W^- values obtained through 

 Equation (31) will generally be reliable— as was the 

 case with the one-factor model (4)— only when a wide 

 range of weights are included, variability is low, and 

 the correct statistical model is used. 



As a first approach toward an improved statistical 

 model, one could conceive of a geometric mean 

 multiple regression which, in analogy to a simple 

 geometric mean regression, would be derived from 

 the geometric mean of the parameters of a series 

 of multiple regressions. This approach would in- 

 volve, in the case of n + 1 variables (= Y, Y lt Y 2 , 

 ... Y n ) in the following steps: 



1) Compute the parameters of n + 1 Type I multi- 

 ple regressions, where each regression (j) has 

 another variable as dependent variable (i.e., Y, then 

 Y lt Y 2 , ... to Y n ; see j = 1 to 5 in Table 4). 



2) Solve each of the j equations for the "real" 

 dependent variable (Y = C, see j = 6 to 10 in Table 

 4). 



3) Compute the geometric mean of each partial 

 regression coefficient from 



b- = (V 6 2i -...&„/*. (29) 



4) Compute the intercept of the new Type II 



Table 4. Estimation of parameters in a "mixed" multiple regression (see also text). 



1 Note that body weight (IV) is here expressed in log 10 units. 



835 



