FISHERY BULLETIN: VOL. 84, NO. 4 



multiple regression from 



a = Y - (Vfi + 62^2 • • • + &.T.) (30) 



where the 3^ are the means of the F r values and 

 6/ the geometric mean partial regression coeffi- 

 cients. 



This method cannot be used here without modi- 

 fication because in most cases the multiple regres- 

 sion is "mixed" (Raasch 1983), consisting of vari- 

 ables which can be expected to generate normally 

 distributed residuals when used as dependent vari- 

 ables (here: C, W, T) as well as "dummy" or binary 

 variables (S, M) which cannot generate normally 

 distributed residuals when they are used as depen- 

 dent variables. 



As might be seen in Table 4, the use of dummy 

 variables as "dependent" variables generates un- 

 stable interrelationships between the remaining 

 variables, making the computation of meaningful 

 mean partial regression coefficients impossible. 



The best solution here seems to omit for the com- 

 putation of the mean regression coefficient those 

 multiple regressions which have binary variables as 

 "dependent" variables; Table 4 illustrates this 

 approach. 



The mixed model so obtained is 



C = 0.489 - 0.0738W - 0.01647/ + 0.0175S 



+ 0.0151M 



(31) 



which corresponds to the standard model 



C = 0.62W - 0.90T' + 0.195' + 0.46AT (32) 



in which the original variables C, W, T, S, and M 

 are expressed in standard deviation units and in 

 which the slopes (= path coefficients, see Li 1975) 

 allow for comparing the effects of W, T, S, and M 

 on C. These variables suggest that with regards to 

 their impact on C, 



T > W > M » S. 



(33) 



See Li (1975) for further inferences based on path 

 coefficients. 



In the southern North Sea in late summer-early 

 autumn, Limanda limanda experiences tempera- 

 tures usually ranging between 10° and 20°C (Lee 

 1972). Solving Equation (31) for T = 18°C, the 

 highest temperature in Pandian's experiments (i.e., 

 assuming the higher late summer-early autumn 

 temperatures limit WJ leads to estimates of W = 



500 g for the females and 298 g for the males, com- 

 pared with the values of 756 and 149 g obtained by 

 Lee (1972) on the basis of growth studies. 



Estimating values of /? that are wholly compatible 

 with the latter estimates of W^ is straightforward, 

 however, since it consists of solving Equation (31) 

 forT=18°C,M=0, and the appropriate value of 

 S, based on the equation 



P = 1/log W M (a + VVi + b 2 'V 2 . . . b n 'V n ) (34) 



In the present case, this leads to /3 values of 0.073 

 and 0.089 for females and male dab, respectively. 

 The "average" relationship (if such exists) between 

 food conversion efficiency and body weight in female 

 dab fed herring meat is thus 



K x = 1 - (H7756) 0073 



while for males it is 



K x = \ - (IF/149) 0089 



(35) 



(36) 



with both values of fi within the 95% confidence 

 interval of the first estimate of /3 (in Equation (27), 

 see Table 3). 



DISCUSSION 



The model presented here for the computation of 

 Q/B is not meant to compete against the more 

 sophisticated models whose authors were cited 

 above. Rather, it was presented as a mean of link- 

 ing up the results of feeding experiments with 

 elements of the theory of fishing such that infer- 

 ences can be made on the food consumption of fish 

 populations which 1) do not invoke untenable 

 assumptions, 2) make maximum use of available 

 data, and 3) do not require extensive field sampling. 



A distinct feature of the method is that it does not 

 require sequential slaughtering of fish for the esti- 

 mation of their stomach evacuation rate, nor field 

 sampling of fish stomachs, which may be of rele- 

 vance when certain valuable fishes are considered 

 (e.g., coral reef fishes in underwater natural parks). 



Several colleagues who reviewed a draft version 

 of this paper suggested that Equation (4) should in- 

 corporate an upper limit for K x smaller than unity. 

 This model would have the form 



K x = K lmax - (W/WJP™ 



(37) 



with parameters W^ and (i m identical and analogous 

 respectively to those in Equation (4) and a value of 



836 



