FISHERY BULLETIN: VOL. 84, NO. 4 



W t = W m (1 - e -^- f o))3 



(7) 



(von Bertalanffy 1938; Beverton and Holt 1957), and 

 where W t , the weight at time t, is predicted via the 

 constants K, t , and W^, all three of which are 

 usually estimated from size-at-age data obtained in 

 the field (see Gulland 1983 or Pauly 1984a). 



That W x values obtained via Equations (2) and (6) 

 are realistic can be illustrated by means of that part 

 of the data in Table 1 pertaining to Channa striata 

 (= Ophiocephalus striatus), the "snakehead" or 

 "mudfish" of south and southeast Asia. These data 

 give, when fitted to the traditional model 



K Y = 0.482 If" - 205 . 



(8) 



The same data, when fitted to the new model give 



K x = 1 - (Ml,580) 0073 . (9) 



(See Figure 1 for both models.) The value oiW 00 = 

 1,580 g is low for a fish which can reach up to 90 

 cm in the field (Bardach et al. 1972). However, its 

 growth may have been reduced in laboratory growth 

 experiments conducted by Pandian (1967). 



Equation (6) used here to predict W^ is extreme- 

 ly sensitive to variability in the data set investigated, 

 and two approaches are discussed to deal with this 

 problem. 



The first approach is the appropriate choice of the 

 regression model used. In the example above (Equa- 

 tion (9)), the model used was a Type I (predictive) 

 regression, which is actually inappropriate, given 

 that 



1) the log 10 W values are not controlled by the 

 experimentator and 



2) regression parameters are required, rather 

 than prediction of C values (see Ricker 1973). 



The use of a Type II ("functional", or "Geometric 

 Mean") regression appears more appropriate; con- 

 version of a Type I to Type II regression (with 

 parameters a, b') can be performed straight- 

 forwardly through 



b' = bl\r\ 



and 



a = C - b' log 10 W 



(10) 



(11) 



where r is the correlation coefficient between the 

 C and the log 10 W values (Ricker 1973). In the case 



of the example here, one obtains with r = 0.942 a 

 new model: 



K x = 1 - (W71,290) 0077 



(12) 



close to that obtained using a Type I regression, due 

 to the high value of r of this example. However, in 

 cases where the fit to the model is poor, the use of 

 a Type II regression can make all the difference 

 between realistic and improbable values of W^. 



Another approach toward optimal utilization of 

 the properties of the new model (4) is the use of "ex- 

 ternal" values of asymptotic weight, which will here 

 be coded W^ to differentiate them from values of 

 W x estimated through the model. In such case, (i 

 can be estimated from 



P = C/(log 10 W M - log 10 W) 



(13) 



in which W {ao) is an asymptotic size estimated from 

 other than food conversion and weight data, e.g., 

 from growth data or via the often observed close- 

 ness between estimates of asymptotic size and the 

 maximum sizes observed in a given stock (see Pauly 

 1984a, chapter 4). 



These two approaches are illustrated in the exam- 

 ple below, which is based on the data in Table 1 per- 

 taining to the grouper Epinephelus guttatus. When 

 Equation (6) is interpreted as a Type I regression, 

 these data yield a value of W^ > 12 kg, which is far 

 too high for a fish known to reach 55 cm at most 

 (Randall 1968). Interpreting Equation (5) as a Type 

 II regression leads to a value of W x = 3.5 kg which 

 is realistic, although still not close to the asymptotic 

 weight of 1,880 g estimated by Thompson and 

 Munro (1977). Finally, using the latter figure as an 

 estimate of W {oo) yields the model 



K x = 1 - (W/1,880) 0136 



(14) 



as a description of the relationship between K x and 

 weight in Epinephelus guttatus (Fig. 2). The value 

 of p in Equation (14) lies within the 95% confidence 

 interval of the value of p = 0.060 which generated 

 the first unrealistically high estimate of W m . 



MODEL FOR ESTIMATING 



THE FOOD CONSUMPTION 



OF FISH POPULATIONS 



When feeding experiments have been or can be 

 conducted under conditions similar to those prevail- 

 ing in the sea (food type, temperature, etc.), the 



830 



