PAULY: ESTIMATING FOOD CONSUMPTION OF FISH POPULATIONS 



ly, these parameters do not provide information 

 which can be interpreted via another model. 



2) The model implies values of K 1 > 1 when a~ llb 

 > W > 0, which is nonsensical. 



3) The model implies that, except when W = 0, 

 K x is always > 0, even in very large fish, although 

 it is known that fish cannot grow beyond certain 

 species-specific and environment-specific sizes, 

 whatever their food intake. 



The new model proposed here has the form 



K x = 1 - (W/Wy (4) 



with ft as a constant and W m as the weight at which 

 K x = 0. The model implies that K x = 1 when W = 

 0, whatever the values of p and W^ (see Discussion 

 for comments on using values other than 1 as up- 

 per bound for K x in Equation (4)). The new model 

 can, as the traditional model, be fitted by means of 

 a double logarithmic plot: 



C = p log 10 W„- p log 10 W 



(5) 



where C = -log 10 (1 - K x ), the sign being changed 

 here to allow the values of C to have the same posi- 

 tive sign as the original values of K x . Interesting- 

 ly, it also appears that negative values of K x (based 

 on fish which lost weight), which must be ignored 

 in the traditional model, can also be used in this 

 model (as long as they do not drag the mean of all 

 available K x values below zero, see Table 1), 

 although their interpretation seems difficult. 



The new model requires no more data, nor 

 markedly more computations than the old one. It 

 produces "possible" values of K x over the whole 

 range of weights which a given fish can take. The 

 values of W^, which represent the upper bound of 

 this range can be estimated from 



W^ = antilog 10 (C intercept/ 1 slope |). (6) 



Thus, while p has no obvious biological meaning, 

 the values of W x obtained by this model do have a 

 biological interpretation, which is, moreover, anal- 

 ogous to the definition of W x in the von Bertalanffy 

 growth function (VBGF) of the form 



Table 1 .—Data on the food conversion efficiency of Channa striata (= Ophiocephalus 

 striatus) (after Pandian 1967), Epinephelus striatus (after Menzel 1960), and Hola- 

 canthus bermudensis (after Menzel 1958). 



'Mean of starting and end weights. 

 2 Growth increment/food intake. 



3 Note that the experiment considered here was conducted with a food which led to deposition 

 of fat, but not of protein (see also Table 2), a consideration that is ignored for the sake of this example. 



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