PAULY: ESTIMATING FOOD CONSUMPTION OF FISH POPULATIONS 



K lmax to be estimated independently prior to fitting 

 Equation (37) to data. 



Data do exist which justify setting the upper limit 

 of K x at or near unity. They pertain to fish em- 

 bryos, whose gross conversion efficiency can be 

 defined by 



Kx = 



W h 



w e - w y 



(38) 



where W h is the larval weight at hatching, W e the 

 egg weight, and W y is the weight of the yolk sac at 

 hatching. Values of K x as high as 0.93 have been 

 reported using this approach (From and Rasmussen 

 1984), extending further toward unity the range of 

 K x values reported by earlier authors, e.g., 0.85 in 

 Solea solea (Fliichter and Pandian 1968), 0.79 in Sar- 

 dinops caerulea (Lasker 1962), and 0.74 in Clupea 

 harengus (Blaxter and Hempel 1966). 



Thus, for a wet weight of 0.5 mg corresponding 

 to a spherical egg of 1 mm diameter, one obtains, 

 using Equation (14) for E. guttatus, a value of K 1 

 = 0.87 which is within the range of K x values given 

 above. This example is not meant to suggest that 

 K x values pertaining to large fish should be used in 

 combination with the model presented here to 

 "estimate" K 1 in eggs or larvae. Rather, it is 

 meant to illustrate the contention that, of the possi- 

 ble choices of an upper bound for K x in Equation 

 (4), the one selected here has the feature of making 

 the model robust, particularly with respect to high 

 values of K x and extrapolations toward low values 

 of W. 



Apart from (1, the key elements of the model 

 (isometric von Bertalanffy growth, constant ex- 

 ponential decay, steady-state population) are all 

 parts of other, widely used models. Thus, whether 

 estimates of QIB obtained by this model are con- 

 sidered "realistic" or not will depend almost entirely 

 on the value of (i used for the computation. 



There are several ways of reducing the uncertain- 

 ty associated with p. The following may need special 

 consideration: 



1) Feeding experiments used to estimate p could 

 be run so as to mimic as closely as possible the 

 crucial properties of the habitat in which the popula- 

 tion occurs whose QIB value is estimated, inclusive 

 of seasonally oscillating factors. 



2) Further research and study should lead to the 

 identification of anatomical, physiological, and 

 ecological properties of fish correlating with their 

 most common value of ft. 



3) An additional parameter could be added to 



account for fish reproduction, which is not explicit- 

 ly considered in Equation (22). 



Little needs to be said about item 1 which should 

 be obvious since (except in the context of aquacul- 

 ture) feeding and growth experiments are conducted 

 in order to draw inferences on wild populations. 

 With regards to item 2, it suffices to mention that 

 relative gill area ( = gill surface area/body weight), 

 which appears to a large extent to control food con- 

 version efficiency (Pauly 1981, 1984b), should be a 

 prime candidate for correlational studies. Item 3 

 could cause QIB values obtained by the model pre- 

 sented here to substantially underestimate actual 

 food consumption, were it not for three circum- 

 stances which produce opposite tendencies: 



a) The assumption that the energy needed by fish 

 to develop gonads is taken from the energy other- 

 wise available for growth may not apply (lies 1974; 

 Pauly 1984b). Rather, the reduction of activity 

 occurring in some maturing fish may more than 

 compensate for the energy cost of gonad develop- 

 ment (Koch and Wieser 1983). 



b) Growth parameters are usually computed using 

 size data from fish whose gonads have not been 

 removed, thus accounting for at least a fraction of 

 the food converted into gonad tissue. When the 

 value of Z used in the model is high, this fraction 

 will be large because the contribution of the older 

 fish to the overall estimate of QIB will be small. 



c) Experimental fish are usually stressed and 

 therefore have lower conversion efficiencies than 

 fish in nature, even though they may spend little 

 energy on food capture (see Edwards et al. 1971). 

 This effect leads to low values of ft and hence high 

 estimates of QIB. 



Because of these factors, the values of QIB obtained 

 by the method proposed here may lack a downward 

 bias. 



ACKNOWLEDGMENTS 



I wish to thank R. Jones (Aberdeen), as well as 

 E. Ursin (Charlottenlund), A. McCall (La Jolla), J. 

 J. Polovina (Honolulu), P. Muck (Lima), and the two 

 anonymous reviewers for their helpful comments on 

 the draft of this paper. 



LITERATURE CITED 



Allen, K. R. 



1971. Relation between production and biomass. J. Fish. 



837 



