Xiao: Use of the original von Bertalanffy growth model to describe the growth of barramundi, Lates cakanfer 



839 



mum rate on 3 or 4 March (i.e. at the start of autumn) 

 (Fig. 1). Thus, its length gi'ows fastest on 3 or 4 March (i.e. 

 at the start of autumn), grows less until a full stop on 17 

 July (i.e. in the middle of winter), shrinks until 19 or 20 

 October (i.e. in the middle of spring), and resumes a posi- 

 tive gi'owth for another cycle. Thus, barramundi does not 

 grow in length for three months in a year, from 17 July 

 (i.e. in the middle of winter) to 19 or 20 October (i.e. in 

 the middle of spring). However, Equations 8 and 11 have 

 different assumptions and predict different amplitudes of 

 seasonally varying growth rate. Such a strong seasonality 

 in gi'owth rate might be related to seasonal changes in the 

 availability of food and in water temperature. 



Similarly, tagging may adversely affect the growth of 

 barramundi perch and bias estimates of parameters in a 

 growth model, where its effects are not taken into proper 

 account. In fact, Xiao (1994) has already interpreted the 

 same set of data in terms of the effects of tagging. How- 

 ever, it is impossible to identify the right model from all 

 possible models, because of the inductive nature of model- 

 ing and because of our poor understanding of the underly- 

 ing mechanisms of growth and how tagging affects growth. 

 In a preliminary analysis, I have constructed a model, and 

 have attempted (but failed) to estimate, simultaneously, 

 both the effects of tagging and seasonally varying growth 

 rates. Such a failure is not surprising because the amount 

 of information in a set of tagging data is limited. Further 

 progress can be made only by better understanding the 

 underlying mechanisms of growth. 



This work also puts some of Pauly's (1981) work into 

 perspective. For example, or'''*y/K and K//3 in Equation 9 

 can be interpreted respectively as the average maximum 

 size and growth rate of a species. As Pauly (1981) pro- 

 posed, the product (or'''*)'/K)(K//3) = cr'''*y/j3 is indeed an 

 index of growth performance because it is in direct pro- 

 portion to the mean anabolic rate. Similarly, or"'V/K and 

 yiji in Equation 12 can be interpreted respectively as the 

 average maximum size and growth rate of a species. The 

 quotient (}'//3)/(or"'^7/K) = a'''T<//3 is an index of catabolic 

 performance, because it is in direct proportion to the mean 

 catabolic rate. 



Finally, anabolic and catabolic rates of animals can be 

 estimated from data from a mark-recapture experiment 

 on two distinct lengths of the same individual measured at 

 different times. Thus, the present work has demonstrated 

 a way to estimate anabolic and catabolic rates of animals. 

 Such field-based estimates can be compared with those 

 obtained under laboratory conditions. 



Acknowledgments 



1 wish to thank three anonymous referees for their very 

 constructive and valuable comments on the manuscript, 

 Kate Watt (SARDI Aquatic Sciences Centre) for producing 

 Table 1, and Roland K. Griffin (Northern Territory Depart- 

 ment of Primary Industry and Fisheries) and Tim L. O. 

 Davis (CSIRO Division of Fisheries) for supplying L. cal- 

 carifer data. Roland K. Griffin also provided some refer- 

 ences on L. calcarifer. 



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