NOTE Francis et al.: Uncoupling otolith and somatic growth in Pagrus auratus 



163 



The key factor that must be considered when decid- 

 ing which back-calculation method to use is the accu- 

 racy with which it estimates back-calculated lengths. 

 Comparison of mean back-calculated lengths with mean 

 observed lengths can detect only gross errors (Francis 

 1990), and is not a good test for accuracy. Campana 

 (1990) used simulations to show that his method re- 

 moved much of the bias associated with a sagitta- 

 somatic growth-rate effect. The existence of a strong 

 growth-rate effect in juvenile snapper suggests that 

 Campana's method should be used to overcome the 

 expected bias. 



Campana's (1990) equation 4 corrects for growth- 

 rate variability among fish, while assuming linear 

 sagitta-somatic trajectories for individual fish. The need 

 for the latter assumption can be overcome by incorpo- 

 rating time-varying growth into the model (Campana 

 1990, eq. 7). However, there are two obstacles to use of 

 the time-varying model for snapper: First, the model 

 takes no account of sagitta and somatic size-at- 

 capture, which limits its use to back-calculation of 

 mean lengths; second, the model requires width mea- 

 surements from all daily increments between the bio- 

 logical intercept and capture, plus a proportional rela- 

 tionship between increment width and somatic growth. 

 For snapper, the relationship between increment width 

 and somatic growth is unknown. Furthermore, recent 

 work on other species has shown that changes in in- 

 crement width may lag or be unrelated to changes in 

 somatic growth (Molony & Choat 1990, Wright 1991). 

 For these reasons, we recommend that back-calcula- 

 tion of snapper lengths from daily increments be done 

 using Campana's equation 4. 



Acknowledgments 



We thank the University of Auckland for providing 

 research facilities and technical help at the Leigh Ma- 

 rine Laboratory. In particular, we thank M. Kampman, 

 B.S. Doak, and W Jackson for assistance in the field. 

 R.I.C.C. Francis advised on data analysis. Helpful com- 

 ments on the manuscript were given by J.D. Neilson, 

 D.H. Secor, J.M. Kalish, R.I.C.C. Francis, M.J. 

 Kingsford, and an anonymous reviewer. 



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