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Fishery Bulletin 105(4) 



Appendix 



The spreadsheets of the computer application Microsoft 

 Excel (Microsoft Co., Tokyo, Japan) were used as an 

 analysis platform, and an add-in tool solver was used 

 for the optimization of the present OL-FL equation. The 

 solver has been standard add-in tool in Excel since the 

 Excel 95 version. The optimized value of the parameters 

 and the Akaike's information criterion (AIC) in the pres- 



ent equations were identical with the use of Excel 2003 

 and Excel 2007. The modified spreadsheet of a Microsoft 

 Excel workbook shows how to fit the two-phase allome- 

 tric smoothing function for the otolith length (OL) and 

 fork length (FL) relationship (Appendix Table below). 

 The most suitable equation to describe the relation 

 between otolith length and somatic length was chosen 

 if it accorded with the minimum AIC. 



