Schirrlpa: An evaluation of back calculation methodology using simulated otolith data 



791 



1500 



00 10 20 3.0 4.0 





D 



3 4 1.0 



Otolith radius (mm) 



20 



3.0 



4 



Figure 1 



Scatter plot of the four simulated otolith radius-total length relations (OR-TLs). (A) OR-TL/SIG = 

 sigmoid shaped; t B I OR-TIVLIN = linear shaped; ( C ) OR-TL/EXP = exponentially shaped; (D) OR-TL/ 

 ASYM = asymptotically shaped. 



D _ D 333 



O^ was then calculated as 



O^ = Bjx0.5. 

 Otolith radius-total length relation 



(5) 



(6) 



The OR-TL relation was fitted as closely as possible to 

 that reported for striped bass by Heidinger and Clodfelter 

 1 1987 ). Modeling the conversion factor o^ ( Eq. 3 ) as a func- 

 tion enabled me to generate four different OR-TL relations 

 typically found in nature. A sigmoid shaped OR-TL (OR- 

 TL/SIG) relation (Fig. lA) relation was achieved by setting 

 the parameter a,, = 0.08 and modeling the parameter 04 as 

 a function of body length: 



a^ =9-(-(-7xSin(0.006xLen^//!)-h5). 



(7) 



A linear shaped OR-TL (OR-TL/LIN) relation (Fig. IB), as 

 found in striped bass (Heidinger and Clodfelter, 1987) was 

 achieved by setting the parameter Oj (from Eq. 1) to 0.85 

 and modeling otolith radius as a function of brain length 

 (the parameter 04 was not necessary for this relation). 

 An exponential OR-TL( OR-TL/EXP) relation (Fig. IC), 

 similar to that found for vermilion snapper, Rhomhoplites 

 aurorubens, (Grimes, 1978) was achieved by again setting 



the parameter a., to 0.08 and modeling the parameter a^ 

 as a linear function of otolith weight: 



= 25-(1.75xO„ 



(8) 



An asymptotic OR-TL (OR-TL/ASYM) relation (Fig. ID), 

 similar to that found for walleye, Stizostedion vitreum, 

 (Heidinger and Clodfelter, 1987), was achieved by keeping 

 the parameter Cg = 0.08 and modeling the parameter a^ as 

 a function of total length: 



a, = Q.1\1E- 12 xLength\ 



(9) 



Mortality 



Mortality could occur from three sources: direct starvation, 

 random natural mortality based on length, and fishing mor- 

 tality. If a fish lost more than a specified percentage of its 

 maximum attained body weight (359f for larvae and 50% 

 for juveniles), it died from starvation. Fishing mortality was 

 described first as an overall value (F=0.4) and then divided 

 by 365 to calculate a daily value. In order to ensure that 

 there would be no sampling bias due to gear selectivity, fish- 

 ing mortality was assumed to be nonselective (random). 



The four simulated OR-TL relations were described by 

 using four different functions: 1) ordinary least squares 

 (OLS) linear regression (model I) 



