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



793 



the fish from which they are calculated become older) or a 

 similar effect would result in a negative slope. If there is 

 no bias caused by this approach, the expected value of this 

 slope is zero when randomly sampled from an unfished 

 population. 



The accuracy of each of the twenty methods of back-cal- 

 culation was evaluated by plotting the percent error of the 

 estimated length-at-age in relation to the true value. As 

 an overall evaluation of the method, a sum-of-squares (SS) 

 was calculated by squaring the percent error between the 

 estimated length-at-age and the true length-at-age and 

 summing across all ages. 



tion of the age used in the back-calculation. This lack of 

 trend, and the high degree of similarity between the mean 

 length-at-age of the population and catch suggested that 

 the catch was a random and representative sample of the 

 population. 



Methods 2, 4, 6, 8, and 9 resulted in the least bias and 

 method 1 the most bias when the slopes were examined 

 across the various shapes of the OR-TL relation (Fig. 3). 

 The linear shaped OR-TL (OR-TL/LIN) relation resulted 

 in the least amount of bias, and the exponential shaped 

 OR-TL (OR-TL/EXP) relation resulted in the most when 

 the various relations were examined across methods. 



Results 



The true underljdng mean length-at-age of both the sur- 

 viving population and the catch (Table 2) was calculated 

 and tabulated in standard back-calculation type tables. 

 There was no apparent trend in the estimates as a func- 



Sigmoid-shaped OR-TL relation 



Of the four functions fitted to the OR-TL/SIG relation 

 (Table 3), the Weibull cumulative function resulted in the 

 highest coefficient of determination (r'-=0.914); however 

 the coefficient of determination of the quadratic fit was 

 very similar (r^=0.913). 



