370 



Fishery Bulletin 90(2). 1992 



Figure I 



Comparison of the bias- 

 correction and IMMAGE 

 approaches to estimating 

 instantaneous mortality 

 rate (M) from selection- 

 biased length-frequency 

 data. Bias correction Oeft 

 column) begins by dividing 

 (a) the observed length- 

 frequency distribution by 

 estimates of capture prob- 

 ability to estimate (b) the 

 unbiased length distribu- 

 tion. The unbiased length 

 distribution is then con- 

 verted to (c) an age distribu- 

 tion, and M is estimated 

 with (d) linear regression. 

 IMMAGE (right column) 

 begins by creating (e) an 

 unbiased age distribution 

 using initial estimates of M 

 and the number of day-0 

 larvae, N„. The unbiased 

 age distribution is con- 

 verted to (f) an unbiased 

 length distribution using 

 the ageing sample, (g) The 

 unbiased length distribution 

 is multiplied by the capture 

 probabilities to estimate the 

 sampled length distribution 

 (solid line), then mortality 

 estimates are varied itera- 

 tively to minimize the resid- 

 ual sum of squares between 

 the observed (histogram) 

 and the estimated length 

 distributions. 



BIAS CORRECTION 



IMMAGE 



150 

 12S 



£100 



75 



, I r?' , lU 



flHr. , ,,, T i, 



4 6 10 12 14 16 ie 20 22 24 26 26 30 

 Langth (mm) 



4 6 B 10 12 14 16 16 20 22 24 26 28 30 

 L*ngth (mm) 



•| 10 



4 6 9 10 12 14 16 16 20 22 24 26 26 30 



Length (mm) 



4 6 10 12 14 16 162022 24 26263032 34 



Length (mm) 



"300 



I 200 



I 200 



i 



I 



wm 



Hf^^nnr 



012345676 9 10 1112 13 14 15 

 Age (days) 



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 Age (days) 



MORTALITY 

 ESTIMATE 



0123456769 101112131415 

 Age (days) 



surement is associated with an age. Ageing samples 

 are considered biased when used in growth parameter 

 estimation but are considered unbiased when used in 

 mortality parameter estimation. This distinction is made 

 because mortality parameters can be influenced by 



selection bias in ageing samples as well as by selection 

 bias in the length-frequency samples. To simplify inter- 

 pretation of the results and avoid compounding the ef- 

 fects of the two sources of bias, bias in the ageing 

 samples has been ignored in the mortality estimation. 



