Somerton and Kobayashi: Inverse method for mortality and growth estimation 



373 



Figure 3 



Mean length-at-age in the simulated population (•), mean 

 length-at-age estimated without correction for size selection 

 (■), and mean length-at-age (±2 SE) estimated with IM- 

 MAGE (vertical bars). 



of the linear growth function [cf. Eq. (1)] were both 

 unbiased, as were all of the estimates of mean length- 

 at-age over the entire age range (Fig. 3). This indicates 

 that, at least for linear growth, IMMAGE provides un- 

 biased estimates of growth parameters from biased 

 length and age samples. 



Mortality 



For mortality estimation, the primary effect of the 

 decrease in capture probability with increasing larval 

 length is that relative abundance is progressively 

 underestimated with increasing age (Fig. 2b). If ig- 

 nored, such a progressive underestimation would result 

 in positively biased mortality estimates. In the sim- 

 ulated population, for example, mortality estimates 

 obtained from the observed length-frequency samples 

 (M = 0.450 ± 0.004) had a highly significant positive bias 

 of 125% (Fig. 4a). 



Elimination of the biased length-frequencies was only 

 partially effective in reducing the bias in estimated 

 mortality rates, because the mortality estimates (M = 

 0.364 ± 0.007) still had a highly significant positive bias 



of 80% (Fig. 4b). In practice, length elimination is likely 

 to be even less effective than it appears here, because 

 it is usually applied to cases where the capture prob- 

 abilities are crudely known, whereas exact knowledge 

 is assumed in the simulations. 



Figure 4 (right) 



Frequency distribution of 1000 simulated estimates of instantaneous 

 mortality rate computed from (a) observed length-frequency data, (b) 

 observed length-frequency data after eliminating all length-frequencies 

 with a capture probability of < 0.95, (c) observed length-frequency data 

 divided by estimates of capture probability, (d) corrected age-frequency 

 data after eliminating all age-frequencies with a capture probability of 

 <0.95, and (e) observed length-frequency data using IMMAGE. 



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