FISHERY Hl'LLETIN: VOL. 86, NO. 4 



contributing to tlie high estimates of K. First, the 

 relatively fast growth rate and high mortality re- 

 sulted in early overlapping or accumulation of dis- 

 tributions and in large fish being rare so that team 

 B could never identify more than 3 out of 4 modes 

 corresponding to fished age classes using the Bhat- 

 tacharya method in any sample (Fig. 2a). Second, 

 the third mode was consistently overestimated 

 because the distributions for age classes 3 and 4 

 were merged together. Third, the young-of-the-year 

 fish do not appear in the samples as a well-defined 

 distribution until late in the monthly time series of 

 samples because recruitment does not take place un- 

 til June. Finally, we found that estimates of /iT using 

 the Gulland and Holt plot in the LFSA package were 

 very sensitive to small deviations in the estimates 

 of modal lengths obtained using the Bhattacharya 

 method. 



Total mortality estimates for situation 1 using 

 the estimated K and L^ values were not good for 

 either package. Estimates of Z using the actual K 

 and L^ values used in the simulations were within 

 35% and 45% of the expected Z (Table 2). 



Situation 2 was the sparid/lutjanid type, character- 

 ized by a single recruitment peak per year and 5 

 distributions corresponding to the 5 fished cohorts 

 in the catch (Fig. 2b). Both methodologies gave 

 similar estimates of K, close to the actual value. 

 However, L^ was overestimated by ELEFAN and 

 underestimated by the LFSA package. The mean 

 estimate of Z was within 32% of the expected Z for 

 the ELEFAN catch curve analysis and within 13% 

 for the LFSA package analysis. Mean Phase H 

 estimates of Z were 20% and 15% above the ex- 

 pected Z (Table 2). 



Situation 3, the sparid/lutjanid type with two re- 

 cruitment peaks per year (Fig. 2c) produced good 

 results using ELEFAN. However, modal progres- 

 sion estimates of K were low, with corresponding 

 underestimates of Z (Table 2). Component distribu- 

 tions were poorly defined compared to situation 2; 

 age classses 4 and 5 were often obscured by the age 

 class 3 distribution. Incorrect separation of distribu- 

 tions and bad estimates of growth parameters were 

 therefore not unexpected. 



For the last situation, the sparid/lutjanid type with 

 stochastic recruitment (Fig. 2d), estimates of K, 

 L^, and Z were generally good for both packages. 

 However, as shown by the standard deviations, the 

 range of estimates for certain parameters was 

 quite high. This was the case for K estimated by 

 ELEFAN and L^ estimated by modal progression 

 analysis in the LFSA package. 



DISCUSSION 



This preliminary study has shown that, as ex- 

 pected, the structure of the data has a big effect on 

 the estimates derived using length-frequency pack- 

 ages. In general, the results were encouraging. 

 However, it should be noted that the simulated 

 length-frequency distributions can be regarded as 

 representing high-quality samples of the hypothe- 

 tical populations in terms of lack of bias, sample 

 size, and frequency of sampling. In other words, 

 real life length-frequency data is seldom of this 

 quality. 



The modal progression analysis implemented by 

 Sparre (1986) was more sensitive to the structure 

 of the length-frequency samples. Worst results in 

 terms of estimation of growth parameters were ob- 

 tained under multiple recruitment (situation 3) and 

 fast growth and high mortality (situation 1). A fun- 

 damental problem with the Bhattacharya method 

 is the inability to identify modes at the upper end 

 of the size spectrum, particularly when there is fast 

 growth or many age groups. Identification of modes 

 using the Bhattacharya method might have been im- 

 proved by using smaller size class intervals, par- 

 ticularly for situation 1. However, even when there 

 was little ambiguity in the selection of modes using 

 the Bhattacharya method, it was found that the 

 Gulland and Holt plot for estimating K and L^ was 

 very sensitive to small underestimates and over- 

 estimates of the modes considered to represent 

 growth over time. 



Length converted catch curve estimates of total 

 mortality are highly dependent on the estimated 

 growth parameters. Consequently, estimates of Z 

 generally paralleled estimates of K and L^ and 

 were not as good as estimates of Z obtained using 

 the actual simulation values of K. These latter esti- 

 mates of Z were generally close to actual Z values 

 for all situations despite the fact that the length- 

 frequency data necessarily did not meet steady-state 

 assumptions because of variable recruitment and 

 mortality. However, the variability of mortality 

 rates was deliberately kept small because the pri- 

 mary objective was to examine the effects of differ- 

 ent recruitment patterns. 



ELEFAN, the Bhattacharya, and the modal pro- 

 gression method of the LFSA package all require 

 subjective decision making by the user. It would 

 seem that ELEFAN is less subjective or that poor 

 choices are less likely to be made by the user than 

 in the selection of modes by the Bhattacharya 

 method and in the choice of modes for the modal 



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