CASTRO AND ERZINI: COMPARISON OF LENGTH-FREQUENCY PACKAGES 



normal. The decomposition of each length-frequency 

 sample into component distributions is carried out 

 by plotting a logarithmic transformation of the dif- 

 ferences between successive length frequencies. A 

 normal distribution appears as a series of values 

 making up a straight line with a negative slope. In 

 the LFSA package, which implements the Bhat- 

 tacharya (1967) method, the user selects the points 

 believed to make up a normal distribution, and the 

 mean, standard deviation and various other 

 statistics are computed. In the next step, the means 

 of all distributions are plotted against time and the 

 mean lengths thought by the user to reflect the pro- 

 gression of a cohort are linked. Finally, growth 

 parameters are computed from the linked modes by 

 a method referred to as a Gulland and Holt plot 

 (Gulland and Holt 1959). 



In both packages, the growth parameters are used 

 to create age based catch curves for estimation of 

 instantaneous annual total mortality, Z. Therefore, 

 except for the estimation of Z, the methodologies 

 of the two packages are quite independent. However 

 they are both characterized by a certain degree of 

 subjectivity. 



Methodology 



Following the suggestion of Hampton and Maj- 

 kowski (1987), two different teams were formed. 

 One (team A) created the simulated samples (10 

 cases of 12 monthly samples for each situation), and 

 another (team B) ran the length-frequency analysis. 

 The 40 cases were given arbitrary filenames and 

 were mixed by team A prior to analysis by team B. 

 This was done to avoid influencing the choice of ini- 

 tial values or parameter ranges, required by some 

 of the methods applied. In estimating the growth 



parameters using the LFSA package, constraints 

 on the limit of acceptable estimates of L^ were 

 guided by the value of the midpoint of the largest 

 size class in each particular case. For analysis by 

 ELEFAN I & II, the size of the largest length class 

 also helped guide the choice of range of potential 

 values of L^. Team A provided information to 

 team B in different phases. In phase 1, samples were 

 provided to team B with information on mesh size, 

 and only broad descriptions of the type of species, 

 and indications of fishing mortality levels. Team B 

 analyzed the length-frequency samples with both 

 packages to the best of his ability. In Phase 2, exact 

 information on growth, mortality, and number of 

 age classes was provided and new estimates of Z 

 were obtained using both packages. The results pro- 

 duced by team B are presented in Table 2. 



It should be noted that expected values for Z in 

 Table 2 are less than the sums of F and M in Table 

 1. This is because Table 1 values are inputs, and F 

 is subsequently corrected for selectivity. 



RESULTS 



In situation 1, the sardine-type species with one 

 recruitment peak per annum, the samples were 

 simulated using growth parameters typical of a 

 small clupeid with high fishing effort expressed by 

 a high value oiF and small mesh size. Thus a typical 

 length-frequency sample consists of 4 component 

 distributions or 4 cohorts (Figure 2a). While esti- 

 mates of the growth parameters by ELEFAN were 

 very good, the LFSA package estimates of i(^ were 

 surprisingly high. 



Close examination of the length frequencies, the 

 Bhattacharya method and Gulland and Holt plot im- 

 plemented by Sparre revealed a number of factors 



Table 2.— Results of estimation of growth and mortality parameters (mean and standard deviation) using 

 ELEFAN and LFBFSA packages. Z, and Zj are total mortalities calculated using estimated and actual K 

 and L„ values. 



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