COMPARISON OF TWO LENGTH-FREQUENCY BASED PACKAGES FOR 



ESTIMATING GROWTH AND MORTALITY PARAMETERS USING 



SIMULATED SAMPLES WITH VARYING RECRUITMENT PATTERNS 



Margarida Castro and Karim Erzini' 



ABSTRACT 



Length-frequency distributions were simulated for species with recruitment patterns characteristic of 

 many tropical fish; 1 ) one recruitment peak per year, fast growth and very high mortality, 2) one recruit- 

 ment peak per year, slow growth and moderate to high mortality, 3) two recruitment peaks per year, 

 slow growth and moderate to high mortality, and 4) random recruitment, slow growth and moderate 

 to high mortality. Two microcomputer program packages— one incorporating the ELEFAN I & II pro- 

 grams and the other implementing a form of Modal Progression Analysis— were used to estimate growth 

 and mortality parameters, and these were compared with the initial parameters used to generate the 

 simulated samples. The results, while generally encouraging, suggest that multiple recruitments per year 

 make it difficult to estimate growth and mortality parameters using these two packages. 



Information concerning growth, mortality, and 

 recruitment patterns is of great importance in 

 lengtli-frequency analysis. The purpose of this paper 

 was to evaluate two sets of methods used in length- 

 frequency analysis in terms of their ability to 

 produce accurate estimates of growth and mortal- 

 ity parameters in the absence of such biological 

 information. 



The methodology chosen consisted of generation 

 of length-frequency distributions with known pa- 

 rameters to which the length-frequency methods 

 were applied. The results obtained with the method 

 were compared with the initial conditions. This pro- 

 cedure has been used in other studies (Hampton and 

 Majkowski 1987; Jones 1987). 



The development of the program for simulating 

 length frequencies was guided by assumptions im- 

 plicit in the length-frequency methods and by known 

 factors concerning the biology offish. These include 

 1) average individual growth in accordance with the 

 von Bertalanffy growth curve, 2) little variation in 

 natural mortality throughout the exploited phase, 



3) exponential decline in the numbers of a cohort, 



4) length distributions normal for each age class, 

 and 5) recruit numbers random. Some other fea- 

 tures of the program, such as the selectivity of the 

 gear (logistic type) are not standard assumptions of 

 length-frequency methods but are options for pa- 

 rameters necessary to describe the effect of fishing. 



'Graduate School of Oceanography, Narragansett Bay Campus, 

 University of Rhode Island, Narragansett, RI 02882. 



The authors believe that the simulated length fre- 

 quencies accurately reflect the assumptions of the 

 length-frequency methods and therefore the gener- 

 ated samples can be used to test, correct, and pos- 

 sibly improve these methods. The simulated sam- 

 ples might also help to define a range of situations 

 when a specific length-frequency method can or can- 

 not be used. 



Traditionally, length-frequency analysis methods 

 have been used as validation methods for age deter- 

 minations made independently. Recently, these tech- 

 niques have grown in importance and frequency of 

 use, in particular in tropical fisheries, where age 

 determinations based on direct reading of check 

 marks in hard parts of the fish are difficult, and in 

 crustaceans, which do not have permanent hard 

 structures. As a result, length-frequency analysis 

 has been used in situations where very little is 

 known about the biology of the species. 



It is the purpose of this work to contribute to the 

 understanding of the possible errors that are made 

 when length-frequency analysis is used without 

 biological information on mortality levels, growth 

 parameters, and, in particular, recruitment pat- 

 terns. It might be argued that such methods of 

 length-frequency analysis are particularly useful in 

 the situations described above, precisely because 

 they do not require a priori knowledge of biological 

 information. The question then becomes, is it legit- 

 imate to use length-frequency analysis techniques 

 in the absence of minimum biological information? 

 And if the answer to this question is no, then what 



Manuscript accepted July 1988. 



FISHERY BULLETIN: VOL. 86. NO. 4, 1988. 



645 



