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Fishery Bulletin 88(4), 1990 



NORMSEP; 1971), Yong and Skillman (computer pro- 

 gram ENORMSEP; 1975), McNew and Summerfelt 

 (1978), and MacDonald and Pitcher (computer program 

 MIX; 1979). The distribution mixture method of 

 Schnute and Fournier (1980) uses a growth model to 

 impose these constraints. A second category of pro- 

 cedures assumes a specific growth function (usually the 

 von Bertalanffy) and attempts to match predicted 

 length modes to those observed. Among these methods 

 are the ELEFAN I procedure of Pauly and David 

 (1981), and Shepherd's length composition analysis 

 (1987). 



The Shepherd length composition analysis method 

 (SRLCA) (Shepherd 1987) relies on a goodness-of-fit 

 score function which varies according to the corre- 

 spondence of observed and predicted length-frequency 

 modes for given pairs of von Bertalanffy growth 

 parameters (L,„f and K), thus presumably constraining 

 the indication of optimal parameters to within biolog- 

 ically realistic bounds. SRLCA has fewer subjective 

 input requirements than the distribution mixture 

 methods (Shepherd 1987). Basson et al. (1988) per- 

 formed Monte Carlo tests of SRLCA and noted that 

 although SRLCA provided biased results for simulated 

 data with large variation in !ength-at-age, SRLCA 

 generally performed better than ELEFAN L 



To test the performance of SRLCA on an observed, 

 potentially difficult-to-interpret data set, as suggested 

 by Shepherd (1987), we applied a version of SRLCA 

 using the von Bertalanffy growth equation to research 

 trawl survey data for Gulf of Maine northern shrimp 

 Pandaliis borealis, and compared our results with ac- 

 cepted interpretations of the data. Currently, simple 

 visual inspection and information on sexual character- 

 istics are used to resolve survey length frequency to 

 age frequency, providing subsequent estimates of 

 relative adult stock abundance, recruitment success, 

 and total instantaneous mortality rates (Z) (Mclnnes 

 1986, NSTC 1987). Survey results reveal that this stock 

 has experienced variable recruitment and growth dur- 

 ing 1982 to 1988 (NSTC 1984, 1985, 1986, 1987, 1988). 

 Although true ages for northern shrimp are not avail- 

 able for use as "ground truth" in this evaluation of 

 SRLCA performance, we feel our assessment of the 

 method is valuable since it is based on application to 

 real data of the type which in practice might require 

 the use of length-based assessment methodolog}'. 



Methods 



Analysis 



SRLC'A compares the observed length-frequency dis- 

 tribution with that expected from the von Bertalanffy 



equation for given test pairs of L,„f and K by applica- 

 tion of a continuous, periodic test function of the form: 



T, = ((sin n {t„„„ - t„„„}] / (n {t,,,., - t„„„}]) 



X (cos 2n [t|,,„. - ts]) 



where T, is the value of the function for a given length 

 interval i, t,„ax and tmin are ages at the upper and 

 lower bounds of the interval for a given test set of 

 growth parameters, ti,ar is the average of t,,,^^ and 

 t^jn , and ts is the date of observation, expressed as a 

 fractional part of the age (e.g, annual) cycle (Shepherd 

 1987). 



A measure of goodness-of-fit is then used to deter- 

 mine the best fitting set of growth parameters for the 

 observed length-frequency distribution. This measure, 

 the score function S, is given by: 



S = X T,N,"^ 



where i indexes the length intervals, T is as indicated 

 previously, and N is the number of animals in each in- 

 terval. Taking the square root of N helps reduce the 

 sensitivity of the score function to unusually large 

 numbers of animals in a given length interval (e.g., in 

 the event of exceptional recruitment; Shepherd 1987). 

 Cumulative scores are large and positive when length 

 modes predicted for a given pair of growth parameters 

 are consistent with observed len.gth-frequency modes, 

 with negative scores indicating inconsistency. Shep- 

 herd (1987) suggested that regions of nearly constant 

 scores within the K by L,,,,- score matrix may provide 

 an indication of the shape of the confidence interval 

 around pairs of parameters (e.g.. Shepherd suggests 

 a region equal to one-half of the maximum score might 

 approximate the 95% confidence interval). Typically, 

 several regions (hereafter called ridges) of high scores 

 will be observed for each length-frequency distribution 

 analyzed, with local maxima in each ridge that provide 

 alternative interpretations of the data. 



Length-frequency data 



(kilf of Maine northern shrimp are protandric her- 

 maphrodites, with the females the target of a valuable 

 winter/spring fishery in the western Gulf of Maine (see 

 Mclnnes 1986 for an overview of the fishery). A re- 

 search vessel trawl survey was implemented in 1983 

 to provide a fisheries-independent source of data for 

 the stock. A stratified random trawl survey is con- 

 ducted annually during late July through mid-August 

 aboard the Northeast Fisheries Center (NEFC) RV 

 Gloria Michelle in the western Gulf of Maine (Fig. 1). 



