Abstract.- We applied Shep- 

 herd's length composition analysis 

 (SRLCA) to research trawl survey 

 catches of Gulf of Maine northern 

 shrimp Panddlug horealis to test the 

 efficiency of the method in interpret- 

 ing the age structure of a length- 

 freiiuency distribution incorporating 

 significant variation in growth and 

 recruitment rates. We evaluated the 

 performance of the method by com- 

 paring the von Bertalanffy growth 

 parameters provided by SRLCA antl 

 subsequently derived age frequen- 

 cies and instantaneous total mortal- 

 ity rates with previously accepted 

 results based on simple visual inspec- 

 tion of the annual length-frequency 

 distributions. 



In spite of the variable growth and 

 recruitment rates exhibited by the 

 stock, SRLCA yielded information 

 providing a resolution of the length- 

 frequency data close to a priori as- 

 sumptions, although information ex- 

 ternal to the procedure was needed 

 to select the best interpi'etation from 

 among several locally optimal solu- 

 tions. 



A Practical Assessment of the 

 Performance of Shepherd's Length 

 Composition Analysis (SRLCA): 

 Application to Gulf of Maine 

 Northern Shrimp Pandalus 

 borealis Survey Data 



Mark Terceiro 

 Josef S. Idoine 



Woods Hole Laboratory, Northeast Fisheries Science Center 



National Manne Fisheries Service, NOAA, Woods Hole, Massachusetts 02543 



Manuscript accepted 18 June 1990. 

 Fishery Bulletin, U.S. 88:761-773. 



The analysis of length-frequency modes 

 was the first method used l)y aquatic 

 biologists to delineate successive co- 

 horts in fish and invertebrate popula- 

 tions. Simple visual inspection of modes 

 was developed first (e.g., the "Peter- 

 sen" method [Petersen 1891]); this 

 relies heavily on the intuition of the 

 scientist for the cori-ect separation of 

 age groups. Later workers assumed 

 a normal distribution underlying the 

 observed length modes, and graph- 

 ical methods using normal probabil- 

 ity paper were used to resolve length 

 distributions to cohorts by the suc- 

 cessive identification and removal of 

 suspected age groups. The method of 

 Cassie (1954) is probably the best 

 known of these graphical procedures, 

 which rely to a large degree on sub- 

 jective decisions of the scientist. Dif- 

 ficulty in defining modes for older 

 age groups, problems in interpreta- 

 tion caused by variable growth rates 

 and recruitment, and an inability to 

 reproduce the interpretation of age 

 groups from one worker to the ne.xt 

 have limited the utility of these sim- 

 ple methods. 



For most finfish stocks, the inter- 

 pretation of growth intervals on hai'd 

 body parts (e.g., scales, otoliths, spines, 

 and vertebrae) has evolved as the 

 ageing method of choice, replacing 

 length-composition analysis methods. 



For many taxa, however, the inter- 

 pretation of growth intervals from 

 age structures is difficult, either due 

 to problems in identifying periodic 

 marks or because of the lack of suit- 

 able hard structure. For fast-grow- 

 ing, short-lived tropical finfish, and 

 invertebrates such as lobsters, crabs, 

 shrimps, and squids, the resolution to 

 ages of modes in length-frequency 

 distributions continues to be the pri- 

 maiy method used to estimate growth 

 and age structure of populations. Re- 

 cently developed methods directed to 

 interpreting length-frequency distri- 

 butions generally fall into two cate- 

 gories. The first group treats the 

 problem as one of statistically resolv- 

 ing a mixture of distributions, and 

 usually assumes an underlying nor- 

 mal distribution for the components. 

 The parameters resulting in the best 

 match between the area under the 

 theoretical distribution and the area 

 under the observed length distri- 

 bution are selected by employing 

 chi-square or maximum likelihood 

 methods. These distribution mixture 

 methods require some prior constraint 

 on the number of length modes and 

 the bounds of the parameters to 

 prevent biologically unrealistic re- 

 sults. The lineage of this approach in- 

 cludes the methods of Hasselblad 

 (19(i6), Tomlinson (computei- progi-am 



761 



