A statistical method for evaluating 

 differences between age-length keys 

 with application to Georges Bank 

 haddock, Melanogrammus aeglefinus 



Daniel B. Hayes 



Woods Hole Laboratory, Northeast Fisheries Science Center 



National Marine Fisheries Service, NOAA 



1 66 Water Street, Woods Hole, MA 02543-1 097 



Age-length keys are a critical com- 

 ponent of many methods used to es- 

 timate catch at age (Southward, 

 1976; Kimura, 1977; Gavaris and 

 Gavaris, 1983; Quinn et al., 1983; 

 Lai, 1987; Martin and Cook, 1990). 

 When formulating age-length keys 

 for use in stock assessment, the ap- 

 propriate time interval for data col- 

 lection and aggregation is an im- 

 portant consideration. Potentially, 

 an age-length key derived from data 

 taken at a single time during the 

 year could be used to compute catch 

 at age for the entire year. This prac- 

 tice runs the risk of producing in- 

 accurate estimates of catch at age, 

 however. Finer time intervals for 

 age-length keys are typically used 

 (e.g., quarterly or monthly) but at a 

 cost of increased sampling require- 

 ments. Generally, intensive sam- 

 pling over brief time intervals 

 provides the most accurate repre- 

 sentation of age at length in the 

 population (Kimura, 1977; Westr- 

 heim and Ricker, 1978). In practice, 

 however, such a strategy is expen- 

 sive to implement because of the 

 labor-intensive nature of collecting 

 and processing large numbers of 

 fish for age data. For the efficient 

 and cost-effective use of sampling 

 resources, it is desirable to sample 

 and age the fewest fish, giving ad- 

 equate precision while avoiding bi- 

 ased results. The data needed can 

 be considerably reduced if appropri- 

 ate time intervals for age-length 

 keys can be defined. 

 550 



A further problem facing fishery 

 scientists is the need for evaluation 

 of samples collected with different 

 gears. Although fishing gears may 

 select for fish size, the question here 

 is whether the gears select for fish 

 with different proportions of age at 

 length. For example, the Northeast 

 Fisheries Science Center (NEFSC) 

 of the National Marine Fisheries 

 Service samples most of the com- 

 mercially important fish stocks off 

 the northeastern United States with 

 bottom trawls during the spring and 

 autumn. The fish collected in these 

 surveys have a substantially differ- 

 ent size composition than the com- 

 mercial catch because the standard 

 survey trawl has a small mesh 

 codend liner. However, it is un- 

 known whether fish of a given 

 length caught in the research sur- 

 vey trawl differ in age composition 

 from fish of the same length har- 

 vested commercially. If the age at 

 length of fish captured is the same 

 for these gears, then a pooled key, 

 including data from research sur- 

 veys, will increase precision by in- 

 creasing sample size but will not 

 bias catch at age estimates. How- 

 ever, if age-length keys differ, then 

 pooling can introduce bias into es- 

 timates of catch at age (Westrheim 

 and Ricker, 1978). 



The primary objective of this 

 study is to present a method for de- 

 termining whether two age-length 

 keys differ statistically. This method 

 is then applied to Georges Bank 



haddock to determine what time in- 

 tervals should be used for age- 

 length keys for this stock and to 

 determine if research trawl-survey 

 age data can be combined with age 

 data from commercially harvested 

 haddock. The benefit (in terms of 

 increased precision) of pooling age- 

 length keys, where appropriate, is 

 also determined. 



Methods 



Biological sampling 



Scales were collected from commer- 

 cially landed haddock in the NEFSC 

 port sampling program. Because 

 sampling requests to this program 

 are filled quarterly, age-length keys 

 and the age structure of landings 

 were computed on a quarterly ba- 

 sis as in previous stock assessments 

 (Clark et al, 1982; Gavaris and Van 

 Eeckhaute, 1990). Length at age by 

 month was averaged over several 

 years (1980 to 1988) to determine 

 growth on a monthly basis. Had- 

 dock scales were also collected in 

 the NEFSC bottom trawl research 

 survey. The NEFSC conducts this 

 survey during the spring and au- 

 tumn each year, providing a fishery 

 independent source of age struc- 

 tures. These surveys are conducted 

 from Cape Hatteras, North Caro- 

 lina, to Nova Scotia, Canada, with 

 the use of a stratified random 

 sampling design. Further details 

 concerning sampling procedures 

 in the NEFSC survey are outlined 

 in Grosslein ( 1969) and Azarovitz 

 (1981). 



Scales were removed from the lat- 

 eral line region below the second 

 dorsal fin. After removal, scales 

 were dried and then impressed on 

 a laminated plastic slide. Scales 

 were viewed at approximately 40 x 

 magnification to determine age. 

 Ages were determined following cri- 



Manuscript accepted 2 April 1993. 

 Fishery Bulletin: 91:550-557 1 1993) 



