NOTE Salthaug: Dynamic age-length keys 



453 



The corresponding observed proportion of each age group 

 was N^ /N, where N^ is the observed number of individuals 

 in age group a. Only months with more than 300 sampled 

 individuals were used in the testing of the age-length keys. 



Results 



The predicted age distributions from the model (based on 

 monthly length distributions) were generally quite simi- 

 lar to the observed age distributions, although they varied 

 between the investigated years (Fig. 3). Deviations from 

 the observed age distributions were especially large in the 

 years 1992-94. The commercial catches were dominated by 

 the age groups 4-6, and there was a sHght tendency that 

 the model underestimated proportions. It is also worth 

 noting that points from the same age group within years 

 often seemed to form a line with a slightly different slope 

 or intercept from the diagonal. 



Discussion 



The application and testing of the theoretical age-length 

 keys is only an indication of the quality and usefulness of 

 the method. An important assumption about the samples 

 from the commercial catches is that individuals are sam- 

 pled randomly within the 5-cm size groups from the popu- 

 lation. If some age groups are over- or under-represented 

 within size groups in the catches, in relation to the true 

 population, there will be deviations in the proportion of age 

 groups seen in Figure 3. Catches (and thereby the samples) 

 are often taken from a restricted area within the total dis- 

 tributional area of the cod stock, where the length-at-age 

 of individuals may differ from the rest of the population or 



where particular age groups dominate. In addition, errors 

 in the age readings may occur. 



The model's potential inability to capture the true age- 

 size structure in the population may also lead to deviations 

 in Figure 3. The estimates of the parameter values may suf- 

 fer from sampling error, and simplifying assumptions may 

 lead to errors (e.g. linear length increment between years 

 and equal mortality rates for all age groups within years). 

 Monthly growth rates for gadoids in temperate areas often 

 vary seasonally (Jorgensen, 1992; Hayes, 1993). In addi- 

 tion, both the fishing mortality and the natural mortality 

 are expected to vary for different ages and sizes because of 

 ecological factors, fishermen's strategy, and the selection 

 properties of commercial fishing gears. 



By reading the age of a limited number of individuals 

 at different times during the season, the resulting average 

 lengths at age can be used to estimate the current value of 

 1.1^^. Another solution is to model the dynamics in average 

 length more exactly (see e.g Schnute and Fournier, 1980). 

 The seasonal change in the (relative) number offish in each 

 age group can be estimated by using available information 

 about the fishing mortality. More complex modeling of struc- 

 tured populations than the approach described here, which is 

 quite simple, can of course be used (see e.g. Tuljapurkar and 

 Caswell, 1997). However, the main point is to use a method 

 that gives a fairly accurate estimate of the age-length dis- 

 tribution in the population at a given time, and a complex 

 model is not necessarily a better one in this respect. 



Acknowledgments 



I thank the Research Council of Norway for financial sup- 

 port. Ulf Dieckmann and Mikko Heino are thanked for 

 assistance with aspects of the theoretical model. 



