270 



Fishery Bulletin 90(2). 1992 



with spawning, migration, and feeding, which 

 would have to be accounted for in a model 

 before analyzing environmental influences on 

 growth. 



Underlying this seasonal pattern of variation 

 in weight is the length-weight relationship 

 characteristic to a species, determined by the 

 overall shape of the fish. Extreme departures 

 from the typical length-weight relationship are 

 unlikely to persist. Fish that are heavy in rela- 

 tion to their length in one year would tend to 

 grow faster in length than average, while 

 underweight fish would tend to experience 

 slower growth in length. Adjustments to an in- 

 dividual's annual reproductive effort can also 

 dampen departures from the typical length- 

 weight relationship (Tyler and Dunn 1976). 



During the period covered by this analysis, 

 the length-weight relationship of Pacific whit- 

 ing has varied from year to year, most notice- 

 ably in 1983, when mean weight was extremely 

 low at a given length (Dorn and Methot 1990). 

 The link between anomalies in the length- 

 weight relationship and annual growi;h incre- 

 ments is best demonstrated by the results of 

 a trial model that used the anomaly in the 

 estimated weight at 45 cm from the annual length- 

 weight regression (Dorn and Methot 1990) as the only 

 predictor variable for the annual growth increment. 

 This variable was highly significant in the model 

 (P< 0.001), indicating that the annual growth incre- 

 ment is low during years where the length-weight rela- 

 tionship is below average. This result also supports the 

 hypothesis that variation in Pacific whiting length-at- 

 age is caused by environmental processes that affect 

 the availability of food. 



The analysis presented in this paper is based ex- 

 clusively on fishery data. It should be acknowledged 

 that there are numerous problems associated with the 

 use of fishery statistics to infer growth patterns of fish 

 within a population. Incomplete, size-dependent re- 

 cruitment to a fishery can make fishery data on length- 

 at-age a biased estimate of population length-at-age. 

 Ageing error can distort the estimates of length-at-age 

 when the year-classes have large differences in abun- 

 dance. Shifts in the geographic and temporal pattern 

 of the fishery, or shifts in the geographic distribution 

 of the population itself, can cause spurious changes in 

 estimates of length-at-age. The lengths for less abun- 

 dant age-groups are not estimated as precisely as those 

 for abundant age-groups. This is particularly true of 

 extremely young and old fish, as these age-groups may 

 be represented in fishery samples by only one or two 

 individuals which determine the mean length for that 

 age-group. 



100 



1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 

 Year 



Figure 6 



Percent of the Pacific whiting Merliiccius productvs catch biomass taken 

 north of Cape Falcon flat. 46°45'N) near the mouth of the Columbia 

 River, during 1978-88. Catch of Pacific whiting from the Canadian zone 

 is included in the calculations. 



The severity of some of these problems can be re- 

 duced by using the procedures described in the Appen- 

 dix for compiling strata estimates of length-at-age and 

 calculating variance estimates. Length-at-age for tem- 

 poral and geographic strata can be examined separately 

 before being combined to produce annual summary 

 statistics. Length-at-age estimates based on only a few 

 individuals can be discounted in the analysis by using 

 the estimated variances of length-at-age as weights. 

 Nevertheless, some factors affecting growth can only 

 be addressed by modeling fisheries as both a source of 

 information on the stock and a major influence on its 

 dynamics. The growth-increment regression model 

 used in this paper assumes that the fishery samples the 

 population without bias, so it is not the appropriate 

 framework for studying these processes. Models with 

 size-selective fishing mortality and stochastic growth 

 have been developed for exploited fish populations 

 (Deriso and Parma 1988, Parma and Deriso 1990). The 

 practical application of these models is limited by the 

 difficulty of distinguishing between different sources 

 of growth variability using only catch data. 



Size-selective mortality may have played a role in 

 causing variation in length-at-age of Pacific whiting 

 over the years covered by this analysis. Since the length 

 ANOVA found a significant increase in length from 

 south to north, a northward shift in the fishery would 

 tend to increase length-at-age in the catch. At the same 

 time, however, the length-at-age of the survivors of the 



