FISHERY BULLETIN: VOL. 87, NO. 4, 1989 



exploited populations of S. alutus, for example, 

 very old age groups may have smaller mean 

 lengths than younger age groups, suggesting 

 some type of growth-dependent mortality 

 (Leaman'). Markedly smaller mean lengths at 

 age have not been observed, however, for very 

 old specimens of either S. pinniger or S. dip- 

 loproa (Boehlert and Yoklavich 1984; Wilson 

 1985). A genetic basis for differences in gi-owth 

 and age at sexual maturity has been suggested 

 for cod, Gadus morhua (Borisov 1979) and 

 brown trout, Salmo triitta (Favro et al. 1979). 

 An investigation of the biochemical genetics of S. 

 diplopwa by using electrophoresis at 29 loci has 

 shown no variation associated with age (L. W. 

 Seeb and G. W. Boehlert unpubl. data). Al- 

 though negative results cannot rule out a differ- 

 ence, our gi'owth results did not show a con- 

 sistent trend supporting a genetic basis for 

 growth differences. 



Data Analysis and Interpretation 



Yearly means of GI(i)'s were calculated and 

 were the values upon which further analysis was 

 made. Standardized growth anomalies (Z-scores) 

 were calculated so that each time series of 

 growth for both species had a mean of zero and a 

 standard deviation of one. This allowed com- 

 parison of the growth anomalies in different 

 growth years, standardized for the effects of 

 gi'owth increment magnitude. Comparisons be- 

 tween species were also facilitated by this con- 

 version. A growth anomaly value of zero corre- 

 sponded to normal gi'owth rate, averaged over 

 the period of the data record. 



Within species, there were both similarities 

 and differences between the time series of differ- 

 ent age gi'oups. Covariability between different 

 age groups was extracted by principal com- 

 ponent analysis (Hotelling 1933) of the six-by-six 

 cross correlation matrix, which expressed inter- 

 relationships among the six series of standard- 

 ized growth anomahes of each species over the 

 period of analysis. The principal component ex- 

 pansion of gi'owth increments can be written as 



Gl(x,t) = E F,M-)a,,(ty, (1) 



11=1 



where x is the age class (1-6), t is time, and the 



index n corresponds to component number (1-6). 

 The loadings F„{x) are the eigenvectors of the 

 cross correlation matrix. The amplitude time 

 series a„{t) are referred to as the principal com- 

 ponents of covariability. The dominant loadings 

 across age groups (those reducing the largest 

 proportions of total variance in the original data 

 set) and the associated principal component time 

 series were interpreted in terms of physical and 

 biological processes influencing gi'owth rate var- 

 iability. An attempt was made to relate the prin- 

 cipal component time series as dimensionless, 

 uncorrelated expressions of growth for each 

 species to time series of environmental and bio- 

 logical data. Environmental data (upwelling, 

 wind speed, and wind stress curl at lat. 45°N, 

 long. 125°W; sea-surface temperature at Neah 

 Bay, WA, lat. 48°22'N) from 1946 to 1977 were 

 provided by the Pacific Fisheries Environmental 

 Group, Monterey, CA. Sea level data from San 

 Francisco (lat. 38°N) were taken from Prager 

 and MacCall-. 



RESULTS 



A total of 942 S. pinniger (616 males and 326 

 females) and 802 S. diplopwa (651 males and 151 

 females) were used in this study. Specimens of 

 S. pinniger ages 2-60 years corresponded with 

 birth dates from 1920 to 1978 (Fig. 2A); S. dip- 

 loproa ages 1-86 years corresponded with birth 

 dates from 1896 to 1979 (Fig. 2B). Total numbers 

 of gi'owth increments measured were 5,600 for 

 S. pinniger and 4,714 for S. diploproa. 



Mean annual size of growth increments for 

 both species showed a reduction with age gi'oup, 

 which is typical in fishes. Mean size of incre- 

 ments decreased dramatically (between twofold 

 and threefold) from age gi'oups 1 and 2, then 

 slowly from age gi'oups 2-6 (less than twofold). 

 Growth anomalies for all ages were character- 

 ized by significant interannual variability for 

 both species (Figs. 3, 4). The standardized time 

 series for S. pinniger (Fig. 3) showed a general, 

 gi'adual decreasing trend in growth rates for age 

 gi'oups 2-4 from the beginning of the record until 

 about 1965 or 1970. Age group 1 showed a gen- 

 erally decreasing trend prior to about 1957 and 

 an increasing trend thereafter. Age gi'oups 5 and 

 6 showed a gi'adually increasing trend virtually 



'B. M. Leaman. Pacific Biological Station, Naiiaimo, B.C. 

 Canada, pers. commun. November 1987. 



-Prager, M. H., and A. D. MacCall. 198(3. An environ- 

 mental data base describing coastal southern California in 

 the years 1920-1984. Part I: Procedures and summaries. 

 Natl. Mar. Fish. Serv., Southwest Fish. Cent. Adm. Rep. 

 LJ-86-31, 50 p. 



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