Dorn: Environmental covanates of Merluccius productus growth 



265 



55 n 



47 



37 



32 



Males 



57 



52 



£ 47 



Appendix for calculating strata esti- 

 mates of length-at-age, and for com- 

 bining the strata estimates to pro- 

 duce an annual estimate (Fig. 3). 

 The decline in length-at-age is evi- 

 dent in graphs of both male and 

 female length-at-age. 



The factorial analysis of mean 

 length variance is given in Table 4. 

 Weighted analysis of variance was 

 used with the sampling variances as 

 weights. The F-tests for age, year, 

 region, sex, and time-period were 

 all highly significant (P< 0.0001). 

 Because of the large number of ob- 

 servations (2072), this result is not 

 surprising. The parameter esti- 

 mates in Table 4 are defined such 

 that the intercept term represents 

 the mean length of a 1-year-old 

 male in the early part of the season 

 in 1978 in the EUR region. Param- 

 eter estimates for the other factor 

 levels can be interpreted as the dif- 

 ference between mean length of 

 Pacific whiting identified by that 

 factor level and those identified by 

 the intercept characteristic with all 

 other factors being held constant. 



The results of the ANOVA can be 

 summarized as follows. Length in- 

 creases with age to age 10, then 

 varies irregularly to age 15 (Table 

 4). Length increases 0.55 cm from 

 the early period (April- June) to the 

 middle period (July-August), and 

 increases an additional 0.46cm from 

 the middle period to the late period 

 (September-November). There is 

 an increase of 1.36 cm from the 

 EUR region in the south to the 

 VNC region in the north, indicating 

 that the larger Pacific whiting of an 

 age-group migrate farther north. On average, female 

 Pacific whiting are larger than males by 0.55cm. Since 

 the ANOVA model does not contain a sex-age interac- 

 tion, this difference in mean length would apply to all 

 ages. In general, these results are consistent with the 

 previously reported findings on the growth of Pacific 

 whiting (Dark 1975, Francis 1983). The ANOVA year 

 coefficients show the decline in length since 1978. Mean 

 length-at-age reached a minimum in 1984. There was 

 a slight rebound in length-at-age from 1984 to 1986, 

 but after 1986 length-at-age began to decline again. 



Models containing interaction terms between factors 



37 



1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 



Females 



■ age 1 



- age 9 



- age 8 

 • age? 



- age 6 



- age 5 



■ age 4 



- age 3 



1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 

 Year 



Figure 3 



Mean U.S. fishery length-at-age estimates by sex for Pacific v/h\tmg Merluccius pro- 

 ductus, 1978-89. The extremely low estimates of mean length for male and female 

 age-3 fish in 1979 were due to asymmetric error in the ageing of the strong 1977 

 year-class. 



were also analyzed. All the two-way interaction terms 

 were statistically significant, but much less so than the 

 main effects. The addition of more than 200 parameters 

 to describe the two-way interactions would make inter- 

 pretation difficult. Yet a model with only main effects 

 is clearly inadequate, since it implies, for example, that 

 both the 2-year-old and 12-year-old whiting declined in 

 mean length by the same amount from 1983 to 1984. 



Growth increment regression 



Before considering the effects of environmental co- 



