BUTLER: NORTHERN ANCHOVY GROWTH IN THE CALIFORNIA CURRENT 



in Bartlett et al. 1984). Thus, comparison of 

 lengths adjusted by age between years of fish 

 hatched during the same calendar month is reli- 

 able. Comparison of lengths of fish hatched at 

 the extremes of the same spawning season may 

 be less reliable than between-year comparisons. 

 Fish hatched in January are four months older 

 than fish hatched in May, and linear extrapola- 

 tion to a common age may introduce error. How- 

 ever, since growth is decelerating, linear extra- 

 polation overestimates mean lengths of fish 

 hatched at the extremes of the spawning season. 

 The fact that lengths of fish hatched in January 

 and May in all years, except 1983, are less than 

 lengths of fish hatched in March indicates that 

 the error is not great. 



The allometric relations of length and weight to 

 otolith radius were estimated using nonlinear re- 

 gression. These relations w^ere used to back-cal- 

 culate age-specific size and gi'owth rates for indi- 

 vidual fish; not all fish were weighed in 1980 and 

 1981, and data were pooled from 1980 to 1982 to 

 determine the allometric relations of both length 

 and weight to otolith radius. Individual relations 

 were determined for 1983 and 1984. 



The gi'owth rates in length and in weight were 

 determined from increment widths and the first 

 derivative of the empirical relationship of fish 

 size and otolith radius. The condition factor (dry 

 weight/length cubed) was significantly less in 

 anchovy juveniles collected in 1983 than in an- 

 chovy juveniles collected in 1980-82. Therefore, 

 the algorithm to convert otolith increment size to 

 growth in dry weight differed among years. The 

 equation used to calculate growth in length was 



\L/M = (lR/At){AL/\R)\ 



(1) 



where AR/At is rate of change of the width of the 

 daily increments, and AL/AR is the slope of the 

 observed relationship of fish length and otolith 

 radius. 



The variance of the product (10 of two varia- 

 bles (X, Z) is given by 



Var(y) = Z'^Yar(X) + jr^Var(Z) 



+ 2XZCovar{XZ) 



(2) 



if the variables are not independent (Goodman 

 1960). The estimate of the variance of iXR/At was 

 the variance of the measurement of increment 

 width of the fish in each gi"oup. If the length, 

 radius relation was linear, the variance of AL/AR 

 was estimated from S^y\x, the variance of 



the slope of the regression of length on otolith 

 radius. If the relation of length to radius was 

 nonhnear, as was often the case, the variance of 

 AL/AR was estimated by partial derivatives. 

 The variance of AW/AR was not calculated; the 

 complex derivative may not be a good estimate 

 of the true variance. 



The author tested the assumption that the 

 covariance was equal to zero by comparing the 

 slopes of the relations of juvenile fish length and 

 otolith radius for 70-100 mm, slow- and fast- 

 growing fish collected in October 1984 that were 

 > 1 year old. The slope was 0.0419 for anchovy 

 older than one year and 0.0314 for fish younger 

 than one year old. These slopes were not signifi- 

 cantly different (P > 0.10, ANCOVA). Conse- 

 quently confidence intervals around back-calcu- 

 lated gi'owth rates were calculated ignoring the 

 third term in Equation (1). 



Lengths of anchovies were significantly differ- 

 ent between months and years {P < 0.01, 

 ANCOVA). Within a spawning season, fish 

 hatched during February, March, and April 

 grew faster than fish hatched in January or May 

 (Fig. 1), although this was not evident for the 

 1983 or 1984 data. The mean of five fish in Jan- 

 uary 1982 was not different from that of the 

 April 1982 sample. The adjusted lengths of ju- 

 veniles collected from the 1983 year class where 

 less than the adjusted lengths of any of those 

 from 1980-82 for all months but May (Fig. 1, 

 Table 1). The adjusted lengths of juveniles from 



Table 1 . — Mean lengths at capture of juvenile northern 

 anchovy hatched in various months of 1980-84, adjusted 

 to a common age of 208 days. SE and N stand for standard 

 error and number of fish, respectively. 



647 



