DARK: AGE AND GROWTH OF PACIFIC HAKE 



Table 7.-Mean radii (cm) of photographed otolith annuli by total age group. 



Table 8.— Back-calculated body length (cm) at various ages for 

 the 1957-61 year classes of Pacific hake. 



corroborates the slow growth rate of the 1961 year 

 class suggested by the length-age data presented 

 previously. The 1961 year class was an extremely 

 large year class numerically, exceeding by far the 

 size of other year classes of record. Perhaps den- 

 sity-dependent growth was operative in this ins- 

 tance. The size of the 1961 year class may have 

 been so large that the competition for food and 

 space noticeably restricted the growth of in- 

 dividuals. It cannot be ascertained whether the 

 members of smaller year classes might undergo 

 density-dependent growth to a lesser extent or if 

 the phenomenon is triggered only by unusually 

 large year classes. 



The von Bertalanffy growth equation is com- 

 monly used to describe asymptotic growth. It is 

 used herein because it fits the data well and is 

 readily incorporated in certain yield models. Von 

 Bertalanffy's equation is /, =/oo 1-e^^' <'-'o))^ where 

 1, = body length at time t;l oo = estimated average 

 maximum body length; k= rate of growth; t^ — 

 theoretical age when growth conforms to the von 

 Bertalanffy equation. Since sexual differences in 

 growth characteristics exist in Pacific hake, 

 separate curves were fitted to male and female 

 length data. Average length at age data from Ta- 

 ble 3 were used to compute the growth curves. In 

 this instance the growth of the 1961 year class was 



considered atypical and it was excluded from the 

 analysis. A computer program' utilizing the 

 method of Stevens (1951) was used to compute the 

 constants for the von Bertalanffy equation. The 

 resulting equations are: /, = 56.29 (l-e-o-39 ('-0.20)) 

 for males and /, = 61.23 (l-e-o-^oc-o.oi)) for females. 

 By comparison, Tillman's (1968) estimates of A: 

 were 0.41 for males and 0.19 for females. He 

 reported that treatment of Best's (1963) data also 

 yielded 0.19 for females. In the present study /oo 

 for both sexes are reasonable estimates of average 

 maximum body lengths. Males as long as 66 cm 

 and females as long as 80 cm have been observed. 

 Growth of Pacific hake is adequately represented 

 by the von Bertalanffy equations as the curves fit 

 the observed lengths-at-age very well (Figure 16). 

 The curves are nearly superimposed until about 

 age 5 when they begin to diverge and continue to 

 do so with age. Although sex-specific growth rates 

 are apparent, the growth rate of the entire Pacific 

 hake population may be best represented by an 

 equation based on data with the sexes combined. 



The growth equation with sexes combined is /, — 

 60.85 (1-e -0-30(^-003)). 



Growth in Weight 



In 1964-69 length and weight data were collect- 

 ed on 2,417 male and 3,117 female Pacific hake 

 taken from Washington to southern California. 

 Lengths and weights were taken from fresh fish as 

 they were unloaded from vessels at the processing 

 plant and from research samples at sea. Fork 

 lengths were taken to the nearest centimeter and 

 weights to the nearest decagram. The majority of 



'Program developed by George Hirschhorn, Northwest 

 Fisheries Center, National Marine Fisheries Service, NOAA, 

 Seattle, Wash. 



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