268 



Fishery Bulletin 90(2). 1992 



Residuals by year 



-1 1 1 1 1 1 1 1 1 1 



1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 



Year 



Residuals by age 



10 11 12 13 14 15 



Figure 5 



Standardized residuals by age and by year for the final model, which 

 included gj, and gi (coefficients modeling asymptotic growth), and coef- 

 ficients for sex, sea-surface temperature, and population density. Lines 

 connect averages of the residuals at each cluster of points. 



Discussion 



Although density-dependent growth has been demon- 

 strated for many fishes (Shepherd and Grimes 1983, 

 Reish et al. 1985, Ware 1985, Ross and Almeida 1986, 

 Peterman and Bradford 1987, Overholtz 1989), few 

 researchers would argue that density-dependent 

 growth is an important characteristic of all fish popula- 

 tions. The age-structured yield models first developed 

 by Beverton and Holt (1957)— currently used to man- 

 age many temperate marine fish stocks— use a fixed 

 schedule of weight-at-age to calculate the yield, re- 

 gardless of the level of population abundance. For a 



stock of Atlantic mackerel, however, the his- 

 torically observed variation in weight-at-age at- 

 tributable to density-dependent growth had a 

 significant effect on the projected yields from 

 the fishery (Overholtz et al. 1991). For Pacific 

 whiting, this potential for changes in weight- 

 at-age to influence yield is taken into account 

 by using the weight-at-age observed in recent 

 years to project the yield for the upcoming year 

 (Dorn and Methot 1990). To obtain a fishing 

 mortality rate that gives the long-term sus- 

 tainable yield, the average weight-at-age over 

 the history of the fishery is used. This strategy 

 tacitly assumes that the current decline in 

 weight-at-age is not a permanent change in the 

 population. 



Parrish et al. (1981) state that the principal 

 resident species of the California Current 

 system do not exhibit density-dependent 

 growth. They contend that the population size 

 of these species is controlled by environmen- 

 tal variability during the larval stages. As a 

 result, the adults are seldom plentiful enough 

 to reach a food -limited carrjang capacity. 



A contrasting viewpoint is found in Boehlert 

 et al. (1989) who present evidence that the 

 large biomass removals oiSebastes spp. in the 

 years 1966-70 off the west coast of the United 

 States resulted in increases in the annual 

 growth of two members of this genus: canary 

 rockfish S. pinniger and splitnose rockfish S. 

 diploproa. They maintain that the decline in 

 the total abundance of Sebastes spp. has had 

 an effect on food availability for individual 

 rockfish species. Although euphausiids are 

 shared by most Sebastes species as the principal 

 prey (Brodeur and Percy 1984), they are also 

 a major link in the food chain of the California 

 Current ecosystem, supporting numerous fish 

 and invertebrate populations. For this reason, 

 it is unlikely that changes in the abundance of 

 Sebastes spp. alone could have had a substan- 

 tial impact on the overall abundance of euphausiids 

 in the California Current ecosystem. However, since 

 rockfish are spatially restricted to habitats with limited 

 area, the density-dependent growth displayed by S. 

 pinniger and S. diploproa may be due to density- 

 dependent changes in the food availability within these 

 habitats. The possibility that cropping by Pacific 

 whiting and other species significantly affects the abun- 

 dance of euphausiids in the California Current eco- 

 system at large has not yet been adequately tested, 

 though Mullin and Conversi (1989) were unable to 

 detect any change in the abundance of euphausiids in 

 the California current system after the start of the 



