GUNDERSON: POPULATION BIOLOGY OF SKBASTES ALVTUS 



TABLE 16. — Example of computations used to estimate exploitable biomass, yield, and population fecundity for a hypothetical Pacific 

 ocean perch population based on No recruits. Input parameters needed are indicated by asterisks. 



Mj' V,' N, 



Natural Vulner- sj Number alive W, ' 



mortality ability Proportion alive at at beginning Mean 



Age coefficient coefficient beginning of age / of age / weight 



8, Mean biomass 



Mean 

 exploitable 



m. 



Popu 

 Fecun- Hon 



biomass Yield dity fecundity 



Q=t c 



M n 



A/ s (=A/ ) W KF \ ° M J 1 -exp -W F+M )\ V B 



FV B m N m 



M, 



V, s, = exp -{V F+M ) A/ s, 



W, 



N.W, 



F , M 11 exp (V,F + M,)| V,8, FV,B, m, A/,m, 



M, 



V 2 s 2 = s,exp -{V,F t/W,) N s 



N 2 W 2 



FV 2 B 2 m 2 N 2 m 2 



M, 



V 3 s 3 =s 2 exp -(V 2 F+M 2 ) N s 



W i v 3 F +M 3 11 ' ex P -< y 3^-M 3 )l ^S 3 



2 WS/ = S' 



FV383 m 3 N 3 m 3 



'Estimated from the age-length data in Table 3 and Westrheim and 

 Thomson's (1971) all-B.C. length-weight relation for females: W = 0.0078571 



L 



3.16734 



Vulnerability coefficients for 8- and 9-yr-olds were assigned arbitrarily. The 

 values used were more conservative than those predicted by extrapolation of 

 the straight line obtained for 10- to 16-yr-olds (0.20 for 8-yr-olds and 29 for 

 9-yr-olds). 



Yield, exploitable biomass, and total fecundity 

 are calculated for each age group, then summed. 

 The results give the annual yield to the fishery, 

 annual production of larvae, and average exploit- 



able biomass on hand during the year for an 

 equilibrium population of Pacific ocean perch. 

 This population is based on a constant number of 

 recruits (N ), with individual growth and mortal- 

 ity being determined by the input values of the 

 constants used to describe mortality, vulnerabil- 

 ity to fishing, and mean weight at each age. 



A computer program 5 was written to carry out 

 the calculations in Table 16 and offers a variety of 

 ways to evaluate the effects of different fishing 

 strategies on a stock. The basic calculations can be 

 carried out for any combination of instantaneous 

 rates of fishing mortality (F) and age of entry into 

 the fishery (t' p ) that the user specifies. 



The mesh size used when fishing for Pacific 

 ocean perch is dictated primarily by convenience, 

 since the incidence of "gilling" and entanglement 

 in the meshes is reduced sharply when using 3.0- 

 inch mesh (internal measure) in the cod end. This 

 was not found to be the case in mesh studies with 

 Atlantic redfish (Templeman 1963), where use of 

 smaller cod end mesh sizes simply "gilled" fish of a 

 smaller size. In the Pacific ocean perch stocks 

 examined in this paper, recruitment to the fishing 

 grounds is quite gradual and the fish that would 

 normally be "gilled" in a 3.0-inch cod end are 

 poorly represented on the grounds. 



Pacific ocean perch offer a special case then, 

 where evaluation of the effects of different size or 

 age restrictions is of no practical interest for 

 fisheries management. Consequently, all analysis 

 in this section was focused on determining the 

 optimal intensity of fishing for the Pacific ocean 



5 D. Gunderson and J. Buss. 1976. Users guide to ASSESS: 

 Assessment of the effects of different fishing strategies on fish 

 populations (FORTRAN IV). Norfish Pap. NC09, 8 p. 



395 



