Ralston et al ; An approach to estimating rockfish biomass from larval production 



139 



175 

 150 

 125 

 100 



75 i 



50 



25 







t iU ^ 



life table prediction 



o observed 



' I ' ' 



10 

 Age (yr) 



15 



20 



Figure 7 



Weight-specific fecundity and its dependency on age. 

 Observed values are means of measured females, brack- 

 eted by ±1.0 standard error and ±1.0 standard deviation 

 (all samples collected by trawl during February-March, 

 1991). The solid line, which is not fitted to the "observed" 

 points, is the predicted relationship from the life table 

 analysis presented in Table 3. 



due to the bias correction that occurs when the fecundity 

 relationship, which was fitted on the log-scale, is back- 

 transformed to the arithmetic scale. Irrespective of the 

 type of data, however, it is evident that weight-specific 

 fecundity is only weakly dependent on age. This finding 

 implies that changing the equilibrium age structure of 

 the population, as mediated through an alteration in the 

 natural mortality rate (M), will have little effect on the 

 population's weight-specific fecundity. 



The assumption that recruitment is constant and uni- 

 form does not appear to appreciably bias the estimate 

 of population weight-specific fecundity derived from the 

 life table analysis (102.17 lai-vae/g of female). Population 

 weight-specific fecundity was also estimated in a Monte 

 Carlo life table simulation that used a more realistic 

 lognormal recruitment model (Fogarty, 1993). Annual 

 recruitments in that simulation were determined as N^ 

 = exp(;/ -I- aX). where N^ is the number of recruits at age 

 1, // = log^,|10,0001, a = 0.921, and X is a standard normal 

 deviate (i.e. X~Af[0,l]). This level of variability in lognor- 

 mal recruitment is comparable to that observed in the 

 widow rockfish fishery (Bence et al., 1993: Hightower and 

 Lenarz*), where 20-fold differences in recruitment have 

 been observed in a 10-yr time period. Results of the simu- 

 lation showed that fluctuating, lognormal recruitment can 



Hightower, J. E., and W.H.Lenarz, 1990. Status of the widow 

 rockfish fishery in 1990. In Status of the Pacific coast ground- 

 fish fishery through 1990 and recommended acceptable biologi- 

 cal catches for 1991. Stock assessment and fishery evaluation, 

 appendix vol. 2, 48 p. Pacific Fishery Management Council, 

 Portland, OR. 



800 -3 



700 ^ 



600 -. 



>, 500 H 



(J 



§ 400 - 



CT : 



'^ 300 -. 

 200 

 100 ^ 







p(91.3 < larvae/g < 106.4) = 0.90 

 > 



X = 101.06 

 n = 5000 



-.nnn 



I T I I I T I j yV t VV 'i " i " i " i " | " i " i " i " i " i " i " i " i " i " |' I I I ' r I I 



70 80 90 100 110 



Population weigtit-specjfic fecundity (larvae/g of female) 



Figure 8 



Results of Monte Carlo simulation evaluating the effect 

 of recruitment stochasticity on calculations of shortbelly 

 rockfish population weight-specific fecundity. 



produce values of population weight-specific fecundity 

 that range from 71 to 110 larvae/g of female, depending 

 on the exact sequence of year classes and their resulting 

 affect on age structure (Fig. 8). Even so, the mean of the 

 sample distribution (.v = 101.06 larvae/g of female, n=5000) 

 did not differ significantly from the life table calculation 

 that had no recruitment variability. In addition, 90'^f of all 

 the lognormal recruitment realizations were within ±10'^f 

 of the constant recruitment result. 



By definition, population weight-specific fecundity rep- 

 resents the number of larvae produced by one gram of 

 female biomass (including immature 1-yr-olds). We ex- 

 panded female biomass to total biomass including males. 

 Results presented in Table 3 show that age-specific male 

 cohort biomass, like that of females, is calculated as the 

 product of numbers-at-age and individual weights-at- 

 age, which when summed over all ages yields the total 

 equilibrium male biomass (347.64 g/male recruit). Total 

 population biomass (i.e. females-t-males) is then 759.01 g, 

 of which females comprise 54.2'7f by weight. Thus, the 

 total biomass is estimated by applying a 1.845 expansion 

 factor to female biomass. 



Larval production 



Sampling with different mesh-size bongo nets (333 and 

 505 pm) allowed an assessment of whether a portion of 

 smaller larvae retained by the smaller mesh was lost with 

 the standard 505-pm mesh. Although shortbelly rockfish 

 are relatively large and stout at parturition (-5.0 mm, 

 Moser et al., 1977), undersampling of small, young larvae 

 could seriously bias larval production estimates. Results 

 presented in Figure 9 show, however, that the standard- 

 ized catches of larvae ( number/| 10 m'-^l ) in the two net sizes 

 were quite similar. A paired t-test of catches (333 minus 



