Table 23. 



-Proportions of females in the estimated population of walleye pollock by age group and geographical area, 1976 

 Bering Sea spring trawl survey. 1 















Age group (yr) 













All ages 



Subarea : 



1 



2 



3 



4 



5 



6 



7 



8 



9 



10 



11 



12 



combined 

















portion 



of femal 





































Inner shelf 





























4N 



0.63 



0.00 























0.61 



4S 



0.47 

























0.47 



1 



— 



0.40 



0.61 



0.20 



0.00 



0.76 



0.68 



0.80 



0.64 



0.74 



0.85 



0.94 



0.51 



Outer shelf 





























and slope 





























3 



0.33 



0.50 



0.49 



0.49 



0.35 



0.11 



0.55 



0.56 



0.68 



0.45 



0.51 



0.59 



0.48 



3 slope 



— 



— 



0.69 



0.56 



0.50 



0.33 



0.72 



0.76 



0.88 



0.78 



0.83 



1.00 



0.66 



2 



0.34 



0.43 



0.37 



0.37 



0.37 



0.36 



0.37 



0.32 



0.33 



0.36 



0.58 



0.70 



0.38 



2 slope 



— 



0.58 



0.56 



0.49 



0.61 



0.57 



0.69 



0.65 



0.66 



0.69 



0.87 



0.% 



0.61 



All subareas 





























combined 



0.46 



0.45 



0.42 



0.41 



0.41 



0.33 



0.41 



0.41 



0.44 



0.41 



0.58 



0.65 



0.43 



'Based upon sampled individuals for which sexes could be determined. 

 : See Figure 3. 



Table 24. 



-Length -weight relationships observed for walleye pollock during the 1976 Bering Sea spring trawl survey, 

 with testing for between-area and between-sex differences. 





Otolith' 

 area 



Number 

 sampled 



FL 

 range (cm) 



Length-weight coefficients 

 b 



Predicted weight-at 



-length 



Sex 



10 cm 



30 cm 



50 cm 





























Males 



B 



116 



19-65 



0.0048 



3.0789 



5.8 



170.9 



823.9 





D 



138 



26-58 



0.0052 



3.0568 



5.9 



169.6 



808.3 





Both areas 



















combined 



254 



18-65 



0.0051 



3.0641 



5.8 



170.1 



813.9 



Females 



B 



299 



18-69 



0.0031 



3.2127 



5.0 



172.4 



889.8 





D 



137 



21-60 



0.0025 



3.2568 



4.4 



158.9 



839.2 





Both areas 



















combined 



436 



18-69 



0.0029 



3.2235 



4.8 



168.1 



872.7 



Overall 





690 



18-69 



0.0034 



3.1775 



5.1 



169.1 



857.3 



Analysis 



of covariance 



























Tests for differences 1 











Slope (ft) 







Common means 







df 





F ratio 



df 





F ratio 



Males between areas B and D 



1:250 





0.03 



1:251 





0.28 



Females between areas B and D 



1:432 





0.32 



1:433 





12.9** 



Between 



sexes in area B 





1:411 





5.78* 



— 





— 



Between 



sexes in area D 





1:271 





2.53 



1:272 





0.35 



See Figure 4. 

 '* = P £0.05, 



P S0.01. 



distributions of observed conditions were summarized in a length- 

 maturity key for each sex. Male and female samples showed either 

 of five stages of gonad condition: Immature, developing, spawn- 

 ing, spent, or inactive (Table 7). 



By applying the estimated number of individuals within the 

 population (for each sex, all subareas combined) at each fork 

 length to the respective length-maturity key, an estimate was ob- 

 tained of the number of individuals within each classification of 

 gonad condition (at each fork length). The rate of attaining 

 reproductive maturity (first spawning condition) was then ex- 

 amined by computing the proportions of immature (condition 

 code 1) and mature (condition codes 2-5) individuals within the 

 population at each fork length. Individuals classified in code 2 

 condition (developing) were included in the mature category 

 because, in one analysis of 570 developing individuals (from 

 Miller Freeman hauls 14-50, 6-16 April 1976), 87% of males and 

 96% of females appeared to be near spawning. 



For each sex, the relationship between fork length and propor- 

 tion mature was found to be fairly well described by a sigmoidal 

 curve of the model: 



= o-be 



P= e 



-cL 



(26) 



where P is the proportion of the population mature at fork length 

 L (cm), e is the natural constant 2.71828 . . ., and b and c are 

 constants (Fig. 34). Because an equivalent form of Equation (26) 



% +b i L > 



(27) 



whereZ= ln(-lnP),a, = lnb,andb, = - c, a least squares 

 linear regression was used to estimate o, and b, and then obtain 

 estimates of b and c. 



The fitted model for males was found to be 



P = e- 



- 0.224L 



(28) 



and the fork length at which 50% of the individuals were mature 

 was 31.0 cm. Females matured at longer lengths than males, and 

 the fitted model was 



45 



