BERGGREN and LIEBERMAN: RELATIVE CONTRIBUTION OF STRIPED BASS 



Table 2. — Quadratic discriminant functions' based on Hudson, Chesapeake, and Roanoke spawning-stock specimens of striped bass 



and used to classify spawning-stock, oceanic, and overwintering specimens.^ 



Hudson; 



''hud =^ 1.489.070559 - 

 + 090968 UZ + 

 + 24 321052 X r 

 Chesapeake 



''CHES = - 1.368 946420 

 + 0.321075 C/Z - 

 + 25 294896 X + 

 Roanoke: 



'^ROAN = - 1.650 902863 

 + 0.228873 UZ 

 + 25 512087 X - 



(0.077516 U^ i 0.256954 W^ > 

 0,047441 WX + 0.023246 WY + 

 7 985031 Y > 381 695141 Z 



- (0.089560 U^* 242459 W? 

 0.092151 WX 0,000861 WY 

 7.014936 Y » 323 469441 Z 



1 171065X2 ^ 

 164200 WZ 



2 536320 Y^ 

 0.457365 Xy 



123 907000 Z2 

 2 799760 XZ 



- 0.019058 UW 

 2.861250 YZ) + 



<- 0.015160 UX - 0.007057 UY 

 8.776221 U + 28,127772 W 



1 122690X2 + 2 155850/2 + 117 554000 Z^- 0.007099 UW + 0.005302 UX 



2 363980 WZ + 381082 XY + 3.623860 XZ - 1 590090 VZ) + 1 1 316822 U 



- (0.107062 U2 

 0.293615 WX 

 22.351388 Y 



+ 0.316254 W2 t 

 + 129292 WY - 

 469 422957 Z 



2 063540X2 

 1 009790 WZ 



0.842590 Y^ + 139.577500 Z2 

 106776 Xy - 606466 XZ + 



062826 UW + 0.015703 UX 

 4 416000 YZ) + 10 320202 U ^ 



0.015500 uy 



21 749040 W 



043640 UY 

 27 000888 W 



'Except for an additive constant ( -2.5 In 2tt) common to each function. 



2F = discriminant score. U = lateral line scale count, W = character index, X = upper-arm gill raker count, Y 

 measurement ratio, and Z = snout length mternostril width ratio. 



first to second annulus/focus to first annulus 



Table 3. — Comparison of correct-classification percentages and estimated and known stock percentages 

 among the total set of spawning-stock specimens of striped bass and cross-validation subsets. 



Correctly 

 Spawning classified 

 stock (%) 



Random set' 



Known 



stock 



(%) 



Estimated 

 stock 

 (%) 



Correctly 



classified 



(%) 



Independent set2 



Known 



stock 



(%) 



Estimatec 

 stock 

 (%) 



Correctly 



classified 



(%) 



T^tal^t^ 



Known 



stock 



(%) 



'Randomly sampled half of total spawmng-stock collections used to determine quadratic functions for cross-validation. 

 ^Remaining half of spawmng-stock specimens classified by quadratic functions based on the random set. 

 ^AII specimens from spawmng-stock collections classified by quadratic functions based on the total set. 



Estimated 

 stock 

 (%) 



tions between estimated and known stock 

 percentages within sets was as much as 9 percent- 

 age points. The quadratic functions thus provided 

 slightly biased estimates of stock percentages 

 when applied to collections composed of 34^^ Hud- 

 son, 46*^ Chesapeake, and 20'7( Roanoke stocks. 



Best Estimator of Relative Contribution 



The best estimate of the percentage of Hudson 

 River specimens in subsamples from the simula- 

 tion studies was the estimate from the third itera- 

 tion of the reclassification procedure (Table 4). On 

 the average, this iterative estimate was less 

 biased than estimates from other iterations, the 

 as-classified estimated (i.e. , estimate from the first 

 iteration), and the adjusted estimate for most per- 

 centages of Hudson stock considered. In addition, 

 the variance of the bias of the iterative estimate 

 was often less than that of the other estimates. For 

 percentages of Hudson stock 'e 50*^ , the iterative 

 and adjusted estimates closely agreed and the bias 

 in each estimate was small ( 'SS percentage 

 points). The iterative estimate will, therefore, be 

 used to estimate Hudson stock contribution in 

 oceanic collections, and the adjusted estimate will 

 be used to substantiate estimates of Hudson con- 



TABLE 4. — Mean and standard deviation of absolute bias' of 

 estimated relative percentages of Hudson River stock of striped 

 bass in replicated random samples from spawning-stock collec- 

 tions.^ 



'Absolute value of the difference between the true relative percentage of 

 Hudson River stock in the subsample and the estimated relative percentage 

 based on nine replicates of varying Chesapeake and Roanoke proportions in 

 the subsamples 



2Estimates were based on random samples from one-half of spawmng-stock 

 collections which were classified as to area of origin by quadratic functions 

 obtained from the other half of the collections. 



^Based on two replicates. 



■■Based on eight replicates. 



tribution « 50^^. The iterative estimate will also 

 be used to estimate Chesapeake and Roanoke 

 stock contributions. 



341 



