Fishery Bulletin 90(1). 1992 



s\ 



M-m 

 M 



ing the sample size (n) for a linear regression was 



(Eq. 8) 



m 



n- 1 = 



According to Hunter et al. (1985), the optimum number 

 of tissue samples can be determined for a given 6 

 (= s^e/s^A). the cost of processing a tissue sample, and 

 the cost of processing a fish. The ratio, K = s^i/s^a. 

 measured the excess variance which is contributed by 

 taking tissue samples rather than counting every ad- 

 vanced oocyte in the ovary. 



We used Dover sole collected during January-Feb- 

 ruary 1987 to determine the optimal number of tissue 

 samples. Two tissue samples were taken from the 

 ovaries of 99 Dover sple. The within-sample variance 

 of oocyte density (s^g = 1053 x lO'*) was obtained from 

 an ANOVA, and the linear regression of Yp on W 

 (Yp = 20,255 -H 40.54 W) gave the MSE (s2^ = 18,469 x 

 10^) (Table 6; Fig. 5, lower middle). Thus is 0.058 

 when calculated from equations (7 and 8) where m = 2. 



Because M was large (range 200-700), was 



M 



assumed to equal 1, and s^a was computed as s^^ - 

 (s^e^^) = 17,942 X 10^. Hence when two tissue samples 

 are used, the variance within tissue samples is only 

 5.8% of the variance around the fecundity-fish weight 

 regression line. To quantify the 

 excess variance due to subsam- 

 pling, we computed K = s-^/s^^ 

 = 1.03. This means the variance 

 around the regression line which 

 was based on two tissue samples 

 per fish (Eq. 4) is about 1.03 

 times that of an equation based 

 on counts of all advanced yolked 

 oocytes in the ovary (Eq. 2). Al- 

 though the vnthin-ovary variance 

 was small, we recommend count- 

 ing two tissue samples per female 

 because the cost of processing 

 the second sample was minimal. 



Cy(b)2 



(Eq. 9) 



Table 6 



Within-sample variance (s%xlO"^) from ANOVA and the 

 MSE (s-(XlO"'') from the regression analysis of fecundity 

 (Yx 10"-) and weight of Dover sole Microstomiis pacificus. 

 California females taken January-February 1987. 



Analysis of variance on total fecundity 



Source 



DF 



SS 



MS 



Fish 

 Error 



Total 



98 

 99 



197 



8,559,008 

 104,201 



8,663,209 



87,337 

 1,053 



Analysis of variance on linear regression 



Source 



DF 



SS 



MS 



Regression 

 Residual 



1 

 97 



2,488,019 

 1,791,468 



2,488,019 

 18,469 



134.72 



Predictor 



Coeff. 



SD 



Constant 



Fish wt. 



202.55 



40.54 



32.03 



3.49 



6.32 



11.61 



Optimal number of females 



In addition to the sample alloca- 

 tion based on cost of processing 

 fish and cost of processing tissue 

 samples, the number of females 

 needed for a regression estimate 

 of total fecundity was determined 

 by modifying a procedure sug- 

 gested by Thigpen (1987) to the 

 1987 fecundity data for Dover 

 sole. The equation for determin- 



OREGON 

 N = 67 



1-^ 



100 



200 ] — 



o 



o 

 o 

 _i 

 < 



I- 

 o 



OREGON 

 N = 36 



OREGON & CALIFORNIA 



CAL DECEMBER 



CAL JANUARY 



CAL MARCH 



ORE DECEMBER 



ORE MARCH 



100 

 200, — 



CALIFORNIA 

 N = 31 



DECEMBER 



FEMALE WEIGHT (g) 



Figure 5 



Total fecundity of Dover sole Microstomus pacificus as a function of female wet weight 

 in grams (without ovary) for various months taken in central California and Oregon. 

 Each point represents a single female; equations are given in Table 9. 



