LO ET. AL.: ESTIMATES OF LARVAL MORTALITY 



0.15 



CV(b) 



— Estimated CV 

 • Observed CV 



120 160 



POSITIVE TOWS (n) 



200 



240 



Figure 8. — The relationship between the coefficient of variation, cv(b), and the number of positive tows, n, derived from 

 the results of the simulation. 1980-87 survey results are also plotted. 



The CV Method 



The CV of the estimate of the difference be- 

 tween two mortahty coefficients, cv(.d) (Equa- 

 tion (1)), was calculated for various mortality 

 differences and sample sizes using the data listed 

 in Table 5. The cvid) decreases linearly with the 

 difference between mortality coefficients (D), 

 increases linearly with the absolute value of the 

 larger of the two mortality coefficients (P2), and 

 exponentially declines with increasing sample 

 size (A^, )i) (Table 6). The required sample size 

 was thus estimated by regressing the number of 



Table 5. — Mean and standard error (SE) of estimated mor- 

 tality coefficient based on 100 computer runs. Five popula- 

 tions were simulated, each with a different mortality coeffi- 

 cient (P). Simulated surveys used three sample sizes {N) 

 with 60% of the plankton tows positive for anchovy larvae 

 (nl 



Sample size N(n) 



50(30) 



100(60) 



200(120) 



positive tows on P2, D, and lnlc('(d)]: 



n = -101 + 24.8 p2 - 150D- 128 ln[cv(d)] . 



For example, estimating the difference be- 

 tween two estimated mortality coefficients, 

 when the true mortality coefficients are 3.0 and 



Table 6. — Coefficient of variation of the esti- 

 mate of the difference between two mortality 

 coefficients, cv{d). calculated for various mortal- 

 ity differences, D, and sample sizes, n. The 

 number of positive tows, n, was 60% of the total 

 number of tows. 



409 



