LO ET. AL.: ESTIMATES OF LARVAL MORTALITY 



L =0.68L 



c 



1 081 



Figure 7. — The effect of net abrasion and preservative on tlie 

 apparent length of anchovy larvae (fi'om Theilacker 1980). L is 

 live larval length; L^. is preserved (captured) larval length, and 

 the length of the plankton tow is 20 minutes. 



transformed Pareto function: 



In(Pt) = MP,,) - p ln{t/t,,) . 



Each simulation that produced an estimate of 

 mortahty rate was repeated many times. The 

 collection of estimates of mortality rates was 

 used to assess the accuracy and precision of esti- 

 mates of mortality rates. 



Sample Size for Detecting a Difference of 

 Mortality Rates 



The minimum sample size required to detect a 

 difference between two mortalities was com- 

 puted by two methods. 



The CV Method 



The coefficient of variation (cv) of the estimate 

 of the difference between two mortality coeffi- 

 cients (D = (Bo - (3i) was calculated by 



cv(d) 



[var(bi) + var(62)]' 

 D 



|0.5 



for D iF 



(1) 



where d is the estimate of D, the difference be- 

 tween mortality coefficients Pi and ^oiD = P2 ~ 

 Pi); 61 and 62 are the estimates of Pi and P2; 

 var(6i) and var(52) varying with sample size are 

 computed in the simulation. The relationship be- 

 tween the sample size in) and two elements, 



cv{d) and D, enables us to determine the min- 

 imum sample size for a given ciid) and D. 



The Power Method 



The probability of detecting a difference in two 

 mortality rates, given that there is a difference, 

 was calculated as 



P[d > c(Pi,«) i D] = P[Z > 2(pi,P2,H)] (2) 



where d follows a normal distribution with a 

 mean of Z) and a variance of [SE((/)]-; Z follows a 

 normal distribution with a mean of and a vari- 

 ance of 1: 



c(Pi,70 =2SE(f/) = 2V^SE(6) 



forpi = p2(Z) = 0) (3) 



2((3l,P2,«) = 



c(pi,»)-D 



SEW) 



and SE(J) = [var(6i) + varibo)^^ 



forP2#Pi(/)^0). 



A normal distribution table was used to obtain 

 the probability values. 



Relationship Between Growth and 

 Mortality 



The mortality coefficient (p) was fixed. Five 



407 



