LO ET. AL.: ESTIMATES OF LARVAL MORTALITY 



APPENDIX 



Assignment of Larval Ages Using the Pareto Function 



The standing stock (SS) of larvae, between the ages of//, and 20 days, is 

 the integi'al of the production curve (Fig. 5) over these ages: 



r 20 r 20 



SS= P,di = P„(t/t„)-Hi 



= [1 - (20/<,)-<P-i'] Jllji- for p <> 1, 



(3- 1) 



= [ln(20) - Mt,,)]t,P,, for (3 = 1. 



Similarly the number of larvae younger than age t is 



SS, = [1 - m,,)-'^-''^ ^"^" for p <> 1, 



(P- 1) 



= [ln(0 - ln(^,)] t^Pf, for p = 1. 



The proportion of larvae that are younger than age t is 



m = SS,/SS = ^ ^ ^^ ,^ ^^ for p <> 1, 



1 - (20//;,)-<P-i' 



\n{t/t„) 



for p = 1, 



ln(20//y,) 



where < r(t) < 1. 



By rearranging terms, t can be expressed as 



t = t,,[l - r{t )(1 - (20/6,)"'""^*]"^'"'"" for 6 <> 1, 



= th(20/t,,y^'^ for 6 = 1, 



where 6 is a normal random variable with mean = p and standard error = 

 0.2 p (0.2 is an arbitrarily chosen value for the coefficient of variation (b) and 

 )it) is a uniform random variable between and 1). 



Sample Allocation 



The allocation of tows to each region and month was based on the 1984 

 sampling pattern (Table 2, Fig. 2). For a total of A'^ tows, the number of 

 positive tows allocated to month ; and region j was computed as 



n(i,j) = N * p{i) * q{j\i) * r{j\i) 



where pd) is the proportion of tows for month i and Sp(0 = 1 



gi i\i) is the proportion of tows made in region / during month / and 



^qij\i) = 1 

 r{j\i) is the proportion of positive tows for region / during month i 

 and < = rOlO < = 1. 



415 



