Dorn: Environmental covariates of Merluccius productus growth 



275 



Var(lj) = 



1 



2.(liPj-Aj)2 '- + ^ '- - 2.Zqiqhqijqhj(liPj-Aj) — '-^-^ 



i#h 



Combining length-at-age from different strata 



An estimate of combined mean length-at-age is 



'-m'- 



where Ijh is the length-at-age in the hth stratum, and Cjh is the catch-at-age for the same stratum. 

 Again using a delta-method approximation, 



Var(lj) = IVar(Cjh) 



h 



(IjhCj - Xcjh Ijh) 

 h 



+ IVar(ljh) 



h 





The complete expression should include a term involving Cov(Cjh, Ijh)- This term was always negligible com- 

 pared with the other two terms, and depended on the method used to calculate the catch-at-age. Consequently, 

 it is not included here. The variance estimator for combined length-at-age for several strata requires an estimate 

 of the variance of catch-at-age. A method for obtaining this is given in Kimura (1989). 



