nor purse seines are designed to estimate sex ratio 

 it can only be stated that the anchovy sex ratio has 

 not been adequately estimated. 



Collins (1969) showed that females are greater 

 in length and weight at age than males. However, 

 since Collins' estimates are based on combined 

 data from three fishing seasons and, since female 

 weights are known to fluctuate within season due 

 to spawning activity, the precision with which the 

 data can be used for estimation purposes is open 

 to speculation. 



For the present purpose of estimating c the sex 

 ratio of the number of females to males plus 

 females as estimated from the February 1978 

 midwater trawl survey (Hunter and Goldberg 

 1979) will be used. Reexamining original data 

 used by Hunter and Goldberg (1979, table 5) the 

 ratio estimate is 



c 

 Var(c) 



0.550 

 0.001. 



This assumes, of course, an equal weight at age. 



In the future, the best estimate of c is likely to be 

 the ratio of the actual sampled weights of males 

 and females; these were not available for the 



proximations. P may not be constant for as long a 

 time interval as assumed here. Observed b' was 

 found to be consistent for time of day, weight of 

 fish, and geographic location. This may not prove 

 to be the case under more intensive sampling. 

 Another problem in estimating the spawning 

 fraction is in determining female sexual maturity. 

 This problem may be particularly acute for recent- 

 ly spawned young females where microscopic 

 analysis is necessary to separate the recently 

 spawned from the sexually immature. Misclassi- 

 fying recently spawned as immature would tend to 

 inflate the estimated b. 



By the delta method (Seber 1973), the variance 

 of Sis 



[ 



Var(S) = {ab'cV^ d^VariP) + P^Varid) 



+ {PdY 



r Var(a 



) Var(6') Var(c) 



+ 



b'- 



+ 



& 



]] 



.(4) 



Dividing Equation (4) by the square of Equation 

 (3) and then taking the square root we have the 

 coefficient of variation (CV) of spawning biomass 



CV(S) = J[CY{P)f + [Cy{a)f + [CV(6)]' + [CV(c)]' + [CV{d)f, (5) 



February 1978 survey. This would, of course, 

 require the assumption that the sex ratio can 

 differ from 1:1, that the weight distribution of the 

 two sexes can change with time, and that a sample 

 estimate is a better estimate than any hypothe- 

 sized or long-term average value. 

 Using the following estimates 



P = 2.321 X lO'-'eggs/d 



eggs/t 



a = 3.96 X 10 

 b' = 0.159 



8 



c 

 d 



0.550 

 1.080 



the estimated S is approximately 0.72 million t. 

 This is reasonably close to the estimate by the 

 Smith procedure (Stauffer and Parker^) of 1.17 t. 

 At this time caution should be exercised in inter- 

 preting the general range described by these two 

 estimates. The parameters of Smith's procedure 

 have not been formally estimated. The parameter 

 estimates of this new method are only first ap- 



=^StaufTer, G. S., and K. R. Parker. 1978. Estimate of the 

 spawning biomass of the northern anchovy central subpopula- 

 tion for the 1978-79 fishing season. U.S. Dep. Commer., NOAA, 

 NMFS/SWFC Adm. Rep. LJ-78-9, 10 p. 



which is the component vector of the coefficients of 

 variation of the estimated parameters, right side 

 of Equation (3). Since possible covariance terms 

 are neglected, Equation (5) may be somewhat 

 oversimplified. However, Equation (5) allows a 

 first approximation to delegating the relative 

 impact of the precision of the individual param- 

 eter estimates. The squared coefficients of varia- 

 tion are as follows: 



[CV(P)]^ = 0.339 

 [CYia)f = 0.005 

 [CV(6)]=' = 0.018 



[cy(c)v 



[CY{d)f 



0.003 

 0.013. 



ThusCV(S) = 0.614. P contributes approximately 

 8 times more to the coefficient of variation of the 

 spawner biomass estimate than all other param- 

 eters combined. In the future, additional effort 

 will be allocated to estimating production. 



The utility of the direct method, Equation (2), 

 lies in the fact that all the parameters can be 

 estimated. The same samples used for estimating 

 b' can be used to estimate a and c. This can be 

 done with 2 wk of midwater trawling. It is hoped 



543 



