FISHERY BULLETIN: VOL. 72. NO. 2 



the period between the given sampHng date and 

 the previous sampling date plus one-half the 

 period between the given sampling date and the 

 next following sampling date. 



The ANP equals the sum of all net production 

 increments over the year. 



tn=n 



ANP = SUM NP t„ (tn 4 ; -t, - ; )/2. 



tn — J- 



(3) 



In the equation tn refers to the nth sample date, 

 ^Ptn refers to the mean rate of net production per 

 day on the nth sample date, and ANP is the mean 

 value of the annual net production for any life 

 history stage being considered. For the first and 

 last sampling dates of the year, the mean rates per 

 day were applied over one-half the following 

 sampling date interval and one-half the previous 

 sampling date interval, respectively. Calculations 

 using Equation (3) were carried out separately for 

 postlarvae, larvae, and eggs at station 5 off 

 Scripps, and the total for all life history stages is 

 the sum of the annual values for the eggs, larvae, 

 and postlarvae at that station. ANP was also cal- 

 culated at stations 1, 3, and 6 for postlarvae only. 

 The variance of the mean value of the ANP at a 

 given station was calculated as the product of the 

 variance of the mean rate of net production per 

 day and the square of the time interval over which 

 it was applied, summed for all time intervals dur- 

 ing the year. The equation was derived from the 

 variance formula of a dependent variable which 

 equals the product of two independent variables 

 (net production over a time interval, a t, equals 

 the product of the mean net production per day 

 and zi^), by solving for the square of the differen- 

 tial of net production over a time interval a^ The 

 covariance term is zero since the daily net produc- 

 tion and time interval between sampling dates are 

 independent. The term for the square of the mean 

 daily net production multiplied by the variance of 

 A Ms presumed to be small, because sampling dur- 

 ing the year was within a few hours at the same 

 time of the day for all sampling dates. 



t„=n 



Var(ANP)=SUM Var(A^P^J(^„4i-^„_im.(4) 



n ^ 1 



The symb ols a re as given above in Equation (3), 

 and Var (ANP) and Nd,x{NPtn) refer to the var- 



iance of mean annual net production and the var- 

 iance of mean daily net production on sampling 

 date tn, respectively. 



Results 



During the field study from 8 March 1970 to 2 

 June 1971, 100 mortality values were obtained for 

 postlarvae and larvae. On any one sampling date 

 it was not possible to calculate mortality values 

 for all size classes, especially with small sample 

 sizes in older stages. Therefore, the mortalities 

 from all sample dates were grouped into seven 

 time periods and seven size classes (excluding 

 eggs) in order to obtain an estimate of mortality 

 for each class over time. The mortalities were 

 grouped according to the subjective criterion that 

 medians of a group would differ from any other by 

 at least 50%. The mortalities for size classes were 

 set by the comparisons of mean numbers per class 

 between successive classes. 



For the time period of 1 May to 18 June 1970 a 

 life table calculation is given in Table 11. The 

 mean hatching success of eggs is 94%. The Ix 

 values are the probability that an individual born 

 will survive to the beginning of each age interval. 

 The instantaneous mortality rates which were 

 used to construct the / ,: schedule are as follows: 1) 

 0.170 for larvae ofage 1-19 days, 2) 0.021 for stage 

 1-2 mm postlarvae ofage 19-45 days, 3) 0.150 for 

 stage 3-4 mm postlarvae of age 45-53 days, 4) 

 1.047 for stage 5 mm postlarvae ofage 53-54 days, 

 5) 0.572 for stage 6 mm postlarvae ofage 54-55 

 days, 6) 0.378 for stage 7-8 mm postlarvae ofage 

 55-63 days, and 7) 0.260 for stage 9-13 mm post- 

 larvae ofage greater than 63 days. These mortal- 

 ity rates were applied equally for each age inter- 

 val over the duration of the respective stages. Note 

 that up to age 53 days (4.5 mm) the first 45 live 

 births give a net reproduction of 1 .0405 (60% of the 

 total), enough to replace the population. The next 

 53 live births add 23% of the total net reproduc- 

 tion. The enormous potential reproductive capac- 

 ity at age 61-63 days and older is not fully realized 

 because of the miniscule numbers which survive 

 to this age. These results show the great impor- 

 tance of early reproduction in size classes 1-2 mm 

 toward the net reproduction. 



The population parameters and stable age dis- 

 tributions in May-June and three other time 

 periods, each with its own schedule of survival and 

 the mean schedule of births, are shown in Table 

 12. For the 1 May to 18 June period, the observed 



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