HIROTA: NATURAL HISTORY OF PLEUROBRACHIA BACHEI IN LA JOLLA BIGHT 



DEMOGRAPHY AND NET 

 PRODUCTION 



Methods 



Computations of stage-specific instantaneous 

 mortality rates (hereafter referred to as mortality 

 rates or mortalities) were made in order to use 

 these values in other calculations to estimate 

 population parameters and rates of net produc- 

 tion. Mortalities were calculated using field data 

 on stage frequencies treated as a composite of all 

 samples taken on each sampling date and labora- 

 tory data on rates of development, with tempera- 

 ture and food concentrations being similar to aver- 

 age values observed in the field study area. The 

 growth or development rate data are from 

 laboratory cultures at 15°C and 35 /jg C/liter food 

 concentration. The mortalities were computed by 

 a computerprogram (Fager, 1973) which solves an 

 equation to fixed level or error by a specified 

 number of iterative calculations. 



N,+ 1 IN^ = t, (1 - e ~'^^v + 1 )lt, + 1 (e ^'x - 1). (1) 



The variables ^r and tx^^ i are the duration of 

 development in days for stage x andx+1, respec- 

 tively; variables A^v andA^v+i are the numbers of 

 each stage in the composite divided by the respec- 

 tive duration of development. The mortality rate 

 on a per day basis from stage x to stage x + 1 is M; 

 for an organism with continuous growth, such as a 

 ctenophore, a "stage" is a size category. Positive, 

 mortalities can be calculated only when Nx ex- 

 ceeds A'^;^ + 1 . Implicit in the calculation are the 

 assumptions that: 1) successive stages of the or- 

 ganisms were born during a period of constant 

 recruitment and 2) successive stages have lived 

 together in spatial proximity, or emigration is 

 balanced by immigration in the water parcel. . 



The life table calculations were based on the 

 estimated mortalities for different time periods of 

 field sampling and the mean schedule of live 

 births from laboratory cultures at IS'^C. The equa- 

 tions used to calculate population parameters and 

 stable age distributions are from Birch (1948). 



The rate of net production per day of each de- 

 velopmental stage is a function of the numbers 

 and weights of the animals and their instantane- 

 ous rate of tissue growth and of mortality on a per 

 day basis; the rate of net production by a species 

 population of a given age structure is simply the 



sum of the rates for each stage. These rates are 

 calculated from the equation of Ricker (1958), 

 which relates the rate of net production to the 

 mean daily standing stock and the rates of growth 

 and mortality. 



NP, = G,B,il - e 



Gi-M 



)/(M,-G,) = G,Bi.(2) 



In this equation , and M, are the mean exponen- 

 tial coefficients or mean instantaneous rates of 

 growth and mortality of the ith stage on a per day 

 basis. The variables Bi and B, are the calculated 

 standing stocks per sample in milligrams organic 

 matter per square meter of the ith stage at the 

 beginning of the day (B, ) and the average over a 

 24-h period (Bi ). This function equates the rate of 

 net production per day for the ith stage (NP, has 

 units of milligrams organic matter per square 

 meter over a 24-h period) to the instantaneous 

 rate of tissue growth times the standing stock at 

 the beginning of the day (the beginning of the day 

 is the time a field sample is taken) corrected for 

 differential increases due to tissue growth and 

 differential decreases due to mortality. For 

 further details refer to the work of Ricker (1958) 

 and Mullin and Brooks (1970). Note that the rate 

 of net production per day is actually an average 

 value, because it is calculated using means for 

 growth and mortality rates. 



The rates of net production for postlarvae and 

 larvae of P. bachei were calculated according to 

 Equation (2) above. No values for mortality rates 

 of eggs were calculated, but the hatching time of 

 eggs at 15°C is about 24 h. In calculation of the net 

 production of eggs per day, it is assumed a steady 

 state in the standing stock of eggs with a hatching 

 time of 24 h. This is equivalent to the assumption 

 that the rate of net production of eggs per day is 

 equal to the standing crop at the time of sampling 

 the eggs. 



From calculations of the net production per day 

 of postlarvae for each replicate sample at each 

 station, the mean value and the variance of the 

 mean are calculated according to standard 

 parametric statistics. At a given station, the total 

 amount of organic matter produced over some in- 

 terval of time, i^, equals the product of the mean 

 rate per day and the time interval in days. For 

 calculations of the annual net production (ANP), 

 it is assumed that the mean rate per day on a given 

 sampling date at one station applies linearly over 

 an interval of time equal to the sum of one-half 



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