FISHERY BULLETIN: VOL. 71, NO. 4 



MODEL STRUCTURE 



A flow-chart of GXPOPS indicating the op- 

 tional life history sectors is presented in Fig- 

 ure 1. Each sector is described by the equations 

 below. The basic time period for calculations in 

 GXPOPS is monthly with all processes summed 

 or averaged annually. There are three output 

 options: 1) annual summaries only, 2) monthly 

 and annual summaries by age class, and 3) 

 monthly listings by age class as well as monthly 

 and annual summaries. 



year class, / 

 natural and 

 can evaluate 

 patterns such 

 seasons, etc. 

 of selectivity 

 incorporated, 

 class I during 



= 1. . . n, and j - 1. . . 12. With 

 fishing mortality so general one 



the effects of seasonal mortality 



as mass winter mortalities, closed 

 The coefficient A allows patterns 

 or seasonal availability, etc. to be 



The average number alive of year 



month j is given by 



-Z; 



N;j = NiAl-e ^J)IZ, 



'I] 



'ij 



ij- 



(3) 



(^ 



OF 



PLANKTONIC 

 LARVAE 



&- 





e 



^-oa I 



IMMATURES -^-^ MALES ►*!— • 



I I 



f-*<] 



i. 



FEMALES 



*---*ci 



CATCH 



NATURAL 

 DEATHS 



Figure 1. — Simplified flow chart of the computer pro- 

 gram, GXPOPS. Boxes represent state variable compart- 

 ments, solid lines represent material flows, dashed lines 

 represent information flows, and circles represent regula- 

 tory functions; CF = copulation function, FF = fishing 

 mortality function, MF = sex specific maturation func- 

 tion, and RF = recruitment function. 



Growth 



The growth in weight of the animals is rep- 

 resented by one of two options, the von Berta- 

 lanffy growth equation or a linear segmental 

 growth curve as in POPSIM (Walters, 1969). 

 The von Bertalanffy formulation is 



Wlj = Woo 



[l-.-^<12,^y-13-<o)|3 (4, 



Wj; is the average weight of an individ- 



where 



ual in year class / at the beginning of the 

 month j, and Woo , K and t^ are parameters of 

 the von Bertalanffy growth equation. The seg- 

 mental growth option is formulated as 



Wlj = a + b A t 



(5) 



Mortality 



Mortality may be age-specific on a monthly 

 basis and is assumed to be representable by an 

 exponential decline such that 



with 



^i, y + 1 = ^if ~^^J 



Z^Mij^A^jFij 



(1) 



(2) 



where Nij is the number of animals belonging 

 to the z'thyear class at the beginning of month 

 j, Mij is the instantaneous coefficient of nat- 

 ural mortality, Ay is an availability multi- 

 plier, Fij is the potential instantaneous coef- 

 ficient of fishing mortality of a fully available 



where a 



W; 



i, j - 1 



b = 



(Wij - 



w 



u-i) 



and 



A^ = 1. Using the segmental option, any shape 

 growth curve may be approximated, including 

 the stepwise growth pattern of ciTistaceans and 

 many temperate fishes and mollusks. 



Yield 



Yield is computed monthly both in numbers 

 and weight for each year class under either the 

 von Bertalanffy or linear segmental growth 

 option. 



YNij=^ijFijNij 



(6) 



where YNij is the yield in numbers. Under the 

 von Bertalanffy growth option, the yield in 

 weight, Yioij , is computed as j 



1020 



