FOX: POPULATION SIMULATOR 



Constant recruitment of size l/a-i may be 

 simulated with GXPOPS by selecting equation 

 (28) and setting a^ ^ 0- 



Timing in the Simulator 



Reference in this study is made to a year di- 

 vided into 12 mo because the reproductive cycles 

 of many exploited fish populations are annual. 

 It is just as easy to consider the "year" as a 

 reproductive cycle (16 days, 3 yr, etc.) divided 

 into 12 time periods of equal length. 



The conventional notation, for numbering 

 timestream entities, is for the initial or first 

 instance to be denoted as 0. The computer, 

 however, begins with 1 in executing "DO" 

 loops, etc., therefore, the ordinal numbering 

 system is used in GXPOPS. The first month 

 and year are denoted as 1, as are the initial 

 numbers and yields of the first month and 

 year, and the young of the year. The simulator 

 takes the hatching time, f^, as time 1 (i.e., 

 L^ — L\) and the year is carried on a biologi- 

 cal fiscal basis. For example, if hatching oc- 

 curs on April 1, recruitment to the main popu- 

 lation on July 1 of the first year of life, and 

 breeding begins October 1 and ends December 

 1; then 



tY^ = 1, ^^ = 3, t^ = 7, and t^ = 8, 



respectively. If recruitment does not occur 

 until July 1 of the third year of life, then t^ = 



27. 



EXAMPLE: A PANDALID SHRIMP 

 POPULATION 



GXPOPS was designed to be useful for ex- 

 amining the responses of many life history pat- 

 terns to exploitation. The impetus, however, 

 was to examine the response to exploitation 

 of a pandalid shrimp life history (Fox, 1972). 

 Pandalid shrimps are protandric hermaphro- 

 dites — i.e., individuals mature as males but 

 later transform to function as females (Berke- 

 ley, 1930), fertilization is accomplished through 

 copulation, the females carry fertilized eggs 3-9 

 mo until hatching, and they exhibit pronounced 



stepwise growth. While the extensive simula- 

 tion studies investigating the effects and man- 

 agement implications of all sectors of the 

 pandalid shrimp model will be published subse- 

 quently, one particular study of the effect of 

 season length on the simulated fishery is useful 

 for illustrating the utility of GXPOPS. 



Table 1 contains the parameters of the simu- 

 lated pandalid shrimp population which 1) 

 consists of six year classes, 2) is fully recruited 

 to the fishable population during the third year 

 of life (at 2 yr old), 3) breeds over 2 mo, 4) 

 carries its eggs 5V2 mo until hatching, 5) re- 

 cruits to the main population during the fourth 

 month of life (3 mo after hatching), 6) matures 

 as males during the third year of life (at 2 yr 

 old), and 7) transforms into females during the 

 fourth year of life (at 3 yr old). The stepwise 

 growth in weight is given in Figure 2. 



Exploiting the sinrmlated pandalid shrimp 

 produced the relationship between equilibrium 

 yield and fishing effort (= instantaneous fish- 

 ing mortality coefficient since the catchability 

 coefficient was assumed to be 1.0) given in Fig- 

 ure 3. An equilibrium yield was achieved with 

 fishing effort up to 1.4, with the maximum 

 equilibrium yield occurring at about 1.0. Fish- 

 ing above a level of 1.4 did not result in equil- 

 ibrium within 25 yr of simulated fishing, and 

 continued fishing somewhere between 1.4 and 

 2.0 would eventually result in extinguishing 

 the population. By not including the effect of 

 random mating (copulation), i.e., k^, — °o , 

 the simulated population achieved equilibrium 

 out to nearly F = 1.8 (Fox, 1972). This exhibits 

 some need for considering the implications of 

 copulation success in evaluating management 

 alternatives. 



The equilibrium yields given in Figure 3 are 

 for an annual pandalid shrimp fishery. Several 

 states, however, have closed seasons during that 

 part of the year when females are carrying 

 fertilized eggs — ovigerous period — (Dahl- 

 strom, 1970). For the simulated pandalid shrimp 

 population, the ovigerous period lasts 6 mo 

 (months 7-12). It is of interest to compare the 

 results of the closed ovigerous season strategy 

 with other possible season lengths, all begin- 

 ning subsequent to hatching and running con- 

 tinuously until reaching the closed season. 





1025 



