ATKINSON: FISH POPULATION DYNAMICS 



4000 



ESTIMATED 



FROM SARDINE 



DATA BY MURPHY (1966) 



ESTIMATED FROM 

 ANCHOVY DATA 

 BY MURPHY (19661 



1932 



36 



40 



44 



48 



52 



YEAR 

 (a) SARDINES AND ANCHOVY 



8000 — 



_ 6000 



V) 



z 

 o 



I- 



8 

 < 



g 



CQ 



4000 — 



2000 



1932 



36 



48 



52 



40 44 



YEAR 



(b) COMPETITOR AND PREDATOR GROUPS 



Figure 7.— Simulation run for assumed models of increased sar- 

 dine fishing rate and fluctuating sardine larvae survival rate. 



single population group 

 • spatial and temporal variations. 



The sardine subsystem within the California Cur- 

 rent region was modeled using the multispecies dif- 

 ference model and simulations computed for the 

 sardine's collapse period of 1932-52. Input drivers 

 perturbing the system included representations of 

 the increased sardine fishing pressure and the fluc- 

 tuating sardine larvae survival rates during this 

 period. Simulation results were shown to compare 

 favorably with the available population history data. 

 The increased fishing pressure was indicated to be 



1000 



ANCHOVY 



1932 



36 



40 44 



YEAR 



48 



52 



Figure 8.— Simulation run for assumed constant pre-1932 fishing 

 rate but with fluctuating sardine larvae survival rate. 



the fundamental cause for the sardine collapse; the 

 estimated yearly fluctuations in sardine larvae sur- 

 vival could not by themselves have caused this sud- 

 den event. 



These simulation results demonstrate the use of 

 the discrete-time difference model as an efficient 

 simulation tool. There appear to be many applica- 

 tions for the model in theoretical and applied multi- 

 species fisheries studies. 



ACKNOWLEDGMENTS 



This work was based on a part of a dissertation 

 submitted in partial satisfaction of the requirements 

 for the Ph.D. degree at the University of Califor- 

 nia, Los Angeles. S. E. Jacobsen, chairman of the 

 dissertation committee, provided guidance and en- 

 couragement throughout these studies. D. A. Kiefer 

 of the Department of Biological Sciences, Univer- 

 sity of Southern California, reviewed early versions 

 of this paper and made helpful comments. 



LITERATURE CITED 



Anderson, K. P., and E. Ursin. 



1977. A multispecies extension to the Beverton and Holt 

 theory of fishing, with accounts of phosphorus circulation 

 and primary production. Medd. Dan. Fisk. Havunders. 

 7:319-435. 

 Atkinson, C. A. 



1980. Analysis of perturbed dynamic systems under param- 



547 



