SILLIMAN: EXPERIMENTAL EXPLOITATION OF FISH POPULATIONS 



Oscillatory Fluctuations 



The substantial oscillatory deviations evident in 

 comparisons of observed and simulated biomass 

 levels (Figures 12, 13) suggest the need for special 

 study. Deviations can be evaluated more readily if 

 they are plotted along a straight baseline (Tables 

 12, 13; Figure 14). Viewed in this manner, devia- 

 tions appear at least roughly regular with respect 

 to time. Also, they tend to be similar for control 

 and test populations of the guppy for comparable 

 periods. They did not, therefore, result solely from 

 perturbations due to exploitation, although in the 

 test populations deviations were somewhat 

 greater post-exploitation than pre-exploitation. 



Oscillations of the type described above seem to 

 be basic to many populations. Walter (1973) points 

 out that such a fluctuation occurred in Lake 

 Michigan alewives. He developed delay-differen- 

 tial equations which are compatible with "an os- 

 cillatory sort of behavior centered about the 



equilibrium level." Although it would be of 

 interest to apply such models to the guppy-sword- 

 tail data, it is unlikely that they would provide 

 substantially different results insofar as the basic 

 relations between exploitation and yield are con- 

 cerned. It is with such relations that I am 

 primarily concerned in this paper. 



Since there were some fluctuations in water 

 temperature (Figure 1) during the course of the 

 experiments, it seemed possible that these might 

 have caused all or part of the oscillatory population 

 changes. To test this, a regression was erected for 

 periods 33-75, when temperature fluctuations were 

 fairly regular. The independent variable was 

 water temperature, and the dependent variable 

 was deviation of the control guppy population 

 biomass from that predicted by the simulation 

 model (Table 12, Figure 14). Results showed no 

 significant correlation between biomass devia- 

 tions and temperature (r = 0.087, P>0.1). 



It is worthwhile in this discussion of oscillatory 



Table 12. -Deviations of actual biomass from theoretical, on 

 basis of fitted model, guppy. 



Table 13.— Deviations of actual biomass from theoretical, on 

 basis of fitted model, swordtail. 



'Reconstruction interval. 



'Reconstruction interval. 



885 



