FISHERY BULLETIN: VOL. 73, NO. 4 



;o.6- 



1.2 1.6 2.0 



EFFECTIVE EFFORT 



.6 .8 1.0 



EFFECTIVE EFFORT 



1.2 



1.6 



1.8 



20 25 30 



BIOMASS (groms) 



45 



Figure 10. -Fox (1970) model fitted to yield data for the guppy. 

 Exploitation rates are 0.000, 0.257, and 0.326 per 3-wk period 

 fleft-to-right in upper panel, reversed in lower panel). 



12 16 20 



BIOMASS (grams) 



Figure U.-Fox (1970) model fitted to yield data for the sword- 

 tail. Exploitation rates are 0.000, 0,100, and 0.157 per 4-wk period 

 (left-to-right in upper panel, reversed in lower panel). 



11). Effective exploitation rates shown varied 

 slightly from the "target" rates because of lack of 

 infinite divisibility of the populations and because 

 of errors. The fitted Fox models yielded values of A- 

 of 0.260 per 3 wk and 0.321 per 4 wk for the guppy 

 and swordtail, respectively. Comparable values for 

 the Gompertz curves were 0.193 and 0.260. It was 

 considered more appropriate to use the values 

 from the Fox model because the analyses were 

 based on that model. To place the swordtail on the 

 same time scale as the guppy, the value of k was 

 multiplied by %, or %(0.321) = 0.241. 



Data of catch and biomass for the competing 

 populations (Table 8) were used to calculate 

 exploitation rates. Again the effective rates 

 varied from the target rates as explained in the 

 preceding paragraph. Also, it was again necessary 

 to adjust the effective rates for the swordtail to 

 the same time scale as the guppy. This was done by 

 the formula m = 1 - {1 - m.'y\ where ni' is the 

 unadjusted rate. Finally, for use in the differential 

 equations, the 3-wk rates must be converted to 



instantaneous rates. The formula is: F = -log^, (1 - 

 m), from Ricker (1958). 



The use of instantaneous exploitation rates as 

 employed herein assumes that P declines con- 

 tinuously, whereas the experimental technique 

 was to remove all the fish at the beginning of the 

 brood interval. It can readily be shown, however, 

 that the reduction in population resulting from the 

 application of rn at the beginning of a period is 

 exactly the same as the application of the 

 equivalent F throughout the period, even if both 

 are superimposed on a constant natural mortality. 



A summary of all the constants used in applying 

 Formulae (7) and (8) to biomass data from the 

 competing populations is given in Table 9. Where 

 both unadjusted and adjusted data are shown, the 

 latter were the ones used. 



Application of the Model 



Using standard analog computer techniques 

 (Ashley 1963) values of guppy and swordtail 



882 



