FISHERY BULLETIN: VOL. 70, NO. 3 



Both recorded and unrecorded natural mor- 

 talities occurred. Recorded mortality represent- 

 ed finding of dead fish in the tanks. Unrecorded 

 mortality, as mentioned above, is demonstrated 

 by negative values of R,nt (Table 3) , 



CHANGES UNDER EXPLOITATION 



Responses of the populations varied with ex- 

 ploitation rate. At the 10% rate, numbers in 

 each population declined while biomass remained 

 relatively constant (Figures 1 and 2). At the 

 25% rate, both numbers and weights declined. 

 Further consideration of stock changes will be 

 limited to data of biomass, since the biomass 

 curves are more regular than those of numbers 

 and represent both recruitment and growth. It 

 is evident that the initial rise in weight of catch 

 at the 25% rate was due almost entirely to crop- 

 ping off the biomass accumulated at the 10% 

 rate (Figure 2). The response of both popula- 

 tions to an increase in exploitation rate thus fol- 

 lowed classical conceptions based on theoretical 

 grounds (for instance, those of Thompson and 

 Bell, 1934). 



EQUILIBRIUM YIELDS 



In a relatively short experiment, such as this, 

 covering only 13 exploitation periods, the attain- 

 ment of complete equilibrium at either of the ex- 

 ploitation rates is obviously impossible. The last 

 two exploitation periods at each rate encompass 

 relatively small changes in stock and catch (Fig- 

 ure 2) ; they will thus be considered equilibrium 

 periods for the purposes of the analyses reported 

 below. 



Table 3. — Recruitment and unrecorded mortality, Tilapia 

 macrocephala. R,^t = P„ + i - P„ + M,nt + Cj^t, 

 where INT is interval between counts n and n+1, R is 

 net change,' P is stock, M is recorded mortality, and C is 

 catch, all in numbers. 



'■ ^j^f > indicates recruitment of at least the incJicoted number of 

 fish, K.f^rp < indicate.s unrecorded mortality of at least the indicated 

 number, and ^.j^^ = indicates either no recruitment and unrecorded 

 mortality, or the two exactly balanced. 



gression method employed for fitting does not 

 perform well when only two points are avail- 

 able. There is no opportunity for com.pensating 

 errors, and slight errors are greatly magnified 

 when the regression is extrapolated to the F-in- 

 tercept to estimate the maximum stock. Also, 

 since there are zero degrees of freedom, there is 

 no way of assessing variability. 



The above difficulties can be circumvented by 

 fitting a single general curve to both populations. 

 For individual population characteristics, devi- 

 ations from the general curve can be studied. 

 Four points were available for fitting the regres- 

 sion line — two from each population (Figure 3) . 

 The fit seems reasonably good for an experiment 

 of this type. 



POPULATION MODEL 



The exponential surplus-yield model of Fox 

 (1970) is simple to fit and has been found suit- 

 able for experimental populations with short 

 brood intervals (Silliman, 1971); it was there- 

 fore chosen for use with the data from the T. 

 macrocephala experiment. Ideally, the model 

 would be fitted to S and L separately. The re- 



COMPARISON OF YIELDS 



Deviations from the general curve (Figure 3) 

 may be considered with respect to the crowding 

 eflfect. It is seen that at the lower exploitation 

 rate (10% target) and larger population, the 

 population in the smaller tank (S) has a large 

 positive deviation whereas that in the larger 

 tank (L) is close to the curve. Conversely, at 

 the higher exploitation date (25% target) and 



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