FISHERY BULLETIN; VOL. 78, NO. 3 



Figure 14. — Visualization of proposed 

 adult-juvenile stock-recruitment model. 

 See text for explanation. 



^e/v,^'o 



-2,0 py 



more extreme would be the expected fluctuations 

 in recruitment at the same adult stock densities. 

 Variability in recruitment would be increased 

 with a decrease in adult stock, as would be caused 

 by fishing. 



If, instead of juveniles of the same species, 

 juveniles (or perhaps adults) of another species 

 interact with fry (or larvae) in a similar manner, 

 one may begin to imagine the complexity of 

 possible "true" recruitment mechanisms in fish 

 populations. Standard simple stock-recruitment 

 relations may require more dependence of recruit- 

 ment on adult stock alone than is justified. In- 

 traspecific or interspecific interactions of the 

 type observed in these experimental populations 

 clearly create complex recruitment processes, in- 

 capable of even approximate description on the 

 basis of adult stock alone. If recruitment theory is 

 to be of practical significance in the management 

 of fish populations, it seems that the numerical 

 dynamics of given populations will have to be 

 examined as unique biological phenomena, per- 

 haps only rarely susceptible to standardized 

 mathematical descriptions such as the Ricker 

 stock-recruitment model. 



One may, of course, deny the relevance of the 

 above conclusions, derived from single species 

 laboratory populations maintained under fixed 

 food supply, for the modeling of natural popula- 

 tions. In particular, it may be questioned whether 

 the extreme variability in numerical population 

 growth observed in experimental populations does 

 in fact also occur in natural populations. And it 



may also be questioned whether natural popula- 

 tions actually exhibit such extreme response of 

 individual growth rates to variations in popula- 

 tion density. Several aspects of guppy life history 

 and empirical observations from natural popula- 

 tions together argue that experimental variation 

 in numerical population growth indeed has clear 

 parallels in natural populations. The second issue, 

 that concerning density dependence of growth, is 

 less easily resolved. 



The extreme variability in numerical popula- 

 tion growth observed in these experimental pop- 

 ulations arises primarily from small population 

 size. This variation is inherent and depends on the 

 guppy reproductive cycle. Since all statistical 

 analyses were based on expectations of events, 

 and since in small populations the discrepancy 

 between actual outcomes of events and their 

 expectations may be large, statistical analysis and 

 prediction of numerical growth patterns were 

 inherently weak. For example, fry survival rate 

 estimates were based on the expected number of 

 births in a 2-wk interval rather than on actual 

 births which were unknown. At initiation of 

 populations only five adult females were present. 

 The initial "biweekly" sampling interval was 16 d 

 so the probability of an individual female deliver- 

 ing a brood within the first interval was 16/31 = 

 0.516. Since broods of females are delivered in- 

 dependently of one another, one may reasonably 

 assume that the number of broods delivered in the 

 first interval among five adult females was bi- 

 nomially distributed with parameters n ( = 5) and 



574 



