HANKIN: A MULTISTAGE RECRUITMENT PROCESS 



p ( = 0.516). The mean of this distribution, n p, 

 is the expected number of broods delivered in the 

 first period, or: 5 x 0.516 = 2.58 broods. 



Further, taking the mean initial weight of adult 

 females to be 0.5 g, the fecundity relation predicts 

 an expected brood size of 11.14 fry and a possible 

 range of from 5 to perhaps 20/brood. Thus, the 

 expected number of births iEB) is: 2.58 broods 

 X 11.14 births/brood = 28.73 births = npu 

 where: u = expected outcome of a success (i.e., 

 expected number per brood). But the range of 

 possible values for the random variable "number 

 of births in a biweekly interval" was from 

 (0 broods x 5 births/brood) to 100 (5 broods x 

 20 births/brood) births. Assuming that perhaps 

 70% of the fry born in the first interval survived, 

 since adult predator densities were very low, the 

 collected statistic API could have had a range 

 from to about 70. Hence the estimated fry 

 survival rates could have had a range of from 

 (APLEB = 0/28.73), had no broods been de- 

 livered, to as high as 2.44 (70/28.73), if all five 

 females delivered broods. Estimated fry survival 

 rates at adult densities of eight or nine during the 

 first 4 wk reflected this possible variation in 

 actual numbers of broods delivered and number 

 of births per brood and ranged from to 1.38. 

 Thus large variation among estimated fry sur- 

 vival rates at low adult densities is possible and 

 unavoidable if the actual number of births is 

 unknown. 



In natural populations fluctuations in year- 

 class strength, the natural analog to numerical 

 experimental population increase, due to varia- 

 tion in early life survival, often range over two 

 orders of magnitude (Forney 1976). While the 

 primary causes behind such variations (often at 

 the same or similar stock densities) seem to be 

 usually environmental, unlike experimental pop- 

 ulations under controlled conditions, this varia- 

 tion seems at least equal to that observed in these 

 experiments. Guppy reproductive features, includ- 

 ing small brood size, very high but variable fry 

 survival, and high variability in timing of brood 

 delivery, are replaced in most natiu-al fish popula- 

 tions by high fecundity and extremely low and 

 variable early life survival. Thus, although under- 

 lying causes differ markedly, observed fluctua- 

 tions in numerical population growth of natural 

 populations at least equal those observed in ex- 

 perimental populations. 



The striking density dependence of growth ob- 

 served in these populations may, however, repre- 



sent an exaggeration of probable levels of growth 

 response to density that may exist in natural 

 populations. Many natural populations are prob- 

 ably not directly limited by their food supply, but 

 rather by competing species, suitable habitat for 

 all life stages, and/or harvest by man. Natural 

 population biomass may in general fall below that 

 which the underlying food supply could in theory 

 support. Also, variation in food supply would 

 make field observations of density-dependent 

 growth less striking. Finally, empirical observa- 

 tions suggest that such intense growth depression 

 with high population density is rarely a feature of 

 commercial fish populations. Rather, observations 

 of extreme stunting of fish size have been collected 

 from simple single species populations in many 

 respects analogous to the experimental popula- 

 tions. Stunting among high density pond and 

 small lake populations of yellow perch, Perca 

 flauescens, and eastern brook trout, Saluelinus 

 fontinalis , is well known. Although extreme den- 

 sity dependence of growth does occur in natural 

 populations, it seems unlikely for most exploited 

 populations, especially when population biomass 

 has been reduced to perhaps one-half of unex- 

 ploited levels. 



SUMMARY 



The ultimate interest in laboratory study of the 

 stock-recruitment process is to gain insight into 

 this fundamental problem and to apply such 

 insight to the study and modeling of natural 

 populations. These experiments illustrate that 

 the stock-recruitment process may involve more 

 than a single adult stock -related feedback control 

 and that more complex mechanisms may involve 

 interactions among several stock components. 

 While mathematical models of more complex 

 stock-recruitment processes may be constructed, 

 that such complex analytic models may be use- 

 fully applied in practice is far from clear. Two 

 serious application problems exist and these prob- 

 lems seem inherent to analysis of stock-recruit- 

 ment relations for any temperate species. The 

 time frame and economic expense necessary to 

 collect data suitable for statistical analysis of 

 possible complex stock-recruitment models and 

 the probably inherent variability of the recruit- 

 ment process argue that if, indeed, such complex 

 models are to be of practical use, major rethinking 

 of analysis and data collection approaches is 

 required. 



Data collection during these experimental stud- 



575 



