HANKIN: A MULTISTAGE RECRUITMENT PROCESS 



Analyses of these experimental populations 

 show that there are two distinctly different com- 

 ponents of experimental population growth and 

 that these two components should be separated in 

 mathematical treatments of population dynamics. 

 Numerical growth in experimental populations is 

 an extremely variable population phenomenon, 

 only weakly predictable through convential mod- 

 els and statistical techniques. Total biomass 

 growth is a relatively invariant population pro- 

 cess, highly predictable, and nearly immediately 

 responsive to slight disturbances in food supply. 

 From a modeling perspective, these considera- 

 tions imply that population biomass growth might 

 be adequately described by a simple deterministic 

 model, such as logistic growth, while description 

 of numerical growth may require more complex 

 and perhaps stochastic models. 



Description of numerical dynamics is, of course, 

 the province of stock-recruitment theory. Neglect- 

 ing the issue of the extreme variability in numeri- 

 cal behavior of these populations for the moment, 

 these experiments reveal at least two likely bio- 

 logical complications which may render simple 

 stock-recruitment theory of limited practical ap- 

 plication. The observed strong juvenile-fry inter- 

 action shows that recruitment may depend not 

 only on parent adult stock but also on juvenile 

 stock, perhaps at different times and in different 

 places. Simple stock-recruitment theory clearly 

 requires modification to account for such inter- 

 actions. Also, density-dependence of growth may 

 further compound the complexity of the recruit- 

 ment process. While numerical change within 

 sampling intervals may be adequately, although 

 imperfectly, described by the model developed, 

 eventual recruits, say in terms of adult females, 

 are evidently not a simple fraction of numerical 

 increase some fixed number of weeks previous. 

 Models of recruitment in fish populations have not 

 explicitly dealt with complications that might be 

 introduced by the density-dependence of year- 

 class growth, dependence that may occur after a 

 year class has been established. 



The probable general effects of a strong juvenile- 

 fry interaction may be examined by making a few 

 simplifying assumptions (none of which are more 

 than only approximately met by guppies) and then 

 to recast the experimental numerical dynamics 

 model as a more general relation similar in form to 

 the simple stock-recruitment model first proposed 

 by Ricker (1954). These assumptions are: 1) The 

 expected number of births is proportional to the 



number of reproductive females rather than to the 

 biomass of females. 2) The number of reproductive 

 females is proportional to the total number of 

 adult predators. 3) The correlation between size 

 and age is perfect and growth rates of individuals 

 are density independent. Then, letting A = num- 

 ber of adult predators, J = number of interacting 

 juveniles, and a, b^ , 6-2 = constants, the experi- 

 mental numerical dynamics model, 



API - EB exp(BiXi + B^X^), 



may be reexpressed as (using assumptions 1) 

 and 2)): 



API = aA exp(6i A + b^J) 



and if recruits are a constant fraction of numerical 

 increase in a given period (using assumption 3) ): 



R = a' A exp(6iA + bzJ) 



where a' = constant 



R — "recruitment." 



Three dimensions are required for visualization 

 of a hypothetical stock-recuitment relation incor- 

 porating a juvenile-fry interaction. To examine 

 such a relation, experimental estimates of b^ 

 (-0.031) and of 62 (-0.160) were taken from the 

 mean nonlinear estimates for 5.0 mm refuge fence 

 populations. Based on ratios of expected number of 

 births to numbers of adult predators, a rough 

 estimate for a' was obtained (= 2) by assuming 

 that recruitment was determined at the end of a 

 sampling period. A plot of the adult-juvenile stock- 

 recruitment relation thus produced is given in 

 Figure 14. 



There is a pronounced flattening of the recruit- 

 ment surface with increasing juvenile density. At 

 high juvenile density (15 on the graph), recruit- 

 ment is low, nearly constant, and is essentially 

 independent of adult stock. If such interactions 

 occur within populations of fish simple plots of 

 recruitment against adult stock would reveal 

 little trend at high juvenile densities. At low 

 juvenile densities, however, recruitment appears 

 strongly related to adult stock in the classic dome- 

 shaped manner. At low levels of adult stock 

 recruitment may fluctuate considerably, indepen- 

 dent of adult stock, as a response to high or low 

 juvenile densities. In general the more intense the 

 inhibition of fry survival rates by juveniles, the 



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