HANKIN: A MULTISTAGE RECRUITMENT PROCESS 



multiple linear regressions is the natural loga- 

 rithm of estimated survival rates, while for the 

 nonlinear regressions it is actual observed popula- 

 tion increments. 



If the model were correct one would expect that 

 statistical analyses should give: 



1) estimates of the B^ coefficient similar in 

 all populations, 



2) estimates of the B2 coefficients which are: 



a) close to in the 4.5 mm populations, 



b) some negative number in the 5.0 mm 

 populations, 



c) some negative number larger in absolute 

 value than in b) for 5.5 mm populations. 



No juvenile interactions would be expected in the 

 4.5 mm treatment group and J5 individuals 

 contributing to predation in the 5.5 mm popula- 

 tions, but not included in X2 , would be expected 

 to increase the 82 coefficient. Numbers of J4 5 

 individuals present at the beginning of intervals 

 during Phase I were estimated from total numbers 

 and weights recorded for the combined J4 cate- 



gory monitored during Phase I (see Hankin 1978b 

 for details). 



Results of multiple regression analyses of orig- 

 inal and long-term 5.0 mm populations appear in 

 Table 11 and of treated populations during Phase 

 II in Table 12. Squared multiple correlation coeffi- 

 cients (r^), when both adults and juveniles were 

 included in regressions, ranged from 0.8003 to 

 0.9272 in Phase I populations indicating that 

 about 80 to 907c of the uncorrected sums of squares 

 of the natural logarithms of estimated fry survival 

 rates could be explained by regression on adult 

 and juvenile densities. Estimates of adult preda- 

 tion coefficients were similar for all populations, 

 and estimates of juvenile predation coefficients 

 differed in the expected order among treatment 

 groups. Differences among juvenile predation co- 

 efficients were less striking than had been antici- 

 pated. Mean estimates of B2 for 4.5, 5.0, and 5.5 

 mm treatment groups were -0.0280, -0.1009, 

 and -0.1249. 



Alternative estimates of 5i and B2, obtained 

 by minimizing the squared deviations between 

 actual and predicted biweekly adjusted popula- 



Table 11. — Estimates of predation coefficients (Bj, fij' ^nd squared multiple correlation 

 coefficients (r ) for Phase I guppy populations. Based on multiple regression analysis of the 

 hypothesized model: ln[lAP/ + 1)/EB] = B^Xi + B^X^. See text for explanation of model 

 parameters. 



Table 12. — Estimates of predation coefficients (Bj, B^) and squared multiple correlation 

 coefficients (r ) for treated guppy populations during Phase II. Based on multiple regression 

 analysis of the hypothesized model: ln([AP/ -1- l]IEB) = B,Xi -t- B^X^- See text for explana- 

 tion of model parameters. 



571 



