FISHERY BULLETIN: VOL. 78, NO. 3 



tion increments, were strikingly different among 

 treatment groups. Mean estimates of B2 in 4.5 

 mm and 5.0 mm treatment groups were -0.0024 

 and - 0.0857. Estimates for the three 5.5 mm pop- 

 ulations were -0.0494, -0.1523, and "- . Large" 

 (fails to converge to finite negative number), 

 again indicating strong interaction by juveniles 

 (Table 13). However, alternative fits of actual 

 population increases against adult and juvenile 

 densities could account for an average of only 59% 

 of the variation in the uncorrected sums of squares 

 of the adjusted population increment variable. 

 Still, given initial population states at the begin- 

 ning of intervals, the patterns of predicted incre- 

 ments exhibited pronounced pulses and generally 

 behaved well relative to actual population his- 

 tories (Figure 13). 



Table 13. — Estimates of predation coefficients (Bj and fij' 

 and squared multiple correlation coefficients (r ) for all treated 

 guppy populations for specified intervals. Based on iterative 

 Taylor Series approximation analysis of the hypothesized model; 

 API = EB X exp(B,X, + B2X2). Estimates which fail to 

 converge ( — .Large) are not included in means. 



DISCUSSION 



In no earlier population experiments with 

 guppies have detailed analyses of numerical pop- 

 ulation growth been attempted. Analyses em- 

 ployed in this study were designed with two 

 purposes in mind. Comparisons of numerical 

 dynamics measures, while perhaps unsatisfying 

 to those demanding rigorous statistical tests or 

 parameter estimates, allowed qualitative distinc- 

 tions to be drawn among treatment groups and 



S 

 U 



M 



O 160 



F 



P 

 

 P 



u 



L 



A 



T 



I 



O 



N 



I 



N 

 C 



R 



E 

 M 

 E 

 N 

 T 

 S 



120 



80 



40 



6 12 18 24 30 36 



WEEKS 



Figure 13. — Sum of observed (solid line) and predicted (dots) 

 population increments for guppy population 4 during Phase I. 



showed clear differences in the patterns and 

 variability of numerical population growth. Least- 

 squares regression techniques, while shedding no 

 light on the qualitative features of numerical 

 increase, allowed evaluation of the fit of the 

 hypothesized numerical dynamics model to col- 

 lected experimental data and also allowed esti- 

 mation of adult and juvenile stock predation 

 coefficients. That multiple regression analysis 

 failed to indicate as striking differences in ju- 

 venile predation coefficients among treatment 

 groups as did nonlinear least-squares regression 

 illustrates a strong relation between analysis 

 technique and analysis result. Clearly, parameter 

 estimates based on linear fits of a survival equa- 

 tion are not comparable with those obtained by 

 minimizing squared deviations between observed 

 and predicted population increments, although 

 the underlying numerical dynamics model and 

 experimental data used are identical for both 

 analyses. In the absence of detailed data specify- 

 ing the true error component of the underlying 

 model it is unclear which regression technique is 

 appropriate. Regardless of such technical issues, 

 all analyses support the hypothesis that altera- 

 tion of refuge habitat quality may significantly 

 change biological interactions among components 

 of a population. This finding is compatible with 

 earlier studies and also unifies the "conflicting" 

 results of previous studies with and without ref- 

 uge areas. 



572 



