Table l.--Form and results of analysis of variance of population performance for height at age 16 



Source of variance Degrees of freedom Components expected in each mean square Mean square F 



Sites 3 a| + 203.43a2^g + 1503. 95o2 



489,559 



3.38** 



Blocks in sites 30 a| + 203.43o2^g 



144,829 



18.21** 



Populations 35 + 43.74o2g + 174. 210^ 



27,335 



3.44** 



Populations x sites 105 a| + 43.74a^g 



7,952 



1.55** 



Kesiauai dizd oJ; 



E 



5,124 





**Statistical significance at the 1 percent level of probability. 







Patterns of population differentiation were related to physiognomic 



criteria of 



the seed 



source by multiple regression: 







= bQ + biXi + i>2^2 + i^3^3 







where 







y^ - least squares mean for population i on all sites as calculated 



in preceding 



I analysis. 



bQ = intercept, 



bi to 253 = regression coefficients, 



Xi to X3 = independent variables of elevation (meters) , latitude (degrees -40) and 

 longitude (degrees -100) , respectively. 



Effects of habitat types (recurring plant communities of potential climax) on population 

 differentiation were also tested in multiple regression analyses. For these tests, the previous 

 model was adjusted by including constant terms for each habitat type represented by the 36 popula- 

 tions. But, as shown previously (Rehfeldt 1980), inclusion of the effects of habitat types did 

 not improve the fit of the data to the model. Habitat types apparently have little effect on 

 differentiation and are subsequently ignored. 



The regression model presented above was also used on least squares mean height of popula- 

 tions from each of the four sites. As detailed later, however, the mean height of populations 

 between ages 11 and 16 was so strongly correlated among sites that the results of the separate 

 regression analyses essentially duplicated those presented previously (Rehfeldt 1980). Conse- 

 quently, results of separate analyses for each site are not presented. 



Guidelines for seed transfer were developed from patterns of population differentiation. 

 According to techniques used previously (Rehfeldt 1979), the analysis of variance allows 

 calculation of the least significant difference (isd) among population means that provide for 

 statistical detection of mean differences at given levels of probability (Steele and Torrie 

 1960). A value of Isd was calculated at the relatively low level of probability of 0.2 in 

 order to guard against making the error of accepting no differences among populations when 

 differences actually exist. Then, the expression Isd^Q . 2) /i> , where b is the regression 

 coefficient, provides the distance in elevation, latitude, and longitude associated with mean 

 differences at the 80 percent level of probability. These distances are proposed as guidelines 

 for limiting seed transfer. 



Possible genetic gains within seed zones were estimated from quantitative genetic analyses 

 made for each site according to a model of random effects (table 2) . These analyses allowed 

 estimates of family heritabil ities , individual heritabilities , and genetic gains expected 

 after alternative plans of seed orchard development. Estimates of genetic gains from family 

 selection and individual selection within families followed Namkoong (1979). 



2 



