where Yi is the performance of population i ; Ei is the 

 elevation of population i ; Xiji^ is geographic variable k for 

 population i in geographic region j; and Pq, pi, P2, Yjk' 

 6ji^ are regression coefficients, j = 1 . . A, k = 1 . . A. 



Adequacy of a model was judged according to the 

 goodness of fit {R^), residual variance (s^.J, and patterns 

 displayed by residuals (Draper and Smith 1981). 



RESULTS 



Environmentally diverse planting sites strongly influ- 

 enced growth and development of seedlings (table 1). 

 While the average tree at PREF 640 was 106 cm tall, that 

 at PREF 1,500 and Lost Valley was only 76 cm and 

 62 cm, respectively. Values for adjusted height imply that, 

 even if all trees had been the same height at age 5, by 

 age 7 those at PREF 640 would still have been about 

 10 cm taller than trees on the other sites. Main effects of 

 test environments are also expressed by the occurrence of 

 snow damage only at Wgh elevations and by the relatively 

 high incidence of needle cast, shoot borers, and frost in- 

 juries at low elevation. Environmental effects on late 

 growth also were pronounced; similar stages of shoot 

 elongation occurred about 1 month later at PREF 1,500 

 than at PREF 640. 



In these heterogeneous planting environments, mean dif- 

 ferences between populations were statistically significant 

 for all traits except adjusted height (table 1). Pronounced 

 effects of populations were associated w\th mean differ- 

 ences as large as 55 cm in 7-year height, 5 cm in late 

 growth, 78 percent in leaves infected with needle cast, and 

 65 percent in number of trees exhibiting snow damage. 

 Weak effects of populations were evident for mites, spring 

 frost damage, and shoot borers largely because of low in- 

 cidence for each variable. Thus, mites occurred on only 

 10 percent of the trees, but as many as 33 percent of the 

 trees from one population were infested. The proportion of 

 trees damaged from a spring frost was only 2 percent, but 

 mean values for populations ranged up to 11 percent. And 

 the incidence of shoot borers for most populations was in- 

 cidental <5 percent), but 19 percent of the trees were in- 

 jured in one of the British Columbia populations. 



Interactions of provenances and test environments were 

 also significant for all variables measured on more than 

 one site (table 1). Interactions for late growth and 7-year 

 height obviously represented a scale effect because simple 

 correlations of population means for the same variable at 

 different sites ranged from 0.80 to 0.92. The interaction 

 for adjusted height most likely resulted from various 

 maladaptations that have accumulated between ages 5 and 

 7 and have differentially affected the height of populations 

 at each planting site. This interaction is clarified by subse- 

 quent analyses that consider adjusted height at each test 

 site as separate traits. 



Simple correlations (table 2) describe a relationship 

 between the height of populations at ages 8 and 7 that is 

 nearly perfect (r = 0.94). Other extremely strong correla- 

 tions (table 2) show that the tallest populations at ages 3 

 and 7 also (1) produced the most 7-year elongation after 

 midsummer (late growth) regardless of test site, (2) grew 

 the most from a common height at age 5 when planted at 

 low elevation, (3) suffered little needle cast and few in- 

 juries from spring frost when planted at low elevation, but 

 (4) were the most susceptible to snow damage at high 

 elevations. Populations that were short also had little late 

 growth, suffered the least snow damage, but were most 

 susceptible to needle cast at low elevations. Table 3 illus- 

 trates that the tallest populations suffered the most injury 

 from autumn freezing tests (Rehfeldt 1980) and displayed 

 the greatest growth and longest duration of elongation in 

 studies of the periodicity of shoot elongation involving 

 2-year-old trees (Rehfeldt and Wykoff 1981). 



Regression models for relating variation among popula- 

 tions to the elevation and geographic location of the seed 

 source were not only statistically significant for all vari- 

 ables but also accounted for over 80 percent of the genetic 

 variance in five variables (table 4). These models, however, 

 included between 10 and 20 independent variables and 

 were therefore subject to overfitting, the fitting of vari- 

 ables to individual samples rather than to the group 

 (Draper and Smith 1981). Consequently, biological signifi- 

 cance of the results is judged with respect to the least 

 significant difference (Steel and Torrie 1960) at the 

 95 percent level of probability, Isd (.05), calculated from 

 analyses of variance and presented in figure 3. 



Table 1-— Results of analyses of variance expressed as intraclass correlations. o|, 

 Op, Op^, Oo,p,, and are variance components associated with the ef- 

 fects of environments and populations, interaction, plots in populations, 

 and error variance within plots, of is the sum of all components 



Variable 







If/of 







7-year height 



0.39** 



0.16** 



0.03** 



0.12** 



0.30 



Adjusted height 



.72** 



-.00 



.12** 



.05** 



.11 



Late growth 



.05** 



.29** 



.20** 



.05** 



.41 



Needle cast 





.52** 





.07** 



.41 



Mites 





.05** 





.95 





Shoot borer 





.05** 





.95 





Spring frost injury 





.09** 





.91- 





Snow damage 





.40** 





.60 





•'Statistical significance of F-value at the 1 percent level of probability. 



4 



