Idaho (Wright and others 1977), the four populations of greatest longitude (fig. 1) 

 were excluded from the following analyses. 



The hardiness of 47 populations for each phase of cold acclimation was used as 

 a dependent variable in the following model: 



where: 



= predicted injury for population 



X^l = degrees latitude at the origin of population ij 



X^2 - degrees longitude at the origin of population 

 -2 



= meters (1x10 ) elevation at the origin of population ^J 



X .1^ to X .J - constant terms (values of zero or one) that respectively code 

 the Pseudotsuga menziesi-ij Abies grandis^ Thuja oacidentalis , and Tsuga heterophylla 

 series of habitat types. 



Under this model, effects of the Abies lasioaarpa series of habitat types are 

 contained within the intercept (Zpq) . Consequently, values of regression coefficients 

 for constant terms {bif. to by) are deviations from the mean value for seedlings from 

 Abies lasioaarpa habitat types. 



Because multiple regression models are partially interpretable from inter- 

 correlations among independent variables, it is instructive to note that significant 

 associations were apparent between latitude and longitude (r = 0.56) and between longi- 

 tude and elevation (r - -0.32). For the populations represented, habitat types accounted 

 for significant proportions of variance in none of the other independent variables. 



In accordance with the techniques of Morgenstern and Roche (1969), concepts of 

 selection were used to estimate population change associated with the geographic and 

 ecologic variables. This technique uses the expression for genetic gain: 



R - ihOj^ 



where: 



R = selection response, 



h?- - heritability, 



a^. = additive genetic variance, 



i = selection intensity. 



The selection intensity is estimated by assuming that = 1 , is estimated by 



the standard error of regression (s ^ ) , and R is estimated by the regression coefficient 



(fc) . Because the intensity of selection depends only on the proportion of the 

 population in the selected group, the proportion of a population that is similar to a 

 neighboring population one geographic unit distant is estimated directly from the 

 selection intensity (fig. 11.3, Falconer 1960). 



4 



