An analysis of variance of the estimated damage was 

 used to determine significant differences among stands. 

 A balanced AN OVA (SAS 1982) was used for variables 

 blocks (replications) and stands. Stepwise multiple re- 

 gression analyses were used to relate the degree of GPM 

 damage to elevation and geographic location of the seed 

 source. Independent variables included elevation, lati- 

 tude, longitude, northwest-southeast coordinates, 

 southwest-northeast coordinates, and their squares. The 

 northwest-southeast coordinates equaled latitude x longi- 

 tude and the southwest-northeast coordinates equaled 

 (1/latitude) x longitude. The geographic variables were 

 nested within two geographic regions: (1) Idaho north of 

 the Salmon River and (2) Montana west of the Continen- 

 tal Divide. A stepwise multiple regression procedure for 

 maximizing R 2 (SAS 1982) was followed. 



Predicted percentage of GPM damage for geographic 

 area was computed using the best fit multiple regression 

 equation for a constant elevation. Contour lines 

 (isopleths) separating statistically equal levels of the 

 estimated damage were determined by using the least 

 significant difference formula (Steel and Torrey 1960) at 

 a t- value of 0.2. 



RESULTS 



The regression of total current shoots per tree (7T) for 

 the sample resulted in regression coefficients of a = -68.0, 

 and b = 22.6 shoots per foot, R 2 = 0.69. The goodness-of- 

 fit procedure yielded a chi-square of 1.38, which was 

 highly significant but probably somewhat underestimated 

 since in the sample 60 percent of the trees were not in- 

 fested with GPM. 



The average level of estimated percent damage by GPM 

 was 6 percent. Individuals varied from to 85 percent, 

 and stands varied from to 17 percent. The frequency of 

 damage classes by individuals is summarized in table 1. 

 Differences among stands were highly significant 

 (table 2). 



Regression coefficients for the stepwise multiple regres- 

 sion equation that produced the best fit resulted in an R 2 

 of 0.46, a mean square of 0.0062 with 9 degrees of free- 

 dom, and an error mean square of 0.0008 with 82 degrees 

 of freedom resulting in an F value of 7.7, significant at 1 

 percent level of significance (table 3). 



Midge damage by seed source is shown in figure 1, and 

 predicted values from the multiple regression equation 

 are shown in figure 2. The dotted line represents the 

 average predicted value, and the solid contour lines are 

 derived from +V2 lsd from the mean at the 0.2 level of 

 significance. 



2 



