Table 1— Model for analysis of variance and expected mean squares 



Source of 



variation df 1 Expected mean squares 



Block 4 o 2 w + pa 2 £ +pfo 2 B 



Stand 47 o 2 w + po 2 E + pbo 2 F/s + pf*bo 2 s 



Family in stand 188 o 2 w + pa 2 E + po 2 F/s 



Experimental error 892 o 2 w + pa 2 E 



Within plot 2,644 a 2 w 



Where: b = 5, S = 48, f = 234, f =4.8 harmonic mean of families in 

 stands; p = 3.01 harmonic mean of individuals within plots. 



1 Degrees of freedom were reduced by 44 for missing plots. 



Data were taken as described for the provenance test. 

 Table 1 shows the analysis of variance and expected mean 

 squares. Heritability was calculated using the following 

 formula: 



For individual 



4o 2 f/s 



h 2 j = 



F/S 



For family 



hK = - 



° 2 w 



F/S 



r. 2 



F/S 



+ 



o 2 w 

 pb 



+ 



° 2 E 



where h 2 j = heritability based on individuals, h 2 F = 

 heritability based on families, 4o 2 F/s is the estimated addi- 

 tive variance for individuals, o 2 FIS for families, and o 2 w , 

 o 2 E , pb, and 6 are defined in table 1. 



Relationship of infection and the 1985 height was deter- 

 mined by regression analysis using the GLM procedure 

 (SAS 1982). 



RESULTS 

 Provenance Test 



The level of infection by L. baculiferum varied from 

 none (1 percent of the trees) to almost complete defoliation 

 of 1983 needles (22.1 percent of the trees). Table 2 sum- 

 marizes the amount of infection for both tests. Figure 1 

 shows the actual percentage of damage for each stand. 



Analysis of variance of the levels of infection demon- 

 strated that differentiation among stands for infection was 

 highly significant (table 3). 



Regression coefficients for the multiple regression equa- 

 tion that produced the best fit are listed in table 4. These 

 resulted in an R 2 of 0.37, a mean square of 0.0386 with 9 

 degrees of freedom, and an error mean square of 0.0072 

 with 82 degrees of freedom, resulting in an F value of 5.4, 

 significant at 1 percent level of significance. 



Predicted values from the multiple regression equation 

 at the mean elevation of all stands— 3,282 ft (1,000 m)— 

 are shown in figure 2. The center line represents the 

 average predicted value, and lines depicting + 1/2LSD 

 from this mean at the 0.2 level of significance were drawn 

 north and south from this line. 



Table 2— Level of infection (percent) by Lophodermium 



baculiferum on 2-year-old foliage of ponderosa pine by 

 category 



Amount of 

 foliage damaged 



Test trees 



Category 



Meat 



Range 



Provenance 



Progeny 







<1 



<1 



1 



2.5 <5 7.4 



4.8 



2 



21.0 6-36 36.3 



34.2 



3 



53.0 37-69 34.2 



32.8 



4 



85.0 >70 22.1 



28.1 



Table 3- 



-Analysis of variance of infection by Lophodermium 





baculiferum on ponderosa pine 





Source of Mean 





variance df 1 square 



F 



Block 



9 0.136 





Stand 



81 .103** 



3.32 



Block x 



stand 783 .031 





1 Degrees of freedom were reduced by 36 for missing plots. 





"Significant at the 1 percent level of probability. 





Table 4- 



-Intercept and regression coefficients 







from the best fit multiple regression 







equation for infection of ponderosa 





pine by Lophodermium baculiferum 



Factor 



b value 



Intercept 



-247.86612619 



Elevation 



- .00008780 



Elevation 2 



.00000001 



Northwest 



.01251327 



Southwest zone 1 



.00678625 



Latitude 



- 1 .44985788 



Longitude 



4.99039460 



Longitude zone 1 



.49234995 



Longitude 2 



- .02442355 



(Southwest zone 1) 2 



3.30576505 



3 



