HERITABILITY AND RUST RESISTANCE IN WHITE FIVE 399 



The models from which estimates of genetic parameters were obtained 

 to predict selection gains in stages B and C follow. 



>DDELS 



STATISTICAL 



Each elevation was analyzed separately and the general formula for 

 the statistical model was : 



x ijk = » + T i * */ + ^ho * r k + b m + e m * d ijk 



%-ijk = adjusted and transformed proportion of healthy seedlings, from the 

 cross of the ith tester and the jth candidate, in the feth replication; 

 \t = general mean; x-: = effect of ^th tester; x^ - = effect of j'th candidate 

 (ix)ij = effect of interaction of the ith tester and the jth candidate; 

 Rfc = effect of the feth replication; &£jfc = binomial sampling effect; 

 e ijk = effect of plot; fZ£jfc = individual effects within a plot. 



The candidates and testers were considered to be random with the 

 replications fixed. 



The basic data of the experiments consisted of the proportions, 

 number healthy seedlings fa^ffe) divided by the total number (w^^) per 

 plot . 



p. 



K w< 



ijk m . .- 



d 13k 



An adjustment was made to the proportion (Bartlett, 1947) to minimize 

 fluctuations, due to small sample sizes, as follows. 



When r.- k = mtjk 



and when r_-,-> = 



?.., - 1 - 



ijk 4 m m 



ijk 4 w 4 .„ 



The adjusted proportions were transformed to arc sin of square root of 

 the proportion (Bartlett, 1936) to stabilize the variance. The variance 

 of the proportions was 



a 2 ^ = i P(l-P) - ia 2 



where P(l-P) = a 2 £, and is the binomial sampling variance, o 2 ^ is the 

 variance of the inequality of the probabilities of each seedling being 

 healthy (see Kendall and Stuart, 1963, p. 127 and Appendix to this paper) 

 and m is the harmonic mean of the number of seedlings per plot. With the 

 adjusted proportions transformed to arc sin the binomial sampling variance 

 is constant (Scheffe*, H. , 1959) and equal to 821 (Fisher and Yates, 1948, 

 and see Appendix for explanation) and therefore 



