FIXING TRANSGRESSIVE VIGOR IN NICOTIANA RUSTICA 165 



plant height and leaf length, the data, as taken, could be used without 

 serious error in partitioning the variance of segregating generations. For 

 node number it was indicated that some correction should be made with 

 the data before further biometrical analysis was undertaken. 



Mather suggested that difficulties of the sort encountered in these data 

 with node number may be overcome by finding a transformation of scale on 

 which they would be minimized. The transformations \/X, X'^, X^, and 

 \/a -\- bx on the individual measurements were made. In the latter transfor- 

 mation b is the linear regression coefficient and a the intercept. Also, for 

 ^ya + bx — K, \/—K was taken as —\/K. In some cases the transforma- 

 tions reduced the departure from the preferred relationship in one test, only 

 to make the transformed data less preferable by another test. No transforma- 

 tion tried resulted in a consistent improvement over the original scale, and 

 consequently none was used. 



It is evident that the significantly different variances in node number of 

 the two parental types were due mainly to different interactions between 

 genotype and environment. From previous experience we know that under 

 ideal conditions of growth, Olson 68 and strain 34753 show approximately the 

 same variability. The adverse weather conditions of the 1949 season were ob- 

 served to have a more deleterious effect on leaf number in strain 34753. Con- 

 sequently it was considered that the greater variability of this variety, com- 

 pared to Olson 68, could be attributed to a greater phenotypic interaction 

 between genotype and environment. In view of these relationships, the 

 analysis of the data on node number was approached in another way, as 

 mentioned below under "Partitioning Phenotypic Variance." 



First Generation Hybrids 



Deviations of the Fi means from mid-parent values (arithmetical average 

 between parental means) can be used to estimate the preponderance of 

 dominant gene effects, acting in one direction, at loci by which the parental 

 complements differ. Mid-parent values were calculated from the 1947 da- 

 ta on the four original varieties. The results for each line are summarized in 

 Table 10.4. The data shown were obtained by first calculating the difference 

 between the Fi mean and the mid-parent (Fi — MP) for each cross, then tak- 

 ing the average of the differences for each group of three F/s involving the 

 parent variety under consideration. The ratio of the deviation of the Fi from 

 the mid-parent to half the parental difference, Fi — MP/\{P2 — Pi) , is a meas- 

 ure of the relative potence (Mather, 1949; Wigan, 1944) of the gene sets. Po- 

 tence ratios, calculated from averages, are shown in Table 10.4. For plant 

 height and leaf length the Fi means fall, on an average, about .6 of the dis- 

 tance from the mid-parent toward the larger parent. For leaf number the Fi 

 means fall, on an average, about .7 of the distance from the mid-parent 

 toward the smaller parent. 



