FIXING TRANSGRESSIVE VIGOR IN NICOTIANA RUSTICA 169 



between the environmental variances of the Pi, P2, and Fi is assumed, so 

 that a% of the Fi = 1/2((t% of Pi + al of P2), then a% of the Fi = 6.78. 

 The environmental variance of Bi may then be equated to 1/2 (variance of 

 Pi+ variance of Fi), which is 5.12. By a similar relation, the environmental 

 variance of B2 is equal to 8.44. The pooled heritable variance of Bi + B2, i.e., 

 l/2ah + 1/2(7?,, may be equated to: (W.49 - 5.12) + (9.45 - 8.44). This 

 gave 6.38. The heritable variance of the F2, i.e., l/2ao + l/4o-i), may be 

 equated to (10.52 — 6.78). This gave 3.74. Solving: <t% = 10.56 and <to = 

 2.20. The former, (xjj, has a somewhat larger value than that obtained by 

 the original analysis (8.16, Table 10. 6j; the latter, cc, is the same. 



Heritability of a character was estimated as the ratio, expressed in per 

 cent, of the variance component due to additive, fixable gene effects (aa) to 

 the sum, <r% -\- a]) -\- a%. Heritability of plant height was calculated to 

 be 54.9 per cent, of leaf length 11.5 per cent, and of node number 12.4 per 

 cent. 



Estimates of the number of effective factors (Ki) were made on the as- 

 sumptions inherent in the equation A'l = (Pi — P^^l^a'a. The values ob- 

 tained (Table 10. 6 j were 0.81 for plant height, 1.38 for leaf length, and 0.83 

 for number of nodes. These estimates were undoubtedly too low, due in part 

 to non-isodirectional distributions of + and — genes in the parents. Ex- 

 perimental evidence of non-isodirectional distribution was afforded by the 

 fixing of transgressive characteristics in inbred selections following hybridiza- 

 tion between varieties. Some -\- genes were contributed by each parent, and 

 consequently could not have been concentrated in one. Linkage in coupling 

 phase and/or differences in magnitude of effect of the individual genes or 

 gene blocks might also have contributed to the low estimates of the number 

 of effective factors. 



In the absence of data on Fa's, biparental progenies, and double back- 

 crosses (Mather, 1949), the errors of the estimates of 0%, a\,, and 0% for each 

 character were computed as follows. From the eight replications, four means 

 were calculated by grouping replications 1 and 2, 3 and 4, 5 and 6, and 7 

 and 8. The standard error of the four independent means was then obtained 

 (Table 10.6). These errors are maximum estimates since there was a pro- 

 nounced gradient of environmental effects from replication 1 to replication 8. 



Mather (1949) is in the process of making an extensive biometrical genetic 

 analysis of plant height in a Xicotiana rustica cross, and it was of interest to 

 compare his published results with corresponding statistics presented in this 

 study. From his data so far reported, the average values (mean of 1946 and 

 1947) for components of variance for plant height are: 9.30 for 0%, 9.25 for 

 (To, and 18.05 for (7%. The heritability calculated from these estimates is 44.1 

 per cent. The results reported in this discussion are similar in that heritabil- 

 ity is high and <!% has about twice the value of a]}. 



