HYBRIDIZATION IN THE EVOLUTION OF MAIZE 181 



the proportion of outcrossing. The formula is based upon the assumption that 

 gene action is, on the average, additive. 



It is obvious (according to this formula) that the percentage of hybrid 

 vigor retained in later generations of a cross will approach but never fall be- 

 low kjl. Since the value of k in the case of maize lies usually between .9 and 

 1.0, it is apparent that the amount of hybrid vigor retained in later genera- 

 tions of maize crosses will (with random mating) seldom fall below the 

 one-half, which is characteristic of the Fs- 



There are experimental data which tend to show that advanced genera- 

 tions of maize crosses behave approximately as would be expected from the 

 formulae of Wright and Stephens. 



Kiesselbach (1930) compared the Fi,F2,andF3of 21 single crosses with the 

 parental inbred lines. The average yield of the inbreds was 24.0 bushels. The 

 average yield of the Fi was 57.0 bushels. The theoretical yield of the Fo is 

 40.5 bushels. The actual yield was 38.4 bushels which does not differ signifi- 

 cantly from the theoretical. The yield of the F3 was 37.8 bushels which is 

 almost identical to the F2 yield. 



Neal (1935) compared the yield in Fi and F2 of 10 single crosses, 4 three- 

 way crosses, and 2 double crosses. The theoretical reduction in yield be- 

 tween the Fi and F2 in these three groups (based upon Wright's formula) 

 should have been 31.1 per cent, 21.0 per cent, and 15.2 per cent respectively. 

 The actual reduction was 29.5 per cent, 23.4 per cent, and 15.8 per cent. The 

 agreement could scarcely have been closer. 



There is abundant evidence from maize crosses to show that equilibrium 

 is reached in F2, and that in the absence of selection there is no further reduc- 

 tion in yield in the F3. Data from the experiments of Kiesselbach (1930), 

 Neal (1935), and Sprague and Jenkins (1943) are summarized in Table 11.2. 



The data so far presented are concerned with crosses of inbred strains. Do 

 hybrids of open-pollinated varieties behave in the same w^ay? Since open- 

 pollinated varieties, although not homogeneous, are stable in productiveness 

 they should behave in crosses in the same way as inbred strains. Data from 

 advanced generations of topcrosses presented by Wellhausen and Roberts 

 (1949) indicate that they do. The theoretical yields of the F2 of a topcross 

 can be computed from a formula suggested by Mangelsdorf (1939). 



W'ellhausen and Roberts compared the Fi and F2 generations of 31 dif- 

 ferent topcrosses each including the open-pollinated variety Urquiza and 

 two inbred lines of unrelated varieties. The latter were in all cases first-gener- 

 ation selfs. The mean yield of the 31 Fi hybrids (in terms of percentage of 

 Urquiza) was 132 per cent. The mean yield of the corresponding 31 F2 hy- 

 brids was 126 per cent. Since the yields of the first-generation selfed lines 

 entering into the cross is not known, it is impossible to calculate with pre- 

 cision the theoretical yield of the F2. However, it is known that good homozy- 

 gous inbreds yield approximately half as much as open-pollinated varieties 



