Heterosis pp. 180-183 (1952)
Hybrid Vigor in Advanced Generations
Paul Mangelsdorf

The rate at which hybrid vigor diminishes in a population after the F2 generation is related to the proportion of outcrossing. This is true whether hybrid vigor depends upon heterozygosity or upon the cumulative action of dominant genes, and irrespective of the number of genes involved and the degree of linkage. With complete selfing the amount of hybrid vigor retained is halved in each succeeding generation. With complete outcrossing the amount of hybrid vigor falls to one-half in the F2 and thereafter remains constant. With a mixture of selfing and outcrossing an intermediate result is to be expected. This can be calculated from the following formula presented by Stephens (1950):

h = 1/2 [ (1 - k) h' + k].

In this formula h is the proportion of F1 vigor retained in the current generation, h' is the proportion retained in the preceding generation, and k is 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 below k/2. 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 generations of maize crosses will (with random mating) seldom fall below the one-half, which is characteristic of the F2.

There are experimental data which tend to show that advanced generations of maize crosses behave approximately as would be expected from the formulae of Wright and Stephens.

Kiesselbach (1930) compared the F1 ,F2, and F3 of 21 single crosses with the parental inbred lines. The average yield of the inbreds was 24.0 bushels. The average yield of the F1 was 57.0 bushels. The theoretical yield of the F2 is 40.5 bushels. The actual yield was 38.4 bushels which does not differ significantly 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 F1 and F2 of 10 single crosses, 4 three-way crosses, and 2 double crosses. The theoretical reduction in yield between the F1 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 reduction 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 different topcrosses each including the open-pollinated variety Urquiza and two inbred lines of unrelated varieties. The latter were in all cases first-generation 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 hybrids 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 precision the theoretical yield of the F2. However, it is known that good homozygous inbreds yield approximately half as much as open-pollinated varieties (Jones and Mangelsdorf, 1925; Neal, 1935) which means that inbreds, selfed once and having lost half of their heterozygosity, should yield 75 per cent as much as the open-pollinated varieties from which they were derived. Assuming that the single-cross combinations involved are at least equal to the topcross combinations — 132 per cent — we compute the theoretical F2 yield of the topcrosses at 117 per cent, which is considerably less than the 126 per cent actually obtained in the experiments. From the results it can be concluded that hybrid combinations including open-pollinated varieties of maize retain a considerable proportion of their vigor in advanced generations.

TABLE 11.2
SUMMARY OF EXPERIMENTS DEMONSTRATING EQUILIBRIUM REACHED IN F2 AND
NO ADDITIONAL YIELD REDUCTION IN F3 OF MAIZE CROSSES

Investigators Class of Hybrids No. Hybrids Tested Yield in Per Cent of F1
      F1 F2 F3
Kiesselbach, 1930 Single crosses 21 100 68.0 66.0
Neal, 1935 Single crosses 10 100 70.5 75.7
Neal, 1935 3-way crosses 4 100 76.6 75.8
Sprague and Jenkins, 1943 Synthetics 5 100 94.3 95.4
Total and averates   40 100 76.9 78.2

There is also some evidence to indicate that the amount of heterosis which occurs when open-pollinated varieties are used in hybrid combinations may be considerably higher with Latin-American varieties than with varieties commonly grown in the United States. Wellhausen and Roberts report single topcrosses yielding up to 173 per cent of the open-pollinated variety and double topcrosses up to 150 per cent. A recent report from the Ministry of Agriculture of El Salvador (1949) shows four different hybrids between open-pollinated varieties yielding about 50 per cent more than the average of the parents. Such increases are not surprising, since the varieties used in the experiments are quite diverse, much more so than Corn Belt varieties.

All of the data which are available on the yields of advanced generations of maize crosses, whether the parents be inbred strains or open-pollinated varieties, tend to show that a substantial part of the hybrid vigor characteristic of the F1 is retained in subsequent generations. Thus maize under domestication is potentially and no doubt actually a self-improving plant. Distinct more-or-less stable varieties or races evolve in the isolation of separated regions. Man brings these varieties or races together under conditions where cross-fertilization is inevitable, and a new hybrid race is born. Repeated cycles of this series of events inevitably lead to the development, without any direct intervention of man, of more productive races. If, in addition, natural selection favors the heterozygous combinations as it does in Drosophila (Dobzhansky, 1949), then the retention of hybrid vigor in advanced generations of maize crosses will be even greater than that indicated by the experimental results.