A model for heterosis

--Donald S. Robertson

It has been suggested that many quantitative trait loci (QTLs) may be wild type alleles of loci for which qualitative mutants involving quantitative traits have been found--e.g., dwarfs (plant height), defective kernels (seed size), etc. (MNL 58:10, 1984; J. Theor. Biol. 117:1, 1985). This hypothesis suggested that quantitative patterns of inheritance occurred because there were slight differences in the efficiency of gene products as a result of the molecular polymorphism found in wild type alleles. Such slightly different alleles, all of which produce basically the same, but nonetheless slightly different phenotypes, are called isoalleles. The effect of such isoalleles has been shown by Hageman et al. (Adv. Agron. 19:45, 1967) to be primarily additive. An additive model will explain the classical quantitative inheritance pattern (see Figure 1). Such a simple model, however, does not explain heterosis.

Figure 1. The classical model for the inheritance of quantitative traits assuming additivity.
Assumptions:
1. All quantitative genes for a trait are completely additive.
2. 10 loci
3. Two lines are crossed a. Line X - each allele contributes 10 quantitative units above the basic wild type of 1000. Line X would equal 1200 units.
b. Line Y - each allele contributes 5 quantitative units above the basic wild type of 1000. Line Y would equal 1100 units.


Results expected in the F1 and F2 populations:
1. The F1 population would show very narrow variation around a value of 1150.
2. The F2 population would show the typical bell-shaped curve for the distribution of phenotypes in the F2 populations. The extreme values of this curve would approach those of the parents.

 Figure 2 presents the basic assumptions for a proposed model (the Biochemical Pathway Model) to explain how wild type isoalleles might explain both the classical model of quantitative inheritance and heterosis. Figure 3 is a schematic presentation of the model. The biochemical pathways involved in the expression of any quantitative trait are probably much more complicated than this illustration. It is known that there are other mechanisms regulating biochemical pathways besides the efficiency of the gene products of the individual genes in the pathway (e.g., feedback inhibition, end product inhibition, suppressors, inducers, etc.). As implied above, for most quantitative traits there may be more than one pathway involved in the expression of a trait. For example, it is known that the gibberellin biosynthetic pathway is involved in the expression of plant height. Yet not all plant height qualitative mutants (e.g., dwarfs, brachytic, etc) are gibberellin responsive. Figure 2. The biochemical pathway model of quantitative inheritance and heterosis.
Assumptions:
1. A given quantitative trait is the end result of a product or products produced by one or more biochemical pathways.
2. Each step in these pathways is under the control of unlinked genes and the products they produce (enzymes).
3. The gene products for each step can vary in efficiency depending upon variation in the wild type isoalleles.
4. All variant gene products function above the minimum level necessary for the expression of wild type.
5. For a given step, some wild type isoalleles produce products that function at higher levels above the minimum wild type level than others.
6. The final amount of the end product for any pathway is determined by the most inefficient reaction in the pathway.
7. The effect of gene products from isoalleles is additive but the total effect of the products from two isoalleles can not exceed 100% of the potential wild type phenotype. If this model is correct, inbreds most likely have many biochemical steps controlled by low efficiency gene products. Two inbreds that show good combining ability as hybrids have in toto all steps functioning at a higher level than either inbred considered alone. This would mean that for each low efficiency gene product functioning for one step in inbred X, the other inbred, Y, will have a high efficiency product functioning for the same step. For those inbreds that do not have good combining ability, they both probably have relatively low efficiency gene products functioning for one or more of the same steps.

Figure 3. The biochemical pathway model of quantitative inheritance and heterosis: an example.

The effect of gene products from isoalleles does not have to be completely additive. The model will still work even if dominance is found for some loci.

Recent results reported in Science (Stewart et al., Science 241:1216, 1988) support The Biochemical Pathway Model. These workers demonstrated that the level of gibberellin production was low in the four inbreds tested and, as expected, the inbreds were shorter than hybrids. In addition, the inbreds showed significant growth response to exogenously applied gibberellin. Most of the hybrids between these inbreds, on the other hand, were taller than either parent (heterosis) and showed very little if any response to exogenously applied gibberellin. B. O. Phinney has shown that some dwarf mutants block steps in the gibberellin biosynthetic pathway (Plant Growth Substances, Springer-Verlag, p. 55, 1985). Thus the wild type alleles at these dwarf loci produce enzymes regulating steps in this pathway. It is obvious that in the inbreds studied by Stewart et al., the gibberellin pathway was not functioning to its full potential. Otherwise, the inbreds would not respond to exogenously applied gibberellin. This low gibberellin production could be the result of wild type isoalleles in the inbreds at one or more steps that produce low efficiency gene products that limit the total amount of gibberellin produced. Most hybrids had complementing isoalleles that would allow full or near full production of gibberellin (as suggested by the model). In such a situation, exogenously applied gibberellin has little effect. One hybrid did not show a heterotic response as measured by gibberellin production in seedlings. This hybrid had a correspondingly greater response to exogenously applied gibberellin than the other hybrids tested. Again, this is a result predicted by the model for inbreds with poor combining ability for plant height. Such inbreds have isoalleles responsible for enzymes with low efficiencies for the same step(s) in the gibberellin biosynthetic pathway.

This model is not proposed as the sole explanation for heterosis. There is undoubtedly more than one mechanism responsible for this complex phenomenon. Enhanced biosynthesis due to enzymatic polymorphism, as proposed by Schwartz and Laughner (Science 166:626, 1969), also could be responsible for a portion of the heterotic response, along with other, as yet, undiscovered mechanisms.

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