The heritability theory of heterosis and its meaning for global agriculture

This paper begins with the overthrow of the concept of combining ability in crossbreeding by the concept of heritability. The reason is that general combining ability changes with the number and kind of pure strains in the foundation stock and hence special combining ability changes also, so that work with different kinds of pure strains in the foundation stock cannot be compared. Hence combining ability is useless as a parameter to predict the amount of heterosis expected in the next generation. On the other hand, since each cross has a separate heritability, it can be applied to a cross population just as successfully as in purebreeding. Since the same concept holds in both cases, resort to any other concept would be superfluous. That's why combining ability must be rejected. Another reason (not given in the full text) is, an infinite number of pure strains would be required in the foundation stock for its results to be comparable with those of the heritability theory, which disposes of its utility altogether. The main content of the thesis is then the centennial enigma of heterosis can be resolved by Descarte's theoretic method of deduction. Accordingly we start from the definition of heterosis. [formula: see text] where H is heterosis, F1 is the first generation offspring, MP is the mean of the parents or midparent, and from the use of a binomial random variable and its extension to the multinomial case derive the basic relations of heterosis with its components. Starting with second degree statistics, we obtain [formula: see text] where V and cov stand for variance and covariance. The equations of heterosis are [formula: see text] where N is number of genes controlling a trait, a = (Pi - Pj)/2, d is deviation from midparent, while the variance components are all indicated by their names under the respective terms. It turns out that all these can be easily computed from the data so that the problem becomes a simple one which any college student may solve. In other words, the right answers are found when the right questions are asked. Who had ever shown that the heritability principle is inapplicable in crossbreeding, e.g., in a crossing of two pure strains? From this cue arose the realization that the F1 of a cross of two pure strains must also be a Mendelian population, with p and q both equal to 1/2 which simplifies the algebra outright. This Heritability Theory of Heterosis, or HTH in capital letters, rests on 2 initial arguments: 1) Since 0.5 + 0.5 = 1, crossing two pure strains gives a population which is only a special case of pure-breeding, therefore a heritability coefficient must exist for the F1; 2) Our problem reduces to that of finding that coefficient; the answer is given by the additive component divided by VF1, i.e., (1/2) Na2/VF1. which is readily found from the solution of the heterosis equations. Thus the eternal enigma of heterosis is resolved! This happened at the end of the 20th century. We now come to the second point of the discovery, the new genetic parameter crossheritability which will rise in size with the increase of the number of times it's used and form the link between breeding and evolution. The advent of the Age of Evolution Engineering in the 21st century marks a totally new era, showing that artificial will ultimately supercede natural selection, with the long span of time element eliminated. For agriculture at least, it means there is no limit to the increase of food supply by the new method, with the concentration of desirable genes by hybridization in place of the old theory of their fixation. Genetic gain is achieved through artificial selection, with an 80% saving of time, labor and cost by adoption of the new method. Applied to a further increase in all kinds of agricultural products including hybrid rice, it means that a huge escalation, in fact a New Green Revolution, on a much larger scale than that of any such before, is in view, provided it is adopted in our research and educational institutions as early as possible, ere its spread elsewhere. The possibilities from the evolution point of view can only be pictured by science fiction.