The American Naturalist 55(637): 116-133 (1921)

A STIMULATION of growth has come to be recognized as one of the results of hybridization. The phenomenon is of so much importance, practical as well as theoretical, that it has been given a special designation, heterosis. (Shull, 1914.)

1 The theory has been further elucidated in the monograph on "Inbreeding and Outbreeding'' by East and Jones (1920).

New interest has been given to the study of the causes of this increased vigor by the work of Dr. Donald F. Jones1 (1917 and 1918). Briefly stated the theory accepted by Jones is that growth is affected by a number of different characters or factors, the dominant members of each character pair being favorable and the recessive unfavorable to growth. Each strain or variety possesses some dominant and some recessive characters. When two strains are crossed the first generation of the hybrid exhibits the dominant characters of both parents and is in consequence more vigorous than either parent. In subsequent generations the number of dominant characters in any individual can not be greater than in the first generation and in a large majority of instances will be less, hence the average vigor of the second generation, although still above that of the parents, will be below that of the first.

The theory is not new, but has not been generally accepted because of outstanding objections. Dr. Jones has reviewed the earlier work and has advanced a very ingenious and entirely novel explanation of the objections. This explanation will be discussed later.

Bruce (1910) from purely mathematical considerations, showed that if dominance is correlated with vigor, crossing would produce "a mean vigor greater than the collective mean vigor of the breeds." Only a few days later appeared the paper of Keeble and Pellew (1910) with a concrete illustration and the suggestion that the "greater height and vigor which F1 generations commonly exhibit may be due to the meeting in the zygote of dominant growth factors of more than one allelomorphic pair." It appears to me unfortunate that in elaborating this theory, Jones has retained the form of statement used by Keeble and Pellew, and describes the phenomenon of heterosis as due to the accumulation of dominant growth factors instead of placing the emphasis on the suppression of deleterious recessive characters. It may seem that the difference is only verbal since a dominant growth factor presupposes a recessive allelomorph. There is, however, a difference in the point of view, especially if the evolutionary significance of the phenomenon is considered. In speaking of dominant growth factors we seem to assume as a starting point, strains of low vigor subsequently improved by the appearance of dominant mutations. It is known that advantageous variations, whether dominant or recessive, are of extremely rare occurrence and while evolutionary progress as a whole must be dependent on such rare progressive changes the effect of these is negligible as a factor explaining heterosis.


In all varieties of maize there are to be found plants that are abnormal in some particular and these abnormal individuals are almost always deficient in vigor and yield. When varieties are self-pollinated for a series of years at least a large part of the degeneration that follows is caused by these abnormalities.

The bearing of abnormalities on heterosis will be more easily understood if the behavior of two or three examples is described.

A very common abnormality consists of small yellow spots thickly distributed on all the leaves which develop later than the seedling stage. While undoubtedly interfering with the proper functioning of the chlorophyl, the effect of this abnormality is not serious. Even in breeding experiments seed may be saved from a spotted plant and in a population containing these partly chlorotic individuals many of the ovules on the most vigorous plants will be fertilized by pollen from affected plants. It is easy to see how characters of this kind persist.

A more serious and less common abnormality is one that prevents the leaves from unrolling properly, with the result that the plant is bent and contorted and in extreme cases never reaches maturity. Seed would seldom be saved from plants affected with this disorder, but they frequently produce pollen in normal quantities and the character in consequence is widespread and difficult to eliminate.

Albino seedlings may be taken as an example of a still more serious type of abnormality. In this case all individuals that show the character die in the seedling stage. It might appear at first that disorders of this type would be self-eliminating. The character is recessive, however, and in many strains there are plants which are hybrid for the albino character. These hybrid plants show no trace of the character, yet one half of the pollen grains and one half of the ovules carry albinism. If either of these unite with one of their kind an albino plant results, while if they unite with a normal gamete another hybrid plant like the parent is produced. Such characters may be carried along in this manner for any number of generations in a completely latent form, coming into expression only when pollen grains and ovules both bearing the character chance to unite.

Breeding experiments have shown that the more conspicuous of these abnormalities are recessive Mendelian characters which have come into expression through the chance meeting of male and female gametes both bearing the character. Only a few of the more obvious of these abnormalities have been studied, but there is no line of demarcation between these conspicuous changes and those that are less evident down to variations that can not be distinguished visually from environmentally induced fluctuations.

2 The term character has been used in many places in this paper where it would have been more in conformity with current usage to employ the term factor.

Different varieties possess different assortments of deleterious characters and in a cross between two unrelated strains all of the recessive lethal or semi-lethal characters2 not common to both parents are kept from' expression, since the recessive characters of each parent are brought into combination with, and suppressed by, their dominant allelomorphs in the other parent. Freed from the depressing effects of these recessive characters, the first generation of a hybrid is usually more vigorous than either parent. In subsequent generations the old recessive characters again come into expression in some of the plants, thus reducing the general vigor below that of the first generation.

Since heterosis results from the combined action of independent units it might seem proper to call these units factors. Taken individually, however, each of the units is assumed to produce a tangible effect and is, properly speaking, a character.

If the above explanation of heterosis is to be accepted it should follow that a majority of the departures from the normal must be deleterious and recessive while those which are advantageous are dominant.

The existence, on the other hand, of advantageous recessive, or deleterious dominant, variations would operate to make F1 populations less vigorous than the average of their parents and conversely inbreeding would tend to increase vigor.


None of the recorded Mendelian variations of maize is of a nature that would be advantageous to a wild plant and most of them are obviously detrimental. Moreover, if variations occur at random the chances are almost infinitesimal that any particular variation would constitute a favorable addition to the complex mechanism of a highly specialized plant or animal. A chance alteration in the parts of a machine would seldom improve its efficiency.

Of the recorded heritable variations in maize the departure from the normal condition is recessive in a great majority of the cases. Aside from a number of widespread characters where neither member of the allelomorphic pair may be considered more normal than its mate, the only dominant variations in maize that come to mind are pod corn and fasciated or bear's foot ears.

On the other hand, the recessive variations already described number more than 20 and it would be safe to say that hundreds of others are known to maize breeders.

In a complex organism we may expect that deleterious variations will occur more frequently than beneficial variations, but that such a large proportion of the characters should be recessive calls for comment. East and Jones hazard the suggestion that natural selection has suppressed the tendency to produce dominant unfavorable variations while the tendency to produce unfavorable recessive variations has been tolerated.

It should be kept in mind that the observed preponderance of recessive characters does not necessarily imply that a corresponding preponderance of mutations or germinal changes are recessive. Dominant disadvantageous variations are eliminated much more promptly than recessive and the gradual accumulation of recessive characters soon would place them in the majority in any cross-bred species. It seems not improbable that the great preponderance of recessive over dominant characters is a measure of the extent to which dominant characters are eliminated. In a cross-bred form even variations that result in sterility or death may persist indefinitely if recessive. It may well be that the rate at which dominant characters appear represents roughly one half of the germinal changes that are taking place, new recessive characters originating at approximately the same rate. The preponderance of recessive characters would then be explained, as the result of their preservation in a hybrid condition.


This assumption is made necessary by the fact that the abnormalities which are sufficiently conspicuous to be identified and isolated will account for a part only of the reduction of vigor that follows inbreeding. A part must be due to the combined effect of minor unfavorable variations, the effect of individual variations being insufficient to produce changes that can be distinguished from environmental fluctuations.

That minor variations are more numerous than major is almost self-evident if large and small variations form a continuous series, as they seem to do, since there is a limit to the largeness of variations but none to their smallness. If further proof is needed it follows from the fact that most major variations can be resolved into less comprehensive variations and these subsidiary or minor variations must be more numerous than the major variations of which they form parts.

As East has noted, our classification of variations into large and small may have only a remote relation to the importance of characters in the plant's economy. But whether judged by the change in appearance or by their importance to the organism, it is certain that larger or more fundamental changes must occur less frequently than smaller or less important variations.


The appearance of deleterious characters when maize is inbred and their disappearance when crosses are made, would follow whether the characters were the result of recombination or of mutation.

There seems to be no sure way of distinguishing between the behavior of characters that appear as the resuit of recombination and those that result directly from a germinal change. Changes that occur in homozygous strains must be mutations. lit is, however, theoretically impossible to be certain that a strain is homozygous regardless of the number of generations that it has been selfed and, practically, the criterion of homozygosity is fixed by the accuracy with which comparisons can be made. With quantitative characters in maize it is difficult to detect with certainty differences of less than 10 per cent., yet sister progenies of strains that have been selfed for as many as 8 or 9 generations usually show differences too large to be ascribed to chance. This difficulty of obtaining uniformity may be due to the large number of factors involved, but also may be due to the frequency of minor mutations. If a new character appears in a relatively uniform strain that has been selfed for a number of generations and the character behaves as a simple Mendelian unit, it usually is ascribed to a mutation. Even in such cases, however, the character may be due to recombination. If the two factors of a dihybrid recessive character arose independently in nearly the same position on homologous chromosomes, the close linkage of the dominant allelomorph of one factor with the recessive allelomorph of the other would long postpone the appearance. of an individual with both recessive factors and when it did appear the departure of its behavior from that of a simple character would be difficult to detect.

Although the nature of variations does not affect the bearing which the preponderance of recessive characters has on the explanation of heterosis, there are practical as well as theoretical reasons for wishing to know whether new characters that appear in breeding stocks are mutations or result from the combination of factors already present in the germ plasm. If the undesirable characters that appear from time to time, even in well bred varieties, are the result of recombination, the breeder will be encouraged to expend the time and labor necessary to eliminate them. If, on the other hand, these new characters are the result of an unstable germ plasm other means must be sought.

Already the importance of deleterious recessive variations has found application in the breeding of maize. It soon was realized that to successfully eliminate recessive characters it is necessary to bring the characters into expression by inbreeding. Once a strain has been freed of undesirable characters, vigor may be restored by combining the inbred lines or the full advantage of dominance may be realized by growing first-generation hybrids of the better strains.

This method of breeding will be relatively unsuccessful if unfavorable mutations are of frequent occurrence. It is perhaps too early to be sure that this is not the case, but it is encouraging that in strains self-pollinated for 13 generations Jones finds no conspicuous variations after about the 7th generation. The next step is to demonstrate that no unfavorable variations appear when the selfed lines are crossed. This has been shown to be the case in the first-generation, but a certain percentage of multiple factor recessives are to be expected in subsequent generations.

If linkage is operative these recessive characters would come to light slowly, much as they appear in successive generations of an open-bred variety. As already pointed out, there is as yet no way of distinguishing between mutations and multiple factor characters, when the factors are linked.


In discussing the nature and causes of the reduction of vigor that follows inbreeding, it is necessary to choose words with great care. To state the questions at issue in such a way as to distinguish between differences of fact and differences in the use and meaning of words will tax the possibilities of the language.

Many of the older writers on heredity, have held that inbreeding is a cause of degeneration. In avoiding ambiguous words "cause" is one of the first that must go. If forced to define their position this school would probably be content with the statement that degeneration is a necessary consequence of inbreeding, the intermediate steps or nature of the process being unknown. Is this conception really at variance with the idea that degeneration results from the increased number of unfavorable recessive characters brought into expression by increasing homozygosity? Does not this conception rather amplify the older, general and indefinite position by explaining how the degeneration may be brought about?

It excites unnecessary opposition, and is not entirely fair, to read into the early writings the idea that inbreeding was held to be the immediate and direct cause of the subsequent degeneration. Such words as "cause" and "per se" have perhaps been used, but is there not sufficient latitude in their meaning to allow the later discoveries to be looked upon as explaining rather than refuting the old doctrine?

In the attempt to bring the two views into sharp contrast the newer explanation is sometimes stated in terms which likewise must be interpreted with latitude if the explanation is to be accepted. Thus East and Jones (p. 123) state one of the results of inbreeding maize as follows: "There is a reduction in size of plant and productiveness which continues only to a certain point and is in no sense an actual degeneration." It is difficult to imagine a degeneration more "actual" than that usually following the inbreeding of maize.

In another place (p. 139) the same authors say: "The only injury proceeding from inbreeding comes from the inheritance received." Such statements have an unfortunate air of finality that probably was not intended. The relation between inbreeding and degeneration has been greatly clarified by the work of these authors, but the above statement taken literally places them in a position similar to that of the older writers who stated that inbreeding was the "cause" of degeneration. There may well be other and important ways in which inbreeding is associated with degeneration.

There is for example definite evidence that vigor is reduced by continued asexual reproduction (Shull, 1912), and although it may be urged that this result is associated with the phenomenon of senescence, so may be the decline of vigor that follows inbreeding.

Furthermore, it has been shown by Calkins (1919) that in the ciliate, Ursoleptus, conjugation between sister cells of an asexually propagated line increases vigor.


Two objections have stood in the way of accepting dominance as an explanation of heterosis. The first of these is that if this explanation is the correct one it should be possible to obtain an occasional F2 individual, homozygous for all dominant allelomorphs, the progeny of which should be uniformly as vigorous as the F1. It is held that no such F2 individual has been found. The second objection is that the distribution in F2 should be skew with the mode above the mean while in fact F2 populations show a symmetrical distribution.

Jones has proposed a novel and ingenious explanation of both objections. He has pointed out that it is only necessary to assume that the phenomenon of linkage, which plays such an important rôle in the inheritance of Drosophila, is operative also in maize.

If groups of characters are inherited as units with little or no crossing over, both dominant and recessive characters being represented in any particular unit, the first generation would still exhibit all the dominant characters of both parents, but when segregated into pure lines each pure line would again exhibit recessive characters, with a consequent decline in vigor.

This assumption of group inheritance or linkage would also meet the objection that F2 populations exhibit a normal and not a skew distribution.

There are a number of instances of coherence or linkage known in maize, but if the characters studied to date are a fair sample the rôle of linkage must be of minor importance. Linkage relations have not been studied in sufficient detail even to state with assurance that the characters are arranged in linear series corresponding to the number of chromosomes, although this conclusion is indicated. The linkages of most of the Mendelian characters are very loose and it would seem necessary to conclude that, if the characters of maize are arranged in a linear series, the chromosomes must be either very long or very flexible.

While admitting that linkage would meet the objections urged against the simple hypothesis that the suppression of recessive characters explains heterosis, it may be well first to make sure that any such assumption is necessary. An examination of the maize literature indicates that the difficulty of securing uniform strains with the vigor of the first generation has been assumed rather than demonstrated. No case was found where selection following hybridization had been continued long enough to approximate homozygosity. There are also very few cases where the more vigorous F2 individuals have been chosen as parents of the F3. The most extensive series of experiments are those of Emerson and East (1913).

Height is probably the most satisfactory character to use as a measure of heterosis. There are 23 comparisons of F1 and F2 populations in the work of Emerson and East. To these six can be added from our own experiments.

In these 29 cases the mean of the F2 was below that of the F1 in every instance but in ten of the 29 cases the largest of the F2 plants equalled or exceeded the largest of the F1 individuals and in every case where a progeny was grown from a plant near the upper limit of the range of the F2 its mean exceeded that of the F1.

Other characters reported by Emerson and East for which the F1 was measurably larger than the mid-parental value are length and diameter of ear and length of internode. With respect to length of ear (Tables XIII-XV), there are 13 F2 progenies that may be compared with the F1. In 10 the mean was higher than the mean of F1. Four F3 progenies were grown from F2 individuals above the mean of F1 and in 3 of these the mean exceeded the mean of F1.

With respect to diameter of ear (Tables XVIII and XIX), 8 F2 progenies may be compared with the F1. In 2 of the 8 instances it would appear that the mean was above that of F1. Seven of the 18 F3 progenies were grown from F2 individuals above the mean of F1 and in every case the F3 mean exceeded the mean of F1.

Length of internode is the character showing the most decided increase in F1 over the mid-parental value. In the two crosses reported (Tables XXXIII and XXXIV) this increase was 33 and 27 per cent. None of the F2 progenies grown the same season as the F1 equalled the F1. The mean of the F1, however, was exceeded by the mean of 5 of the F3 progenies grown the following season, although the parents were not selected for internode length. The results with these characters give little or no evidence of non-heritable vigor in the F1, neither is there any proof that it is difficult to select progenies with the vigor of F1.


In the absence of experimental data, to secure which will require very extensive experiments extending over many years, it may be instructive to consider what results may be expected if suppression of semi-lethal characters is the true explanation of heterosis.

The difficulty of obtaining individuals homozygous for all or even a limited number of characters has been frequently pointed out, but the bearing of this on the difficulty of retaining the vigor of the first generation seems not to have been appreciated.

With a sufficiently large number of characters influencing vigor it would be impossible in practice, even without the assumption of linkage, to obtain homozygous individuals having the vigor of the first generation.

Thus with 10 pairs of characters over 700,000 individuals would have to be grown before there would be an even chance of obtaining an individual homozygous for all of them.

More than ten separately inherited Mendelian character differences affecting growth have been identified and there is no reason for believing that more than a small proportion have been isolated or that more than a small proportion produce conspicuous morphological changes that would be readily detected.

A near approach to the vigor of the F1 night be expected, of course, without complete homozygosity.

Some idea of the chances of isolating strains that are practically homozygous may be obtained by calculating the size of the populations that must be grown to insure a reasonable chance of finding an individual homozygous for say 70 per cent. of the characters.

Table I indicates the size of the populations necessary to fulfil these conditions with the number of character pairs ranging from 10 to 30.


It will be seen that to have a reasonable chance of obtaining an individual homozygous for even 70 per cent. of the character pairs it is necessary to limit the character pairs to 15 or less. Another way of gaining a quantitative idea of the degree of homozygosity that may be expected is presented in Table II, which gives the number of individuals necessary to provide an even chance of obtaining at least one individual homozygous for different numbers of characters in crosses when from two to 15 character pairs are involved. It should be kept in mind that even though one should obtain an individual homozygous for a sufficiently large percentage of the characters involved to approximate closely the F1 in vigor, it would be necessary to grow a progeny from this individual before its inherent vigor could be demonstrated. The numbers given in the tables might thus be taken to represent F3 progeny rows instead of F2 individuals.


The conclusion is that perjugate progenies equalling or even closely approximating F1 in vigor are hardly to be expected in breeding experiments and consequently no assumptions are necessary to account for their nonappearance.


The second objection, that of the failure of F2 progenies to show a skew distribution, may now be considered. There can be no question that a series of independent, dominant characters influencing size would bring about a skew distribution. Assuming the characters to have equal effect, two characters would give a distribution of 1, 6, 9, three, a distribution of 1, 9, 27, 27, and with four characters the distribution would be 1, 12, 54, 108, 81. It is apparent that with an increase in the number of characters the skewness becomes less pronounced. It may be of interest to determine whether, with a reasonably large number of characters, the skewness would be detected in populations of the size usually grown in experiments.

With 20 pairs of characters giving 21 classes 1,099,514,627,776 individuals would have to be grown to obtain a representative population. Of this population 99.91 per cent. would fall in the 12 classes with the largest number of dominant characters. That is, populations of over 700 would have to be grown before there would be an even chance of getting any individuals smaller than those represented in these 12 classes. With ordinary sized populations then the distribution would be fairly represented by the distribution of the 12 largest classes.

The distribution among these 12 classes would be as follows:

No. Dominant
Proportion of
Individuals Expected
9   3  
10   1.0  
11   2.7  
12   6.1  
13   11.2  
14   16.9  
15   20.2  
16   19.0  
17   13.4  
18   6.7  
19   2.1  
20   3  

A distribution of this nature, with populations of approximately 500 individuals, conforms to the normal frequency curve as closely as would be expected. The mode departing from the mean by only 3/100 of a class.

The theoretical distribution of an F2 population involving 20 pairs of characters of equal weight with complete dominance is shown in the accompanying diagram. It will be noted that although the curve as a whole is skew, the portion to the right of the class with 9 dominant characters, which comprises 99.91 per cent. of the area, is practically symmetrical.

With 10 character pairs there would be 11 classes and 99.65 per cent. would fall in the 7 largest classes and in this portion of the theoretical population the mode would be separated from the mean by only 3/10 of a grade.

Distribution of individuals In F2 population Involving 20 pairs of characters of equal weight and showing complete dominance.

Even should it be possible to grow F2 populations sufficiently large to detect departures from a normal frequency distribution there is yet another reason for questioning that a skew distribution should be expected, when plotted in the customary way. It has come to be accepted that the effect produced by a given growth factor is dependent on the size of the organism.. For example, if a growth factor increases the length of the internode by a given amount, it is clear that the height of a plant with 30 internodes will be increased more than that of a plant with only 15 internodes. In other words, the effects are factorial instead of additive. A convenient method of classifying a population on a factorial basis has been proposed by Zeleny (1920), who takes the range of each class as a constant percentage of the value of the midpoint of the class. The result of this change in plotting is to increase the range of sizes included in the higher classes and consequently to raise the mode.

In conclusion it would seem, therefore, that the assumption of linkage, while perhaps not improbable, is superfluous so far as the explanation of heterosis is concerned, since neither of the objections which it was framed to meet have foundation in fact.

It is, perhaps, too much to assert that the suppression of deleterious recessive characters completely explains heterosis or that the reappearance of these characters is the only factor in the decline in vigor that follows inbreeding, but the behavior of maize is in full accord with this explanation.