heterosis and the inheritance of quantitative characters

Heterosis and the Inheritance of Quantitative CharactersAuthor(s): Eric AshbySource: Proceedings of the Royal Society of London. Series B, Biological Sciences, Vol. 123, No.833 (Aug. 17, 1937), pp. 431-441Published by: The Royal SocietyStable URL: http://www.jstor.org/stable/82072 .

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575.I25 575--8I

Heterosis and the Inheritance of Quantitative Characters

BY ERIC ASHBY

From the Department of Botany, The University, Bristol

(Communicated by V. H. Blackman, F.R.S.-Received 19 February- Revised 5 May 1937)

In three recent papers (Ashby 1930, I932, I937) observations have been

recorded on the physiological basis of heterosis. These data suggest no obvious genetical interpretation, though they draw attention to the need for a re-examination of the existing hypothesis. This paper considers the

requirements for a theory of heterosis and discusses the bearing of heterosis on other aspects of size inheritance.

THE POLYMERIC FACTOR THEORY OF SIZE INHERITANCE

Heterosis involves quantitative characters. It is in fact usually described in plants with reference to height, for while many other qualities are

affected in heterosis, increase in height is the most obvious phenomenon and the most easily measured. Any genetical theory of heterosis must

therefore be consistent with a theory of the inheritance of size characters in general.

The hypothesis of size inheritance still most widely accepted dates from

1908-10, when Nilsson-Ehle and, independently, East published data on

the inheritance of characters which exhibited no clearly marked segre-

gation. The literature now abounds with examples of the inheritance of

quantitative characters. Most of these examples accord in showing an F1 population which is not more variable than its parents, and which is

intermediate between them in size (except where heterosis is manifested), and an F2 population apparently symmetrically distributed about a mean

intermediate between those of the grandparents, and exhibiting a greater variance than either the grandparents or the F1. Families bred from

individuals from various points of the F2 distribution differ markedly in

their means and variance. This summary of a great mass of data is

[ 431 ] 2G2



432 E. Ashby

necessarily incomplete, but it specifies the requirements which a theory of size inheritance must satisfy.

East's theory is adequate to account for many of the results of size crosses, but it involves three assumptions which require modification in the light of modern work. These are: (i) lack of dominance among the factors determining size, (ii) an equal influence of these factors on the size character in question, and (iii) a linear relationship between the number of factors present and the size of the character upon which they operate. East pointed out that on these assumptions the distribution of size classes in an F2 population is according to the terms of a binomial expansion, (I + )2n, and under these conditions the distribution is symmetrical.

It is obvious that formal and simplified assumptions have to be made in

any theory of size inheritance, but these particular assumptions are not

acceptable for the following reasons: (i) The suggestion that size factors do not as a whole show dominance is contrary to experience, for some

degree of dominance is characteristic of most genetic factors which have been isolated, including those which control size. East himself admits this

(i916), though he does not suggest any corresponding modification of the

theory. Moreover, the assumption was made to account for the symmetry of F2 distributions. There was no proof of this symmetry, and indeed Fisher, Immer and Tedin (1932) have shown that significant skewness does exist in some of the apparently symmetrical distributions of size characters published by Emerson and East (I9I3). In other instances, where many factors operate in determining size, dominance bias may be present even

though it cannot be disclosed by analysis; for the mean and the mode of a binomial distribution fall in the same class whether the distribution is skewed or not, and the distribution of the individuals in a small sample may be quite unlike the distribution of the whole population from which the sample is taken. This is illustrated by the following, suggested to the writer by Professor J. B. S. Haldane. If n factors, located on different chromosomes and exhibiting full dominance, affect a size character, the mean of the resulting F2 is np = 3n/4. The variance is npq = 3n/16, the value of the third moment statistic, y1 is - (p - q)/ V(npq) = - 2//(3n), and the variance of y, is /(6/M), where M is the number of individuals in the

population. When ten factors operate, as in fig. 1, the mean is 7 5, the variance is 1-875, and the skewness is -0-3675. In order to obtain a

probability of 0-98 that the distribution is asymmetrical it is necessary to use about 500 individuals. It is unnecessary therefore to postulate non- dominance of size factors: even with considerable dominance the bias may be difficult to detect. (ii) The second assumption, that all factors controlling



Heterosis and the Inheritance of Quantitative Characters 433

a quantitative character have an equal effect in determining its size, is not

supported by analytical work on size inheritance. It is commonly found that size is governed by relatively few "principal" factors and a number of modifiers. Examples of this are to be found in the work of Punnett and

Bailey (I914), Emerson (I916), Frost (I923), Lindstrom (1929), Sirks (I932), Rasmusson (I935). (iii) The third assumption, that there is a linear

relationship between the number of factors and the size of the character

upon which they operate, is somewhat misleading, in that it implies that

300,000 - /

X 200,000- / \

0

100 /

I 100,000- / \

1 - l - i I I I I I I -

0 1 2 3 4 5 6 7 8 9 i0 Number of dominant factors

FIG. 1-The theoretical distribution of ten independently segregating dominant factors in an F2 population. Note that in a small sample individuals with less than five dominant factors would be rare and the distribution would appear superficially to be symmetrical.

the factors are acting on a single process, whereas the size of an organ is the resultant of several more or less independent processes. Rasmusson has recently (I933) substituted for this assumption the suggestion that the effects of factors on size follow a law of "diminishing returns". This, however, carries the same implications as the assumption that factors are additive in their effect, and it may be noted that if factors acted in this

way the skewness already present due to dominance bias would be greatly augmented.

THE GENETICAL HYPOTHESIS OF HETEROSIS

It is necessary to specify these difficulties inherent in East's theory of size inheritance, because this theory is at variance with the hypothesis of



heterosis put forward by his co-worker, Jones. Jones's genetical inter-

pretation of heterosis (1917) replaced the various "stimulus" hypotheses, and is still generally accepted. It explains heterosis as due to the comple- mentary action of dominant linked factors derived from both parents. Jones's scheme provided for the occurrence of heterosis in F1, for an assumed symmetrical distribution of size characters in F2, and for the belief that individuals as large as those in the F, could not be bred true in subsequent generations. The scheme may be illustrated by the following diagram:

Parent 1 Parent 2 AA EE JJ aa ee jj bb ff kk BB FF KK CC GG LL cc gg 11 dd hh mm DD HH MM

Hybrid Aa Ee Jj bB fF kK Cc Gg LI dD hH mM

The letters symbolize factors (in this example showing complete linkage) located in three pairs of chromosomes, and affecting the size of the

organism carrying them. The factors are homozygous in the parents and

they combine to give a hybrid heterozygous for them all. On the assumptions of East's theory of size inheritance there is no

heterosis according to this scheme; the "size value" of the hybrid is the same as that of its parents. Jones, on the other hand, assumes that size factors as a whole do show some dominance, and only when this assumption is made will his scheme provide even a formal analysis of heterosis.

In order to account for the apparent absence of dominance bias in the

progeny of a population showing heterosis Jones postulated that the two inbred parents should make approximately equal contributions to the size of the hybrid. If this is not postulated the distribution of size in the F2

population will be skewed, notwithstanding linkage. But the postulate is

contrary to Jones's own data, for if the parents make approximately equal contributions of size factors to the hybrid, and if the size factors are equal in their potency, then ex hypothesi the parent plants should be about the same size for the character in question. Reference to the data on which the hypothesis is built shows that in height, for instance, the parents may differ by 40 % and there are instances of weight heterosis where the parents differ in weight by 100% (Ashby I930). Crossing-over, while it might reduce skewness in F2 would not eliminate the inequality in number of

434 E. Ashby




dominants in the gametes if this inequality were initially large, and in the limiting case (random assortment of factors) there should still be skewness due to dominance bias. However, the assumption made by Jones is un-

necessary, for there is no convincing evidence that the progenies of populations showing heterosis are not skewed.

It is not the purpose of this criticism to discredit the factorial hypothesis of heterosis, but to remove from the hypothesis one of those features which impair its application. Collins (I92I) pointed out that Jones's attempts to account for symmetrical F2 distributions were superfluous, in that there was no evidence that symmetry was present, but his suggestions were overlooked. In essentials, however, Jones's hypothesis :is in accord with the facts. It may be restated in its modified form as follows: If two inbred strains carrying different sets of factors exerting a favourable effect on size, and showing some degree of dominance, are crossed, the hybrid may show heterosis due to the combined operation of the "favourable " factors derived from its parents. Dominance bias in the F2 population may be detectable, or it may be concealed on account of the large number of factors contributing to it.

The hypothesis does not provide a very satisfactory basis for the analysis of heterosis, and it is significant that it has received very little direct test from experiment. Two pieces of evidence support it. Fisher, Immer and Tedin (I932) have shown, by comparing the distribution of skewness in F3 populations with the covariance of the first and second degree statistics for the populations, that heterosis is probably due to dominance favouring the larger size. Richey (1927) and Richey and Sprague (I93I) by a series of back-crosses of hybrids on their parents, have shown that the most

heterozygous races show the greatest heterosis. Apart from these examples the hypothesis is justified only in that it has not been proved wrong.

A WORKING HYPOTHESIS OF SIZE INHERITANCE

Heterosis as explained by Jones is a particular instance of the operation of polymeric factors in size inheritance. A drawback to the theory of size inheritance as it stands, apart from its unsatisfactory assumptions (vide p. 432), and despite Rasmusson's suggested modifications, is that the theory is not helpful in indicating experiments which might carry the analysis of size further. It does not take account of the fact that factors determining size operate on different processes and at different times in the history of the organism. Analyses of Fe distributions may be deceptive; metrical bias may obscure the bias due to dominance; and estimates, from analysis of



E. Ashby

F2 distributions, of the number of genes involved in size inheritance are too uncertain to carry conviction (see Rasmusson 1933; Serebrovsky I928). A fresh statement of the theory of size inheritance, which is implicit in some modern work (e.g. Goldschmidt 1927; Ford and Huxley 1929; Sinnott I935; Sinnott and Dunn I935) and which emphasizes a new mode of attack on the problems, may be made in the following terms: (i) size characters are generally under the control of several genetic factors; (ii) these factors are unlikely to be arithmetically cumulative in their effect

upon one single process; but the factors will operate upon various determinants of size, e.g. some upon initial size of primordia, some upon growth rates, some upon rates of differentiation, etc.; (iii) the parts played by the several genetic factors in determining size will depend upon the level of the environment and the time in the life cycle at which the factors come into operation.

The theory stated in this form indicates how the problem may be

approached from another angle-by analysing size into the processes which determine it and studying the inheritance of these processes. Thus, the final size of a leaf may be resolved into the following determinants: (i) the number of cells in the primordium; (ii) the rate of cell division; (iii) the rate of cell expansion; (iv) the period over which growth is maintained; (v) the rate of differentiation; (vi) the final size of the cells. Each of these processes will be controlled by various genetic factors, and the contribution which the factors make to leaf size will be subject to the condition of the environment. The final size of the leaf is a function of so many variables that it is of little value as a measure of genotypic constitution, but the mode of inheritance of the several determinants of size may be simpler.' Data on maize, for instance (Ashby I930), show that the dry weight in the grand period of growth is referable to embryo weight and efficiency index. Two races were found to have the following values:

Embryo weight Efficiency g. index

Race 1 0-038 0-069 Race 2 0-013 0.097

After 43 days' growth plants from these two strains had the same mean dry weight (1*099 g.). In the one case it was reached by a small capital increasing quickly; in the other case by a larger capital increasing more slowly. The higher efficiency index was shown to behave as a complete dominant in the F, and the indices segregated in F2. The segregation of embryo weights is obscured by the effect of the maternal environment,

436




in particular the size of the testa, and it needs further analysis. This instance also draws attention to the confusing testimony of size data, for the two genotypes in question fall on different parts of a distribution for

weight at different times in their development. From 0 to 43 days race 1 is heavier than race 2. At 43 days the two genotypes fall into the same

weight class. From the 43rd day onwards race 2 falls into a higher class than race 1. The shape of the distribution curve depends upon the time at which the population is sampled. Such fragments of data indicate that the genetics of size may be profitably studied through a consideration of the inheritance of processes which determine size.

One unexpected fact is already emerging from these analyses: there is an indication that hereditary size differences are commonly determined by initial sizes of primordia rather than by the time relations of subsequent development. Analysis of data for maize (Jones I917; Ashby I932), tomatoes (Ashby I937; Luckwill 1937), guinea-pigs (Castle, see Ashby 1937), and pigs (Roberts and Laibile; see Ashby I937), shows that differences in size between different genotypes are referable to initial differences (i.e. at birth or germination) and are not due to differences in growth rate during post-embryonic development. Kopec's work on mammals (I923, I926, 1933) points to the same conclusion, in that birth weight is highly correlated with subsequent size. The situation is not without exceptions, for differences in size between genotypes may depend on differences in relative growth rate (Ford I928; Livesay I930; Ashby I930), but in most instances on

record the ratio of sizes of adults in two strains is no greater than the ratio of sizes at birth or germination, and the genetics of size must be studied

through the genetics of embryo development.

THE PHYSIOLOGY OF HETEROSIS

This method of analysis has been applied to the study of size heterosis

(Ashby 1930, I932, I936, I937; Luckwill I937). The results may be summarized in the following terms: (i) heterosis in certain strains of maize and tomatoes is manifested as greater height, dry weight, leaf area, leaf number, etc.; (ii) the plants showing heterosis do not exhibit relative

growth rates greater than both their parents in any of these particulars, nor have they a relatively greater respiration or assimilation rate; (iii) size heterosis is associated with larger primordia in the embryos of the F1

population, and the additional vigour is referable in some cases entirely to this initial advantage in size. These conclusions are illustrated by the data assembled in Table I, from some unpublished experiments of Luckwill,



E. Ashby

working with the present writer. It is evident from entries 1-7 in this table that heterosis was manifested in a variety of ways. It is evident from entries 8-14 that various rates of development were not greater in the hybrid, but that the higher parental rate was inherited in the manner of a complete dominant in the F1. Heterosis can be attributed to the

initially larger primordia in the F1 embryos, and this is in accordance with Jones's hypothesis, but the general absence of higher metabolic rates in the hybrid after germination is not what would be expected according to the hypothesis.

TABLE I-SUMMARY OF DATA ON THE DEGREE OF HETEROSIS AND THE

RATES OF DEVELOPMENT IN A HYBRID AND ITS PARENTS. PARENT 1

is Lycopersicum racemigerum AND PARENT 2 IS L. esculentum, RE-

CESSIVE FOR BRACHYTIC STEM, FASCIATED FRUIT, AND "WILTY

FOLIAGE '

Dry weight after 23 weeks (g.) of:

1 Stem ... ... ... 2 Leaf ... ... ... 3 Total ... ... ... 4 Leaf number ... ... 5 Mean area per leaf (cm.2) ... 6 Mean dry weight per leaf (g.) ... 7 Embryo weight (mg.) ... . 8 Mean efficiency index ... 9 Relative growth rate as height ...

Relative growth rate as weight of: 10 Stems ... ... ... 11 Leaves ... ... ... 12 Differential growth ratio between

stem and leaf ... . 13 Mean relative rate of leaf pro-

duction ..... 14 Mean assimilation rate ... ...

*s. = significant;

Parent 1 Parent 2 Hybrid

90 67

157 284

19-2 0-129 0-680 0-226 0-102

15 32 47 99 28-8

0-183 0-818 0-156 0-065

130 144 274 319

37-1 0-246 1-005 0-226 0.090

Significance of increase in hybrid

over parents

S.*

S. S. s. S. s. s.

n.s. n.s.

0-243 0-173 0-244 n.s. 0.190 0-157 0-193 n.s.

1-32 1-06 1-30

0-141 0-102 0-142 n.s. 0-394 0-321 0-383

n.s. = not significant.

There seem to be three possible interpretations of these results:

(i) There may be practically no variety in genes controlling growth rates

among different inbred races; this implies that the parent strains carry of the same factors for metabolic and developmental rates. If this were true

crossing would not produce strains with relatively higher rates of development than existed in the parents, and there would be no segregation for these rates in generations subsequent to F1.

438




(ii) Rates of development under experimental conditions may be determined by environment rather than by heredity, so that although two strains may differ in their hereditary potentiality as regards growth rates, these differences may be suppressed by the limiting influence of the environment. This would account for the fact that hybrids, despite heterosis, show no higher relative rates of development than their parents, and at the same time for the fact that hereditary differences in embryo size are apparent, for the primordia of embryos develop in a totally different environment. Suppression by the environment of potentialities for embryo growth is frequently encountered in the writer's work; the sizes of embryos from reciprocal crosses may differ greatly, and depend upon the size of the testa which encloses them.

On either of these interpretations the genes effective in determining size differences would operate early in the life cycle, and the manifestation of heterosis would depend on these genes. Data from two recent papers by Faberge (I936a, b) may be interpreted in the same way. It was found that the relative growth rates of tetraploid tomatoes showed no evidence of segregation among different strains, and did not differ significantly from the relative growth rates of diploids. Neither Faberge's results nor those of the present writer indicate which of these interpretations is the more

probable. (iii) The third possibility, which must not be excluded from consideration,

is that there is some stimulus to development of the embryo consequent upon fertilization by a "foreign" male gamete. East originally advocated this view (East and Hayes I912) and Jones (I917) is careful not to reject it in favour of his own hypothesis. One or two more recent works support implicitly the idea of a non-Mendelian cause of heterosis (Calkins I919; Umeya I930). The present writer's data are consistent with such a view, though they do not provide evidence in favour of it.

I am grateful to Professor Macgregor Skene for his criticism of the

manuscript.

SUMMARY

The assumptions inherent in the polymeric-factor theory of size inheritance and the genetical theory of heterosis are discussed. Both theories make unsatisfactory postulates in order to account for the absence of dominance bias in F2 populations, but in fact dominance bias can some- times be demonstrated, and even when it is concealed the distribution



E. Ashby

cannot be assumed to be symmetrical. Therefore the assumptions to explain this symmetry may be removed from the theories. When this is done the theories become consistent with one another and with the facts of size inheritance. They may, however, be stated in a form which emphasizes a fresh method of investigation; namely, the study of size inheritance through an analysis of the inheritance of the developmental processes which determine size.

Recent work on the physiology of heterosis, of which some new examples are given, is not at variance with a Mendelian hypothesis, but it is necessary to postulate either (i) that there is practically no variety in genes controlling growth rates among different inbred races, or (ii) that genetic differences between races, affecting rates of development, are suppressed by the limiting influence of the environment. There are no indications from the data as to which of these suggestions is the more probable.

REFERENCES

Ashby, E. 1930 Ann. Bot., Lond., 44, 457. - 1932 Ann. Bot., Lond., 46, 1007. - I936 Amer. Nat. 70, 179. - 1937 Ann. Bot., Lond., N.S. 1, 11.

Calkins, G. N. iI99 J. Exp. Zool. 29, 121. Castle, W. E. I929 J. Exp. Zool. 53, 421. Collins, G. N. I92I Amer. Nat. 55, 116. East, E. M. I9I0 Amer. Nat. 44, 65.

- 1916 Genetics, 1, 164. East, E. M. and Hayes, H. K. 1912 Bull. U.S. Bur. P1. Ind. No. 243. East, E. M. and Jones, D. F. I919 "Inbreeding and Outbreeding," Philadelphia. Emerson, R. A. I916 Res. Bull. Neb. Agric. Exp. Sta. No. 8. Emerson, R. A. and East, E. M. 1913 Res. Bull. Neb. Agric. Exp. Sta. No. 2. Faberge, A. C. 1936a J. Genet. 33, 365.

- I936b J. Genet. 33, 383. Fisher, R. A., Immer, F. R. and Tedin, 0. I932 Genetics, 17, 107. Ford, E. B. 1928 J. Genet. 20, 93. Ford, E. B. and Huxley, J. S. I929 Arch. EntwMech. Org. 107, 67. Frost, H. B. 1923 Genetics, 8, 116. Goldschmidt, R. 1927 "Physiologische Theorie der Vererbung." Berlin. Jones, D. F. 1917 Genetics, 2, 466. Kopec, S. 1923 J. Genet. 13, 371.

- 1926 J. Genet. 17, 187. - I933 Z. indukt. Abstamm.- u. VererbLehre, 53, 94.

Lindstrom, E. W. I929 Amer. Nat. 53, 317. Livesay, E. A. 1930 Genetics, 15, 17. Luckwill, L. C. 1937 Ann. Bot., Lond., (in the Press). Nilsson-Ehle, H. i908 Bot. Not. 257. Punnett, R. C. and Bailey, P. G. I914 J. Genet. 4, 23. Rasmusson 1933 Hereditas, Lund, 18, 245.

- I935 Hereditas, Lund, 20, 161.

440



Heterosis and the Inheritance of Quantitative Characters 441 Heterosis and the Inheritance of Quantitative Characters 441

Richey, F. D. 1927 Amer. Nat. 51, 430.

Richey, F. D. and Sprague, G. F. I93I Tech. Bull. U.S. Dep. Agric. No. 267. Roberts, E. and Laibile, R. J. 1925 J. Hered. 16, 383.

Serebrovsky, A. S. I928 Z. indukt. Abstamm.- u. VererbLehre, 48, 229. Sinnott, E. W. I935 Genetics, 20, 12, lxi. Sinnott, E. W. and Dunn, L. C. 1935 Biol. Rev. 10, 123. Sirks, M. J. 1932 Genetica, 13, 210.

Umeya, Y. 1930 Genetics, 15, 189.

612.662 :599.82

The Menstrual Cycle of the Primates

X-The Oestrone Threshold of the Uterus of the Rhesus Monkey

BY S. ZUCKERMAN, Beit Memorial Research Fellow

From the Department of Human Anatomy, Oxford

(Communicated by W. E. Le Gros Clark, F.R.S.-Received 31 March 1937.)

Uterine bleeding occurs in spayed rhesus monkeys a few days after the cessation of a series of oestrin injections (Allen 1927). The fact that

bleeding also follows either the removal of ovaries which do not contain functional corpora lutea or injury to large ovarian follicles (Allen 1927; van

Wagenen and Aberle 193 I) is now related to the occurrence of post-oestrin bleeding, and these various observations, together with parallel and in some cases long-established clinical findings, have been made the basis of what is known as the oestrin-withdrawal theory of menstruation. The experimental study of the menstrual cycle necessarily requires detailed knowledge of the

varying reactions of the primate uterus to oestrin. The available observations on this question are very few, and for that reason the following study was undertaken.

1-MATERIAL AND METHODS

The experiments reported in this paper were performed on one prepu- bertal and on twenty-four adolescent and mature ovariectomized rhesus

monkeys (Macaca mulatta). The maximum and minimum weights of the

Richey, F. D. 1927 Amer. Nat. 51, 430.

Richey, F. D. and Sprague, G. F. I93I Tech. Bull. U.S. Dep. Agric. No. 267. Roberts, E. and Laibile, R. J. 1925 J. Hered. 16, 383.

Serebrovsky, A. S. I928 Z. indukt. Abstamm.- u. VererbLehre, 48, 229. Sinnott, E. W. I935 Genetics, 20, 12, lxi. Sinnott, E. W. and Dunn, L. C. 1935 Biol. Rev. 10, 123. Sirks, M. J. 1932 Genetica, 13, 210.

Umeya, Y. 1930 Genetics, 15, 189.

612.662 :599.82

The Menstrual Cycle of the Primates

X-The Oestrone Threshold of the Uterus of the Rhesus Monkey

BY S. ZUCKERMAN, Beit Memorial Research Fellow

From the Department of Human Anatomy, Oxford

(Communicated by W. E. Le Gros Clark, F.R.S.-Received 31 March 1937.)

Uterine bleeding occurs in spayed rhesus monkeys a few days after the cessation of a series of oestrin injections (Allen 1927). The fact that

bleeding also follows either the removal of ovaries which do not contain functional corpora lutea or injury to large ovarian follicles (Allen 1927; van

Wagenen and Aberle 193 I) is now related to the occurrence of post-oestrin bleeding, and these various observations, together with parallel and in some cases long-established clinical findings, have been made the basis of what is known as the oestrin-withdrawal theory of menstruation. The experimental study of the menstrual cycle necessarily requires detailed knowledge of the

varying reactions of the primate uterus to oestrin. The available observations on this question are very few, and for that reason the following study was undertaken.

1-MATERIAL AND METHODS

The experiments reported in this paper were performed on one prepu- bertal and on twenty-four adolescent and mature ovariectomized rhesus

monkeys (Macaca mulatta). The maximum and minimum weights of the



heterosis and the inheritance of quantitative characters

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