Genetics 45: 1457-1465 (1960)

John innes Horticultural Institution, Bayfordbury, Hertford, Herts, England
Received May 20, 1960

AMONG outbreeding species of animals and plants, the nongenetic or environmental component of variability has been shown to he inversely proportional to the level of heterozygosity (MATHER 1950; ROBERTSON and REEVE 1952; LERNER 1953; McLAREN and MICHIE 1956). Owing to fundamental dissimilarities in genetic architecture and behaviour between outbreeders and inbreeders, the relative variability of heterozygotes and homozygotes belonging to species with different breeding systems might be expected to show clear and constant differences. The information that is at present available on the relative variability of inbred and hybrid lines of inbreeding species does not, however, form a consistent pattern (LERNER 1953). This may be attributed partly to the fact that many of the data on variability have been presented in support of studies designed to answer other problems, with the result that it is not always possible to establish, with any reliability, the significance of the published estimates. When this is recognized, and only the most reliable data from the standpoint of experimental layout are admitted, a somewhat less contradictory picture emerges.

The evidence from studies on tomato (POWERS 1942), on Galeopsis (HAGBERG 1952). and on Nicotiana species (JINKS and MATHER 1955; PAXMAN 1956; SMITH and DALY 1959), all show that the variability of F1 hybrids in the inbreeding species studied fall within the range of the inbred parents. The most serious challenge to this conclusion is found in the extensive study of mutants in barley (ROBERTSON and AUSTIN 1935) and in their further analysis and interpretation by GUSTAFSSON (1946). The ratio of the coefficient of variation between homozygotes and heterozygotes in the barley material suggests that the heterozygotes were more variable, but the average ratio over all comparisons was very close to unity, 1.067 ± 0.025. It is doubtful whether a difference in variability of this magnitude has any biological meaning even if it is proved to be real. LEWIS (1954), following a study of flower number in the tomato and an examination of other published data, attempted to generalize the behaviour of inbreeding species by correlating the level of variability directly with dominance. Since only the one character which LEWIS himself studied showed dominance of the smaller parent, most of the relative variabilities on which his conclusions were based might simply be a reflection of a positive relation between the variance and the mean.

The present study on eight inbred lines and six hybrids in the tomato was undertaken, as a further contribution to the understanding of patterns of variability in inbreeders, and the design chosen for the experiments was such as would provide the replication necessary to make valid comparisons between the calculated estimates of variability.


The material comprised eight inbred lines intercrossed to give the six F1 hybrids, XT/1, XT/2, XT/3, XT/19, XT/23 and XT/27, as shown in Tables 1 and 2 of the text. The inbred lines represent commercial varieties which have been multiplied by selfing over very many generations, and their breeding behaviour (which is typical of an obligate, inbreeding species) indicates that they are pure lines. Two trials, each consisting of four inbreds and three hybrids, were conducted. The first (experiment 1) was sown on the 20th April, 1959, to take advantage of the high light conditions of early and midsummer, and the second (experiment 2) was commenced on the 10th June, 1959, to provide a contrast in growing conditions. All the material was grown under glass where variability, due to environmental fluctuations, is high as compared with open ground. Experiment 1 consisted of ten replicates of 20 plants in each plot set out in randomized complete blocks in various parts of the glasshouse area. The position of the blocks represented quite wide differences in site aspect and type of glasshouse and, therefore, in the light and temperature conditions under which they were grown. Experiment 2 differed from above in that only seven replicates were available and the number of plants per plot varied between 20 and 36.

Means and their standard deviations of the ten replicate means of four inbred lines and three F1 hybrids in experiment 1

  59 x 42 x 5 x 18
  |______ _____________ ______| |______ _____________ ______| |______ _____________ ______|
Character |
No. of fruit 11.74 ± 0.55 20.93 ± 0.96 22.41 ± 1.01 20.76 ± 1.36 13.83 ± 0.79 16.22 ± 0.88 11.30 ± 0.79
Av. wt. per fruit 4.14 ± 0.011 2.52 ± 0.07 2.44 ± 0.07 2.61 ± 0.05 3.54 ± 0.09 3.54 ± 0.08 3.27 ± 0.08
Wt. per plant 47.80 ± 3.28 49.66 ± 3.40 50.79 ± 4.77 49.98 ± 4.04 44.96 ± 3.38 50.21 ± 4.01 31.07 ± 2.67
Flower no. 7.67 ± 0.18 9.19 ± 0.38 9.19 ± 0.28 9.55 ± 0.24 9.31 ± 0.30 9.15 ± 0.29 9.87 ± 0.22
Flowering date 3.80 ± 0.19 2.88 ± 0.15 6.99 ± 0.27 3.90 ± 0.23 3.43 ± 0.20 3.74 ± 0.18 4.71 ± 0.18

Relative variability of different characters of parents and F1 hybrids in experiment 1 summarized from Table la

Character Mean σ* of
least variable parent
Mean σ* of
most variable parent
Observed mean σ* of
F1 hybrids
No. of fruit 0.71 0.94 1.07
Av. wt. per fruit 0.08 0.10 0.07
Wt. per plant 3.11 4.31 3.82
Flower no. 0.23 0.30 0.31
Flowering date 0.19 0.25 0.19
All characters 0.86 1.18 1.09
* =σ of mean of ten replicate means.

Means and their standard deviations of the seven replicate means of four inbred lines and three F1 hybrids in experiment 2

  43 x 125 x 7a x 59c
  |_______ _____________ ______| |______ _____________ ______| |______ _____________ ______|
Character |
No. of fruit 14.95 ± 0.63 14.59 ± 0.54 8.51 ± 0.37 11.63 ± 0.49 9.06 ± 0.72 11.17 ± 0.61 8.01 ± 0.34
Av. wt. per fruit 1.54 ± 0.06 1.86 ± 0.04 2.59 ± 0.42 2.37 ± 0.08 2.02 ± 0.08 2.39 ± 0.09 3.17 ± 0.13
Wt. per plant 22.98 ± 1.52 26.83 ± 1.27 21.23 ± 1.68 27.33 ± 2.13 18.32 ± 2.31 26.84 ± 2.30 25.06 ± 1.70

Relative variability of different characters for parents and F1 hybrids in experiment 2 summarized from Table 2a

Character Mean σ* of
least variable parent
Mean σ*of
most variable parent
Observed mean σ* of
F1 hybrids
No. of fruit 0.36 0.69 0.55
Av. wt. per fruit 0.08 0.32 0.07
Wt. per plant 1.63 2.10 1.90
All characters 0.69 1.04 0.84
* = σ of mean of seven replicate means.

Five characters were recorded on each plant in experiment 1 and three in experiment 2. The data on fruit characters refer to records over the first three weeks of fruiting, and all weights are given in ounces. Flower number refers to the number of flowers on the first inflorescence, and the figure for flowering date is the mean for the first flower on the first florescence. Plants that flowered on the first day were scored 1, those on the second day were scored 2, etc., until flowering was complete.


Variability of plot means: The stability of plot (population) means, over a range of conditions, reflects the ability of the genotype to direct and maintain the development of a large number of individuals within certain limits. Given a character with a symmetrical curve of distribution, uniformity among means of genetically identical populations would indicate that development is regulated by the genotype along one predominant pathway and at one predominant rate, irrespective of environmental influences. Where the character distribution is skewed, the use of means to compare interpopulation stability is less informative, and the mode would be more meaningful statistically in respect of developmental processes. But since previous work on this subject has been based on the assumption that the frequency distributions of quantitative characters are usually normal and discussion has centered exclusively on comparison of means, the use of the mode in the treatment of the present data was not adopted.

A measure of the relative stability of the inbred lines and the hybrids over the different conditions under which the replicates were grown, is given by the standard deviation of the mean of ten plot means of each line in experiment I and of seven plot means in experiment 2. These are presented in Tables 1 and 2.

Of the 24 comparisons of stability between F1 hybrids and their parents in Tables la and 2a, 15 of the hybrids fall within the range of the parents in respect of the variability of the mean of the replicates. The estimates for the remaining nine hybrids fall on either side of the parental range—four being above and five below the range of their parents. None of these, however, differed greatly from the corresponding highest or lowest parent. The relative stabilities for the different characters in the two experiments can be assessed from Tables 1b and 2b. Apart from fruit number in experiment 1 the mean standard deviation of characters in F1 hybrids do not fall outside the values of the parents, and the average for all characters is very close to the midparental point. There is no suggestion in this material that hybrids are any more, or any less stable over the range of environments than are the inbred parents. It is worth noting that in respect of the characters, average weight per fruit and flowering date, the hybrids are as stable as the most stable parent, whereas other characters are either intermediate in this respect, or else show "dominance" in the opposite direction. It seems likely that the direction and degree of "dominance" in respect of stability differs for different characters, and therefore, that the degree of stability of the F1 hybrid is a specific property established by the parental genotype rather than that of a genotypic state such as heterozygosis.

Variability of individuals in one environment: Comparisons of the standard deviations of individual plot means (Tables 3. 4 and 5) gives a measure of the relative stability of the different genotypes in the face of small, random. fluctuations during development. Whereas the estimates of variability of the different means examined in the previous section is an attempt to measure the rigidity of genotypic regulation of the mean developmental pathway in various populations, the variability of individual means measures the latitude allowed by a genotype to each individual in development.

Mean standard deviations and their standard deviation of the ten replicates
of four inbred lines and three F1 hybrids in experiment 1

  59 x 42 x 5 x 18
  |______ _____________ ______| |______ _____________ ______| |______ _____________ ______|
Character |
No. of fruit 2.11 ± 0.25 3.04 ± 0.15 3.97 ± 0.37 3.37 ± 0.33 2.71 ± 0.26 3.49 ± 0.22 2.83 ± 0.21
Av. wt. per fruit 0.39 ± 0.04 0.46 ± 0.01 0.28 ± 0.01 0.24 ± 0.02 0.26 ± 0.04 0.40 ± 0.03 0.48 ± 0.03
Wt. per plant 7.63 ± 0.83 7.08 ± 0.67 7.68 ± 0.88 8.54 ± 1.27 9.24 ± 0.96 9.46 ± 0.91 7.16 ± 0.58
Flower no. 1.81 ± 0.16 2.61 ± 0.21 1.79 ± 0.12 2.40 ± 0.20 2.02 ± 0.22 2.24 ± 0.24 3.05 ± 0.19
Flowering date 0.66 ± 0.06 0.70 ± 0.04 2.16 ± 0.21 1.05 ± 0.05 0.90 ± 0.13 0.82 ± 0.07 1.13 ± 0.09

Mean standard deviations and their standard deviation of the seven replicates
of four inbred lines and three F1 hybrids in experiment 2

  42 x 125 x 7a x 59c
  |______ _____________ ______| |______ _____________ ______| |______ _____________ ______|
Character |
No. of fruit 3.33 ± 0.31 3.25 ± 0.29 2.68 ± 0.05 2.81 ± 0.23 2.37 ± 0.25 2.32 ± 0.34 1.83 ± 0.04
Av. wt. per fruit 0.21 ± 0.02 0.30 ± 0.02 0.53 ± 0.04 0.43 ± 0.02 0.32 ± 0.02 0.32 ± 0.04 0.55 ± 0.04
Wt. per plant 4.95 ± 0.44 5.59 ± 0.49 5.64 ± 0.32 6.33 ± 0.76 5.07 ± 0.79 5.46 ± 0.59 5.21 ± 0.55

Relative variability of different characters for parents and F1 hybrids summarized from Tables 3 and 4

Character Mean σ* of least
variable parent
Mean σ* of most
variable parent
Observed mean
σ* of F1 hybrids
No. of fruit 2.40 3.19 3.05
Av. wt. per fruit 0.28 0.46 0.36
Wt. per plant 6.26 7.11 7.08
Flower no. 1.87 2.29 2.42
Flowering date 0.82 1.82 0.86
All characters 2.57 3.20 3.03
* = σ of single plot means.

Summary of covariance, analysis of means and standard deviations in experiments 1 and 2

Character Experiment no. Coefficient of
Coefficient of
Variance ratio
(for testing
adjusted means)
Fruit no. 1 0.1687 0.0438 ± 0.033 ...
2 0.0717 0.0265 ± 0.057 ...
Av. fruit weight 1 -0.0819 -0.0291 ± 0.045 ...
2 0.4704 0.1684 ± 0.049 3.19
Wt. per plant 1 0.2411 0.0592 ± 0.030 ...
2 0.4441 0.1377 ± 0.043 0.64
Flower no. 1 0.3715 0.1380 ± 0.044 1.14
Flowering date 1 0.6553 0.4471 ± 0.063 5.36
For r,  n=68 in experiment 1 and 47 in experiment 2.
For V.R.   n1=6 and n2=62 in experiment 1 and n1=6 and n2=41 in experiment 2.

Of the 11 F1 means which fall outside the range of the parents in the 24 comparisons given in Tables 3 and 4 only three (fruit number in XT/27 and flower number in XT/1 and XT/2) are significant using the F test at one percent probability. It will be shown in Table 6 that differences in levels of variability in respect of flower number are entirely dependent on the magnitude of the means. There is, therefore, no evidence to suggest that the heterozygous individuals possess any characteristic stability over and above that which they inherit from both parents. It will be noted from Table 5 that the stability of flowering date among individuals shows a decided "dominance" of the least variable parent. The same trend in the direction of "dominance" was observed in respect of the stability of plot means for this character (Table ib). Most other characters showed "dominance" in the opposite direction, which also agrees with the observations on the different plot means.

Variability, and the magnitude of the mean: The extent to which variability is dependent on the size of the mean was tested by covariance analysis. A summary is presented in Table 6.

From the data given in the previous tables there appeared to be no reason to suspect a difference between the inbred lines and the hybrids in respect of possible correlations between the means and their standard deviations. The data from all the lines were, therefore, analyzed together for covariance. Four clear instances of correlation between the mean and the standard deviation are established by the analysis. In two of these, weight per plant in experiment 2 and flower number in experiment 1, the variance ratio for testing significance of adjusted plot means shows that the difference between the standard deviations of the different lines can be attributed entirely to differences in their means. The variance ratios for the other two characters which showed a correlation between the mean and the standard deviation suggest that the latter differ to a greater extent than would be expected if the differences were entirely due to the level of the means. In other words, the standard deviation of the different stocks are inherently different, as well as being tied to the magnitude of character expression.

Where there is no correlation between the means and the standard deviations, relative variability can be determined by direct comparisons of the standard deviations given in Tables 3 and 4. Of the characters which behave in this way, only fruit number in the hybrid XT/27 has a significantly different level of variability when compared with both parents. Differences in variability between inbred lines are significant in many cases.


The present data together with those quoted previously for other inbreeding species emphasize the difference that exists between inbreeders and outbreeders in respect of the control of enviromentally induced variability. The mechanism governing the various forms of stability or flexibility which have been recognized in treatments of this subject (see THODAY 1953) are so imprecisely understood, and the evolutionary meaning of variability estimates is so vague (see SIMPSON 1944, pp. 37-42) that a general discussion on the nature and significance of this difference would not seem justified. Nevertheless, there are a few points that appear noteworthy. In discussing the greater developmental homeostasis of heterozygotes in outbreeders, LERNER (1953, p. 108) stressed that the condition was a manifestation of previous selection, and that departure from the breeding system that is normal for the species leads to reduced buffering of developmental process in individuals and, therefore, to greater variability resulting from differences in the environment. On the basis of this hypothesis one is led to expect that in inbreeders, where selection operates mainly on homozygotes, and where hybrids represent a complete departure from the normal breeding system, most inbred lines would show less variability than the F1 hybrid both on the intra- and interpopulation level. Clearly, either the argument developed to explain the variability characteristics of heterozygotes in outbreeders is false, or else the differences in genetic structure resulting from the two breeding systems lead, under selection, to a different pattern of variability control. Of these two possibilities the latter appears to provide the more likely explanation for the failure of extrapolation from the behaviour of outbreeding species. One obvious, relevant difference between the two breeding systems is that homozygotes in outbreeders are relatively more frequent than heterozygous combinations in inbreeders. In the former, where fitness depends on a certain level of obligate heterozygosity, homozygous combinations will appear relatively frequently through segregation, and, thus, selection will operate on both genotypic classes. In obligate inbreeding species, on the other hand, heterozygotes appear only rarely, being dependent only on the rate of mutation. Furthermore, the chance of survival of the rare heterozygote in an inbreeder is extremely low; it will be rapidly eliminated following self-fertilization. Thus in species where self-fertilization is obligatory, selection will operate almost exclusively on homozygous genotypes. The almost complete absence of the heterozygote in inbreeders may explain why the consequences of homozygosity and heterozygosity in respect of the control of variability is not as sharply defined in inbreeders as it is in outbreeders. It may also provide a clue to the cause of the apparent contradiction between breeding systems in relation to LERNER'S general thesis on developmental homeostasis in cross-fertilizing species.

A brief reference may be made to the observations made in the present material on the control by the genotype of the environmental, or nongenetic component of variability. Similar observations have been reported by GILBERT (1960). The inbred, homozygous lines used in the present experiments showed significant differences in interplant variability, and for flowering date there was evidence that the variability level of the least variable parent was transmitted as a "dominant" character. Differences in variability in this material must therefore be due to differences in gene content and not to states of homozygosity or heterozygosity of the genotype. Variability, like everything else, is under the control of the gene, and in inbreeding species no great advantage in exercising the control belongs to either of the genotypic states. Thus, hybrid lines of naturally self-fertilizing species, such as the tomato, do not possess intrinsic advantages in uniformity of behaviour such as have contributed to the success of F1 hybrids in outbreeding species of crop plants.


(1) The relative level of nongenetic variability in respect of five quantitative characters has been compared in six F1 hybrids and eight inbred lines of the tomato.

(2) Both the inter- and intrapopulation level of variability of the F1 hybrids fell within the range of their respective parents. None of the data suggests any intrinsic difference between inbred lines and hybrids in respect of their ability to buffer or to eliminate the variability that is induced by the environment.

(3) In four out of eight instances, the level of variability for certain characters was shown to be correlated with the magnitude of the mean. In two cases where there was significant correlation between the mean and the standard deviation, the differences in variability could not be entirely explained by differences in the means, and in these, different homozygous genotypes conditioned different levels of variability irrespective of the size of the mean.

(4) The characteristic levels of variability of certain parents were found to be transmitted to the F1 hybrids. Generally, the variability of F1 hybrids fluctuated around the mid parental value, but in respect of flowering date low variability was transmitted as a dominant character.

(5) These findings are briefly discussed in relation to the known variability patterns of outbreeding species, and possible reasons for differences in variability patterns resulting from the two breeding systems are suggested.


I wish to thank DR. F. YATES, F.R.S. for the use of the Rothamsted computer, and MR. N. E. GILBERT who has given much valuable advice and assistance with the work.