Genetics 24: 668-696 (1939)
Missouri Botanical Garden and Washington University, St. Louis, Missouri
Received March 20, 1939


IN THE field of mathematics there are numerous problems difficult to solve with finite numbers which become relatively simple when the concept of infinity is introduced. Similarly, though the genetics of species crosses is obscure when considered in terms of single factors, it seemed possible that it might be illuminated if one attempted to consider the total recombination of specific differences. The recombinations in any particular cross could be compared, as a whole, with the particular species combinations from which they arose, or the total recombination in one cross compared with that in another. Such an experiment with Nicotiana Langsdorffii and N. alata was started in 1930 at the John Innes Horticultural Institution. It was carried forward at the Missouri Botanical Garden the following year and at the Bussey Institution of Harvard University from 1931 to 1933 while the author was a staff member of the Arnold Arboretum. Grateful acknowledgment is made to these institutions and to DR. HENRY W. EDMONDS and MRS. RUTH OWNBEY for faithful and expert assistance in collecting the data and preparing it for publication. I am indebted to DR. PRISCILLA AVERY of the University of California for unpublished information in regard to chiasma frequencies. A preliminary account was presented at the Sixth Genetics Congress (ANDERSON 1932), and the chief conclusions were incorporated in a technique (ANDERSON 1936) for the study of hybrid populations. Publication in extenso has been deferred until the conclusions could be checked experimentally with other genera and until certain phases of the work (ANDERSON 1939) could be given a more complete statistical treatment. Though the method is simple it leads to somewhat unexpected conclusions. It furnishes new criteria for the recognition and analysis of hybridization in natural or artificial populations and should prove of practical assistance to the plant breeder.


The species chosen for the cross were two species of Nicotiana which are native to South America (AVERY 1938), Nicotiana alata and N. Langsdorffii. For such an experiment it was desirable to have morphologically dissimilar species which yield hybrids with a high degree of fertility. These conditions are met in relatively few genera. Species which are partially fertile inter se and yet which are morphologically as dissimilar as these two species are most exceptional. In the author's experience they are to be found elsewhere only among the orchids and in the genera Narcissus and Aquilegia. These all present cultural difficulties which prevent their use in large scale experiments. These two species of Nkotiana, however, can be grown readily in greenhouses of experimental gardens and several generations can be grown in one year.

The Nicotiana alata used in the experiment is the clear white, large-flowered sort grown in gardens under the name of N. affinis, COMES, in his monograph (1899) of the genus, designated it as N. alata Lk. and Otto var. grandiflora and concluded that it was merely a cultivated form of N. alata. For the sake of brevity it will be referred to throughout this paper as N. alata. The strain used was obtained from MESSRS. SUTTONS as N. affinis in 1930. Ten plants were grown and were found to belong to at least five inter-fertile, intra-sterile classes, in so far as their cross-sterility relationships were concerned. Two inter-fertile plants, nos. 86-5 and 86-7, were chosen for the experiment. It should be pointed out that such strains as this one have been grown in flower gardens for many years and have been consciously and unconsciously selected during that me for size of flower, whiteness of flower, and proportionally long corolla tubes. They probably therefore have accumulated a number of modifiers for these three characters which might conceivably affect the results of the experiment.

The N. Langsdorffii was obtained from the Royal Botanic Gardens, Kew, England. The plants as grown at the John Innes Horticultural Institution all seemed uniform. An open-pollinated seed capsule from one plant gave rise to sixteen seedlings, all essentially similar. Nos. 55-11 and 35-13 were chosen for the experiment. Nicotiana Langsdorffii has also been garden-grown for many generations but since it is a botanical curiosity rather than a flower for the perennial border, the strain used in this experiment is probably not greatly different genetically from the wild species.

To guard against exceptional results due to the interaction of self-sterility alleles and to detect the presence of exceptional gene differences within the species, the crosses were made as shown in figure 1. Two individuals of each species were selected, and reciprocal intra-specific as well as inter-specific crosses were made. The cross N. alata x N. Langsdorffii is usually sterile but with persistence a number of capsules were obtained. All these crosses were made numerous times so that the parental species could be grown for comparison with each generation. The second generation was obtained in two ways, by selfing F1 plants and by crossing two plants of the F1 with each other. The theoretical basis for discriminating between these two types of F2's has been published elsewhere (ANDERSON 1935) and is discussed below under Selective Fertilization (page 681).

For several reasons the experiment was confined to a study of the flowers: (a) As shown by EAST (1913, 1916) in his classical work on quantitative characters, flower size is less affected by environmental variables than is the size of vegetative parts. (2) Nicotiana alata and N. Langsdorffii do not differ as strikingly in vegetative characters as they do in floral characters.

FIGURE 1.—Chart illustrating the relationships of the families used in this experiment. Rectangles represent families, circles denote individual plants.

Typical flowers of the two species are shown in figure 2 drawn to the same scale. The chief differences may be tabulated as follows:

Nicotiana alata N. Langsdorffii
Corolla clear white Corolla green
Pollen ivory Pollen bright blue
Night blooming Day blooming
Corolla tube long (5.8-8.9 cm) Corolla tube short (1.7-2.1 cm)
Corolla limb wide (2.5-4.0 cm) Corolla limb narrow (0.6-0.9 cm)
Corolla limb deeply lobed Corolla limb scarcely lobed
Corolla lobes serrate, acuminate Corolla lobes broadly crenate

Not all of these differences could be scored readily. Day blooming versus night blooming is affected by temperature and humidity as well as by daylight. After a number of trials this character had to be abandoned. Pollen color is affected by the age of the pollen, particularly in various hybrid combinations which have dark blue pollen in young flowers which fades in bright sunlight to a barely perceptible blue. This character was also difficult or impossible to score in plants which were sterile or semi-sterile and it was therefore abandoned. The crenation of the corolla lob is a very interesting character but the F2 and successive generations presented such variability that it was not possible to work out a simple method of scoring the shapes.

The other characters presented fewer difficulties. When large numbers of plants are grown the green-flowered and white-flowered plants are not absolutely discontinuous in the F2 as had been reported in previous experiments in which fewer plants were grown SACHS-SKALINSKA 1921; EAST 1916). The ratios of green to white suggested that a single gene was involved plus a large number of modifiers. For the purposes of this experiment the plants were scored as pure white (opening flowers pure white untinged by green), yellowish (opening flowers yellow, more or less tinged with green, some of these flowers fading to an almost pure white) and green (flowers various shades of green, not fading to a clear yellow, never appearing whitish). The length of the flower was measured in two ways: (1) The length of the tube. (2) The length of the style (and stigma) from the top of the ovary to the tip of the stigma.

The size of the corolla limb and amount of lobing were scored by measuring the length of the longest lobe and of the shortest of the two adjacent sinuses. The lobing is scored by obtaining the ratio of these two figures, "maximum lobe/adjacent sinus." This gives values of around 1 for N. Langsdorffii and of about 2 or 3 for N. alata. Aside from the fact that it introduces a ratio (or a difference if turned into logarithms) into correlation tables this proved to be an efficient and objective way of scoring lobing and has been used by other experimenters (SMITH 1937).


It will be remembered that the object of the investigation was to consider the actual recombination obtained in the second generation as compared with the total imaginable recombination of all the characters of both parents. For the reasons given above we shall confine our data largely to the corolla. The chief differences between the corollas of the two parental species (fig. 2) are (1) in tube length, (2) in limb width. (3) in the lobing of the limb, and (4) in the color of the corolla. There are many other slight differences, notably in the shape of the margin (irrespective of the lobing), in the pouching of the corolla throat, in pollen color, in time of blooming, etc. A study of the recombination of these four characters, however, will give us an excellent approximation to total recombination of corolla differences.

FIGURE 2.—Representative flowers of (A) Nicotiana alata and (B) Nicotiana Langsdorffii; (C) corolla of N. Langsdorffii.

Tube length and limb width. The correlation diagram in figure illustrates the recombination actually obtained in one F2 of 118 plants. The values of the parental species and of the F1 are shown for comparison. It will be seen that the values of the F2 fall entirely within an ellipse running diagonally across the diagram. Although there is much variability from plant to plant in the second generation, in so far as recombinations of these two characters are concerned, it is as a whole mostly in one direction, that is, from a combination of characters more or less like that of N. Langsdorffii to one more or less like that of the F1 to one more or less like that of N. alata. There is nothing like free recombination of the two characters and the frequencies suggest that, even with an infinitely large F2, a plant with a tube as long as that of N. alata and limb as short as that of N. Langsdorffii would not be achieved.

FIGURE 3.—Correlation between limb width (maximum lobe) and tube length in Nicotiana Langsdorffii, N. alata, one F1 family of 41 plants, and one F2 family of 118 plants. Open circles represent the F1, solid circles the F2, numbers N. Langsdorffii (lower left) and N. alata (upper right).

Tube length and degree of lobing. In figure 4 are presented the data on these two characters, from the same plants which furnished the data for figure 3. It will be seen that though there is a little more freedom of recombination than in the previous case, the recombinations are confined to a diagonal band across the correlation diagram.

FIGURE 4.—Correlation between tube length and lobing in the plants represented in figure 3.

Limb width and degree of lobing. The recombinations of these two characters, for the same F2, are summarized in figure. It will be seen that the situation is substantially the same as in the other two cases.

FIGURE 5.—Correlation between limb width and lobing in the plants represented in figure 3.

Corolla color and corolla shape. The recombination of corolla color and shape are presented graphically in figure 6. For this purpose data from a number of F2 families, all grown in the same year on the same plot, have been summarized. It will be seen that there is a very strong tendency for the flowers which are most like N. alata in shape to be white or whitish and for those which are shaped like N. Langsdorffii to be green. This tendency would appear even more clearly if a three dimensional diagram were prepared which included limb width as well as lobing and tube length This particular phase of recombination has been studied exhaustively by SMITH, in the very similar cross between N. alata and N. Sanderae. He found definite evidence of linkage between corolla shape and genes affecting corolla color (SMITH 1937).

FIGURE 6.—Diagram showing the correlation between tube length, lobing of the corolla, and color of the corolla. Combined data from five F2 families, representing 337 plants. Stippled areas (shown in part) represent values of Nicotiana Langsdorffii (lower left) and N. alata (upper right). Open circles denote plants with white corollas; solid circles, with green corollas; and cross-barred circles, with yellowish (intermediate) corollas. Dots somewhat grouped due to the use of two-place logarithms.

Corolla length and style length. The very slight recombination in these two characters was commented upon by EAST (1916) in his classical experiments. Actual data are presented in figure 7. It will be noted that in this case there is very strong correlation in these two characters in the F1 as well as in the F2. The significance of this fact is discussed below. For the present we need only note that, as in the case of the other flower characters, recombination in the F2 is limited to a narrow ellipse running diagonally across the correlation diagram.

FIGURE 7.—Correlation between tube length and style length in the F1 and F2 represented as in figures 3, 4, and 5.

From the evidence submitted above it is clear that the combinations of the F2, bewildering in their variety though they may seem, are far from a complete shuffling of the traits of the two species. Just how far they fall short of being a complete assortment may be determined by generalizing the data in figures 3 to 7. If we consider the recombinations of any two characters, the actual recombinations obtained form more or less of an ellipse running diagonally across the correlation rectangle from one parental combination to the other.

The frequencies of the correlation diagrams suggest that if larger F2's were raised the ellipses might eventually reach and just include the areas of the parental species. In other words they approach this value as a limit and even in an infinitely large F2 the combinations would still fall in an ellipse whose edges (on its cross axis) would be only slightly nearer to the upper left hand and lower right hand corners than they are in the F2's reported above. As will be shown below there are also good theoretical grounds for such an hypothesis.

FIGURE 8.—Diagrammatic generalization of F2 correlation for two multiple factor characters Solid black: areas of parental species; stippled: area of the F2.

Had we obtained all possible recombinations of these two characters they would be distributed over the entire rectangle. The ratio of the kinds of combinations actually obtained (the frequencies are another matter) to the total combinations which might he imagined will therefore be the ratio of the area of the dark colored ellipse in figure 8 to the area of the entire square. The exact ratio in any particular example will depend upon the shape of the ellipse. It is possible, however, to consider the general case. Whatever the figure of the ellipse it tends to be symmetrical on both its axes. [Exceptions are for the most part due to the use of a scale which is warped in one way or another. The elaboration of a scale which would measure units of equal biological value (WRIGHT 1926) for N. alata, N. Langsdorffli and their recombinatious is an exceedingly intricate, though rather irrelevant, problem. The unadjusted metric scale used in figures 3, 4, 5 and 7 is obviously progressively "inflated" in the direction of N. alata, whose total variability on a true biological scale would be only slightly greater than that of N. Langsdorffii. No simple transformation is very much better. A logarithmic scale is only a slight improvement (fig. 6). In studying figures 3 to 7, therefore, it should be remembered that on scales whose units were of equal biological magnitude along their whole length, the areas of N. Langsdorffii and N. alata would be approximately equal and approximately circular, and the recombination bands across the figures would be symmetrical ellipses.] We may therefore make the easier comparison of one-quarter of the ellipse to one-quarter of the rectangle. In figure 8 this will be the ratio of the area ABC to ABD. Since these two areas have one dimension in common (AB), the ratio between them will be given by some function of a/t. If AC were a straight line both areas would be triangles and the actual ratio would be a/t. We may use it for the purposes of generalization, remembering that the value in any particular example will be somewhat higher or lower, depending upon whether the line AC circumscribes somewhat more area or somewhat less area than would a straight line between these points.

If we consider the recombinations of three characters our correlation surface becomes a correlation solid and the recombinations obtained fall in a spindle-shaped solid connecting two diagonal corners (fig. 11). The spindle and the rectangular solid have one dimension in common and differ by two dimensions. In each of these latter the ratio between the spindle and the outer solid is a/t. The ratio of actual recombinations to total recombinations will therefore be some function of (a/t)2. The general ratio we are looking for will be a function of (a/t)n-1, where n is the number of character differences which are being considered.

In Nicotiana alata x N. Langsdorffii, for example, if we consider only the differences in tube length, in the lobing index, in style length. and in limb width, the ratio will approach (a/t)4-1. From an inspection of figures to the ratio of a to t is seen to be somewhere in the neighborhood of 1 to 4. This means that the recombinations obtained are only (1/4)3=1/64 of the kinds of recombinations which might be obtained with free assortment. These four characters, however, represent only a few of many differences which might be considered between N. alata and N. Langsdorffii. It is therefore certain that the recombinations which we have obtained are only an insignificant fraction of the recombinations possible under free assortment.

FIGURE 9.—Extreme recombinations to be expected with complete recombination of tube length, limb width and lobing of N. alata and N. Langsdorffii. Letters correspond to those used in figures 10 and 11.   FIGURE 10.—Actual extremes obtained among 347 plants of the F2. Letters correspond to those used in figures 9 and 11.

To a non-mathematical mind this may seem too strong a statement. When the data are presented, as for the most part they necessarily must be, in terms of the recombination of two characters at a time, it takes a peculiar sort of geometric imagination to see that the proportion of actual recombinations to total recombinations becomes increasingly smaller as more characters are considered. Anyone who has examined second-generations or backcrosses of species hybrids will have been so impressed by their variability that it will be difficult for him to accept the conclusion that such a mélange is only a small fraction of total recombination. For such biologists, and as a sort of graphical summary of all the data, figures 9 and 10 have been prepared. In figure 9 are illustrated the extreme types of corollas which might be expected in the second generation if there were free recombination of tube length, limb width and lobing. In figure 10 are shown the closest approaches to these extremes, which were actually obtained among 347 F2 plants. In figure ii the data of figures 3 to 7 have been slightly idealized and combined into a three way correlation diagram showing the relation between total recombination for these three characters and the actual recornbinations obtained in the experiment. A comparison of figures 9 and to with figure 11 will show that the mathematical deductions are indeed correct The second generation extremes which at first seemed so variable become impressively uniform when compared to the imaginary recombinations of figure 9.


The data reported above show that the recombinations of the F2, however manifold they may seem, are in reality but a narrow segment the total imaginable recombinations of the parental species. There are in other words, powerful restrictions to character recombination in the F2. These restrictions come under at least four headings:

  1. Gametic elimination
  2. Zygotic elimination
  3. Pleiotropy
  4. Linkage
FIGURE 11.—Diagram of correlation cube for three characters, showing the relation between complete recombination (total cube) and actual recombination (central spindle). Letters mark the positions of the ideal (A to F) and actual (A' to F') extreme recombinations illustrated in figures 9 and 10. Three recombinations (A', B' and C') are supposed to be on the far side of the solid spindle.

Gametic elimination is particularly important in plants because of the long and intricate gametophytic existence preceding the production of the sperm and egg. An indication of the amount of this elimination can be obtained by examining the pollen of the F1 plants. AVERY has recently (1938) made a critical cytological study of the F1 between N. alata and N. Langsdorffii, and reports an average of 44 percent of good pollen as judged by its morphology and staining reactions. While the bulk of the non-viable pollen must, according to her observations, be due to gross irregularities in chromosome distribution (see below, page 689, under linkage), a small percentage may well be due to the formation of gametically inviable recombinations of the two species. It might logically be expected that such combinations would be found more often among extreme recombinations than among those which are close to the original parental types.

How much recombination would be restricted by further gametic elimination during pollen germination, and fertilization we have as yet no means of knowing.

Gametic elimination also occurs due to selective fertilization by the F1 pollen. Precise information is available for only one locus in the germplasm, the self-sterility alleles having been the subject of detailed investigation. Such work as that of JONES (1928), however, makes it probable that various other loci may be affected. The action of the self-sterility locus has been the subject of detailed analysis by EAST and his students (EAST 1929).

The theoretical effect of the interaction of the self-sterility alleles upon character recombination in species crosses has been discussed elsewhere (ANDERSON 1935), and will be considered here only in relation to the cross under discussion. Nicotiana Langsdorffii is homozygous for the self-sterility alleles SfSf. At this locus in N. alata there are a series of self-sterility alleles designated as S1, S2, S3, etc. The essential feature of these self-sterility alleles is that pollen bearing any one of them will not grow rapidly enough to cause fertilization in the styles of a plant which possesses the same allele. A plant of the constitution S3S4, for instance, cannot be fertilized by either S3 or S4 pollen. If we designate the alata parent of the cross we are studying as thereby indicating any two of the self-sterility alleles, (actually one of the alleles was identical with EAST's S10) half of the F1 plants will be of the constitution SfSn and the other SfSm. It is possible to derive an F2 from these plants in two different ways, by selfing an F1 plant, or by crossing plants of these two different constitutions. The results will be as follows:

SfSn selfed = SfSf + SfSn
SfSn x SfSm = SfSf + SfSn + SfSm + SnSm

In the first (selfed F1) there is selective fertilization due to the interaction of the SfSn style and Sn pollen. In the second (F1 x F1) there is complete assortment of the four alleles. For the self-sterility locus the make-up of the F2 will be three-quarters from N. Langsdorffii and only one-quarter from N. alata, instead of the normally expected half and half. The self-sterility gene, however, will not be alone, but will be accompanied by a whole segment of alata genes, probably a half of a chromosome or more (see below). In so far as the genes within this segment affect the morphology of the plant we may expect the first type of F2 to be slightly less like N. alata on the average, than is the second type.

Suppose for instance, that the difference in tube length between N. alata and N. Langsdorffii were due to ten essential genes, one in each chromosome. N. alata would be of the genetic constitution AABBCCDDEEFFGGHHIIJJ and N. Langsdorffii aabbccddeeffgghhiijj and the F1, AaBbCcDdEeFfGgHhIiJj. If we assume no dominance and an additive effect for each gene, then the tube of Langsdorffii would be K+0 units long, that of alata K+20 and the F1 K+10 units long. The frequencies for tube lengths from K+0 to K+20 in the F2 without selective fertilization will be given by the coefficients of (a +b)20 since there are 10 pairs of genes. If one of these ten, however, is closely linked with the self-sterility allele then the frequencies of the male gametic combinations will be given by (a+b)9 rather than by (a+b)10 and the frequencies of the F2 will consequently be those of (a+b)19. These theoretical frequencies for the two types of F1's are graphed in figure 12 for comparison with actual frequencies for tube length and lobing index, obtained in these two types of F1's. Crosses with DR. EAST'S homozygous stock plants made it possible to distinguish between SfSn and SfSm individuals. (One of the sterility alleles was identified as S10 by its cross-incompatibilities, the other was not located among the homozygotes available for test This reaction, however, made it possible to distinguish with certainty between SfSn and SfS10 individuals among the F1's). The theoretical curves are seen to be very similar to those actually obtained. (To make the curves roughly comparable the frequencies have been graphed as percentage of total frequency). It will be seen that the curves for (a+b)20 and (a+b)19 when adjusted to the same total frequency differ (1) in position, (2) in shape, the theoretical curve for selective fertilization having a broader peak. The curves for tube length and lobing index show similar differences. In each case the curve for F1 selfed (selective fertilization) is slightly nearer the range of N. Langsdorffii than is the curve for F1 x F1. Furthermore, in each case, the F2's in which selective fertilization is taking place have a slightly higher proportion of values near the mode.

The differences between the two types of F2's are not quite as great, however, as those predicted on the basis of one gene per chromosome. If, as the work on linkage suggests (see SMITH (1937) and below pp. 684 to 691] there are two or more essential genes per chromosome then we should predict a difference of just such a magnitude between the two types of second generations as was actually observed.

Zygotic elimination. As to how many recombinations are eliminated after fertilization we have as yet no precise information. There are indications that such elimination can take place in the seed capsule, in aging seeds, and shortly after germination. The complexity of the problem is indicated by a comparison of F2's grown in the Bussey greenhouse and in the experimental plots out-of-doors. In the greenhouse the plants were subject to infection with mosaic disease from several interspecific hybrids of Nicotiana which because of their scientific interest were not destroyed in spite of their diseased condition. Though isolated in another range of the greenhouse there was always a small percentage of infection. Out-of-doors there was almost no mosaic but in wet seasons a wilt disease was common.

Since Nicotiana alata is fairly susceptible to mosaic though resistant to wilt while Nicotiana Langsdorffii is susceptible to wilt but very resistant to mosaic, zygotic elimination was quite different in the greenhouse from what it was in the field. The plants which were killed by the wilt were for the most part not yet in flower, yet from those which flowered it was evident that they closely resembled N. Langsdorffii. While the numbers in the greenhouse were too small to be significant the opposite tendency was evident there. No records were kept of these two F2's, which had been grown for another purpose. A precise experiment was planned for the next year but a drier season and better seed-bed sanitation practically eliminated the wilt. From these experiments, however, and from observations of natural hybrids (some of them under controlled conditions) the author is of the opinion that an F2 between any two species is a very sensitive indicator of the environment. The complexion of any particular F2 will be determined by the particular environment in which it was grown as well as by the possibilities inherent in the germ cells which begot it. Even under the so-called standard conditions of a scientific experiment there are numerous uncontrolled variables to which any two species will react differentially. These will include such factors as time of year, sunshine, humidity, temperature, crowding, fumigation, and others. For every differentially selective factor in the environment there will tend to be a selection of F2 segregates. An ideal F2 is as impossible as an ideal environment.

Pleiotropism. One of the severe hindrances to character combination in species crosses is the pleiotropic effect of the genes by which the species differ. As GRÜNEBERG points out in his introduction to the analysis of a lethal mutation in the rat (1938). "The number of observable 'characters' in an organism is infinite. The number of genes which control development is limited. It follows that many, perhaps most, genes must not affect only one organ or character but several at a time. Their effect is manifold." GRÜNEBERG then proceeds to distinguish between "genuine pleiotropism” in which the gene exerts its manifold effect through different primary effects and "spurious pleiotropism" in which a single primary effect results ultimately in manifold effects. He concludes that the cases of pleiotropism which have been reasonably well analyzed are all spurious pleiotropism and that genuine pleiotropism if it does indeed exist will be difficult to demonstrate.

FIGURE 12.—Frequency distributions of F2’s obtained by selfing an F1 (broken line) or crossing two completely compatible F1's (solid line). Left to right: (A) actual results for tube length, (B) actual results for corolla lobing, and (C) theoretical expectations for one gene per chromosome.

There is good evidence that "spurious pleiotropism" is one of the hindrances to recombination in the cross between N. alata and N. Langsdorffii. If a gene exerts its primary effect in more than one chain of developmental processes it may be predicted that other factors, including various environmental agents, will also affect both chains and as a result variation in the two end characters will be correlated even in the absence of gross genic differences, as in the F1. The F1 correlations will therefore be a good measure of the "spurious pleiotropism" of the genes governing their development. The more highly correlated they are in the F1, the greater will be the proportion of common developmental processes and the less will be the chance that a gene may affect one character without affecting the other in a corresponding way.

The characters studied in this experiment which showed significant F1 correlations (table 1) were style length vs. corolla tube length, r = +.89, and lobing vs. limb width, r = +.31. The high correlation of style length and corolla-tube length in the second generation of this cross was commented upon by EAST (1916), though he apparently did not note that it was almost as high in the genicly uniform F1 as in the genicly diverse F2. The fact that the F2 correlation is only slightly higher than that for the F1 would suggest that N. alata has few if any germplasmic differences making for a longer style in addition to those which affect the corolla. A hybrid with the corolla as short as that of N. Langsdorffii and a style as long as that of N. alata (or vice versa) is therefore a physiological impossibility.

Correlation coefficients in the F1 and the F2 of width of corolla limb (m.l.),
corolla lobing (m.l./a.s.), corolla tube length (t.1.), and style length (s.l.).

F1 F2
-.0255 ± .1191 .7196 ± .0299
(m.1. / a.s.)
-.0950 ± .1181 .5326 ± .0445
.8867 ± .0255 .9553 ± .0054
(m.l. / a.s.)
.3105 ± .1077 .7186 ± .0300

Similarly, as might be expected, the lobing of the corolla, is to a certain extent dependent upon its size. The larger the corolla, the greater will be the proportional depth of the sinuses. In this case, however, the F2 correlation (+.71) is much higher than the F1 (+.31). It is evident therefore that N. alata not only has genes which make the limb proportionately larger (and at the same time somewhat more lobed) but also other genes which tend to accentuate the lobing.

The growth of the limb and the amount of its lobing seem to be physiologically independent of the development of the tube. At least they do not have enough developmental processes in common so that fluctuations in one, under ordinary conditions are accompanied to any appreciable extent by corresponding fluctuations in the other.

Genuinely pleiotropic genes, affecting both corolla tube length and limb width or lobing, cannot be excluded as a possibility though at the present time there is no clear-cut evidence either for or against such an assumption.

"Spurious pleiotropism" certainly imposes a severe restriction upon character combinations of the plant as a whole. Nicotiana Langsdorffii is generally in both leaf and flower a smaller, coarser, stubbier species than N. alata. Such general specific differences, affecting aspect and texture throughout the organism, must rest upon factors which are "spuriously pleiotropic" and which therefore exert similar influences in different developmental sequences (ANDERSON and WHITAKER 1934). As might be expected, therefore, the hybrids as a whole present a picture of correlated intermediacies. Although difficult to measure or even to describe in exact terms, each hybrid exhibits a series of correlated characters affecting texture, aspect, leaf-form, flower shape, and inflorescence development. Furthermore in the group as a whole it can be seen that the general degree of intermediacy tends to be the same throughout any particular plant.

Linkage. The following discussion of the hindrance to recombination caused by linkage has been worked out on the basis of the multiple factor hypothesis. In the opinion of the author, this hypothesis, however useful it may be as a working approximation, rests upon slight and indirect evidence. One might better say that it has never been disproved than that it has been conclusively established. Though it will be used in its simplest form in the following discussion, certain modifications would fit the facts quite as well. The better part of the evidence for the multiple factor hypothesis is merely evidence for intranuclear inheritance. From what little is known of the morphology and physiology of chromosomes it would seem possible that in addition to genes there might also be some ground substance (such as long protein chains) which were chemically uniform throughout a chromosome but which differed in species or races. So far as the author is aware there is as yet no evidence, even remotely critical, which will decide between the hypothesis of "genes alone" and that of "genes plus ground substance."

The data reported above contain two independent bits of evidence which, though they will not decide between the original multiple factor hypothesis and such modifications of it, are at least evidence for it or for some very similar hypothesis.

The first of these is the morphological difference between the F2's resulting from an F1 selfed and those from F1 x F1. As has been demonstrated on pp. 680 to 681 the results actually obtained are in harmony with theoretical predictions.

The second piece of evidence relates to the degree of recombination between various multiple factor characters. It will be seen from figure 13 that the three characters, tube length, limb width, and lobing, differed in the extent to which the parental values are recovered among the F2's. Tube length falls far short of reaching the parental extremes, limb width just barely does so, while in lobing the parental mean values are achieved. On the multiple factor hypothesis this would be explained as resulting from the number of essential gene differences for these three characters. The tube length differences on this hypothesis would rest upon the largest number of gene differences, and lobing upon the least. The larger the number of genes in a multiple factor character the greater is the chance of linkages with other characters. We would therefore predict that tube length and limb width would show the greatest amount of linkage and lobing and limb width the least, with the linkage between tube length and lobing being intermediate in value. The correlations of table 1 show that this is indeed the case. The result is somewhat obscured by the physiological correlation between lobing and limb width (shown by the F1 correlation). Were it not for this fact the correlation would be even lower. The results are therefore in accord with the predictions of the multiple factor hypothesis.

FIGURE 13.—Comparison of the degree to which the three characters, tube length, limb width, and lobing, reached the parental values in the same F2. Broken line: 91 plants of Nicotiana Langsdorffii; dotted line: 166 plants of N. alata; solid line 118 F2 plants (LALA-14).

Although no case of multiple factor inheritance has been even approximately worked out factorially, it is evident from what little is known that a very large number of factors must be assumed. One student of problem, RASMUSSON, goes so far as to say (1933) that the number of genes involved in such characters will prove to be nearer to 100-200 than to 2-20 and supports his statement as follows: "The Swedish group of geneticists, most of whom have been occupied for many years in practical scientific breeding work, seem to be unanimous in assuming 100-200 genes, for most quantitative characters in crosses between types not too closely related. In view of the great bulk of experience behind [their] opinion it seems necessary that preference be given to the assumption that a large number of genes determine the proper quantitative characters." WEXELSEN (1934), another student of quantitative characters, has an only slightly different opinion. He says: "In most cases of the plant breeder a very large number of factors are involved in characters such as yield and similar complex traits. A fruitful genetic analysis of quantitative characters should, however, try to find forms that differ only in a few factors, and no doubt such forms can be found even for the more complex characters." "STUDENT" (1934) has calculated the number of genes necessary to explain the results of the Illinois maize selection experiments. While, as he himself is careful to point out, his calculations involve certain unverified assumptions, he concludes that they "afford some evidence" for a gene number "at least of the order of 20-40, possibly of 200-400, and not at all likely to be of the order 5-10."

Summary of published evidence on linkage between multiple factor characters and marker genes.

SAX (1923) beans weight 1 1 0
LINDSTROM (1926) tomatoes weight 2 2 0
LINDSTROM (1931) maize row number 5 4+ 1?
WEXEI.SEN (1934) barley earliness 4 4 0
RASMUSSON (1935) peas flowering time 2 2 0
SMITH (1937) nicotines corolla size 8 8 0

Whether or not one makes an estimate as extreme as RASMUSSON'S it is evident that the number of factors which must ordinarily be assumed to explain breeding results is fairly high. It is a remarkable fact that linkage between marker genes and particular quantitative characters has been found in all but possibly one of the cases which have been adequately investigated in plant material (table 2). Supposedly these genes and characters have as a whole been selected more or less at random. This would indicate that genes for multiple factor characters must indeed be numerous; that on the average there must be at least one important gene for each character in every crossover segment. This would mean that the number of genes per character must be at least in the neighborhood of 50-100. If the number is indeed of this order then a remarkable secondary hypothesis can be formulated; all quantitative characters of an organism are closely linked with one another.

If two quantitative characters have only one gene each which are tightly linked, they should nevertheless show appreciable linkage. For instance, in a cross between aabbccddwwxxyyzz and AABBCCDDWWXXYYZZ, the first four gene pairs affecting one character and the second four another, the two characters will be linked if a is linked with w, even though the other loci are all independent. In this case the F1 will be aw/AW, B/b, C/c, D/d, x/X, Y/y, z/Z. In the F2 the abcd's will be mainly limited to the w's and the wxyz's to the a's. IF the number of genes per character is so high that it approaches one per character per crossover segment, then they are very tightly linked indeed and the linkage as a whole can only be broken after numerous generations of controlled breeding (ANDERSON 1939).

As a demonstration of the tightness of this linkage figure 14 has been prepared, diagramming the possible F2 combinations (without regard to their frequencies) in a cross between two species. The diagram is restricted to a single pair of chromosomes, which differ in six essential genes affecting two different characters. The question of frequencies is not considered The diagram illustrates all the F2 genotypes which would be possible in an F2 of infinite size. The F1 is furthermore considered to be perfectly fertile and no structural differences affecting pairing or crossing-over have been assumed.

Factorially, the two parental chromosome types are assumed to a1,b1,c1,d1,e1,f1, and a2,b2,c2,d2,e2,f2. The factors in bold face type, 'b', 'd', and 'f', affect one character and 'a', 'c,' and 'e,' affect the other. The species diagrammed in white, is supposed to have a minimum value for each of the two characters and the species diagrammed in black is supposed to owe its greater magnitude to the equal and additive effect of each of the six genes for which it is homozygous. (These assumptions are not necessary to the theory, but they make for a simpler and more readily understandable diagram). Each dumbbell shaped figure in the diagram denotes a single F2 genotype, black representing genes from the large species and white those from the small. As shown at the bottom of the diagram, the upper half of the "dumbbell" represents one of the chromosomes, the lower half the sister chromosome. The chromosome is diagrammatically represented in compact zig-zag arrangement a \ b / c \ d / e \ f so that the three factors, a, c, and e affecting one character are pushed towards the top and the other three, (b, d, and f) are pushed towards the bottom. The smaller species is given a base value of 0 for each character. The larger species, by definition, will therefore carry three units of increase in each of its chromosomes, for each character, and its value on the diagram will be six for each.

The diagram is for a short chromosome which regularly has one chiasma and only one, so that only single crossovers are possible. This limits the possible kinds of gametes very severely. If the six genes were in separate chromosomes, sixty-four types of gametes would be possible. Linkage (wholly aside from its effect on frequencies), reduces the number of kinds to twelve.

The significance of the diagram in practical breeding problems is discussed below. The important point here is the demonstration of the corollary of the multiple factor hypothesis outlined above; IF THE NUMBER OF FACTORS AFFECTING A CHARACTER EQUALS OR EXCEEDS ONE PER CROSSOVER SEGMENT, THEN ALL SUCH CHARACTERS WILL BE TIGHTLY LINKED, WITHOUT REGARD TO THE FURTHER RESTRICTIONS IMPOSED BY FREQUENCIES.

The diagram in figure 14 represents an ideal case in which there were no further restrictions imposed by gross differences in chromosome arrangement. Such cases in hybrids between species will be rather exceptional. In the actual example on which this paper is based (N. alata x N. Langsdorffii), AVERY (1938) has demonstrated that there are at least two translocations.

The chief effect of these rearrangements on character recombination will be to increase the percentage of gametic sterility and to tighten the linkage of characters coming in together from either species. AVERY has found, for instance, that in the bulk of the PMC of the F1 there is an association of one quinquavalent, six bivalents and one univalent (1v+6ii+1i). Whether this univalent always represents the same chromosome or not (AVERY is of the opinion that it probably does) it is a chromosome in which there has been no chiasma and therefore no crossing over.

Interchanges and inversions are apparently one of the commonest barriers which separate species and races (DOBZHANSKY 1937). The effect is to suppress crossing over. In actual crosses between species and races, therefore, whether in nature or in the breeding plot, character recombination of multiple factor characters will be very severely restricted.

While linkage will hinder recombination between any two multiple factor characters, the hindrance will become proportionately greater for every additional character which is considered. The total hindrance in the F2 of a species cross is therefore staggeringly great. Its minimum value is in the neighborhood of (2n/2n)N, where n equals the average number of gene differences per crossover segment and N equal the number of such segments in the germplasm (Anderson 1939). In the cross used in this experiment, I am graciously informed by DR. PRISCILLA AVERY, the chiasma frequency is around eleven. If we suppose that the species differ on the average by only four genes per crossover segment (which seems a ridiculously low value) then the total hindrance is in the neighborhood of 1/2048. This means that even though we were to grow an F2 so large that it occupied all the arable land on the earth, we would still be obtaining less than 1/2000 of the gene combinations possible with no linkage. In our actual F2 therefore we have been obtaining only a fraction of this fraction, and in addition there have been the further restrictions imposed by pleiotropy and gametic and zygotic elimination.

FIGURE 14.—Diagram of all the possible F2 combinations (with single crossing-over) of a cross differing for six genes located in one chromosome. Genes (a2b2c2d2e2f2) derived from the "black" species are diagrammed in black, those from the "white" species (a1b1c1d1e1f1) are in outline. The genes are represented in zig-zag arrangement, those affecting the character measured on the vertical axis are above in each chromosome, those affecting the character measured on the horizontal axis are below. Each "black" gene is supposed to cause an increase of one unit and no dominance is assumed.

It was pointed out in beginning this discussion that there are at least four kinds of hindrances to character recombination in species crosses. The evidence suggests very strongly that all four are operating in this particular cross. The evidence unfortunately is not critical enough to make even the crudest estimate of the proportion of the total restriction imposed by each of these. In particular an estimate of the relative importance of pleiotropy and linkage is of the greatest theoretical importance. The experiments reported above yield no critical evidence. The only conclusion which is justified is that the component of these two restrictive forces is very strong indeed.

Our theoretical considerations, therefore, have led to the same conclusions as did our examination of the actual data (that there are very severe hindrances to character combination in species crosses). Though the second generation of the cross between N. alata and N. Langsdorffii presents a bewildering mélange to the eye, it was found to be only a fraction, and a rather insignificant one at that, of the total imaginable combinations which might be made of the characters of the parents. It seems significant that the data and the theoretical considerations should agree and that both should yield estimates of the same order of magnitude.

It remains to ascertain if these results are general or if they are restricted to this particular cross or to similar crosses. For the flowering plants they are general. In the past five years the author has studied intensively, in the field, hybridization in the genera Tradescantia, Iris, Lindernia, Viola and Aster. In so far as character recombination is concerned these studies are in complete agreement with the results obtained in this experiment. It may therefore be concluded that character recombination in crosses between species and races is limited in the second generation to a relatively insignificant fraction of total combination. The combined effect of the various hindrances is so great that even in future generations it can be completely broken down only in terms of geological time.


Because of their bearing upon the recognition and classification of hybrids it is planned to discuss the taxonomic significance of these conclusions in a separate article. For the present the following brief outline will suggest how they may be used as a basis for morphological criteria for the recognition of hybridization in natural populations. For this purpose we may catalogue hybrids (following DARLINGTON (1937) in part) as, (A) Non-recombination and (B) Recombination hybrids. In the first of these classes will go such more or less exceptional cases as:

  1. Amphidiploids, where doubling of the chromosomes eliminates interparental recombinations more or less completely.
  2. Mules; hybrids in which complete or almost complete sterility prevents recombination.
  3. Structural hybrids in which recombination is more or less prevented by the peculiar architecture of the germplasm (Oenothera).

Recombination hybrids include the bulk of what are ordinarily thought of as hybrids. In such hybrids, since the time of the early hybridizers it has been known that the F1 is if anything less variable than the parental species while the second generations and backcrosses show tremendous variation from individual to individual. The experiments reported above demonstrate that in spite of this variation from plant to plant, in the hybrids as a group, the characters of the parental species tend very strongly to stay together.

This fact gives us three useful morphological criteria for hybrid populations. In such populations:

  1. The intermediacy of separate characters will be correlated. Hybrids intermediate in one character will tend to be intermediate in others. Hybrids which are most like either parent in any one character will tend to resemble that parent in all other characters.
  2. Variation between individuals will lessen as parental character combinations are approached.
  3. The novelty of the hybrids will be due to new combinations of parental characters and not to the appearance of new characters. (The only exceptions are teratological upsets in physiologically ill-adjusted hybrids.)

These criteria have already been incorporated in a technique (1936) for the study of hybrid populations. For a detailed description of their application to a particular problem see ANDERSON and TURRILL (1938) or RILEY (1938).


The above conclusions have important bearings upon plant and animal improvement. They demonstrate that there are very severe limits to recombination in crossing species or races. Seldom or never will it be possible to incorporate one or more characters of one species with those of another species without also affecting other characters. If, for instance, we wish to incorporate the earliness of one species with the hardiness of another we shall probably have to content ourselves with combining an intermediate hardiness with an intermediate earliness. The readily possible combinations can be thought of as occupying a relatively narrow band from one parental combination, to the F1, to the other parental combination. Anything away from this band can be achieved, if at all, only after a careful program of crossing and selection.

Those who have had practical breeding experience with species hybrids will recognize the truth of this generalization. Among the bearded irises, for instance, there has been a concerted attempt by iris breeders to incorporate the yellow of Iris variegata into Iris pallida without bringing along such other variegata characteristics as dwarf habit, foliaceous spathes, a zig-zag stem and pencilling on the haft of the sepals. As a result of this attempt many beautiful new varieties have been produced and although the best of these might be said to approach a yellow Iris pallida they still show unmistakable traces of Iris variegata in other characters beside color.

In the genus Narcissus there has been a prolonged attempt to combine the red corona of the poet's narcissi with the flower form and yellow perianth of the trumpet daffodils. The last decade has seen the introduction of yellow hybrids with long red trumpets, but even in these recombinations the shape of the trumpet and of the perianth is still markedly intermediate.

From the standpoint of practical breeding the most important generalization to be drawn from the above experiments is that recombination in the F2 is very strictly limited when the essential gene differences exceed two per crossover segment. This means that practical breeding programs need methods for deciding how the desired recombination which has started in the F2 can most efficiently be continued through subsequent generations. In other words what kinds of F3's or backcrosses are most likely to lead to more desirable recombinations than have already been achieved in the F2? Theoretically this selection should be comparatively simple when combining a particular character from one parent with one from the other, as for instance the size of flower of one species and the hardiness of the other. Much more difficult, theoretically, would be the selection of the most efficient F3's when the same character is coming into the cross from both sides, as for instance when attempting to select the maximum yielding strain by crossing two high yielding strains.

The diagram in figure 14 can be used to demonstrate the theoretical basis for selecting the most efficient F3's. Selfing desirable F2's may lead to extinction of desirable genes not already present, since the desirable F2's fall near that part of the recombination area where there is the greatest genotypical variation within each phenotype (see below). Crossing the best F2's back to either parent will prevent the incorporation of desirable genes not already brought in from the other parent. The most efficient crosses should be between the desirable combinations which are most like one of the parents in one of the characters with those which are most like the other parent in the other character. In the above example of an attempt to combine flower size from one species with hardiness from another the most efficient F3's should be produced by crossing the hardiest of the F2's with flowers like the large parent with the largest flowered of those F2's which were as hardy as the other parent. Such crosses should conserve desirable combinations already achieved and at the same time prevent the loss of ultimately useful genes from either species.

These same facts can be demonstrated more concretely by reference to figure 14. If we take as the desired combination, the lower right hand coner of the correlation diagram (6, 0) then our closest possible approach to it in an F2 are the combinations in cell (4, 2). Ordinary procedure would be to self these, to cross them together, or perhaps to backcross them to one of the parents. On the theory outlined above we should instead make a cross between the combination in cell (6, 4) and the one in cell (2, 0).

The theoretical results of these various procedures are illustrated in figure 15 which shows on grids having the same values as that of figure 14 all the possible combinations to be expected from (A) the cross recommended above, (C) selfing one of the desirable F2's, (D) crossing two of the desirable F2's, and (E, F, G, and H) crossing the desirable F2's back to either parent.

FIGURE 15—Results of selfing, crossing, and backcrossing different F2's of figure 14. Black dots show the position of the parents in each case. Numbers indicate the number of times a combination in each cell can be obtained (irrespective of cross-over frequencies).

Reference to figure 14 will show that as one approaches the center of the diagram the genotypic variation within each phenotype increases enormously. Cell 3,3 for instance has eight genotypes all of which are heterozygous. This property will go up exponentially as the number of chromosome pairs is increased, so that selections from in or near this area will be very unreliable in actual practice. Even with one chromosome pair, however, it will be seen that the recommended cross gives as high a proportion combinations in the desired direction as do the luckiest selections from the best combinations of the F2.

The problem of the most efficient F2 selections becomes much more difficult when the same multiple factor character is coming in from each side of the cross. There is then no morphological indication of the particular germplasm of each F2 individual. Multiple factors may be thought of as markers for the bulk of the germplasm in the same way that single factor characters are markers for a particular piece of a particular chromosome. A cross in which an attempt is being made to combine the high yielding capacities of both parents cannot be treated in this way because the marker (yield) enters the cross from both sides.

This problem has been carefully worked out by RICHEY (1927) and by RICHEY and SPRAGUE (1931) who by a series of backcrosses and selections have solved the problem of conserving the recombinations already achieved without losing genes of potential value. The only defect in their system (which has proven of practical value) is that it is slow and costly. On the basis of the theory outlined above, the use of multiple factor characters as markers might be suggested. Theoretically at least it should make for greater efficiency. The procedure would be as follows: Two multiple factor characters should be chosen which differentiate the two parental lines. These might conceivably be any character such as leaf width, height, tassel branching, cob shape, etc. Characters easily observed, resting upon a large number of factors, and having no direct effect upon yield would probably be the most useful.

As an example suppose that the two strains are characterized as follows: strain A, very branched tassel, narrow leaves; strain B, slightly branched tassel, wide leaves. Then, if the number of factors affecting yield is indeed in the neighborhood of 100-200 as RASMUSSON (1934) estimates, the most efficient choices among the high yielding F2's would be those which come closest to combining one of the marker characters of one parent with the marker character of the other. To be specific: if among the high-yielding backcrosses to A, there could be selected a line with tassels as branched as those of A but with a wider leaf, and from those to B a line with leaves as wide as those of B but with a more branched tassel, a cross between these should give better and quicker results than a cross between parents selected on the basis of yield alone.

Theoretically, the procedure as recommended here is an advance on that recommended by RICHEY and SPRAGUE. They select for backcrosses resembling the non-recurrent parent in toto. We advise selecting backcrosses which come nearest to combining a character from the non-recurrent parent with a character from the recurrent one. Their method would select backcrosses having the most and the largest chunks of non-recurrent germplasm. Ours would select backcrosses in which the two germplasms had been broken into the smallest pieces and most completely intermingled. If the morphological selection had been made concurrently with those based on yield it is among such backcrosses that permanent improvement is to be looked for.


  1. The study of total recombinations is presented as a technique for analyzing the genetics of crosses between species or races.
  2. The cross between Nicotiana alata and N. Langsdorffii was selected for such a study because it was (a) easy to grow, (b) highly fertile in the F1, and (c) between morphologically very dissimilar parents.
  3. The differences between these two species are tabulated. Reasons are advanced for limiting the study to differences in corolla shape and color.
  4. The F2 recombinations of tube-length and limb-width, of tube-length and degree of lobing, of limb-width and degree of lobing, and of corolla-length and style-length are described and discussed. It is shown that in each case there is not even an approach to free recombination of the parental values. Instead recombination is found to be restricted to a narrow segment of the total, running from combinations more or less like one parent to combinations more or less like the F1 to combinations more or less like the other parent. This generalization is shown to hold when recombinations in shape and color are considered simultaneously.
  5. A mathematical formula is developed for generalizing the results obtained from studying recombinations two at a time. From this formula it is estimated that the actual character recombinations of the above F2's are less than 1/64 of the total imaginable recombinations.
  6. As a graphical demonstration of this assertion, the extreme recombinations of the F2's are compared with the extremes to be expected under total recombination (figures and 10). It is seen that though, the F2's present a bewildering variation from plant to plant they nevertheless are decidedly uniform by comparison with total recombination.
  7. In the light of these results, the known hindrances to character combination are discussed under the following headings: (a) gametic elimination, (b) zygotic elimination, (c) pleiotropism, and (d) linkage. Evidence is brought forward to show that all of these operated to hinder recombination in the above cross.
  8. The hindrances imposed by linkage of multiple factor characters are found to be severe. It is shown that if the number of factors for each such character is as large as is ordinarily postulated then all the multiple factor characters of an organism will be tightly linked with each other, without regard to the further restrictions imposed by frequencies of recombinations.
  9. Theoretical considerations therefore lead to the same conclusion as did the actual data. Recombination in crosses between species and races is limited in the second generation to a relatively insignificant fraction of total recombination.
  10. The application of these conclusions to practical breeding problems is discussed. The limitations of F2 character recombination are shown to impose a severe handicap and methods are described for selecting the most efficient parents for further breeding from among the F2's.
  11. The taxonomic significance of these conclusions is deferred to a future publication. It is shown that they may be used as the basis for morphological criteria for the recognition and measurement of hybridization in natural populations.
  12. The above points summarize the main body of the paper. There are, however, a number of digressions to which reference may be made.
    1. The morphological consequences of gametic elimination through interaction of self-sterility alleles (p. 681).
    2. A description of the effects of pleiotropy in hybrid populations (p. 684).
    3. Two new pieces of evidence favoring the multiple factor hypothesis or some very similar hypothesis.
    4. The suggested use of multiple factor characters as markers for the bulk of the germplasm in the same way that genes are used to mark particular points (p. 695).