Mutation Theory, pp. 515-527 (1909)
Hugo de Vries



When a new science comes into the field, it usually happens that certain groups of phenomena, which up to then had been dealt with under other heads, are found to come within its ken. This is happening at the present moment, with the study of variability and that of the dependence of the growth and development of particular organs and characters on nutrition. This connection with nutrition has been studied chiefly from the experimental and biological point of view; whilst the same phenomena have been dealt with by statistical methods from another point of view.

New boundaries are difficult to define, and it will be a long time before an agreement will be reached as to which sections of the theory of nutrition should be included in the science of variability.

In the historical and critical part (Part I, pp. 133 and 137 etc.) I have urged that we had no right to give up the attempt to provide an answer to the question as to the causes of the fluctuating differences between individuals and between homologous organs of one and the same individual. The science of variability must not be satisfied with being a purely descriptive and statistical one; it must, like every other, seek to determine the causes of the phenomena of which it treats.

If polymorphism is excluded on the one side and mutability on the other, the whole range of variability can be described in terms of QUETELET'S law. Then there is the question of the inheritance of these variations. The deviations of the various individuals from the mean are heritable: but not in their entirety; a part is always lost. Regression always takes place, and this usually involves more than one-half and often as much as two-thirds of the original deviation. This is the source of the third principle in the theory of variability: the possibility of an increase of the deviation by means of selection. This increase, which is sometimes spoken of as a heaping up of similar small differences, leads to the so-called accumulation and fixation of characters and thus to the production of improved races.

Exactly the same deviations from the mean as those with which statistics have made us familiar may be brought about, either by chance or by deliberate experiment, by changes in the conditions of nutriment. Characters and organs whose dimensions may be increased or diminished by selections, are also dependent on the conditions of life and in many cases it is very difficult to decide which of the two causes has been most operative.

The recent researches of MAC LEOD and others clearly point to a very close relationship between nutrition and variability. For, broadly speaking, variability is really nothing more than differences in individual strength. The stronger a plant or a branch on a plant is, the greater is the likelihood of deviations in a positive direction; weak plants and sickly branches tend to fluctuate in the opposite direction.

But "individual strength" points clearly to nutrition, if we use this word in its widest sense and especially if we make it include the better opportunity which a plant has of being nourished, as when it has plenty of room and plenty of light, and so forth.

1See C. FRUWIRTH, Die Zuchtung der landwirthschaftlichen Culturpflanzen, 1901.
2GOEBEL, Bot. Zeitung, 1882, p. 357.

If we view the whole field of nutritional phenomena and that of fluctuating variability1 they appear to interlock only to a certain extent. Many statistical inquiries point as little in the direction of such a connection, as the excessively vigorous or feeble growth of weeds and cultivated plants under extreme conditions seem to point to it. But indications that the two phenomena are in fact connected, are by no means lacking. GOEBEL, for example, observed that in Agrimonia Eupatorium the lower, best nourished, flowers of the inflorescence had many more stamens than the upper more feebly nourished ones.2 In the sugar-beet the capsules on the lower part of the stem contain many seeds; those on the upper part and on the small lateral branches contain few, and often only one. Many varietal characters answer the requirements of the gardener only when they are on strong individuals; if the plants are weak they are developed either too little or not at all (e. g. Celosia cristata).

We must make it our business therefore, on the one hand, to study the results of increased and diminished nutrition, by statistical methods; and on the other to deal with the conditions affecting the different groups of individuals, when studying QUETELET'S curves.

An inquiry of this kind will at any rate have one good result: it will bring out more prominently the fundamental distinction between variability and mutability. There are still so many cases in which it is difficult or even, for the present, impossible to define the limits between these fundamentally different principles, that every contribution to a solution of the problem is of value.

Therefore it is most essential from the point of view of the theory of mutability to have a perfectly clear conception of the nature of variability in the narrower sense of the term. Absolute constancy and high variability are regarded by many as diametric opposites; in fact it is believed by those who hold the modern theory of selection, that variability leads to inconstancy, that is to say to the production of new forms. According to the mutation theory however constancy and variability are perfectly compatible and, in most cases, usually associated. That which is constant is the type or mean, on both sides of which fluctuations may occur.

1Page 135 of this book. 2Pages 138-143
3Page 147 and Othonna crassifolia in Kruidkundig Jaarboek, Gent, 1900, p. 20.
4Over het periodisch optreden van anomalien, Kruidkundig Jaarboek Dodonaea, T. XI, 1899, p. 54; Sur la périodicité des anomalies dans les plantes monstrueuses, Archiv. Néerland. d. Sc. exactes et nat., 2d Series, T. 3, p. 403. Ueber Curvenselection bei Chrysanthemum segetum, Berichte d. d. bot. Ges., Bd. XVII, 1899, p. 84; Ueber die Periodicität der partiellen Variationen; ibid., Bd. XVII, p. 5.
5A. WEISSE, Die Zahl der Randblüthen am Compositenköpfchen, Jahrb. f. w. Bot., Ed. 30, 1897, p. 453 and W. HAACKE, Entwickelungsmechanische Untersuchungen, Biol. Centralbl., 1900.

The ray florets of the common cornflower are variable in number; the weaker the plant or branch the smaller is this number, according to MAC LEOD.1 The secondary fruits of Papaver somniferum polycephalum exhibit the same correlation,2 the tongue-florets in the heads of Othonna crassifolia diminish if the nutrition of the plant is artificially curtailed.3 The same thing happens in Chrysanthemum segetum4 and other Composites.5 And we can easily observe that in the Umbelliferae the number of umbels is small in proportion as the twig, bearing them is weak.

With regard to Papaver somniferum polycephalum we saw in the first part that it was not possible to separate selection from nutrition. I mean, if we choose our seedparent, paying attention to the greater or less beautiful development of the circlet of secondary fruits, we inevitably chose either the strongest or the weakest plants. There seems therefore no escape from the conclusion that the variability of this circlet is simply a phenomenon of nutrition and that selection in one direction merely chooses the most highly nourished individuals; and in the other, the most poorly nourished.

1VON SEELHORST, Journal für Landwirthschaft, Bd. 48, p. 163; Reference in Botan. Centralbl., 1900, No. 41, Bd. 84, p. 54.

In an investigation of this kind one must take into account the susceptible period. One organ will pass through this period earlier; another later, as I have pointed out in the case of the poppy referred to. The same is true of oats and wheat in relation to the amount of water in the soil. In the first vegetation-period this condition influences the number of internodes in the haulm as well as in the panicles, or ears. At the time of shooting, the amount of water in the ground affects the length of the internodes, and the size of the parts of the inflorescence (the foundations of which have already been laid down by this time) as well as the greater or less fertility of the ears. Much water at the time of shooting increases the amount of straw as well as the yield in grain.1

1W. JOHANNSEN, Ueber die Variabilitat der Gerste mit besonderer Rücksicht auf das Verhältniss zwischen Körnergewicht und Stickstoffprocent. Meddelelser fra Carlsberg Laboratoriet, Bd. 4, Heft 4, 1899.

The truth of the theory put forward by SCHINDLER and VON PROSKOWETZ that it is impossible to unite many good qualities in one individual, depends partly on the absolute productive capacity and partly on the correct nourishment of the individual qualities at the sensitive period of their development. JOHANNSEN'S exhaustive and epoch-making researches into the correlation between seed-weight and nitrogenous contents of barley point in the same direction. The heavier the grain the greater is the amount of nitrogen which depreciates the value of the grain.1 Evidently both vary in the same direction under the influence of high nutrition. But if the sensitive periods for the two should not coincide, the supply of nutriment might be so managed that the weight of the seed is increased without effecting a corresponding increase in those constituents of the seed which are rich in nitrogen. At present it is not possible to do this directly, but JOHANNSEN succeeded in getting a much better harvest without having increased its proportion of nitrogen, by selecting the one value in a positive direction and the other in a negative one.

A further series of experiments is necessary before the conclusions (important alike to the pure and applied biologist) based on these remarkable results can be regarded as thoroughly established. I am simply using them here as a proof of the relation between nutrition and selection in general.

For there is yet another method of studying the relation between manuring and selection. We can alter both factors; and allow them to operate either in the same or in opposite directions. We can, so to speak, add their effects or subtract the one from the other. If this experiment succeeds it proves that the two phenomena are of the same order, and suggests a method of determining their relative importance.

I shall therefore describe in this chapter a series of experiments carried out on this principle. They deal with measurable or countable characters which are capable of experimental as well as of statistical treatment. I chose for this purpose the length of the fruits of the ordinary Oenothera Lamarckiana (Figs. 114 and 115, pp. 529 and 530), and also the material employed by LUDWIG which is afforded by the ray florets of Composites and the rays in the umbels of Umbelliferae (Figs. 117-119, pp. 561-565). In the case of the fruits I tried both the addition and subtraction of the factors; but in that of the ray-florets and the rays of the umbels only the simultaneous operation in opposite directions of heavy manuring and negative selection. The result of the experiment was that sometimes the one factor and, at other times, the other predominated.

The inquiry into the effect of nutrition (manuring, plenty of room, light and water, etc.) has led to the discovery of two principles (foreshadowed in the discussions in the first section p. 137) which I think ought to be enunciated here in the interest of a clear understanding of the whole range of phenomena.

 These two principles are the following:

1. The younger a plant is the greater is the influence of external conditions on its variability, that is, on the place which its various characters will occupy in the curves of variability of the whole culture or race.

1Sometimes, however, a greater effect can be produced on variation by a good or bad treatment of the seedlings than by the choice of seeds; for example in Papaver somniferum polycephalum.

2. In connection with this principle the nutrition of the seed on the motherplant has, in many cases at any rate,1 a greater effect on variability than nutrition during germination and vegetative life itself.

It seems to me that these principles which I only appreciated after many years of experimenting, are now perfectly clear and evident.

From these principles there follows the experimental method which I call the Principle of the manuring of the parent-plant. That is to say, the effect of manuring on variability must be studied not only on the plants which have been heavily manured, but mainly on the generation produced by their seeds.

These principles lead to a further problem, the solution of which will perhaps be of great importance from the point of view of the theory of selection. For it is clear that the principle of the manuring of the parentplants is not necessarily confined to one generation. We shall obviously not get the best nourished seeds from ill favored parents; that is from parents which have themselves arisen from poor seeds. On the contrary the operation of high nutrition of the seeds must be capable of accumulation through two or more generations. The same is true of low or defective nutrition. But inasmuch (as a general rule) those individuals which exhibit the character dealt with in a high degree are the best nourished we naturally choose the most highly nourished individuals as seed-parents when we are selecting for any particular character. In the course of generations the effect of nutrition accumulates, and in this way the deviation of the particular character from the original type is continuously increased. The question arises therefore: what part of the result of selection is due to this accumulation of nutrition during the succeeding generations?

1Part I, 9 9, p. 8.c.

These considerations tend to draw selection and nutrition closer and closer together. The exact mode of nutrition seems to me a matter of secondary importance; what is of the first importance is to discover the effects of nutrition on the susceptible periods in development, and to study the accumulation of this effect in the course of some generations. Now, just as nutrition reaches its maximum effect, in practice, in the course of a few generations, so the limit reachable by selection is very soon attained.1 The significance of the parallel between these two limits seems to me to be obvious.

The closer variability is drawn towards nutrition the wider becomes the gulf between variability and mutability.


The effect of nutrition and selection can either be exerted in similar or in opposite directions; the sum of, or the difference between, their effects can thus be determined.

The general effect of both factors is well known. We are not concerned to prove that the effect of high nutrition is to produce large fruits, and that that of insufficient manure is to produce small ones, and so forth. It seems more important to show that the number of rayflorets can either be increased or diminished by selection: but even on this point there is no doubt whatever. The only question is which of these two factors will preponderate in given instances?

1GALTON'S Natural Inheritance is indispensable for a proper understanding of the foundations of this method and the reader is advised to refer to it in conjunction with this chapter.
2My experiments were made in 1892-1894, i.e., before the publications of these authors had appeared.

The experimental part of the work is to provide the nutrition, i.e., generally favorable conditions of cultivation. The results, however, have to be dealt with by statistical methods which were originated by QUETELET and GALTON1 and have been developed in recent years amongst others by PEARSON, LUDWIG, DUNCKER, DAVENPORT and AMANN.2

Let us begin with the latter point and let us seek to delineate the main features of this method in a few short paragraphs in order that we may have a clear idea of the manner in which they are employed. I have chosen GALTON'S method as the simplest and most convenient for the latter purpose.

QUETELET and GALTON have shown that the individual variations of men and other animals follow the laws of probability. The deviations from the type of any fluctuating character can be expressed by a curve since they are grouped symmetrically round the type as a center of greatest density. The more numerous the observations the more exactly does the curve of variability coincide with the curve of probability. The cause of this parallel is, pretty obviously, that the various deviations from the normal are determined by a vast number of external and internal influences.

1See Ber. d. d. Bot. Gesellsch., Bd. XII, 1894, p. 197, where the previous literature is cited.

QUETELET asserted that the above law applied to plants and GALTON demonstrated it by a few experiments. My cultures of races and varieties extending, as they have done, over many years, have given me plenty of opportunity of convincing myself of its general applicability in the vegetable kingdom.1

When it is once proved that the form of the empirical curve of fluctuations in plants coincides with that of the theoretical curve of probability, so far as unavoidable errors in observation permit, the properties of the latter may evidently be ascribed to the former.

The most important property of the curve for our purposes is that it may be definitely described by two magnitudes, (I) the mean value of the character in question and (II) the amplitude or extent of variation. The mean value used by GALTON is that magnitude which half of the individuals exceed, but which the other half do not attain. This he calls the median. It need not be a magnitude which actually exists, but is found by interpolation on the assumption that variation is unbroken and continuous.

GALTON'S median can be determined more easily than the ordinary mean, which is obtained by dividing the sum of all values by the number of observations. It has exactly the same justification and in symmetrical curves the two necessarily coincide.

The second factor is the amplitude of variation which finds its simplest expression in the remoteness of the extreme variants, provided that the number of individuals is not too small. But the rarity of these extremes makes the determination of these limits by their simple observation largely a matter of chance. GALTON therefore uses another value borrowed from the theory of probability, as a measure of the amplitude. This is the magnitude of the deviation from the mean which is exceeded by a quarter of the individuals and therefore analogous to the so-called "probable error." He calls it the Quartile (Q)

There is obviously one quartile on either side of the Median (M) ; these are called Q1 and Q2. If the curve is symmetrical, the two quartiles have the same value; otherwise the dissimilarity of the empirically determined Q1 and Q2 is a measure of the degree of symmetry of the curve. If the difference between the two is within the range of the error of observation, their mean value Q = (Q1+Q2)/2 is the measure of the amplitude of variation of the material under consideration.

1ED. VERSCHAFFELT, Ueber graduelle Variabilität von pflanzlichen Eigenschaften, Ber. d. d. bot. Gesellsch., Vol. XII, 1894, p. 350.

If we wish to compare the amplitude for different characters together we must reduce them to a common measure. This is done by dividing Q by M.1

We see therefore that Q1, M and Q2 are the numbers which have to be determined by observation. The form of the curve is determined by them and any differences between the curves so determined and the actual figures themselves must be ascribed to errors in observation, at any rate in symmetrical curves. The greater the number of observations which go to make a curve the smaller will these differences be.

In the following sections I shall deduce these values from the data; and use them as a basis for discussion. One advantage of this will be that it will render drawings of the curves superfluous, or at any rate only useful for the purpose of demonstration; and that it will compress the numerical material into a few figures.

A few remarks on the subject of construction of these curves (Figs. 115-118) are called for. The number of ordinates is by no means necessarily the same as the number of groups in the tables. This is sufficiently evident where we are dealing with continuous variations. such as length. For here the unit chosen is quite an arbitrary one. For example, if I had measured the fruits of Oenothera accurately to two millimeters only (or if I had measured them in English inches), I should have had fewer ordinates; but if I had measured them to half a millimeter, I should have had twice as many. And in dealing with ray-florets we may consider units or pairs or larger groups. In fact the data may be grouped in any desired way, to suit our purposes.

The number of units to be used in the construction of a curve depends in principle on the number of individuals. If this is small, they must be made correspondingly few. In order to do this the two or three groups of figures, in the midst of which the interpolated value of M lies, are united to form a single ordinate; this forms the apex of the curve. We then deal with the groups to the right and to the left of it in the same way. This is the only way in which the peaks and valleys, in the curve, resulting from an insufficient number of observations can be smoothed away.

Finally, if the various curves are to be compared with one another, the empirical data must of course be reduced to percentages.

Fig. 115. Oenothera Lamarckiana. Curve exhibiting variation in the length of fruits of 568 plants. The dotted line is that given by the Quetelet-Galton law. Hilversum, 1893.

Fig. 116. A, B, C, Oenothera Lamarckiana. Shifting of the variability curves by selection and nutrition. Graphic exhibition of the tables in this section. Curve D, Oenothera rubrinervis, exhibits the result (described in the following section) of high nutrition without selection. The figures under the abscissae are the mean fruit-lengths in millimeters.

Fig. 117. Anethum graveolens. Curves of the rays of the terminal umbel. The numbers under the abscissae refer to the rays of the primary umbel. In accordance with the rule discussed on page 527 the number of ordinates is half the number of groups in the table. The figure 8 therefore means eight and nine rays and so forth.
A. (56 plants) Curve of 1892, irregular on account of the small number of individuals. It is also asymmetrical being drawn out more to the right.
B. (518 plants) Curve of the following generation 1893. As a result of nutrition and selection it has become nearly symmetrical.

Fig. 118. Chrysanthemum segetum. Curves of the ray-florets of the terminal inflorescences. Under the abscissa are the numbers of these florets. The number of ordinates is reduced to the half; 8 therefore means 7-8 ray florets etc. (height: 1 mm = 1%)

A (97 plants) Dimorphic curve from a mixed sowing 1892.

B (162 plants) By the selection of plants belonging to the group with 13-14 florets as seed-parents the curve has become monomorphic in the next generation, 1893.
— The curve for 1894 was almost exactly the same as that for 1893.