On the ground of such a comparison we may thus a.s.sert that, fluctuations, however different the organs or qualities observed, are the same whenever their curves are seen to overlap one [738] another.

Furthermore, whenever an empirical curve agrees in this manner with the theoretical one, the fluctuation complies with Quetelet's law, and may be ascribed to quite ordinary and universal causes. But if it seems to diverge from this line, the cause of this divergence should be inquired into.

Such abnormal curves occur from time to time, but are rare.

Unsymmetrical instances have already been alluded to, and seem to be quite frequent. Another deviation from the rule is the presence of more than one summit. This case falls under two headings. If the ray florets of a composite are counted, and the figures brought into a curve, a prominent summit usually corresponds to the average. But next to this, and on both sides, smaller summits are to be seen. On a close inspection these summits are observed to fall on the same ordinates, on which, in the case of allied species, the main apex lies. The specific character of one form is thus repeated as a secondary character on an allied species. Ludwig discovered that these secondary summits comply with the rule discovered by Braun and Schimper, stating the relation of the subsequent figures of the series. This series gives the terms of the disposition of leaves in general, and of the bracts and flowers on the composite flower [739] heads in our particular case. It is the series to which we have already alluded when dealing with the arrangement of the leaves on the twisted teasels. It commences with 1 and 2 and each following figure is equal to the sum of its two precedents. The most common figures are 3, 5, 8, 13, 18, 21, higher cases seldom coming under observation. Now the secondary summits of the ray-curves of the composites are seen to agree, as a rule, with these figures. Other instances could readily be given.

Our second heading includes those cases which exhibit two summits of equal or nearly equal height. Such cases occur when different races are mixed, each retaining its own average and its own curve-summit. We have already demonstrated such a case when dealing with the origin of our double corn-chrysanthemum. The wild species culminates with 13 rays, and the grandiflorum variety with 21. Often the latter is found to be impure, being mixed with the typical species to a varying extent. This is not easily ascertained by a casual inspection of the cultures, but the true condition will promptly betray itself, if curves are constructed. In this way curves may in many instances be made use of to discover mixed races. Double curves may also result from the investigation [740] of true double races, or ever-sporting varieties.

The striped snapdragon shows a curve of its stripes with two summits, one corresponding to the average striped flowers, and the other to the pure red ones. Such cases may be discovered by means of curves, but the const.i.tuents cannot be separated by culture-experiments.

A curious peculiarity is afforded by half curves. The number of petals is often seen to vary only in one direction from what should be expected to be the mean condition. With b.u.t.tercups and brambles and many others there is only an increase above the typical five; quaternate flowers are wanting or at least are very rare. With weigelias and many others the number of the tips of the corolla varies downwards, going from five to four and three. Hundreds of flowers show the typical five, and determine the summit of the curve. This drops down on one side only, indicating unilateral variability, which in many cases is due to a very intimate connection of a concealed secondary summit and the main one. In the case of the bulbous b.u.t.tercup, _Ranunculus bulbosus_, I have succeeded in isolating this secondary summit, although not in a separate variety, but only in a form corresponding to the type of ever-sporting varieties.

[741] Recapitulating the results of this too condensed discussion, we may state that fluctuations are linear, being limited to an increase and to a decrease of the characters. These changes are mainly due to differences in nourishment, either of the whole organism or of its parts. In the first case, the deviations from the mean are called individual; they are of great importance for the hereditary characters of the offspring. In the second case the deviations are far more universal and far more striking, but of lesser importance. They are called partial fluctuations.

All these fluctuations comply, in the main, with the law of probability, and behave as if their causes were influenced only by chance.

[742]

LECTURE XXVI

As.e.xUAL MULTIPLICATION OF EXTREMES

Fluctuating variability may be regarded from two different points of view. The multiformity of a bed of flowers is often a desirable feature, and all means which widen the range of fluctuation are therefore used to enhance this feature, and variability affords specimens, which surpa.s.s the average, by yielding a better or larger product.

In the case of fruits and other cultivated forms, it is of course profitable to propagate from the better specimens only, and if possible only from the very best. Obviously the best are the extremes of the whole range of diverging forms, and moreover the extremes on one side of the group. Almost always the best for practical purposes is that in which some quality is strengthened. Cases occur however, in which it is desirable to diminish an injurious peculiarity as far as possible, and in these instances the opposite extreme is the most profitable one.

These considerations lead us to a discussion [743] of the results of the choice of extremes, which it may be easily seen is a matter of the greatest practical importance. This choice is generally designated as selection, but as with most of the terms in the domain of variability, the word selection has come to have more than one meaning. Facts have acc.u.mulated enormously since the time of Darwin, a more thorough knowledge has brought about distinctions, and divisions at a rapidly increasing rate, with which terminology has not kept pace. Selection includes all kinds of choice. Darwin distinguished between natural and artificial selection, but proper subdivisions of these conceptions are needed.

In the fourth lecture we dealt with this same question, and saw that selection must, in the first place, make a choice between the elementary species of the same systematic form. This selection of species or species-selection was the work of Le Couteur and Patrick Shirreff, and is now in general use in practice where it has received the name of variety-testing. This clear and unequivocal term however, can hardly be included under the head of natural selection. The poetic terminology of selection by nature has already brought about many difficulties that should be avoided in the future. On the other hand, the designation of the process as a natural [744] selection of species complies as closely as possible with existing terminology, and does not seem liable to any misunderstanding.

It is a selection between species. Opposed to it is the selection within the species. Manifestly the first should precede the second, and if this sequence is not conscientiously followed it will result in confusion.

This is evident when it is considered that fluctuations can only appear with their pure and normal type in pure strains, and that each admixture of other units is liable to be shown by the form of the curves. More over, selection chooses single individuals, and a single plant, if it is not a hybrid, can scarcely pertain to two different species. The first choice therefore is apt to make the strain pure.

In contrasting selection between species with that within the species, of course elementary species are meant, including varieties. The terms would be of no consequence if only rightly understood. For the sake of clearness we might designate the last named process with the term of intra-specific selection, and it is obvious that this term is applicable both to natural and to artificial selection.

Having previously dealt with species-selection at sufficient length, we may now confine ourselves to the consideration of the intra-specific [745] selection process. In practice it is of secondary importance, and in nature it takes a very subordinate position. For this reason it will be best to confine further discussions to the experience of the breeders.

Two different ways are open to make fluctuating variability profitable.

Both consist in the multiplication of the chosen extremes, and this increase may be attained in a vegetative manner, or by the use of seeds.

As.e.xual and s.e.xual propagation are different in many respects, and so they are also in the domain of variability.

In order to obtain a clear comprehension of this difference, it is necessary to start from the distinction between individual and partial fluctuations, as given in the last lecture. This distinction may be discussed more understandingly if the causes of the variability are taken into consideration. We have dealt with them at some length, and are now aware that inner conditions only, determine averages, while some fluctuation around them is allowable, as influenced by external conditions. These outward influences act throughout life. At the very first they impress their stamp on the whole organism, and incite a lasting change in distinct directions. This is the period of the development of the germ within the seed; it begins with the fusion of the s.e.xual cells, and each of them may be influenced [746] to a noticeable degree before this union. This is the period of the determination of individual variability. As soon as ramifications begin, the external conditions act separately on every part, influencing some to a greater and others to a lesser degree. Here we have the beginning of partial variability. At the outset all parts may be affected in the same way and in the same measure, but the chances of such an agreement, of course, rapidly diminish. This is partly due to differences in exposure, but mainly to alterations of the sensibility of the organs themselves.

It is difficult to gain a clear conception of the contrast between individual and partial variability, and neither is it easy to appreciate their cooperation rightly. Perhaps the best way is to consider their activity as a gradual narrowing of possibilities. At the outset the plant may develop its qualities in any measure, nothing being as yet fixed. Gradually however, the development takes a definite direction, for better or for worse. Is a direction once taken, then it becomes the average, around which the remaining possibilities are grouped. The plant or the organ goes on in this way, until finally it reaches maturity with one of the thousands of degrees of development, between which at the beginning it had a free choice.

[747] Putting this discussion in other terms, we find every individual and every organ in the adult state corresponding with a single ordinate of the curve. The curve indicates the range of possibilities, the ordinate shows the choice that has been made. Now it is clear at once that this choice has not been made suddenly but gradually. Halfway of the development, the choice is halfway determined, but the other half is still undefined. The first half is the same for all the organs of the plant, and is therefore termed individual; the second differs in the separate members, and consequently is known as partial. Which of the two halves is the greater and which the lesser, of course depends on the cases considered.

Finally we may describe a single example, the length of the capsules of the evening-primrose. This is highly variable, the longest reaching more than twice the length of the smallest. Many capsules are borne on the same spike, and they are easily seen to be of unequal size. They vary according to their position, the size diminishing in the main from the base upwards, especially on the higher parts. Likewise the fruits of weaker lateral branches are smaller. Curves are easily made by measuring a few hundred capsules from corresponding parts of different plants, or even by limiting the [748] inquiry to a single individual. These curves give the partial variability, and are found to comply with Quetelet's law.

Besides this limited study, we may compare the numerous individuals of one locality or of a large plot of cultivated plants with one another.

In doing so, we are struck with the fact that some plants have large and others small fruits. We now limit ourselves to the main spike of each plant, and perhaps to its lower parts, so as to avoid as far as possible the impression made by the partial fluctuations. The differences remain, and are sufficient to furnish an easy comparison with the general law.

In order to do this, we take from each plant a definite number of capsules and measure their average length. In some experiments I took the twenty lowermost capsules of the main spikes. In this way one average was obtained for each plant, and combining these into a curve, it was found that these fluctuations also came under Quetelet's law.

Thus the individual averages, and the fluctuations around each of them, follow the same rule. The first are a measure for the whole plant, the second only for its parts. As a general resume we can a.s.sert that, as a rule, a quality is determined in some degree during the earlier stages of the organism, and that this determination is valid throughout its [749] life. Afterwards only the minor points remain to be regulated.

This makes it at once clear that the range of individual and partial variability together must be wider than that of either of them, taken alone. Partial fluctuations cannot, of course, be excluded. Thus our comparison is limited to individual and partial variability on one side, and partial fluctuations alone on the other side.

Intra-specific selection is thus seen to fall under two heads: a selection between the individuals, and a choice within each of them. The first affords a wider and the latter a narrower field.

Individual variability, considered as the result of outward influences operative during extreme youth, can be excluded in a very simple manner.

Obviously it suffices to exclude extreme youth, in other words, to exclude the use of seeds. Multiplication in a vegetative way, by grafting and budding, by runners or roots, or by simple division of rootstocks and bulbs is the way in which to limit variability to the partial half. This is all we may hope to attain, but experience shows that it is a very efficient means of limitation. Partial fluctuations are generally far smaller than individual and partial fluctuations together.

Individual variability in the vegetable kingdom [750] might be called seed-variation, as opposed to partial or bud-fluctuation. And perhaps these terms are more apt to convey a clear conception of the distinction than any other. The germ within the unripe seed is easily understood to be far more sensitive to external conditions than a bud.

Multiplication of extremes by seed is thus always counteracted by individual variability, which at once reopens all, or nearly all, the initial possibilities. Multiplication by buds is exempt from this danger and thus leads to a high degree of uniformity. And this uniformity is in many cases exactly what the breeder endeavors to obtain.

We will treat of this reopening of previous possibilities under the head of regression in the next lecture. It is not at all absolute, at least not in one generation. Part of the improvement remains, and favors the next generation. This part may be estimated approximately as being about one-third or one-half of the improvement attained. Hence the conclusion that vegetative multiplication gives rise to varieties which are as a rule twice or thrice as good as selected varieties of plants propagated by seeds. Hence, likewise the inference that breeders generally prefer vegetative multiplication of improved forms, and apply it in all possible cases. [751] Of course the application is limited, and forage crops and the greater number of vegetables will always necessarily be propagated by seed.

Nature ordinarily prefers the s.e.xual way. As.e.xual multiplications, although very common with perennial plants, appear not to offer important material for selection. Hence it follows that in comparing the work of nature with that of man, the results of selection followed by vegetative propagation should always be carefully excluded. Our large bulb-flowers and delicious fruits have nothing in common with natural products, and do not yield a standard by which to judge nature's work.

It is very difficult for a botanist to give a survey of what practice has attained by the as.e.xual multiplication of extremes. Nearly all of the large and more palatable fruits are due to such efforts. Some flowers and garden-plants afford further instances. By far the greatest majority of improved as.e.xual varieties, however, are not the result of pure intra-specific selection. They are due largely to the choice of the best existing elementary species, and to some extent to crosses between them, or between distinct systematic species. In practice selection and hybridization go hand in hand and it is often difficult to ascertain what part of [752] the result is due to the one, and what to the other factor.

The scientist, on the contrary, has nothing to do with the industrial product. His task is the a.n.a.lysis of the methods, in order to reach a clear appreciation of the influence of all the competing factors. This study of the working causes leads to a better understanding of the practical processes, and may become the basis of improvement in methods.

Starting from these considerations, we will now give some ill.u.s.trative examples, and for the first, choose one in which hybridization is almost completely excluded.

Sugar-canes have long been considered to be plants without seed. Their numerous varieties are propagated only in a vegetative way. The stems are cut into pieces, each bearing one or two or more nodes with their buds. An entire variety, though it may be cultivated in large districts and even in various countries, behaves with respect to variability as a single individual. Its individual fluctuability has been limited to the earliest period of its life, when it arose from an unknown seed. The personal characters that have been stamped on this one seed, partly by its descent, and partly in the development of its germ during the period of ripening, have become the indelible characters [753] of the variety, and only the partial fluctuability, due to the effect of later influences, can now be studied statistically.

This study has for its main object the production of sugar in the stems, and the curves, which indicate the percentage of this important substance in different stems of the same variety, comply with Quetelet's law. Each variety has its own average, and around this the data of the majority of the stems are densely crowded, while deviations on both sides are rare and become the rarer the wider they are. The "Cheribon"

cane is the richest variety cultivated in Java, and has an average of 19% sugar, while it fluctuates between 11% and 28%. "Chunnic" averages 14%, "Black Manilla" 13% and "White Manilla" 10%; their highest and lowest extremes diverge in the same manner, being for the last named variety 1% and 15%.

This partial variability is of high practical interest, because on it a selection may be founded. According to the conceptions described in a previous lecture, fluctuating variability is the result of those outward factors that determine the strength of development of the plant or the organ. The inconstancy of the degree of sensibility, combined with the ever-varying weather conditions preclude any close proportionality, but apart from this difficulty there is, in the [754] main, a distinct relation between organic strength and the development of single qualities. This correlation has not escaped observation in the case of the sugar-cane, and it is known that the best grown stocks are generally the richest in sugar. Now it is evident that the best grown and richest stems will have the greater chance of transmitting these qualities to the lateral-buds. This at once gives, a basis for vegetative selection, upon which it is not necessary to choose a small number of very excellent stems, but simply to avoid the planting of all those that are below the average. By this means the yield of the cultures has often noticeably been enhanced.

As far as experience goes, this sort of selection, however profitable, does not conduce to the production of improved races. Only temporary ameliorations are obtained, and the selection must be made in the same manner every year. Moreover the improvement is very limited and does not give any promise of further increase. In order to reach this, one has to recur to the individual fluctuability, and therefore to seed.

Nearly half a century ago, Parris discovered, on the island of Barbados, that seeds might occasionally be gathered from the canes. These, however, yielded only gra.s.s-like plants of no real value. The same observation was made [755] shortly afterwards in Java and in other sugar producing countries. In the year 1885, Soltwedel, the director of one of the experiment stations for the culture of sugar-cane in Java, conceived the idea of making use of seedlings for the production of improved races. This idea is a very practical one, precisely because of the possibility of vegetative propagation. If individuals would show the same range as that of partial fluctuability, then the choice of the extremes would at once bring the average up to the richness of the best stocks. Once attained, this average would be fixed, without further efforts.

Unfortunately there is one great drawback. This is the infertility of the best variety, that of the "Cheribon" cane. It flowers abundantly in some years, but it has never been known to produce ripe seeds. For this reason Soltwedel had to start from the second best sort, and chose the "Hawaii" cane. This variety usually yields about 14% sugar, and Soltwedel found among his seedlings one that showed 15%. This fact was quite unexpected at that time, and excited widespread interest in the new method, and since then it has been applied to numerous varieties, and many thousands of seedlings have been raised and tested as to their sugar-production.

[756] From a scientific point of view the results are quite striking.

From the practical standpoint, however, the question is, whether the "Hawaii" and other fertile varieties are adequate to yield seedlings, which will surpa.s.s the infertile "Cheribon" cane. Now "Hawaii" averages 14% and "Cheribon" 19%, and it is easily understood that a "Hawaii"

seedling with more than 19% can be expected only from very large sowings. Hundreds of thousands of seedlings must be cultivated, and their juice tested, before this improvement can be reached. Even then, it may have no significance for practical purposes. Next to the amount of sugar comes the resistance to the disease called "Sereh," and the new race requires to be ameliorated in this important direction, too. Other qualities must also be considered, and any casual deterioration in other characters would make all progress illusory. For these reasons much time is required to attain distinct improvements.

These great difficulties in the way of selecting extremes for vegetative propagation are of course met with everywhere. They impede the work of the breeder to such a degree, that but few men are able to surmount them. Breeding new varieties necessitates the bending of every effort to this purpose, and a clear conception of [757] the manifold aspects of this intricate problem. These fall under two heads, the exigencies of practice, and the physiologic laws of variability. Of course, only the latter heading comes within the limits of our discussion which includes two main points. First comes the general law of fluctuation that, though slight deviations from the average may be found by thousands, or rather in nearly every individual, larger and therefore important deviations are very rare. Thousands of seedlings must be examined carefully in order to find one or two from which it might be profitable to start a new race. This point is the same for practical and for scientific investigation. In the second place however, a digression is met with.

The practical man must take into consideration all the varying qualities of his improved strains. Some of them must be increased and others be decreased, and their common dependency on external conditions often makes it very difficult to discover the desired combinations. It is obvious, however, that the neglect of one quality may make all improvement of other characters wholly useless. No augmentation of sugar-percentage, of size and flavor of fruits can counterbalance an increase in sensitiveness to disease, and so it is with other qualities also.

[758] Improved races for scientific investigation can be kept free from infection, and protected against numerous other injuries. In the experimental garden they may find conditions which cannot be realized elsewhere. They may show a luxuriant growth, and prove to be excellent material for research, but have features which, having been overlooked at the period of selection, would at once condemn them if left to ordinary conditions, or to the compet.i.tion of other species.

Considering all these obstacles, it is only natural that breeders should use every means to reach their goal. Only in very rare instances do they follow methods a.n.a.logous to scientific processes, which tend to simplify the questions as much as possible. As a rule, the practical way is the combination of as many causes of variability as possible. Now the three great sources of variability are, as has been pointed out on several occasions, the original multiformity of the species, fluctuating variability, and hybridization. Hence, in practical experiments, all three are combined. Together they yield results of the highest value, and Burbank's improved fruits and flowers give testimony to the practical significance of this combination.

From a scientific point of view however, it is [759] ordinarily difficult, if not impossible, to discern the part which each of the three great branches of variability has taken in the origination of the product. A full a.n.a.lysis is rarely possible, and the treatment of one of the three factors must necessarily remain incomplete.