[276]

LECTURE X

MENDEL'S LAW OF BALANCED CROSSES

In the scientific study of the result of crosses, the most essential point is the distinction of the several characters of the parents in their combination in the hybrids and their offspring. From a theoretical point of view it would be best to choose parents which would differ only in a single point. The behavior of the differentiating character might then easily be seen.
Unfortunately, such simple cases do not readily occur. Most species, and even many elementary species are distinguished by more than one quality. Varieties deviating only in one unit-character from the species, are more common. But a closer inspection often reveals some secondary characters which may be overlooked in comparative or descriptive studies, but which reassume their importance in experimental crossings.
In a former lecture we have dealt with the qualities which must be considered as being due to the acquisition of new characters. If we [277] compare the new form in this case with the type from which it has originated, it may be seen that the new character does not find its mate, or its opposite, and it will be unpaired in the hybrid.
In the case of retrogressive changes the visible modification is due, at least in the best known instances, to the reduction of an active quality to a state of inactivity or latency. Now if we make a cross between a species and its variety, the differentiating character will be due to the same internal unit, with no other difference than that it is active in the species and latent in the variety. In the hybrid these two corresponding units will make a pair. But while all other pairs in the same hybrid individuals consist of like antagonists, only this pair consists of slightly unlike opponents.
This conception of varietal crosses leads to three assertions, which seem justifiable by actual experience.
First, there is no reason for a diminution of the fertility, as all characters are paired in the hybrid, and no disturbance whatever ensues in its internal structure. Secondly, it is quite indifferent, how the two types are combined, or which of them is chosen as pistillate and which as staminate parent. The deviating pair will have the same constitution in both cases, being [278] built up of one active and one dormant unit. Thirdly this deviating pair will exhibit the active unit which it contains, and the hybrid will show the aspect of the parent in which the character was active and not that of the parent in which it was dormant. Now the active quality was that of the species, and its latent state was found in the variety. Hence the inference that hybrids between a species and its retrograde variety will bear the aspect of the species. This attribute may be fully developed, and then the hybrid will not be distinguishable from the pure species in its outer appearance. Or the character may be incompletely evolved, owing to the failure of cooperation of the dormant unit. In this case the hybrid will be in some sense intermediate between its parents, but these instances are more rare than the alternate ones, though presumably they may play an important part in the variability of many hybrid garden-flowers.
All of these three rules are supported by a large amount of evidence. The complete fertility of varietal hybrids is so universally acknowledged that it is not worth while to give special instances. With many prominent systematists it has become a test between species and varieties, and from our present point of view this assumption is correct. Only the test is of little use in practice, as fertility may be diminished [279] in unbalanced unions in all possible degrees, according to the amount of difference between the parents. If this amount is slight, if for instance, only one unit-character causes the difference, the injury to fertility may, be so small as to be practically nothing. Hence we see that this test would not enable us to judge of the doubtful cases, although it is quite sufficient as a proof in cases of wider differences.
Our second assertion related to the reciprocal crosses. This is the name given to two sexual combinations between the same parents, but with interchanged places as to which furnishes the pollen. In unbalanced crosses of the genus Oenothera the hybrids of such reciprocal unions are often different, as we have previously shown. Sometimes both resemble the pollen parent more, in other instances the pistil-parent. In varietal crosses no such divergence is as yet known. It would be quite superfluous to adduce single cases as proofs for this rule, which was formerly conceived to hold good for hybrids in general. The work of the older hybridists, such as Koelreuter and Gaertner affords numerous instances.
Our third rule is of a wholly different nature. Formerly the distinction between elementary species and varieties was not insisted upon, and the principle which stamps retrograde changes [280] as the true character of varieties is a new one. Therefore it is necessary to cite a considerable amount of evidence in order to prove the assertion that a hybrid bears the active character of its parent-species and not the inactive character of the variety chosen for the cross.
We may put this assertion in a briefer form, stating that the active character prevails in the hybrid over its dormant antagonist. Or as it is equally often put, the one dominates and the other is recessive. In this terminology the character of the species is dominant in the hybrid while that of the variety is recessive. Hence it follows that in the hybrid the latent or dormant unit is recessive, but it does not follow that these three terms have the same meaning, as we shall see presently. The term recessive only applies to the peculiar state into which the latent character has come in the hybrid by its pairing with the antagonistic active unit.
In the first place it is of the highest importance to consider crosses between varieties of recorded origin and the species from which they have sprung. When dealing with mutations of celandine we shall see that the laciniated form originated from the common celandine in a garden at Heidelberg about the year 1590. Among my Oenotheras one of the eldest of the recent productions is the O. brevistylis or short [281] styled species which was seen for the first time in the year 1889. The third example offered is a hairless variety of the evening campion, Lychnis vespertina, found the same year, which hitherto had not been observed.
For these three cases I have made the crosses of the variety with the parent-species, and in each case the hybrid was like the species, and not like the variety. Nor was it intermediate. Here it is proved that the older character dominates the younger one.
In most cases of wild, and of garden-varieties, the relation between them and the parent-species rests upon comparative evidence. Often the variety is known to be younger, in other cases it may be only of local occurrence, but ordinarily the historic facts about its origin have never been known or have long since been forgotten.
The easiest and most widely known varietal crosses are those between varieties with white flowers and the red- or blue-flowered species. Here the color prevails in the hybrid over the lack of pigment, and as a rule the hybrid is as deeply tinted as the species itself, and cannot be distinguished from it, without an investigation of its hereditary qualities. Instances may be cited of the white varieties of the snapdragon, of the red clover, the long-spurred violet (Viola [282] cornuta) the sea-shore aster (Aster Tripolium), corn-rose (Agrostemma Githago), the Sweet William (Silene Armeria), and many garden flowers, as for instance, the Clarkia pulchella, the Polemonium coeruleum, the Veronica longifolia, the gloxinias and others. If the red hue is combined with a yellow ground-color in the species, the variety will be yellow and the hybrid will have the red and yellow mixture of the species as for instance, in the genus Geum. The toad-flax has an orange-colored palate, and a variety occurs in which the palate is of the same yellow tinge as the remaining parts of the corolla. The hybrid between them is in all respects like the parent-species.
Other instances could be given. In berries the same rule prevails. The black nightshade has a variety with yellow berries, and the black color returns in the hybrid. Even the foliage of some garden-plants may afford instances, as for instance, the purplish amaranth (Amaranthus caudatus). It has a green variety, but the hybrid between the two has the red foliage of the species.
Special marks in leaves and in flowers follow the same rule. Some varieties of the opium poppy have large black patches at the basal end of the petals, while in others this pattern is entirely white. In crossing two such varieties, [283] for instance, the dark "Mephisto" with the white-hearted "Danebrog," the hybrid shows the active character of the dark pattern.
Hairy species crossed with their smooth varieties produce hairy hybrids, as in some wheats, in the campion (Lychnis), in Biscutella and others. The same holds good for the crosses between spiny species and their unarmed derivatives, as in the thorn-apple, the corn-crowfoot (Ranunculus arvensis) and others.
Lack of starch in seeds is observed in some varieties of corn and of peas. When such derivatives are crossed with ordinary starch-producing types, the starch prevails in the hybrid.
It would take too much time to give further examples. But there is still one point which should be insisted upon. It is not the systematic relation of the two parents of a cross, that is decisive, but only the occurrence of the same quality, in the one in an active, and in the other in an inactive condition. Hence, whenever this relation occurs between the parents of a cross, the active quality prevails in the hybrid, even when the parents differ from each other in other respects so as to be distinguished as systematic species. The white and red campions give a red hybrid, the black and pale henbane (Hyoscyamus niger and H. pallidus) give a hybrid [284] with the purple veins and center in the corolla of the former, the white and blue thornapple produce a blue hybrid, and so on. Instances of this sort are common in cultivated plants.
Having given this long list of examples of the rule of the dominancy of the active character over the opposite dormant unit, the question naturally arises as to how the antagonistic units are combined in the hybrid. This question is of paramount importance in the consideration of the offspring of the hybrids. But before taking it up it is as well to learn the real signification of recessiveness in the hybrids themselves.
Recessive characters are shown by those rare cases, in which hybrids revert to the varietal parent in the vegetative way. In other words by bud-variations or sports, analogous to the splitting of Adam's laburnum into its parents, by means of bud-variation already described. But here the wide range of differentiating characters of the parents of this most curious hybrid fail. The illustrative examples are extremely simple, and are limited to the active and inactive condition of only one quality.
An instance is given by the long-leaved veronica (Veronica longifolia), which has bluish flowers in long spikes. The hybrid between [285] this species and its white variety has a blue corolla. But occasionally it produces some purely white flowers, showing its power of separating the parental heritages, combined in its internal structures. This reversion is not common, but in thousands of flowering spikes one may expect to find at least one of them. Sometimes it is a whole stem springing from the underground system and bearing only white flowers on all its spikes. In other instances it is only a side branch which reverts and forms white flowers on a stem, the other spikes of which remain bluish. Sometimes a spike even differentiates longitudinally, bearing on one side blue and on the other white corollas, and the white stripe running over the spike may be seen to be long and large, or narrow and short in various degrees. In such cases it is evident that the heritages of the parents remain uninfluenced by each other during the whole life of the hybrid, working side by side, but the active element always prevails over its latent opponent which is ready to break free whenever an opportunity is offered.
It is now generally assumed that this incomplete mixture of the parental qualities in a hybrid, this uncertain and limited combination is the true cause of the many deviations, exhibited by varietal hybrids when compared with their [286] parents. Partial departures are rare in the hybrids themselves, but in their offspring the divergence becomes the rule.
Segregation seems to be a very difficult process in the vegetative way, but it must be very easy in sexual reproduction, indeed so easy as to show itself in nearly every single instance.
Leaving this first generation, the original hybrids, we now come to a discussion of their offspring. Hybrids should be fertilized either by their own pollen, or by that of other individuals born from the same cross. Only in this case can the offspring be considered as a means of arriving at a decision as to the internal nature of the hybrids themselves. Breeders generally prefer to fertilize hybrids with the pollen of their parents. But this operation is to be considered as a new cross, and consequently is wholly excluded from our present discussion. Hence it follows that a clear insight into the heredity of hybrids may be expected only from scientific experiments. Furthermore some of the diversity observed as a result of ordinary crosses, may be due to the instability of the parents themselves or at least of one of them, since breeders ordinarily choose for their crosses some already very variable strain. Combining such a strain with the desirable qualities of some newly imported species, a new strain may [287] result, having the new attribute in addition to all the variability of the old types. In scientific experiments made for the purpose of investigating the general laws of hybridity, such complex cases are therefore to be wholly excluded. The hereditary purity of the parents must be considered as one of the first conditions of success.
Moreover the progeny must be numerous, since neither constancy, nor the exact proportions in the case of instability, can be determined with a small lot of plants.
Finally, and in order to come to a definite choice of research material, we should keep in mind that the chief object is to ascertain the relation of the offspring to their parents. Now in nearly all cases the seeds are separated from the fruits and from one another, before it becomes possible to judge of their qualities. One may open a fruit and count the seeds, but ordinarily nothing is noted as to their characters. In this respect no other plant equals the corn or maize, as the kernels remain together on the spike, and as it has more than one variety characterized by the color, or constitution, or other qualities of the grains. A corn-grain, however, is not a seed, but a fruit containing a seed. Hence the outer parts pertain to the parent plant and only the innermost ones to the [288] seedling and therefore to the following generation. Fruit-characters thus do not offer the qualities we need, only the qualities resulting from fertilizations are characteristic of the new generation. Such attributes are afforded in some cases by the color, in others by the chemical constitution.
We will choose the latter, and take the sugarcorn in comparison with the ordinary or starch producing forms for our starting point. Both sugar- and starch-corns have smooth fruits when ripening. No difference is to be seen in the young ripe spikes. Only the taste, or a direct chemical analysis might reveal the dissimilarity. But as soon as the spikes are dried, a diversity is apparent. The starchy grains remain smooth, but the sugary kernels lose so much water that they become wrinkled. The former becomes opaque, the latter more or less transparent. Every single kernel may instantly be recognized as belonging to either of the types in question, even if but a single grain of the opposite quality might be met with on a spike. Kernels can be counted on the spike, and since ordinary spikes may bear from 300-500 grains and often more, the numerical relation of the different types may be deduced with great accuracy.
Coming now to our experiment, both starchy [289] and sugary varieties are in this respect wholly constant, when cultivated separately. No change is to be seen in the spikes. Furthermore it is very easy to make the crosses. The best way is to cultivate both types in alternate rows and to cut off the staminate panicles a few days before they open their first flowers. If this operation is done on all the individuals of one variety, sparing all the panicles of the other, it is manifest that all the plants will become fertilized by the latter, and hence that the castrated plants will only bear hybrid seeds.
The experiment may be made in two ways; by castrating the sugary or the starchy variety. In both cases the hybrid kernels are the same. As to their composition they repeat the active character of the starchy variety. The sugar is only accumulated as a result of an incapacity of changing it into starch, and the lack of this capacity is to be considered as a retrogressive varietal mark. The starch-producing unit character, which is active in the ordinary sorts of corns, is therefore latent in sugar-corn.
In order to obtain the second generation, the hybrid grains are sown under ordinary conditions, but sufficiently distant from any other variety of corn to insure pure fertilization. The several individuals may be left to pollinate [290] each other, or they may be artificially pollinated with their own pollen.
The outcome of the experiments is shown by the spikes, as soon as they dry. Each spike bears two sorts of kernels irregularly dispersed over its surface. In this point all the spikes are alike. On each of them one may see on the first inspection that the majority of the kernels are starch-containing seeds, while a minor part becomes wrinkled and transparent according to the rule for sugary seeds. This fact shows at once that the hybrid race is not stable, but has differentiated the parental characters, bringing those of the varietal parent to perfect purity and isolation. Whether the same holds good for the starchy parent, it is impossible to judge from the inspection of the spikes, since it has been seen in the first generation that the hybrid kernels are not visibly distinguished from those of the pure starch-producing grains.
It is very easy to count the number of both sorts of grains in the spike of such a hybrid. In doing so we find, that the proportion is nearly the same on all the spikes, and only slight variations would be found in hundreds of them. One-fourth of the seeds are wrinkled and three-fourths are always smooth. The number may vary in single instances and be a little more or a little less than 25%, ranging, for [291] instance, from 20 to 27%, but as a rule, the average is found nearly equal to 25%.
The sugary kernels, when separated from the hybrid spikes and sown separately, give rise to pure sugary race, in no degree inferior in purity to the original variety. But the starchy kernels are of different types, some of them being internally like the hybrids of the first generation and others like the original parent. To decide between these two possibilities, it is necessary to examine their progeny.
For the study of this third hybrid generation we will now take another example, the opium poppies. They usually have a dark center in the flowers, the inferior parts of the four petals being stained a deep purple, or often nearly black. Many varieties exhibit this mark as a large black cross in the center of the flower. In other varieties the pigment is wanting, the cross being of a pure white. Obviously it is only reduced to a latent condition, as in so many other cases of loss of color, since it reappears in a hybrid with the parent-species.
For my crosses I have taken the dark-centered "Mephisto" and the "Danebrog," or Danish flag, with a white cross on a red field. The second year the hybrids were all true to the type of "Mephisto." From the seeds of each artificially self-fertilized capsule, one-fourth (22.5%) [292] in each instance reverted to the varietal mark of the white cross, and three-fourths (77.5%) retained the dark heart. Once more the flowers were self-pollinated and the visits of insects excluded. The recessives now gave only recessives, and hence we may conclude that the varietal marks had returned to stability. The dark hearted or dominants behaved in two different ways. Some of them remained true to their type, all their offspring being dark-hearted. Evidently they had returned to the parent with the active mark, and had reassumed this type as purely as the recessives had reached theirs. But others kept true to the hybrid character of the former generation, repeating in their progeny exactly the same mixture as their parents, the hybrids of the first generation, had given.
This third generation therefore gives evidence, that the second though apparently showing only two types, really consists of three different groups. Two of them have reassumed the stability of their original grandparents, and the third has retained the instability of the hybrid parents.
The question now arises as to the numerical relation of these groups. Our experiments gave the following results: [293]

Cross 1. Generation 2. Generation 3. Generation

Mephisto 4. 100% Mephisto
| /
| /
| --- 77.5 % Dom.--
| / \
\ / \
>- All Mephisto 9. all hybrids with
/ \ 83-68% dominants and
| \ 17-32% recessives.
| \
Danebrog --- 22.5 % Rec. 100% Danebrog.

Examining these figures we find one-fourth of constant recessives, as has already been said, further one-fourth of constant dominants, and the rest or one half as unstable hybrids. Both of the pure groups have therefore reappeared [293] in the same numbers. Calling A the specimens with the pure active mark, L those with the latent mark, and H the hybrids, these proportions may be expressed as follows:

1A+2H+1L.

This simple law for the constitution of the second generation of varietal hybrids with a single differentiating mark in their parents is called the law of Mendel. Mendel published it in 1865, but his paper remained nearly unknown to scientific hybridists. It is only of late years that it has assumed a high place in scientific literature, and attained the first rank as an investigation on fundamental questions of heredity. [294] Read in the light of modern ideas on unit characters it is now one of the most important works on heredity and has already widespread and abiding influence on the philosophy of hybridism in general.
But from its very nature and from the choice of the material made by Mendel, it is restricted to balanced or varietal crosses. It assumes pairs of characters and calls the active unit of the pair dominant, and the latent recessive, without further investigations of the question of latency. It was worked out by Mendel for a large group of varieties of peas, but it holds good, with only apparent exceptions, for a wide range of cases of crosses of varietal characters. Recently many instances have been tested, and even in many cases third and later generations have been counted, and whenever the evidence was complete enough to be trusted, Mendel's prophecy has been found to be right.
According to this law of Mendel's the pairs of antagonistic characters in the hybrid split up in their progeny, some individuals reverting to the pure parental types, some crossing with each other anew, and so giving rise to a new generation of hybrids. Mendel has given a very suggestive and simple explanation of his formula. Putting this in the terminology of to-day, and limiting it to the occurrence of only [295] one differential unit in the parents, we may give it in the following manner. In fertilization, the characters of both parents are not uniformly mixed, but remain separated though most intimately combined in the hybrid throughout life. They are so combined as to work together nearly always, and to have nearly equal influence on all the processes of the whole individual evolution. But when the time arrives to produce progeny, or rather to produce the sexual cells through the combination of which the offspring arises, the two parental characters leave each other, and enter separately into the sexual cells. From this it may be seen that one-half of the pollen-cells will have the quality of one parent, and the other the quality of the other. And the same holds good for [296] the egg-cells. Obviously the qualities lie latent in the pollen and in the egg, but ready to be evolved after fertilization has taken place.
Granting these premises, we may now ask as to the results of the fertilization of hybrids, when this is brought about by their own pollen. We assume that numerous pollen grains fertilize numerous egg cells. This assumption at once allows of applying the law of probability, and to infer that of each kind of pollen grains one-half will reach egg-cells with the same quality [297] and the other half ovules with the opposite character.
Calling P pollen and O ovules, and representing the active mark by P and O, the latent qualities by P' and O', they would combine as follows: