Chapter 6

LECTURE XMENDEL'S LAW OF BALANCED CROSSES

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 genusOenotherathe 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 myOenotherasone of the eldest of the recent productions is theO. brevistylisor 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, theClarkia pulchella, thePolemonium coeruleum, theVeronica 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 genusGeum. 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), inBiscutellaand 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 nigerandH. 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:

P + 0giving uniform pairs with the active mark,P + 0'P + 0' giving unequal pairs,P' + 0P' + 0 giving unequal pairs,P' + 0'P' + 0' giving uniform pairs with the latent mark.

In this combination the four groups are obviously of the same size, each containing one-fourth of the offspring. Manifestly they correspond exactly to the direct results of the experiments, P + O representing the individuals which reverted to the specific mark, P' + O' those who reassumed the varietal quality and P + O' and P + O' those who hybridized [298] for the second time. These considerations lead us to the following form of Mendel's,

P + O= 1/4 Activeor 1A,P + O'P' + O= 1/2 Hybridor 2 H,P' + O'= 1/4 Latentor 1 L

Which is evidently the same as Mendel's empirical law given above.To give the proof of these assumptions Mendel has devised a very simple crossing experiment, [299] which he has effected with his varieties of peas. I have repeated it with the sugar-corn, which gives far better material for demonstration. It starts from the inference that if dissimilarity among the pollen grains is excluded, the diversity of the ovules must at once became manifest and vice versa. In other terms, if a hybrid of the first generation is not allowed to fertilize itself, but is pollinated by one of its parents, the result will be in accordance with the Mendelian formula.In order to see an effect on the spikes produced in this way, it is of course necessary to fertilize them with the pollen of the variety, and not with that of the specific type. The latter would give partly pure starchy grains and partly hybrid kernels, but these would assume the same type. But if we pollinate the hybrid with pollen of a pure sugar-corn, we may predict the result as follows.If the spike of the hybrid contains dormant paternal marks in one-half of its flowers and in the other half maternal latent qualities, the sugar-corn pollen will combine with one-half of the ovules to give hybrids, and with the other half so as to give pure sugar-grains. Hence we see that it will be possible to count out directly the two groups of ovules on inspecting the ripe and dry spikes. Experience teaches us [298] that both are present, and in nearly equal numbers; one-half of the grains remaining smooth, and the other half becoming wrinkled.The corresponding experiment could be made with plants of a pure sugar-race by pollination with hybrid pollen. The spikes would show exactly the same mixture as in the above case, but now this may be considered as conclusive proof that half the pollen-grains represent the quality of one parent and the other half the quality of the other.Another corollary of Mendel's law is the following. In each generation two groups return to purity, and one-half remains hybrid. These last will repeat the same phenomenon of splitting in their progeny, and it is easily seen that the same rule will hold good for all succeeding generations. According to Mendel's principle, in each year there is a new hybridization, differing in no respect from the first and original one. If the hybrids only are propagated, each year will show one-fourth of the offspring returning to the specific character, one-fourth assuming the type of the variety and one-half remaining hybrid. I have tested this with a hybrid between the ordinary nightshade with black berries, and its variety,Solanum nigrum chlorocarpum, with pale yellow fruits. Eight generations of the hybrids were cultivated, [299] disregarding always the reverting offspring. At the end I counted the progeny of the sixth and seventh generations and found figures for their three groups of descendants, which exactly correspond to Mendel's formula.Until now we have limited ourselves to the consideration of single differentiating units. This discussion gives a clear insight into the fundamental phenomena of hybrid fertilization. It at once shows the correctness of the assumption of unit-characters, and of their pairing in the sexual combinations.But Mendel's law is not at all restricted to these simple cases. Quite on the contrary, it explains the most intricate questions of hybridization, providing they do not transgress the limits of symmetrical unions. But in this realm nearly all results may be calculated beforehand, on the ground of the principle of probability. Only one more assumption need be discussed. The several pairs of antagonistic characters must be independent from, and uninfluenced by, one another. This premise seems to hold good in the vast majority of cases, though rare exceptions seem to be not entirely wanting. Hence the necessity of taking all predictions from Mendel's law only as probabilities, which will prove true in most, but not necessarily in all cases. [300] But here we will limit ourselves to normal cases.The first example to be considered is obviously the assumption that the parents of a cross differ from each other in respect to two characters. A good illustrative example is afforded by the thorn-apple. I have crossed the blue flowered thorny form, usually known asDatura Tatula, with the white thornless type, designated asD. Stramonium inermis. Thorns and blue pigment are obviously active qualities, as they are dominant in the hybrids. In the second generation both pairs of characters are resolved into their constituents and paired anew according to Mendel's law. After isolating my hybrids during the period of flowering, I counted among their progeny:

128individuals with blue flowers and thorns47individuals with blue flowers and thorns54individuals with white flowers and thorns21individuals with white flowers and without thorns——250

The significance of these numbers may easily be seen, when we calculate what was to be expected on the assumption that both characters follow Mendel's law, and that both are independent from each other. Then we would have three-fourths blue offspring and one-fourth individuals with white flowers. Each of these [301] two groups would consist of thorn-bearing and thornless plants, in the same numerical relation. Thus, we come to the four groups observed in our experiment, and are able to calculate their relative size in the following way:

ProportionBlue with thorns3/4 X 3/4 = 9/16 = 56.25%9Blue, unarmed3/4 X 1/4 = 3/16 = 18.75%3White with thorns1/4 X 3/4 = 3/16 = 18.75%3White, unarmed1/4 X 1/4 = 1/16 = 6.25%1

In order to compare this inference from Mendel's law and the assumption of independency, with the results of our experiments, we must calculate the figures of the latter in percentages. In this way we find:

FoundCalculatedBlue with thorns128=51%56.25%Blue, unarmed47=19%18.75White with thorns54=22%18.75White, unarmed54=22%6.25%

The agreement of the experimental and the theoretical figures is as close as might be expected.This experiment is to be considered only as an illustrative example of a rule of wide application. The rule obviously will hold good in all such cases as comply with the two conditions already premised, viz.: that each character agrees with Mendel's law, and that both are wholly independent of each other. It is clear that our figures show the numerical composition [302] of the hybrid offspring for any single instance, irrespective of the morphological nature of the qualities involved.Mendel has proved the correctness of these deductions by his experiments with peas, and by combining their color (yellow or green) with the chemical composition (starch or sugar) and other pairs of characters. I will now give two further illustrations afforded by crosses of the ordinary campion. I used the red-flowered or day-campion, which is a perennial herb, and a smooth variety of the white evening-campion, which flowers as a rule in the first summer. The combination of flower-color and pubescence gave the following composition for the second hybrid generation:

Number%CalculationHairy and red704456.25%Hairy and white231418.75%Smooth and red462318.75%Smooth and white19126.25%

For the combination of pubescence and the capacity of flowering in the first year I found:

Number%CalculatedHairy, flowering2865256.25%Hairy without stem1282318.75%Smooth and red961718.75Smooth and white4286.25%

Many other cases have been tested by different writers and the general result is the [303] applicability of Mendel's formula to all cases complying with the given conditions.Intentionally I have chosen for the last example two pairs of antagonisms, relating to the same pair of plants, and which may be tested in one experiment and combined in one calculation.For the latter we need only assume the same conditions as mentioned before, but now for three different qualities. It is easily seen that the third quality would split each of our four groups into two smaller ones in the proportion of 3/4 : 1/4.We would then get eight groups of the following composition:

9/16 X 3/4 = 27/64or42.2%9/16 X 1/4 = 9/64"14.1%3/16 X 3/4 = 9/64"14.1%3/16 X 1/4 = 3/64"4.7%3/16 X 3/4 = 9/64"14.1%3/16 X 1/4 = 3/64"4.7%1/16 X 3/4 = 3/64"4.7%1/16 X 1/4 = 1/64"1.6%

The characters chosen for our experiment include the absence of stem and flowers in the first year, and therefore would require a second year to determine the flower-color on the perennial specimens. Instead of doing so I have taken another character, shown by the teeth of the capsules when opening. These curve outwards [304] in the red campion, but lack this capacity in the evening-campion, diverging only until an upright position is reached. The combination of hairs, colors and teeth gives eight groups, and the counting of their respective numbers of individuals gave the following:

HairsFlowersTeethof capsulesNumber%CalculatedHairyRedcurved914742.2%HairyRedstraight157.514.1%HairyWhitecurved231214.1%HairyWhitestraight178.54.7%SmoothRedcurved231214.1%SmoothRedstraight94.54.7%SmoothWhitecurved52.54.7%SmoothWhitestraight1261.6%

The agreement is as comprehensive as might be expected from an experiment with about 200 plants, and there can be no doubt that a repetition on a larger scale would give still closer agreement.In the same way we might proceed to crosses with four or more differentiating characters. But each new character will double the number of the groups. Four characters will combine into 16 groups, five into 32, six into 64, seven into 128, etc. Hence it is easily seen that the size of the experiments must be made larger and larger in the same ratio, if we intend to expect numbers equally trustworthy. For [305] seven differentiating marks 16,384 individuals are required for a complete series. And in this set the group with the seven attributes all in a latent condition would contain only a single individual.Unfortunately the practical value of these calculations is not very great. They indicate the size of the cultures required to get all the possible combinations, and show that in ordinary cases many thousands of individuals have to be cultivated, in order to exhaust the whole range of possibilities. They further show that among all these thousands, only very few are constant in all their characters; in fact, it may easily be seen that with seven differentiating points among the 16,384 named above, only one individual will have all the seven qualities in pure active, and only one will have them all in a purely dormant condition. Then there will be some with some attributes active and others latent, but their numbers will also be very small. All others will split up in the succeeding generation in regard to one or more of their apparently active marks. And since only in very rare cases the stable hybrids can be distinguished by external characters from the unstable ones, the stability of each individual bearing a desired combination of characters would have to be established by experiment [306] after pure fertilization. Mendel's law teaches us to predict the difficulties, but hardly shows any way to avoid them. It lays great stress on the old prescript of isolation and pure fertilization, but it will have to be worked out and applied to a large number of practical cases before it will gain a preeminent influence in horticultural practice.Or, as Bailey states it, we are only beginning to find a pathway through the bewildering maze of hybridization.This pathway is to be laid out with regard to the following considerations. We are not to cross species or varieties, or even accidental plants. We must cross unit-characters, and consider the plants only as the bearers of these units. We may assume that these units are represented in the hereditary substance of the cell-nucleus by definite bodies of too small a size to be seen, but constituting together the chromosomes. We may call these innermost representatives of the unit-characters pangenes, in accordance with Darwin's hypothesis of pangenesis, or give them any other name, or we may even wholly abstain from such theoretical discussion, and limit ourselves to the conception of the visible character-units. These units then may be present, or lacking and in the first case active, or latent.[307] True elementary species differ from each other in a number of unit-characters, which do not contrast. They have arisen by progressive mutation. One species has one kind of unit, another species has another kind. On combining these, there can be no interchange. Mendelism assumes such an interchange between units of the same character, but in a different condition. Activity and latency are such conditions, and therefore Mendel's law obviously applies to them. They require pairs of antagonistic qualities, and have no connection whatever with those qualities, which do not find an opponent in the other parent. Now, only pure varieties afford such pure conditions. When undergoing further modifications, some of them may be in the progressive line and others in the retrogressive. Progressive modifications give new units, which are not in contrast with any other, retrograde changes turn active units into the latent condition and so give rise to pairs. Ordinary species generally originate in this way, and hence differ from each other partly in specific, partly in varietal characters. As to the first, they give in their hybrids stable peculiarities, while as to the latter, they split up according to Mendel's law.Unpaired or unbalanced characters lie side by side with paired or balanced qualities, and they [308] do so in nearly all the crosses made for practical purposes, and in very many scientific experiments. Even Mendel's peas were not pure in this respect, much less do the campions noted above differ only in Mendelian characters.Comparative and systematic studies must be made to ascertain the true nature of every unit in every single plant, and crossing experiments must be based on these distinctions in order to decide what laws are applicable in any case.

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