# Popular Science Monthly/Volume 62/January 1903/Mendel's Law

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* MENDEL'S LAW.
By W. J. SPILLMAN,
U. S. DEPARTMENT OF AGRICULTURE.
NO discovery in recent years has aroused more interest amongst biologists than that of Mendel's Law. If subsequent investigations confirm it as those thus far made have done it can not be considered less than epoch-making. Its importance to plant breeders seems hardly less than that of the atomic theory to the science of chemistry. Professor Bateson, of Cambridge, says there is reason to believe that the plant breeder may eventually be able, by means of this law, to produce a desired hybrid type with the same degree of accuracy as the chemist now constructs a compound. It is impossible, on the threshold of such a discovery, to state just how far-reaching its importance is; we must wait for further investigation before hoping for too much.
As the history of this discovery is not yet generally known, it may be stated that Mendel's original paper was published in an obscure periodical at Brünn, Austria, in 1865. This publication received slight notice until De Vries, in March, 1900, published an exact counterpart of Mendel's theory, including some technical terms proposed by Mendel, and gave some of the results of his own researches to confirm the theory. Shortly after this, Correns of Germany and Bateson of England published results of their own work, showing that each of them had discovered the same law. Meanwhile the writer, working on hybrid wheats in this country, announced the law (but not the theory) in November, 1901. The knowledge of this discovery has become general only during the past few months. It now remains for other investigators to apply it to their own results for confirmation or modification.
As the distinction between varieties and species can not always be drawn with exactness, and particularly since Mendel's law applies alike to crosses and hybrids, it seems justifiable, at least in a discussion such as the present one, to conform to the growing usage of biologists in this country by using the term hybrid to include crosses of all kinds, whether between varieties or distantly related species. I shall, therefore, use the term hybrid in this sense. In the following ​discussion it is to be understood, unless otherwise stated, that the parent forms are all well-established varieties or species (i.e., they come true to type from seed), and that the hybrids are close fertilized (either self-fertilized or fertilized by others like them).
Mendel's law is, briefly stated, as follows: In the second and later generations of a hybrid, every possible combination of the parent characters occurs, and each combination appears in a definite proportion of the individuals.
Mendel did not leave his work unfinished. He proposed a theory, or rather deduced one by a simple course of reasoning that renders the theory almost an established fact as far as results thus far secured are concerned, that explains the facts in the case in a brilliant manner. As I have shown elsewhere, this theory explains most of the so-called exceptions to the law pointed out by several investigators. It explains so many apparent anomalies in such a simple manner that there is danger of applying it too extensively. This point will be brought up again below.
The theory may be illustrated as follows: Suppose the two parent varieties differ with respect to a single character. For instance, a variety of bearded wheat is crossed with one that is smooth (not bearded). When the hybrid thus produced forms its germ cells (pollen and ovules), the characters of the two parents separate, the beard-producing character passing into part of the pollen grains and part of the ovules, the smooth-head character of the other parent passing into the remaining germ cells. The character passing into any single germ cell being governed by chance, on the average half the pollen and half the ovules will receive the character of one parent, the other half that of the other. The results of this separation of characters may be illustrated by the following diagram, in which B stands for the beard-producing character and 8 for its opposite. The reason for the use of a small b in designating the hybrid will appear later.
| | | | | Pollen. | | Ovules |
| B S | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right\}\,$ | Sb (hybrid) | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right.}$ | B S | · | B S | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right\}\,$ | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right.}$ | B $\times$ B$=$B S $\times$ B$=$Sb B $\times$ S$=$Sb S $\times$ S$=$S |
Since the ovules of each kind are offered both kinds of pollen, half of each, on the average, will be fertilized by one and half by the other kind of pollen, giving the four fertilizations shown at the right. (Abundant experience has shown that S X B=B X S.) From this it appears that one fourth of the progeny of the hybrid Sb will be like the parent B, one fourth like S, and one half like the hybrid itself.
​Nothing has been said so far concerning the external appearances of the hybrid, whether it is intermediate between the parents, or resembles one or the other of them. The efforts of investigators since the time of Kölreuter have been directed to the futile attempt to find some law which would enable the breeder to predict the appearance of this hybrid. In general, this can not be done, with our present knowledge. There are two cases to consider. In certain instances hybrids are strictly intermediate between the parents. In others they are unlike either parent. These cases will be noticed later. In the more common case the hybrid either shows a parent character fully developed or shows it not at all. A parent character which is fully developed in the hybrid is said to be 'dominant'; if it is apparently absent it is said to be 'recessive.' In my work with hybrid wheats, beards have always been recessive, hence the designation of the hybrid as Sb.
It will now be seen that, externally, the progeny of the hybrid will consist of only two types, one type (B), constituting one fourth of the progeny, being like one parent, and the other, constituting three fourths of the progeny, resembling the other parent. Of this three fourths, one part (S) is actually like one parent, and will produce progeny like itself. The other two parts (Sb) are hybrids, and will produce progeny of all the types, exactly as the original hybrid did. Plants of the type S may easily be separated from those of the type Sb by planting the seed of each plant separately, and noting the character of the progeny.
The above diagram may easily be extended to any desired number of generations. Extended to the third generation it is:
| B | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | B | $\scriptstyle {\left\{{\begin{matrix}\ \end{matrix}}\right.}$ | B |
| | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | B |
| | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | Sb | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | Sb | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | Sb |
| | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | S |
| S | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | S | $\scriptstyle {\left\{{\begin{matrix}\ \end{matrix}}\right.}$ | S |
Assuming that each of the types S, Sb and B are equally productive, and mixing and sowing all the seed of each generation, the following table shows the percentage of each type in each generation to the sixth:
| Generations. | S | S | Sb | Sb | B | B |
| 1 | | | 100 | | | |
| 2 | 25 | | 50 | | 25 | |
| 3 | 37 | .5 | 25 | | 37 | .5 |
| 4 | 43 | .75 | 12 | .5 | 43 | .75 |
| 5 | 46 | .87 | 6 | .25 | 46 | .87 |
| 6 | 48 | .44 | 3 | 12 | 48 | .44 |
Here it is seen that the hybrid, based on a single pair of antagonistic characters, tends to split up into the two parent types. A hybrid ​whose parents differ in one respect is called a monohybrid; a dihybrid is one whose parents differ in two respects; and so on. Dihybrids and polyhybrids do not tend to split up into the two parent forms, as will be seen later.
Heretofore, plant breeders have been producing hybrids, and then by selecting to type each year from the progeny, trying to fix new types. Let us see what light Mendel's law throws on this practice. In the illustration given above, if the breeder had selected the type B of the progeny of the hybrid, he would have had a fixed type at once. Had he selected for type S, he would have had a mixture of the pure type S with the mixed type Sb. (Professor Bateson proposes the useful terms homozygote for pure types like S, and heterozygote for mixed types like Sb.) Next year the homozygotes S, would reproduce their kind only, while the heterozygotes would produce the three types B, Sb and S in the proportion 1:2:1. The second generation would therefore consist of S, 62.5 per cent.; Sb, 25 per cent.; and B, 12.5 per cent. This method of selection would never result in a fixed type unless the breeder should accidentally choose seed of the type S only. It has already been shown that the fixed type S could have been separated out at once by saving the seed of each selected plant separately, and observing which reproduced true to type. Nature fixes the type whether the breeder selects or not; heretofore, the breeder secured his fixed type by chance selection. With the knowledge of Mendel's law, he now selects his fixed type in a methodical manner, in the third generation.
Dihybrids are much more interesting, since they present the more usual case with which the breeder has to deal. With them, fixed types unlike either parent may be secured in the third generation. It frequently occurs that a breeder finds two characters in different varieties that he wishes to combine in a single variety. This is easily done when the characters obey Mendel's law. To illustrate this case I shall use characters which are of no particular importance, but for which I happen to possess experimental data. The principles are exactly the same for any characters that obey Mendel's law. Suppose we have a variety of wheat that has velvet chaff and another that has smooth heads (is not bearded) and that we wish to combine these two characters in a single variety. It is assumed that neither of the varieties has these two characters already; hence we have to deal with two pairs of opposite characters, namely, beards—no beards, and velvet—glabrous. We may, for brevity's sake, represent these characters by their initial letters, using small letters in cases where they are latent. In my work with wheats, beards have always been recessive, as stated above, and velvet chaff has always been dominant ​(except in a single individual). Hence the cross VB X GS gives us the hybrid VgSb. When this hybrid produces pollen and ovules, the pair of characters V and G separate, V going to half the pollen grains and ovules, and G to the other half. S and B do the same thing, but without reference to V and G. Hence we have four kinds of pollen grains and four of ovules, as shown in the following diagram:
| | | | | Pollen. | Ovules. | |
| VB | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | VgSb | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | VB | VB | Here we have a mixture of four kinds of pollen offered to four kinds of ovules. On the average, one fourth of each kind of ovules will be fertilized by each kind of pollen, giving sixteen equally numerous fertilizations, as follows: |
| | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | VgSb | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | VS | VS | Here we have a mixture of four kinds of pollen offered to four kinds of ovules. On the average, one fourth of each kind of ovules will be fertilized by each kind of pollen, giving sixteen equally numerous fertilizations, as follows: |
| | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | VgSb | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | GB | GB | Here we have a mixture of four kinds of pollen offered to four kinds of ovules. On the average, one fourth of each kind of ovules will be fertilized by each kind of pollen, giving sixteen equally numerous fertilizations, as follows: |
| GS | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | VgSb | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | GS | GS | Here we have a mixture of four kinds of pollen offered to four kinds of ovules. On the average, one fourth of each kind of ovules will be fertilized by each kind of pollen, giving sixteen equally numerous fertilizations, as follows: |
| 1. | VB $\times$ VB $=$ VB. | 9. | VB $\times$ GB $=$ VgB. |
| 2. | VS $\times$ VB $=$ VSb. | 10. | VS $\times$ GB $=$ VgSB. |
| 3. | GB $\times$ VB $=$ VgB. | 11. | GB $\times$ GB $=$ GB. |
| 4. | GS $\times$ VB $=$ VgSb. | 12. | GS $\times$ GB $=$ GSb. |
| 5. | VB $\times$ VS $=$ VSb. | 13. | VB $\times$ GS $=$ VgSB. |
| 6. | VS $\times$ VS $=$ VS. | 14. | VS $\times$ GS $=$ VgS. |
| 7. | GB $\times$ VS $=$ VgSb. | 15. | GB $\times$ GS $=$ GSb. |
| 8. | GS $\times$ VS $=$ VgS. | 16. | GS $\times$ GS $=$ GS. |
Here it will be noticed that (2) and (5) give the same result. Similarly, (3) and (9); (8) and (14); (12) and (15); and (4), (7), (10) and (13). We may, therefore, represent the hybrid and its progeny thus:
| VB GS | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \ \end{matrix}}\right\}\,$ | VgSb | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 1 | VS | This diagram may easily be extended to later generations. VS will produce VS. The progeny of the type VSb will all have the character V, but one fourth of it will have the character S, two fourths Sb, and one fourth B; thus, |
| VB GS | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \ \end{matrix}}\right\}\,$ | VgSb | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 2 | VSb | This diagram may easily be extended to later generations. VS will produce VS. The progeny of the type VSb will all have the character V, but one fourth of it will have the character S, two fourths Sb, and one fourth B; thus, |
| VB GS | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \ \end{matrix}}\right\}\,$ | VgSb | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 1 | VB | This diagram may easily be extended to later generations. VS will produce VS. The progeny of the type VSb will all have the character V, but one fourth of it will have the character S, two fourths Sb, and one fourth B; thus, |
| VB GS | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \ \end{matrix}}\right\}\,$ | VgSb | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 2 | VgS | This diagram may easily be extended to later generations. VS will produce VS. The progeny of the type VSb will all have the character V, but one fourth of it will have the character S, two fourths Sb, and one fourth B; thus, |
| VB GS | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \ \end{matrix}}\right\}\,$ | VgSb | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 4 | VgSb | This diagram may easily be extended to later generations. VS will produce VS. The progeny of the type VSb will all have the character V, but one fourth of it will have the character S, two fourths Sb, and one fourth B; thus, |
| VB GS | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \ \end{matrix}}\right\}\,$ | VgSb | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 2 | VgB | This diagram may easily be extended to later generations. VS will produce VS. The progeny of the type VSb will all have the character V, but one fourth of it will have the character S, two fourths Sb, and one fourth B; thus, |
| VB GS | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \ \end{matrix}}\right\}\,$ | VgSb | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 1 | GS | This diagram may easily be extended to later generations. VS will produce VS. The progeny of the type VSb will all have the character V, but one fourth of it will have the character S, two fourths Sb, and one fourth B; thus, |
| VB GS | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \ \end{matrix}}\right\}\,$ | VgSb | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | | Sb | This diagram may easily be extended to later generations. VS will produce VS. The progeny of the type VSb will all have the character V, but one fourth of it will have the character S, two fourths Sb, and one fourth B; thus, |
| VB GS | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \ \end{matrix}}\right\}\,$ | VgSb | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 1 | GB | This diagram may easily be extended to later generations. VS will produce VS. The progeny of the type VSb will all have the character V, but one fourth of it will have the character S, two fourths Sb, and one fourth B; thus, |
| This diagram may easily be extended to later generations. VS will produce VS. The progeny of the type VSb will all have the character V, but one fourth of it will have the character S, two fourths Sb, and one fourth B; thus, ||
| VSb | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right.}$ | 1 | VS |
| VSb | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right.}$ | 2 | VSb |
| VSb | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right.}$ | 1 | VB |
| 4 parts. ||
In like manner the progeny of the other types may be written out.
Of the nine types produced from the hybrid, four of them, VS, VB, GS, GB, are pure, and will reproduce true to seed. They have no characters hidden in them to crop out in later generations. It will be noticed that each of these pure types constitute one sixteenth of the progeny of the hybrid. Four other types, VSb, VgS, VgB ​and GSb, have each one latent character, and each constitutes two sixteenths of the whole. The type VgSb, having two latent characters, constitutes four sixteenths. In general, a type having n latent characters will be present in the second generation of any hybrid in a proportion 2$^n$ times as great as any type having no latent characters.
Suppose now we sow all these nine kinds of seed and secure mature plants from each. Those of the type GB can easily be distinguished by their appearance. It can be selected out at once, as a new variety fixed in character. The case is different with VS, VB and GS. For example, if we attempt to select GS, we get also GSb, which has exactly the same external characters. But if we take all the plants with glabrous chaff and smooth heads (GS $+$ GSb) and save the seed of each plant separately, we can separate the next generation by noting which plants reproduce true to type; for the seed of GS will produce GS plants only, while that of GSb will produce one fourth GS, two fourths GSb, and one fourth GB, according to Mendel's law. Or, since GS and GSb appear alike, one fourth of the progeny of GSb will be GB (glabrous and bearded), the remaining three fourths being glabrous and smooth. In the same way we can separate VS from VSb, VgS and VgSb, and VB from VgB.
Now VS, VB, GS and GB are all the possible pure (homozygote) combinations of the parent characters, two of them being identical with the two parents, the others constituting new varieties. The practical plant breeder, therefore, does not need to carry his hybrids beyond the third generation to secure all the possible results of a given cross, as far as new fixed varieties are concerned. It should be remembered that this is true only of characters that obey Mendel's law. It is plain, therefore, that it is a matter of the highest practical importance to ascertain how general this law is.
By the same methods outlined above, it is easy to ascertain what types would result from a trihybrid, and from hybrids of all higher orders. In the case of trihybrids, eight permanent combinations result, one like each parent and six new ones. Quadrihybrids give sixteen types, fourteen of which are new; and so on. In general, the number of new fixed types springing from a hybrid is 2″—2, where n is the order of the hybrid.
Percentage of each Type in first six Generations of the Dihybrid VB X GS.
| | | First. | Second. | Third. | Fourth. | Fifth. | Sixth Genera tion. |
| VS | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right\}\,$ | each 0 | 6.25 | 14.06 | 19.10 | 21.97 | 23.46 |
| VB | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right\}\,$ | each 0 | 6.25 | 14.06 | 19.10 | 21.97 | 23.46 |
| GS | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right\}\,$ | each 0 | 6.25 | 14.06 | 19.10 | 21.97 | 23.46 |
| GB | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right\}\,$ | each 0 | 6.25 | 14.06 | 19.10 | 21.97 | 23.46 |
| VgS | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right\}\,$ | each 0 | 12.50 | 9.38 | 5.47 | 2.93 | 1.15 |
| VqB | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right\}\,$ | each 0 | 12.50 | 9.38 | 5.47 | 2.93 | 1.15 |
| VSb | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right\}\,$ | each 0 | 12.50 | 9.38 | 5.47 | 2.93 | 1.15 |
| GSb | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right\}\,$ | each 0 | 12.50 | 9.38 | 5.47 | 2.93 | 1.15 |
| VgSb | | 100 | 25.00 | 6.25 | 1.56 | .39 | .10 |
Hence, if we sow all the seed of each generation, it is seen that each of the homozygote types approaches 25 per cent, of the whole, while all the heterozygote types approach zero, and the larger the number of latent characters in a type, the more rapidly it decreases in proportion. In trihybrids, we should have eight homozygote types, each increasing toward 12$^1$⁄$_2$ per cent. of the whole. Hence the generalization, a hybrid of the nth order tends to split up into 2n fixed types, all types not fixed tending to disappear. The effect of such a law, in the case of accidental hybrids between species and varieties in the wild state, can not fail to be important in the evolution of species. I leave the discussion of this interesting phase of the subject till the law is more generally confirmed. In this connection it may be well to state that, at the recent international conference of plant breeders in New York, Professor Bateson asserted that Mendel's law has been found to hold in every case where it had been thoroughly tested. The groups in which these tests have been made are so varied, representing both plants and animals, that the presumption in favor of the generality of the law is strong enough to warrant breeders in searching for it everywhere.
It has been urged by certain breeders that, even if the law is general, it can not be put to practical use by breeders; for it nearly always happens that the varieties crossed differ in an indefinite number of respects, and we should therefore get so vast a number of resulting types that no two individuals could be classed together. This objection is not altogether valid. In the first place, if we take any established variety and examine the individuals closely, we find no two of them alike. Hence, even if the variety we are trying to produce must consist of an indefinite number of types differing only in minor details, we are no more than duplicating the actual conditions existing amongst present useful varieties. In the second place, a very common problem of the breeder is to unite two characters found ​in related varieties, where the remaining characters of both varieties are unimportant. Hence, in practice, we have in reality to deal with dihybrids in many cases. It should also be remembered that, if we treat a hybrid as a dihybrid, neglecting all but the two characters of most concern, the type we select actually splits up into fixed types with reference to all other characters, so that in a few generations we can secure uniformity, even in minor characters, by selection.
There is a very interesting phase of the subject which, for the sake of clearness, has been purposely overlooked in what has been said above. We have dealt only with the case in which a parent character appears in the hybrid in a fully developed state, or is not apparent at all. This is actually the case with the characters discussed above. Cases are known, however, in which both of a pair of opposite characters appear in the hybrid. This may result in a form intermediate between the parents, as I found to be the case when I crossed short-headed club wheats with the ordinary long-headed varieties. The same phenomenon appeared in crosses between varieties with red chaff and those with white chaff. Sometimes, in crosses between white and red flowers, for instance, the heterozygote types are variegated. It is easy to see that this fact may have an important bearing on the flavor and other characters of hybrid fruits, such as apples, peaches, strawberries, etc. It is highly probable that a great majority of these fruits are heterozygote in character, which fact would explain their well-known variability when grown from seed. It would naturally be expected, since flavors are due to the presence, in various proportions, of certain chemical substances, that entirely new flavors should be found in seedlings of this character, for in almost every seedling we should have a new combination of the flavor-giving substances.
One reason why Mendel's law was not discovered long ago is doubtless to be found in the fact that the large majority of seedlings that have come under the breeder's eye have had heterozygote parents of unknown constitution. If all our leading commercial varieties had been commonly close-fertilized, the law would long ago have forced itself upon us. Professor Bailey's remarkable and careful work on hybrid squashes and pumpkins probably came to naught for this very reason. Had he done the same work with varieties that are normally close-fertilized, he would probably have discovered this law. He was on the right road, but he was in the wrong vehicle.
Let us consider what results would follow the growing of apple seed generation after generation with close-fertilization, if the characters of the apple obey Mendel's law. We start with a tree that is already multihybrid. Suppose it to consist of N pairs of opposite character, A-A′, B-B′, . . . ,N-N′. The hybrid and the first ​generation of its progeny would then be, supposing the primed characters to be recessive:
| Aa′ Bb′ Cc′ Nn′ | $\scriptstyle {\left\{{\begin{matrix}\ \\\ \end{matrix}}\right.}$ | ABC N, ABC Nn′, ABC ...... N′, etc. |
| (hybrid) | $\scriptstyle {\left\{{\begin{matrix}\ \\\ \end{matrix}}\right.}$ | (progeny) |
The total number of types occurring in the progeny is 3″; the number of fixed types (homozygote) is 2″. The number of types with r latent characters is nCr2 $^{n-r}$, where nCr is the number of combinations of n things taken r at a time. Only one type, namely, A′B′C′. . . N′, consisting entirely of recessive characters, could be selected out without getting with it one or more heterozygote types. But by saving the seed of each tree of this generation separately, and observing which, with close fertilization, would reproduce true to type, we could at once secure, in fixed from, all the 2 homozygote types.
If the tree happened to be of the type VgSb, discussed above, in which all the characters of its original parents are present, the above process of analysis would give, not only all its original parents, but all possible combinations of them, and each in a form that would reproduce true to seed, if self-fertilized. If it were of the type VgB, in which some of the parent characters are missing, it would give all the original parents whose characters are all present, together with all their combinations with characters that are present from other parents, some of whose characters are missing. Since apples are confessedly many times multihybrids, it is probable that a very large number of seed would have to be used to secure all the types capable of resulting from combinations of the N pairs of characters.
Suppose we neglect all but essential characters; we might, in the case of the apple, reduce the number of types to a point which would make the task a possible one. If this were done, it would mean much to the plant breeder. Having a large number of fixed varieties of apples, supposing, of course, that Mendel's law holds, we could select parents with a view to producing any combination of characters we desire. Did not Downing, many years ago, assert that much better results could be secured in producing new seedling apples by using seed from strains that had already been propagated several generations from seed? And why? Possibly because the continuous propagation from seed tends to produce pure strains. If the seed used were always produced by self-pollination, there certainly would be a tendency to pure strains if Mendel's law applies. This problem is worth working out, both from practical and from theoretical grounds. It could be done more easily with strawberries, or with some of the common ornamentals that do not reproduce true to seed. This method of analysis is one way of testing Mendel's law in such groups.
This subject is too new to permit of any useful generalizations ​respecting animal breeding. True, Mendel's law has been found to apply with animals so far as the test has been applied, but it will be some time before much use can be made of it in that direction. It will take years to overcome the prevailing prejudices of animal breeders in favor of old-time theories that govern practice in that line.
Exceptions to the Law.
Millardet and others have given accounts of hybrids that immediately split up into the two parent forms, having no, or very few, hybrid progeny, and these have been cited as exceptions to Mendel's law. I have elsewhere shown that Mendel's theory of the separation of parent characters offers a perfectly rational explanation of these cases. If a hybrid is obtained from two varieties each of which prefers its own pollen to that of the other, the resulting hybrid must split up at once into the two parent types, if it obeys the law in question, since each of the two kinds of ovules produced by the hybrid, being offered both kinds of pollen, is fertilized only by its own kind. Yet even in these cases, according to the laws of probability, it ought occasionally to happen that such a hybrid would produce a few hybrids, for it would occasionally happen that an ovule would be offered only one kind of pollen. And this is what actually occurred in hybrids of this class reported by De Vries. A few hybrids occurred along with an excess of both the parent types.
Likewise, when two varieties are crossed, each of which prefers the other's pollen, there will also be an apparent departure from the law; for in this case each of the two kinds of ovules on the hybrid will be fertilized only with the opposite kind of pollen, giving all heterozygotes. Such a hybrid will appear to be fixed in type at once. Such cases have been reported by many observers, including Darwin. In this case it may occasionally happen in later generations of the apparently stable hybrid, that an ovule will be offered only its own kind of pollen and we then get a reversion to one of the parent forms. We may yet find that many sports are to be explained in this manner.
Breeders frequently report entirely new characters in hybrids. If these actually occur we must look further than Mendel's theory for their cause. It must not be overlooked, however, that if the two parents of a hybrid are themselves heterozygote hybrids, Mendel's theory would call for characters unlike any of the visible characters of either parent. In this case, all latent characters in both parents would necessarily crop out in the second generation of the hybrids. We can not dismiss Mendel's theory in such cases until it has been demonstrated that the parents have no latent characters in them.
​It is very probable that marry supposed new characters are merely the peculiar result of the blending of opposite characters, neither of which 'dominates' the other; or it may be that the blending of two unrelated dominant characters gives rise to new characters. As an instance of how this might occur, the presence of two chemical substances, one derived from each parent, might give new flavors in fruit, or new colors in flowers. Bateson has demonstrated a case of the latter and shown that the new and radically different color is not a new character at all, but a blending of parent characters which obey Mendel's law perfectly.
Is it not possible that Mendel has also shown to us an explanation of bud sports? These sports are notoriously common on plants known to be hybrids. May not the separation of parent characters occasionally occur at stages of growth other than the formation of germ cells? If such is the case, bud sports at once come under the law.
It does not seem improbable that, once in a while, the parent characters might fail to separate in the usual manner on the formation of germ cells, so that we might have a few cells inheriting both of a pair of opposite characters, and this might extend over a series of generations before the separation finally occurred. Under such conditions, a recessive character might be carried over any number of generations without showing itself, finally cropping out and giving a case of atavism. Perhaps this is the explanation of atavism. It would be interesting in this connection to know if atavic characters are ordinarily recessive.
It is clear that we have before us a working hypothesis that offers a possible explanation of a large number of phenomena heretofore absolutely inexplicable. It will require time to test the hypothesis, even in the limited number of cases suggested above.
The only data thus far published in this country that may be used as a direct test of Mendel's theory are those I secured from hybrid wheats. At the time these data were arranged for publication similar work in Europe was unknown in this country; they were merely arranged to show that similarly bred hybrids split up into the same types, each type tending to occur in a definite proportion. In all my hybrids characters were present that apparently separated in a manner different from that called for by Mendel's theory. Fortunately, however, the data referred to may easily be arranged to test the applicability of this theory to two characters, namely, beards and velvet chaff. In five out of fourteen crosses one parent was bearded and the other smooth, two of the five being reciprocals. Beards being recessive, theory would call for 25 per cent, of bearded plants ​in the progeny of the hybrids. The seed of each hybrid plant was kept separate and sown as a plat. In three plats from a cross between Valley (♂), a bearded variety, and Little Club (♁), there was an average of 25.7 per cent, of bearded plants. Eleven plats of the reciprocal cross averaged 25.2 per cent, beards. Six plats of a cross between Little Club and Emporium gave bearded plants to the extent of 24.6 per cent.; three plats of Lehigh $\times$ Red Chaff, 25.9 per cent.; and seven plats of Turkey $\times$ Little Club, 30.8 per cent. In the last example there were two aberrant cases, the remaining five lying between 25 and 29 per cent.
Much evidence of a similar nature has been brought forward by De Vries, Correns, Bateson and others, in addition to that given by Mendel. These investigators worked with widely different groups of plants and animals.
Thus far, no one has shown definitely that Mendel's theory is inapplicable to a single case. Correns, however, mentions hybrids which do not behave exactly as called for by theory, but I am not sufficiently familiar with the details concerning them to discuss them here. In my own work I found that the color of the chaff and the length of the head behave in a manner most easily explained by a modification of Mendel's theory. Instead of the pair of opposite characters, long heads and short heads, separating completely on the formation of pollen and ovules, they seemed to separate in all possible proportions, giving in the next generation a series of plants having heads of every possible gradation of length between those of the two parents, and even extending in both directions beyond the parents. In my work I arbitrarily separated the hybrids into three groups— long, semi-long and short heads. As this separation was entirely arbitrary, the results are very irregular, and the original figures do not represent very accurately the actual facts with reference to this character. Exactly the same thing occurred with reference to color of chaff. I have not yet had the opportunity of examining the third generation of these hybrids, so that it can not yet be stated definitely that they really form an exception to Mendel's law.
As is the case with any startling discovery, we are apt either to minimize its importance or to extend its application much beyond legitimate bounds. I fear I shall be accused of the latter. But this new thory is so suggestive and offers a rational explanation to so many hitherto enigmatical phenomena, that a few suggestions as to its possible application can do no harm.
* ↑ Verhandl. d. Naturf. Vereines, Brünn, 1865.
* ↑ Compte Rendus, March 20, 1900.
* ↑ Bul. 115, Off. Exper. Sta., U. S. Dept. Agric.
* ↑ It seems that both Correns and De Vries had arrived at the same theory independently.
* ↑ This does not agree with Correns (l. c.). I think, however, that the cases to which Correns refers may be explained by means of Mendel's law.
* ↑ Science, October 31, 1902.
* ↑ Bul. 115, Off. Ex. Sta. U. S. Dept. Agr.