The Collaborative Mendel Mendel's Paper: A Collaborative Hypertext
Section 8: The Offspring of Hybrids in Which Several Differentiating Characters are Associated

Experiments in Plant Hybridization (1865)
by Gregor Mendel

The Offspring of Hybrids in Which Several Differentiating Characters are Associated.

In the experiments above described plants were used which differed only on one essential character. The next task consisted in ascertaining whether the law of development discovered in these applied to each pair of differentiating characters when several diverse characters are united in the hybrid by crossing. As regards the form of the hybrids in these cases, the experiments showed throughout that this invariably more nearly approaches to that one of the two parental plants which possesses the greater number of dominant characters. If, for instance, the seed plant has a short stem, terminal white flowers, and simply inflated pods; the pollen plant, on the other hand, a long stem, violet-red flowers distributed along the stem, and constricted pods; the hybrid resembles the seed parent only in the form of the pod; in the other characters it agrees with the pollen parent. Should one of the two parental types possess only dominant characters, then the hybrid is scarcely or not at all distinguishable from it.

Two experiments were made with a considerable number of plants. In the first experiment the parental plants differed in the form of the seed and in the color of the albumen; in the second in the form of the seed, in the color of the albumen, and in the color of the seed-coats. Experiments with seed characters give the result in the simplest and most certain way.

In order to facilitate study of the data in these experiments, the different characters of the seed plant will be indicated by A, B, C, those of the pollen plant by a, b, c, and the hybrid forms of the characters by Aa, Bb, and Cc.

 First Experiment: AB Seed parents,  abc Pollen parents,
         A  form round      a form wrinkled
         B albumen yellow   b albumen green

The fertilized seeds appeared round and yellow like those of the seed parents. The plants raised therefrom yielded seeds of four sorts, which frequently presented themselves in one pod. In all, 556 seeds were yielded by 15 plants, and of these there were:

All were sown the following year. 11 of the round yellow seeds did not yield plants, and 3 plants did not form seeds. Among the rest: From the wrinkled yellow seeds 96 resulting plants bore seed, of which: From 108 round green seeds 102 resulting plants fruited, of which: The wrinkled green seeds yielded 30 plants which bore seeds all of like character; they remained constant ab.

The offspring of the hybrids appeared therefore under 9 different forms, some of them in very unequal numbers. When these are collected and coordinated we find:

      38   plants with the sign     AB
      35     "       "       "      Ab
      28     "       "       "      aB
      30     "       "       "      ab
      65     "       "       "      ABb
      68     "       "       "      aBb
      60     "       "       "      AaB
      67     "       "       "      Aab
     138     "       "       "      AaBb
The whole of the forms may be classed into 3 essentially different groups. The first includes those with the signs AB, Ab, aB, and ab : they possess only constant characters and do not vary again in the next generation. Each of these forms is represented on the average 33 times. The second group includes the signs ABb, aBb, AaB, Aab : these are constant in one character and hybrid in another, and vary in the next generation only as regards the hybrid-character. Each of these appears on any average 65 times. The form AaBb occurs 138 times : it is hybrid in both characters, and behaves exactly as do the hybrids from which it is derived.

If the numbers in which the forms belonging to these classes appear be compared, the ratios of 1:2:4 are unmistakably evident. The numbers 33, 65, 138 present very fair approximations to the ratio numbers of 33, 66, 132.

The development series consists, therefore, of 9 classes, of which 4 appear therein always once and are constant in both characters; the forms AB, ab, resemble the parental forms, the two others present combinations between the conjoined characters A, a, B, b, which combinations are likewise possibly constant. Four classes appear always twice, and are constant in one character and hybrid in the other. One class appears four times, and is hybrid in both characters. Consequently, the offspring of the hybrids, if two kinds of differentiating characters are combined therein, are represented by the expression

   AB + Ab + aB + ab + 2ABb + 2aBb + 2AaB + 2Aab + 4AaBb
This expression is indisputably a combination series in which the two expressions for the characters A and a, B and b are combined. We arrive at the full number of the classes of the series by the combination of the expressions:
         A + 2Aa + a
         B + 2Bb + b

Second Experiment: ABC Seed parents,        abc Pollen parents,
         A  form round           a form wrinkled
         B albumen yellow        b albumen green
         C seed-coat gray-brown   c seed-coat white

This experiment was made in precisely the same way as the previous one. Among all the experiments it demanded the most time and trouble. From 24 hybrids 687 seeds were obtained in all: these were all either spotted, gray-brown or gray-green, round or wrinkled. From these in the following year 639 plants fruited, and as further investigation showed, there were among them:

    8 plants ABC     22 plants ABCc    45 plants ABbCc
   14    "   ABc     17    "   AbCc    36    "   aBbCc
    9    "   AbC     25    "   aBCc    38    "   AaBCc
   11    "   Abc     20    "   abCc    40    "   AabCc
    8    "   aBC     15    "   ABbC    49    "   AaBbC
   10    "   aBc     18    "   ABbc    48    "   AaBbc
   10    "   abC     19    "   aBbC
    7    "   abc     24    "   aBbc
                     14    "   AaBC    78    "   AaBbCc
                     18    "   AaBc
                     20    "   AabC
                     16    "   Aabc
The whole expression contains 27 terms. Of these 8 are constant in all characters, and each appears on the average 10 times; 12 are constant in two characters, and hybrid in the third; each appears on the average 19 times; 6 are constant in one character and hybrid in the other two; each appears on the average 43 times. One form appears 78 times and is hybrid in all of the characters. The ratios 10:19:43:78 agree so closely with the ratios 10:20:40:80, or 1:2:4:8 that this last undoubtedly represents the true value.

The development of the hybrids when the original parents differ in 3 characters results therefore according to the following expression:

   ABC + ABc + AbC + Abc + aBC + aBc + abC + abc +
   2ABCc + 2AbCc + 2aBCc + 2abCc + 2ABbC + 2ABbc +
   2aBbC + 2aBbc + 2AaBC + 2AaBc + 2AabC + 2Aabc +
   4ABbCc + 4aBbCc + 4AaBCc + 4AabCc + 4AaBbC +
   4AaBbc + 8AaBbCc.
Here also is involved a combination series in which the expressions for the characters A and a, B and b, C and c, are united. The expressions
         A + 2Aa + a
         B + 2Bb + b
         C + 2Cc + c
give all the classes of the series. The constant combinations which occur therein agree with all combinations which are possible between the characters A, B,C,a,b,c; two thereof, ABC and abc, resemble the two original parental stocks.

In addition, further experiments were made with a smaller number of experimental plants in which the remaining characters by twos and threes were united as hybrids: all yielded approximately the same results. There is therefore no doubt that for the whole of the characters involved in the experiments the principle applies that the offspring of the hybrids in which several essentially different characters are combined exhibit the terms of a series of combinations, in which the developmental series for each pair of differentiating characters are united. It is demonstrated at the same time that the relation of each pair of different characters in hybrid union is independent of the other differences in the two original parental stocks.

If n represent the number of the differentiating characters in the two original stocks, 3En gives the number of terms of the combination series, 4En the number of individuals which belong to the series, and 2En the number of unions which remain constant. The series therefore contains, if the original stocks differ in four characters, 3E4 = 81 classes, 4E4 = 256 individuals, and 2E4 = 16 constant forms: or, which is the same, among each 256 offspring of the hybrids are 81 different combinations, 16 of which are constant.

All constant combinations which in Peas are possible by the combination of the said 7 differentiating characters were actually obtained by repeated crossing. Their number is given by 2E7 = 128. Thereby is simultaneously given the practical proof that the constant characters which appear in the several varieties of a group of plants may be obtained in all the associations which are possible according to the laws of combination, by means of repeated artificial fertilization.

As regards the flowering time of the hybrids, the experiments are not yet concluded. It can, however, already be stated that the time stands almost exactly between those of the seed and pollen parents, and that the constitution of the hybrids with respect to this character probably follows the rule ascertained in the case of the other characters. The forms which are selected for experiments of this class must have a difference of at least 20 days from the middle flowering period of one to that of the other; furthermore, the seeds when sown must all be placed at the same depth in the earth, so that they may germinate simultaneously. Also, during the whole flowering period, the more important variations in temperature must be taken into account, and the partial hastening or delaying of the flowering which may result therefrom. It is clear that this experiment presents many difficulties to be overcome and necessitates great attention.

If we endeavor to collate in a brief form the results arrived at, we find that those differentiating characters, which admit of easy and certain recognition in the experimental plants, all behave exactly alike in their hybrid associations. The offspring of the hybrids of each pair of differentiating characters are, one-half, hybrid again, while the other half are constant in equal proportions having the characters of the seed and pollen parents respectively. If several differentiating characters are combined by cross-fertilization in a hybrid, the resulting offspring form the terms of a combination series in which the combination series for each pair of differentiating characters are united.

The uniformity of behavior shown by the whole of the characters submitted to experiment permits, and fully justifies, the acceptance of the principle that a similar relation exists in the other characters which appear less sharply defined in plants, and therefore could not be included in the separate experiments. An experiment with peduncles of different lengths gave on the whole a fairly satisfactory results, although the differentiation and serial arrangement of the forms could not be effected with that certainty which is indispensable for correct experiment.

When you contribute a comment to MendelWeb you agree to a number of conditions that are outlined in a special notice. Before going further you must acknowledge that you agree to these conditions:

OK, I have read the notice at least once and I agree to the conditions.

What word should the hyperlink come from:

Write your annotation here:

Please tell us your name and what part of the world you're from (required):

Your e-mail address will appear along with your comment if you write it here (optional):

Please check the spelling of everything you've written, since MendelWeb will not run a spell-checker on the text.

Press to submit your annotation, or to erase what you've written.

uber Pflanzen-Hybriden Discussion Questions MendelWeb Notes Homework questions

MendelWeb was conceived and constructed by Roger B. Blumberg