The proportions in which the descendants of the hybrids develop and
split up in the first and second generations presumably hold good for
all subsequent progeny. Experiments 1 and 2 have already been carried
through six generations, 3 and 7 through five, and 4, 5, and 6 through
four, these experiments being continued from the third generation with
a small number of plants, and no departure from the rule has been
perceptible. The offspring of the hybrids separated in each generation
in the ratio of 2 : 1 : 1 into hybrids and constant forms.
If _A_ be taken as denoting one of the two constant characters, for
instance the dominant, _a_, the recessive, and _Aa_ the hybrid form in
which both are conjoined, the expression
_A_ + 2_Aa_ + _a_
shows the terms in the series for the progeny of the hybrids of two
differentiating characters.
The observation made by Gärtner, Kölreuter, and others, that hybrids
are inclined to revert to the parental forms, is also confirmed by the
experiments described. It is seen that the number of the hybrids which
arise from one fertilisation, as compared with the number of forms
which become constant, and their progeny from generation to generation,
is continually diminishing, but that nevertheless they could not
entirely disappear. If an average equality of fertility in all plants
in all generations be assumed, and if, furthermore, each hybrid forms
seed of which one-half yields hybrids again, while the other half is
constant to both characters in equal proportions, the ratio of numbers
for the offspring in each generation is seen by the following summary,
in which _A_ and _a_ denote again the two parental characters, and _Aa_
the hybrid forms. For brevity’s sake it may be assumed that each plant
in each generation furnishes only 4 seeds.
Ratios.
Generation _A_ _Aa_ _a_ _A_ :_Aa_ : _a_
1 1 2 1 1 : 2 : 1
2 6 4 6 3 : 2 : 3
3 28 8 28 7 : 2 : 7
4 120 16 120 15 : 2 : 15
5 496 32 496 31 : 2 : 31
_n_ 2^{_n_}-1 : 2 : 2^{_n_}-1
In the tenth generation, for instance, 2^{_n_}-1 = 1023. There result,
therefore, in each 2,048 plants which arise in this generation 1,023
with the constant dominant character, 1,023 with the recessive
character, and only two hybrids.
THE OFFSPRING OF HYBRIDS IN WHICH SEVERAL DIFFERENTIATING CHARACTERS
ARE ASSOCIATED.
In the experiments above described plants were used which differed only
in one essential character[36]. 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.
[36] [This statement of Mendel’s in the light of present knowledge
is open to some misconception. Though his work makes it evident that
such varieties may exist, it is very unlikely that Mendel could
have had seven pairs of varieties such that the members of each
pair differed from each other in _only_ one considerable character
(_wesentliches Merkmal_). The point is probably of little theoretical
or practical consequence, but a rather heavy stress is thrown on
“_wesentlich_.”]
Two experiments were made with a larger number of plants. In the first
experiment the parental plants differed in the form of the seed and
in the colour of the albumen; in the second in the form of the seed,
in the colour of the albumen, and in the colour 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_.
Expt. 1.--_AB_, seed parents; _ab_, pollen parents;
_A_, form round; _a_, form angular;
_B_, albumen yellow. _b_, albumen green.
The fertilised 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:--
315 round and yellow,
101 angular and yellow,
108 round and green,
32 angular and green.
All were sown the following year. Eleven of the round yellow seeds did
not yield plants, and three plants did not form seeds. Among the rest:
38 had round yellow seeds _AB_
65 round yellow and green seeds _ABb_
60 round yellow and angular yellow seeds _AaB_
138 round yellow and green, angular yellow
and green seeds _AaBb_.
From the angular yellow seeds 96 resulting plants bore seed, of which:
28 had only angular yellow seeds _aB_
68 angular yellow and green seeds _aBb_.
From 108 round green seeds 102 resulting plants fruited, of which:
35 had only round green seeds _Ab_
67 round and angular green seeds _Aab_.
The angular green seeds yielded 30 plants which bore seeds all of like
character; they remained constant _ab_.
The offspring of the hybrids appeared therefore under nine different
forms, some of them in very unequal numbers. When these are collected
and co-ordinated 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 three essentially different
groups. The first embraces 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 thirty-three times. The second group embraces 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 an average sixty-five 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
32, 65, 138 present very fair approximations to the ratio numbers of
33, 66, 132.
The developmental series consists, therefore, of nine classes, of which
four 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_ + 2_ABb_ + 2_aBb_ + 2_AaB_ + 2_Aab_ + 4_AaBb_.
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_ + 2_Aa_ + _a_
_B_ + 2_Bb_ + _b_.
Second Expt.
_ABC_, seed parents; _abc_, pollen parents;
_A_, form round; _a_, form angular;
_B_, albumen yellow; _b_, albumen green;
_C_, seed-coat grey-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, grey-brown or grey-green, round or angular[37]. 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_.
[37] [Note that Mendel does not state the cotyledon-colour of the
first crosses in this case; for as the coats were thick, it could not
have been seen without opening or peeling the seeds.]
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 three characters results therefore according to the following
expression:
_ABC_ + _ABc_ + _AbC_ + _Abc_ + _aBC_ + _aBc_ + _abC_ + _abc_ +
2 _ABCc_ + 2 _AbCc_ + 2 _aBCc_ + 2 _abCc_ + 2 _ABbC_ + 2 _ABbc_ +
2 _aBbC_ + 2 _aBbc_ + 2 _AaBC_ + 2 _AaBc_ + 2 _AabC_ + 2 _Aabc_ +
4 _ABbCc_ + 4 _aBbCc_ + 4 _AaBCc_ + 4 _AabCc_ + 4 _AaBbC_ +
4 _AaBbc_ + 8 _AaBbCc_.
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_ + 2 _Aa_ + _a_
_B_ + 2 _Bb_ + _b_
_C_ + 2 _Cc_ + _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 represent the terms of a series
of combinations, in which the developmental series for each pair of
differentiating characters are associated_. 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, 3^{_n_} gives the number of terms of the
combination series, 4^{_n_} the number of individuals which belong to
the series, and 2^{_n_} the number of unions which remain constant.
The series therefore embraces, if the original stocks differ in four
characters, 3^4 = 81 of classes, 4^4 = 256 individuals, and 2^4 = 16
constant forms; or, which is the same, among each 256 offspring of the
hybrids there are 81 different combinations, 16 of which are constant.
All constant combinations which in Peas are possible by the combination
of the said seven differentiating characters were actually obtained
by repeated crossing. Their number is given by 2^7 = 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
[mathematical] laws of combination, by means of repeated artificial
fertilisation_.
As regards the flowering time of the hybrids, the experiments are
not yet concluded. It can, however, already be stated that the
period stands almost exactly between those of the seed and pollen
parents, and that the constitution of the hybrids with respect to
this character probably happens in the same way as in the case of the
other characters. The forms which are selected for experiments of this
class must have a difference of at least twenty 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 endeavour 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-fertilisation in a
hybrid, the resulting offspring form the terms of a combination series
in which the permutation series for each pair of differentiating
characters are united.
The uniformity of behaviour 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 result,
although the differentiation and serial arrangement of the forms could
not be effected with that certainty which is indispensable for correct
experiment.