Chapter IV: Introduction (3)

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.

THE REPRODUCTIVE CELLS OF HYBRIDS.

The results of the previously described experiments induced further experiments, the results of which appear fitted to afford some conclusions as regards the composition of the egg and pollen cells of hybrids. An important matter for consideration is afforded in _Pisum_ by the circumstance that among the progeny of the hybrids constant forms appear, and that this occurs, too, in all combinations of the associated characters. So far as experience goes, we find it in every case confirmed that constant progeny can only be formed when the egg cells and the fertilising pollen are of like character, so that both are provided with the material for creating quite similar individuals, as is the case with the normal fertilisation of pure species[38]. We must therefore regard it as essential that exactly similar factors are at work also in the production of the constant forms in the hybrid plants. Since the various constant forms are produced in _one_ plant, or even in _one_ flower of a plant, the conclusion appears logical that in the ovaries of the hybrids there are formed as many sorts of egg cells, and in the anthers as many sorts of pollen cells, as there are possible constant combination forms, and that these egg and pollen cells agree in their internal composition with those of the separate forms.

[38] [“False hybridism” was of course unknown to Mendel.]

In point of fact it is possible to demonstrate theoretically that this hypothesis would fully suffice to account for the development of the hybrids in the separate generations, if we might at the same time assume that the various kinds of egg and pollen cells were formed in the hybrids on the average in equal numbers[39].

[39] [This and the preceding paragraph contain the essence of the
Mendelian principles of heredity.]

In order to bring these assumptions to an experimental proof, the following experiments were designed. Two forms which were constantly different in the form of the seed and the colour of the albumen were united by fertilisation.

If the differentiating characters are again indicated as _A_, _B_, _a_, _b_, we have:

_AB_, seed parent; _ab_, pollen parent; _A_, form round; _a_, form angular; _B_, albumen yellow. _b_, albumen green.

The artificially fertilised seeds were sown together with several seeds of both original stocks, and the most vigorous examples were chosen for the reciprocal crossing. There were fertilised:

1. The hybrids with the pollen of _AB_.
2. The hybrids " " _ab_.
3. _AB_ " " the hybrids.
4. _ab_ " " the hybrids.

For each of these four experiments the whole of the flowers on three plants were fertilised. If the above theory be correct, there must be developed on the hybrids egg and pollen cells of the forms _AB_, _Ab_, _aB_, _ab_, and there would be combined:--

1. The egg cells _AB_, _Ab_, _aB_, _ab_ with the pollen cells _AB_.

2. The egg cells _AB_, _Ab_, _aB_, _ab_ with the pollen cells _ab_.

3. The egg cells _AB_ with the pollen cells _AB_, _Ab_, _aB_, _ab_.

4. The egg cells _ab_ with the pollen cells _AB_, _Ab_, _aB_, _ab_.

From each of these experiments there could then result only the following forms:--

1. _AB_, _ABb_, _AaB_, _AaBb_.
2. _AaBb_, _Aab_, _aBb_, _ab_.
3. _AB_, _ABb_, _AaB_, _AaBb_.
4. _AaBb_, _Aab_, _aBb_, _ab_.

If, furthermore, the several forms of the egg and pollen cells of the hybrids were produced on an average in equal numbers, then in each experiment the said four combinations should stand in the same ratio to each other. A perfect agreement in the numerical relations was, however, not to be expected, since in each fertilisation, even in normal cases, some egg cells remain undeveloped or subsequently die, and many even of the well-formed seeds fail to germinate when sown. The above assumption is also limited in so far that, while it demands the formation of an equal number of the various sorts of egg and pollen cells, it does not require that this should apply to each separate hybrid with mathematical exactness.

The first and second experiments had primarily the object of proving the composition of the hybrid egg cells, while the third and fourth experiments were to decide that of the pollen cells[40]. As is shown by the above demonstration the first and second experiments and the third and fourth experiments should produce precisely the same combinations, and even in the second year the result should be partially visible in the form and colour of the artificially fertilised seed. In the first and third experiments the dominant characters of form and colour, _A_ and _B_, appear in each union, and are also partly constant and partly in hybrid union with the recessive characters _a_ and _b_, for which reason they must impress their peculiarity upon the whole of the seeds. All seeds should therefore appear round and yellow, if the theory be justified. In the second and fourth experiments, on the other hand, one union is hybrid in form and in colour, and consequently the seeds are round and yellow; another is hybrid in form, but constant in the recessive character of colour, whence the seeds are round and green; the third is constant in the recessive character of form but hybrid in colour, consequently the seeds are angular and yellow; the fourth is constant in both recessive characters, so that the seeds are angular and green. In both these experiments there were consequently four sorts of seed to be expected--viz. round and yellow, round and green, angular and yellow, angular and green.

[40] [To prove, namely, that both were similarly differentiated, and
not one or other only.]

The crop fulfilled these expectations perfectly. There were obtained in the

1st Experiment, 98 exclusively round yellow seeds;
3rd " 94 " " " "

In the 2nd Experiment, 31 round and yellow, 26 round and green, 27 angular and yellow, 26 angular and green seeds.

In the 4th Experiment, 24 round and yellow, 25 round and green, 22 angular and yellow, 27 angular and green seeds.

A favourable result could now scarcely be doubted; the next generation must afford the final proof. From the seed sown there resulted for the first experiment 90 plants, and for the third 87 plants which fruited: these yielded for the--

1st Exp. 3rd Exp.
20 25 round yellow seeds _AB_
23 19 round yellow and green seeds _ABb_
25 22 round and angular yellow seeds _AaB_
22 21 round and angular green and yellow seeds _AaBb_

In the second and fourth experiments the round and yellow seeds yielded plants with round and angular yellow and green seeds, _AaBb_.

From the round green seeds plants resulted with round and angular green seeds, _Aab_.

The angular yellow seeds gave plants with angular yellow and green seeds, _aBb_.

From the angular green seeds plants were raised which yielded again only angular and green seeds, _ab_.

Although in these two experiments likewise some seeds did not germinate, the figures arrived at already in the previous year were not affected thereby, since each kind of seed gave plants which, as regards their seed, were like each other and different from the others. There resulted therefore from the

2nd Exp. 4th Exp.
31 24 plants of the form _AaBb_
26 25 " " _Aab_
27 22 " " _aBb_
26 27 " " _ab_

In all the experiments, therefore, there appeared all the forms which the proposed theory demands, and also in nearly equal numbers.

In a further experiment the characters of floral colour and length of stem were experimented upon, and selection so made that in the third year of the experiment each character ought to appear in half of all the plants if the above theory were correct. _A_, _B_, _a_, _b_ serve again as indicating the various characters.

_A_, violet-red flowers. _a_, white flowers. _B_, axis long. _b_, axis short.

The form _Ab_ was fertilised with _ab_, which produced the hybrid _Aab_. Furthermore, _aB_ was also fertilised with _ab_, whence the hybrid _aBb_. In the second year, for further fertilisation, the hybrid _Aab_ was used as seed parent, and hybrid _aBb_ as pollen parent.

Seed parent, _Aab_. Pollen parent, _aBb_. Possible egg cells, _Abab_. Pollen cells, _aBab_.

From the fertilisation between the possible egg and pollen cells four combinations should result, viz.:--

_AaBb_ + _aBb_ + _Aab_ + _ab_.

From this it is perceived that, according to the above theory, in the third year of the experiment out of all the plants

Half should have violet-red flowers (_Aa_), Classes 1, 3
" " " white flowers (_a_) " 2, 4
" " " a long axis (_Bb_) " 1, 2
" " " a short axis (_b_) " 3, 4

From 45 fertilisations of the second year 187 seeds resulted, of which only 166 reached the flowering stage in the third year. Among these the separate classes appeared in the numbers following:--

Class. Colour of flower. Stem.
1 violet-red long 47 times
2 white long 40 "
3 violet-red short 38 "
4 white short 41 "

There consequently appeared--

The violet-red flower colour (_Aa_) in 85 plants.
" white " " (_a_) in 81 "
" long stem (_Bb_) in 87 "
" short " (_b_) in 79 "

The theory adduced is therefore satisfactorily confirmed in this experiment also.

For the characters of form of pod, colour of pod, and position of flowers experiments were also made on a small scale, and results obtained in perfect agreement. All combinations which were possible through the union of the differentiating characters duly appeared, and in nearly equal numbers.

Experimentally, therefore, the theory is justified _that the pea hybrids form egg and pollen cells which, in their constitution, represent in equal numbers all constant forms which result from the combination of the characters when united in fertilisation_.

The difference of the forms among the progeny of the hybrids, as well as the respective ratios of the numbers in which they are observed, find a sufficient explanation in the principle above deduced. The simplest case is afforded by the developmental series of each pair of differentiating characters. This series is represented by the expression _A_ + 2_Aa_ + _a_, in which _A_ and _a_ signify the forms with constant differentiating characters, and _Aa_ the hybrid form of both. It includes in three different classes four individuals. In the formation of these, pollen and egg cells of the form _A_ and _a_ take part on the average equally in the fertilisation; hence each form [occurs] twice, since four individuals are formed. There participate consequently in the fertilisation--

The pollen cells _A_ + _A_ + _a_ + _a_
The egg cells _A_ + _A_ + _a_ + _a_.

It remains, therefore, purely a matter of chance which of the two sorts of pollen will become united with each separate egg cell. According, however, to the law of probability, it will always happen, on the average of many cases, that each pollen form _A_ and _a_ will unite equally often with each egg cell form _A_ and _a_, consequently one of the two pollen cells _A_ in the fertilisation will meet with the egg cell _A_ and the other with an egg cell _a_, and so likewise one pollen cell _a_ will unite with an egg cell _A_, and the other with egg cell _a_.

Pollen cells _A_ _A_ _a_ _a_
| \ / |
| \ / |
| x |
| / \ |
| / \ |
\|/ \/ \/ \|/
Egg cells _A_ _A_ _a_ _a_

The result of the fertilisation may be made clear by putting the signs for the conjoined egg and pollen cells in the form of fractions, those for the pollen cells above and those for the egg cells below the line. We then have

_A_/_A_ + _A_/_a_ + _a_/_A_ + _a_/_a_.

In the first and fourth term the egg and pollen cells are of like kind, consequently the product of their union must be constant, viz. _A_ and _a_; in the second and third, on the other hand, there again results a union of the two differentiating characters of the stocks, consequently the forms resulting from these fertilisations are identical with those of the hybrid from which they sprang. _There occurs accordingly a repeated hybridisation._ This explains the striking fact that the hybrids are able to produce, besides the two parental forms, offspring which are like themselves; _A_/_a_ and _a_/_A_ both give the same union _Aa_, since, as already remarked above, it makes no difference in the result of fertilisation to which of the two characters the pollen or egg cells belong. We may write then--

_A_/_A_ + _A_/_a_ + _a_/_A_ + _a_/_a_ = _A_ + 2_Aa_ + _a_.

This represents the average result of the self-fertilisation of the hybrids when two differentiating characters are united in them. In solitary flowers and in solitary plants, however, the ratios in which the forms of the series are produced may suffer not inconsiderable fluctuations[41]. Apart from the fact that the numbers in which both sorts of egg cells occur in the seed vessels can only be regarded as equal on the average, it remains purely a matter of chance which of the two sorts of pollen may fertilise each separate egg cell. For this reason the separate values must necessarily be subject to fluctuations, and there are even extreme cases possible, as were described earlier in connection with the experiments on the form of the seed and the colour of the albumen. The true ratios of the numbers can only be ascertained by an average deduced from the sum of as many single values as possible; the greater the number the more are merely chance elements eliminated.

[41] [Whether segregation by such units is more than purely
fortuitous could probably be determined by seriation.]

The developmental series for hybrids in which two kinds of differentiating characters are united contains among sixteen individuals nine different forms, viz., _AB_ + _Ab_ + _aB_ + _ab_ + 2_ABb_ + 2_aBb_ + 2_AaB_ + 2_Aab_ + 4_AaBb_. Between the differentiating characters of the original stocks _Aa_ and _Bb_ four constant combinations are possible, and consequently the hybrids produce the corresponding four forms of egg and pollen cells _AB_, _Ab_, _aB_, _ab_, and each of these will on the average figure four times in the fertilisation, since sixteen individuals are included in the series. Therefore the participators in the fertilisation are--

Pollen cells _AB_ + _AB_ + _AB_ + _AB_ + _Ab_ + _Ab_ + _Ab_ + _Ab_ +
_aB_ + _aB_ + _aB_ + _aB_ + _ab_ + _ab_ + _ab_ + _ab_.

Egg cells _AB_ + _AB_ + _AB_ + _AB_ + _Ab_ + _Ab_ + _Ab_ + _Ab_ +
_aB_ + _aB_ + _aB_ + _aB_ + _ab_ + _ab_ + _ab_ + _ab_.

In the process of fertilisation each pollen form unites on an average equally often with each egg cell form, so that each of the four pollen cells _AB_ unites once with one of the forms of egg cell _AB_, _Ab_, _aB_, _ab_. In precisely the same way the rest of the pollen cells of the forms _Ab_, _aB_, _ab_ unite with all the other egg cells. We obtain therefore--

_AB_/_AB_ + _AB_/_Ab_ + _AB_/_aB_ + _AB_/_ab_ + _Ab_/_AB_ + _Ab_/_Ab_ + _Ab_/_aB_ + _Ab_/_ab_ + _aB_/_AB_ + _aB_/_Ab_ + _aB_/_aB_ + _aB_/_ab_ + _ab_/_AB_ + _ab_/_Ab_ + _ab_/_aB_ + _ab_/_ab_,

or

_AB_ + _ABb_ + _AaB_ + _AaBb_ + _ABb_ + _Ab_ + _AaBb_ + _Aab_ + _AaB_ + _AaBb_ + _aB_ + _aBb_ + _AaBb_ + _Aab_ + _aBb_ + _ab_ = _AB_ + _Ab_ + _aB_ + _ab_ + 2_ABb_ + 2_aBb_ + 2_AaB_ + 2_Aab_ + 4_AaBb_[42].

[42] [In the original the sign of equality (=) is here represented by
+, evidently a misprint.]

In precisely similar fashion is the developmental series of hybrids exhibited when three kinds of differentiating characters are conjoined in them. The hybrids form eight various kinds of egg and pollen cells--_ABC_, _ABc_, _AbC_, _Abc_, _aBC_, _aBc_, _abC_, _abc_--and each pollen form unites itself again on the average once with each form of egg cell.

The law of combination of different characters which governs the development of the hybrids finds therefore its foundation and explanation in the principle enunciated, that the hybrids produce egg cells and pollen cells which in equal numbers represent all constant forms which result from the combinations of the characters brought together in fertilisation.

EXPERIMENTS WITH HYBRIDS OF OTHER SPECIES OF PLANTS.

It must be the object of further experiments to ascertain whether the law of development discovered for _Pisum_ applies also to the hybrids of other plants. To this end several experiments were recently commenced. Two minor experiments with species of _Phaseolus_ have been completed, and may be here mentioned.

An experiment with _Phaseolus vulgaris_ and _Phaseolus nanus_ gave results in perfect agreement. _Ph. nanus_ had together with the dwarf axis simply inflated green pods. _Ph. vulgaris_ had, on the other hand, an axis 10 feet to 12 feet high, and yellow coloured pods, constricted when ripe. The ratios of the numbers in which the different forms appeared in the separate generations were the same as with _Pisum_. Also the development of the constant combinations resulted according to the law of simple combination of characters, exactly as in the case of _Pisum_. There were obtained--

Constant Axis Colour of Form of
combinations the unripe pods. the ripe pods.

1 long green inflated
2 " " constricted
3 " yellow inflated
4 " " constricted
5 short green inflated
6 " " constricted
7 " yellow inflated
8 " " constricted

The green colour of the pod, the inflated forms, and the long axis were, as in _Pisum_, dominant characters.

Another experiment with two very different species of _Phaseolus_ had only a partial result. _Phaseolus nanus_, L., served as seed parent, a perfectly constant species, with white flowers in short racemes and small white seeds in straight, inflated, smooth pods; as pollen parent was used _Ph. multiflorus_, W., with tall winding stem, purple-red flowers in very long racemes, rough, sickle-shaped crooked pods, and large seeds which bore black flecks and splashes on a peach-blood-red ground.

The hybrids had the greatest similarity to the pollen parent, but the flowers appeared less intensely coloured. Their fertility was very limited; from seventeen plants, which together developed many hundreds of flowers, only forty-nine seeds in all were obtained. These were of medium size, and were flecked and splashed similarly to those of _Ph. multiflorus_, while the ground colour was not materially different. The next year forty-four plants were raised from these seeds, of which only thirty-one reached the flowering stage. The characters of _Ph. nanus_, which had been altogether latent in the hybrids, reappeared in various combinations; their ratio, however, with relation to the dominant characters was necessarily very fluctuating owing to the small number of trial plants. With certain characters, as in those of the axis and the form of pod, it was, however, as in the case of _Pisum_, almost exactly 1 : 3.

Insignificant as the results of this experiment may be as regards the determination of the relative numbers in which the various forms appeared, it presents, on the other hand, the phenomenon of a remarkable change of colour in the flowers and seed of the hybrids. In _Pisum_ it is known that the characters of the flower- and seed-colour present themselves unchanged in the first and further generations, and that the offspring of the hybrids display exclusively the one or the other of the characters of the original stocks[43]. It is otherwise in the experiment we are considering. The white flowers and the seed-colour of _Ph. nanus_ appeared, it is true, at once in the first generation [_from_ the hybrids] in one fairly fertile example, but the remaining thirty plants developed flower colours which were of various grades of purple-red to pale violet. The colouring of the seed-coat was no less varied than that of the flowers. No plant could rank as fully fertile; many produced no fruit at all; others only yielded fruits from the flowers last produced, which did not ripen. From fifteen plants only were well-developed seeds obtained. The greatest disposition to infertility was seen in the forms with preponderantly red flowers, since out of sixteen of these only four yielded ripe seed. Three of these had a similar seed pattern to _Ph. multiflorus_, but with a more or less pale ground colour; the fourth plant yielded only one seed of plain brown tint. The forms with preponderantly violet coloured flowers had dark brown, black-brown, and quite black seeds.

[43] [This is the only passage where Mendel can be construed as
asserting universal dominance for _Pisum_; and even here, having
regard to the rest of the paper, it is clearly unfair to represent
him as predicating more than he had seen in his own experiments.
Moreover in flower and seed-coat colour (which is here meant), using
his characters dominance must be almost universal, if not quite.]

The experiment was continued through two more generations under similar unfavourable circumstances, since even among the offspring of fairly fertile plants there were still some which were less fertile or even quite sterile. Other flower- and seed-colours than those cited did not subsequently present themselves. The forms which in the first generation [bred from the hybrids] contained one or more of the recessive characters remained, as regards these, constant without exception. Also of those plants which possessed violet flowers and brown or black seed, some did not vary again in these respects in the next generation; the majority, however, yielded, together with offspring exactly like themselves, some which displayed white flowers and white seed-coats. The red flowering plants remained so slightly fertile that nothing can be said with certainty as regards their further development.

Despite the many disturbing factors with which the observations had to contend, it is nevertheless seen by this experiment that the development of the hybrids, with regard to those characters which concern the form of the plants, follows the same laws as does _Pisum_. With regard to the colour characters, it certainly appears difficult to perceive a substantial agreement. Apart from the fact that from the union of a white and a purple-red colouring a whole series of colours results, from purple to pale violet and white, the circumstance is a striking one that among thirty-one flowering plants only one received the recessive character of the white colour, while in _Pisum_ this occurs on the average in every fourth plant.

Even these enigmatical results, however, might probably be explained by the law governing _Pisum_ if we might assume that the colour of the flowers and seeds of _Ph. multiflorus_ is a combination of two or more entirely independent colours, which individually act like any other constant character in the plant. If the flower colour A were a combination of the individual characters _A_{1} + _A_{2} + ... which produce the total impression of a purple colouration, then by fertilisation with the differentiating character, white colour, _a_, there would be produced the hybrid unions _A_{1}_a_ + _A_{2}_a_ + ... and so would it be with the corresponding colouring of the seed-coats[44]. According to the above assumption, each of these hybrid colour unions would be independent, and would consequently develop quite independently from the others. It is then easily seen that from the combination of the separate developmental series a perfect colour-series must result. If, for instance, _A_ = _A_{1} + _A_{2}, then the hybrids _A_{1}_a_ and _A_{2}_a_ form the developmental series--

_A_{1} + 2_A_{1}_a_ + _a_
_A_{2} + 2_A_{2}_a_ + _a_.

[44] [It appears to me clear that this expression is incorrectly
given, and the argument regarding compound characters is consequently
not legitimately developed. The original compound character should
be represented as _A_{1}_A_{2}_A_{3} ... which when fertilised by
_a_{1} gives _A_{1}_A_{2}_A_{3} ... a as the hybrid of the first
generation. Mendel practically tells us these were all alike,
and there is nothing to suggest that they were diverse. When on
self-fertilisation, they break up, they will produce the gametes he
specifies; but they may also produce _A_{1}_A_{1} and _A_{2}_A_{2},
_A_{1}_A_{2}_a_, &c., thereby introducing terms of a nature different
from any indicated by him. That this point is one of the highest
significance, both practical and theoretical, is evident at once.]

The members of this series can enter into nine different combinations, and each of these denotes another colour[45]--

1 _A_{1}A_{2}_ 2 _A_{1}aA_{2}_ 1 _A_{2}a_
2 _A_{1}A_{2}a_ 4 _A_{1}aA_{2}a_ 2 _A_{2}aa_
1 _A_{1}a_ 2 _A_{1}aa_ 1 _aa_.

[45] [It seems very doubtful if the zygotes are correctly represented
by the terms _A_{1}aA_{2}a_, _A_{2}aa_, _A_{1}aa_; for in the hybrids
_A_{1}a_, &c. the allelomorphs _A_{1}_ and _a_, &c. should by
hypothesis be separated in the gametes.]

The figures prescribed for the separate combinations also indicate how many plants with the corresponding colouring belong to the series. Since the total is sixteen, the whole of the colours are on the average distributed over each sixteen plants, but, as the series itself indicates, in unequal proportions.

Should the colour development really happen in this way, we could offer an explanation of the case above described, viz. that the white flowers and seed-coat colour only appeared once among thirty-one plants of the first generation. This colouring appears only once in the series, and could therefore also only be developed once in the average in each sixteen, and with three colour characters only once even in sixty-four plants.

It must, however, not be forgotten that the explanation here attempted is based on a mere hypothesis, only supported by the very imperfect result of the experiment just described. It would, however, be well worth while to follow up the development of colour in hybrids by similar experiments, since it is probable that in this way we might learn the significance of the extraordinary variety in the colouring of our ornamental flowers.

So far, little at present is known with certainty beyond the fact that the colour of the flowers in most ornamental plants is an extremely variable character. The opinion has often been expressed that the stability of the species is greatly disturbed or entirely upset by cultivation, and consequently there is an inclination to regard the development of cultivated forms as a matter of chance devoid of rules; the colouring of ornamental plants is indeed usually cited as an example of great instability. It is, however, not clear why the simple transference into garden soil should result in such a thorough and persistent revolution in the plant organism. No one will seriously maintain that in the open country the development of plants is ruled by other laws than in the garden bed. Here, as there, changes of type must take place if the conditions of life be altered, and the species possesses the capacity of fitting itself to its new environment. It is willingly granted that by cultivation the origination of new varieties is favoured, and that by man’s labour many varieties are acquired which, under natural conditions, would be lost; but nothing justifies the assumption that the tendency to the formation of varieties is so extraordinarily increased that the species speedily lose all stability, and their offspring diverge into an endless series of extremely variable forms. Were the change in the conditions of vegetation the sole cause of variability we might expect that those cultivated plants which are grown for centuries under almost identical conditions would again attain constancy. That, as is well known, is not the case, since it is precisely under such circumstances that not only the most varied but also the most variable forms are found. It is only the _Leguminosæ_, like _Pisum_, _Phaseolus_, _Lens_, whose organs of fertilisation are protected by the keel, which constitute a noteworthy exception. Even here there have arisen numerous varieties during a cultural period of more than 1000 years; these maintain, however, under unchanging environments a stability as great as that of species growing wild.

It is more than probable that as regards the variability of cultivated plants there exists a factor which so far has received little attention. Various experiments force us to the conclusion that our cultivated plants, with few exceptions, are _members of various hybrid series_, whose further development in conformity with law is changed and hindered by frequent crossings _inter se_. The circumstance must not be overlooked that cultivated plants are mostly grown in great numbers and close together, affording the most favourable conditions for reciprocal fertilisation between the varieties present and the species itself. The probability of this is supported by the fact that among the great array of variable forms solitary examples are always found, which in one character or another remain constant, if only foreign influence be carefully excluded. These forms develop precisely as do those which are known to be members of the compound hybrid series. Also with the most susceptible of all characters, that of colour, it cannot escape the careful observer that in the separate forms the inclination to vary is displayed in very different degrees. Among plants which arise from _one_ spontaneous fertilisation there are often some whose offspring vary widely in the constitution and arrangement of the colours, while others furnish forms of little deviation, and among a greater number solitary examples occur which transmit the colour of the flowers unchanged to their offspring. The cultivated species of _Dianthus_ afford an instructive example of this. A white-flowered example of _Dianthus caryophyllus_, which itself was derived from a white-flowered variety, was shut up during its blooming period in a greenhouse; the numerous seeds obtained therefrom yielded plants entirely white-flowered like itself. A similar result was obtained from a subspecies, with red flowers somewhat flushed with violet, and one with flowers white, striped with red. Many others, on the other hand, which were similarly protected, yielded progeny which were more or less variously coloured and marked.

Whoever studies the colouration which results in ornamental plants from similar fertilisation can hardly escape the conviction that here also the development follows a definite law which possibly finds its expression _in the combination of several independent colour characters_.

CONCLUDING REMARKS.

It can hardly fail to be of interest to compare the observations made regarding _Pisum_ with the results arrived at by the two authorities in this branch of knowledge, Kölreuter and Gärtner, in their investigations. According to the opinion of both, the hybrids in outer appearance present either a form intermediate between the original species, or they closely resemble either the one or the other type, and sometimes can hardly be discriminated from it. From their seeds usually arise, if the fertilisation was effected by their own pollen, various forms which differ from the normal type. As a rule, the majority of individuals obtained by one fertilisation maintain the hybrid form, while some few others come more like the seed parent, and one or other individual approaches the pollen parent. This, however, is not the case with all hybrids without exception. With some the offspring have more nearly approached, some the one and some the other, original stock, or they all incline more to one or the other side; while with others _they remain perfectly like the hybrid_ and continue constant in their offspring. The hybrids of varieties behave like hybrids of species, but they possess greater variability of form and a more pronounced tendency to revert to the original type.

With regard to the form of the hybrids and their development, as a rule an agreement with the observations made in _Pisum_ is unmistakable. It is otherwise with the exceptional cases cited. Gärtner confesses even that the exact determination whether a form bears a greater resemblance to one or to the other of the two original species often involved great difficulty, so much depending upon the subjective point of view of the observer. Another circumstance could, however, contribute to render the results fluctuating and uncertain, despite the most careful observation and differentiation; for the experiments plants were mostly used which rank as good species and are differentiated by a large number of characters. In addition to the sharply defined characters, where it is a question of greater or less similarity, those characters must also be taken into account which are often difficult to define in words, but yet suffice, as every plant specialist knows, to give the forms a strange appearance. If it be accepted that the development of hybrids follows the law which is valid for _Pisum_, the series in each separate experiment must embrace very many forms, since the number of the components, as is known, increases with the number of the differentiating characters in _cubic ratio_. With a relatively small number of experimental-plants the result therefore could only be approximately right, and in single cases might fluctuate considerably. If, for instance, the two original stocks differ in seven characters, and 100 and 200 plants were raised from the seeds of their hybrids to determine the grade of relationship of the offspring, we can easily see how uncertain the decision must become, since for seven differentiating characters the combination series contains 16,384 individuals under 2187 various forms; now one and then another relationship could assert its predominance, just according as chance presented this or that form to the observer in a majority of cases.

If, furthermore, there appear among the differentiating characters at the same time dominant characters, which are transferred entire or nearly unchanged to the hybrids, then in the terms of the developmental series that one of the two original stocks which possesses the majority of dominant characters must always be predominant. In the experiment described relative to _Pisum_, in which three kinds of differentiating characters were concerned, all the dominant characters belonged to the seed parent. Although the terms of the series in their internal composition approach both original stock plants equally, in this experiment the type of the seed parent obtained so great a preponderance that out of each sixty-four plants of the first generation fifty-four exactly resembled it, or only differed in one character. It is seen how rash it may be under such circumstances to draw from the external resemblances of hybrids conclusions as to their internal nature.

Gärtner mentions that in those cases where the development was regular among the offspring of the hybrids the two original species were not reproduced, but only a few closely approximating individuals. With very extended developmental series it could not in fact be otherwise. For seven differentiating characters, for instance, among more than 16,000 individuals--offspring of the hybrids--each of the two original species would occur only once. It is therefore hardly possible that these should appear at all among a small number of experimental plants; with some probability, however, we might reckon upon the appearance in the series of a few forms which approach them.

We meet with an _essential difference_ in those hybrids which remain constant in their progeny and propagate themselves as truly as the pure species. According to Gärtner, to this class belong the _remarkably fertile hybrids_ _Aquilegia atropurpurea canadensis_, _Lavatera pseudolbia thuringiaca_, _Geum urbano-rivale_, and some _Dianthus_ hybrids; and, according to Wichura, the hybrids of the Willow species. For the history of the evolution of plants this circumstance is of special importance, since constant hybrids acquire the status of new species. The correctness of this is evidenced by most excellent observers, and cannot be doubted. Gärtner had opportunity to follow up _Dianthus Armeria deltoides_ to the tenth generation, since it regularly propagated itself in the garden.

With _Pisum_ it was shown by experiment that the hybrids form egg and pollen cells of _different_ kinds, and that herein lies the reason of the variability of their offspring. In other hybrids, likewise, whose offspring behave similarly we may assume a like cause; for those, on the other hand, which remain constant the assumption appears justifiable that their fertilising cells are all alike and agree with the foundation-cell [fertilised ovum] of the hybrid. In the opinion of renowned physiologists, for the purpose of propagation one pollen cell and one egg cell unite in Phanerogams[46] into a single cell, which is capable by assimilation and formation of new cells to become an independent organism. This development follows a constant law, which is founded on the material composition and arrangement of the elements which meet in the cell in a vivifying union. If the reproductive cells be of the same kind and agree with the foundation cell [fertilised ovum] of the mother plant, then the development of the new individual will follow the same law which rules the mother plant. If it chance that an egg cell unites with a _dissimilar_ pollen cell, we must then assume that between those elements of both cells, which determine the mutual differences, some sort of compromise is effected. The resulting compound cell becomes the foundation of the hybrid organism, the development of which necessarily follows a different scheme from that obtaining in each of the two original species. If the compromise be taken to be a complete one, in the sense, namely, that the hybrid embryo is formed from cells of like kind, in which the differences are _entirely and permanently accommodated_ together, the further result follows that the hybrids, like any other stable plant species, remain true to themselves in their offspring. The reproductive cells which are formed in their seed vessels and anthers are of one kind, and agree with the fundamental compound cell [fertilised ovum].

[46] In _Pisum_ it is placed beyond doubt that for the formation of
the new embryo a perfect union of the elements of both fertilising
cells must take place. How could we otherwise explain that among
the offspring of the hybrids both original types reappear in equal
numbers and with all their peculiarities? If the influence of the
egg cell upon the pollen cell were only external, if it fulfilled
the _rôle_ of a nurse only, then the result of each artificial
fertilisation could be no other than that the developed hybrid
should exactly resemble the pollen parent, or at any rate do so very
closely. This the experiments so far have in no wise confirmed. An
evident proof of the complete union of the contents of both cells is
afforded by the experience gained on all sides that it is immaterial,
as regards the form of the hybrid, which of the original species is
the seed parent or which the pollen parent.

With regard to those hybrids whose progeny is _variable_ we may perhaps assume that between the differentiating elements of the egg and pollen cells there also occurs a compromise, in so far that the formation of a cell as foundation of the hybrid becomes possible; but, nevertheless, the arrangement between the conflicting elements is only temporary and does not endure throughout the life of the hybrid plant. Since in the habit of the plant no changes are perceptible during the whole period of vegetation, we must further assume that it is only possible for the differentiating elements to liberate themselves from the enforced union when the fertilising cells are developed. In the formation of these cells all existing elements participate in an entirely free and equal arrangement, in which it is only the differentiating ones which mutually separate themselves. In this way the production would be rendered possible of as many sorts of egg and pollen cells as there are combinations possible of the formative elements.

The attribution attempted here of the essential difference in the development of hybrids to _a permanent or temporary union_ of the differing cell elements can, of course, only claim the value of an hypothesis for which the lack of definite data offers a wide field. Some justification of the opinion expressed lies in the evidence afforded by _Pisum_ that the behaviour of each pair of differentiating characters in hybrid union is independent of the other differences between the two original plants, and, further, that the hybrid produces just so many kinds of egg and pollen cells as there are possible constant combination forms. The differentiating characters of two plants can finally, however, only depend upon differences in the composition and grouping of the elements which exist in the foundation-cells [fertilised ova] of the same in vital interaction[47].

[47] “_Welche in den Grundzellen derselben in lebendiger
Wechselwirkung stehen._”

Even the validity of the law formulated for _Pisum_ requires still to be confirmed, and a repetition of the more important experiments is consequently much to be desired, that, for instance, relating to the composition of the hybrid fertilising cells. A differential [element] may easily escape the single observer[48], which although at the outset may appear to be unimportant, may yet accumulate to such an extent that it must not be ignored in the total result. Whether the variable hybrids of other plant species observe an entire agreement must also be first decided experimentally. In the meantime we may assume that in material points a difference in principle can scarcely occur, since the unity in the developmental plan of organic life is beyond question.

[48] “_Dem einzelnen Beobachter kann leicht ein Differenziale
entgehen._”

In conclusion, the experiments carried out by Kölreuter, Gärtner, and others with respect to _the transformation of one species into another by artificial fertilisation_ merit special mention. A special importance has been attached to these experiments, and Gärtner reckons them among “the most difficult of all in hybridisation.”

If a species _A_ is to be transformed into a species _B_, both must be united by fertilisation and the resulting hybrids then be fertilised with the pollen of _B_; then, out of the various offspring resulting, that form would be selected which stood in nearest relation to _B_ and once more be fertilised with _B_ pollen, and so continuously until finally a form is arrived at which is like _B_ and constant in its progeny. By this process the species _A_ would change into the species _B_. Gärtner alone has effected thirty such experiments with plants of genera _Aquilegia_, _Dianthus_, _Geum_, _Lavatera_, _Lychnis_, _Malva_, _Nicotiana_, and _Œnothera_. The period of transformation was not alike for all species. While with some a triple fertilisation sufficed, with others this had to be repeated five or six times, and even in the same species fluctuations were observed in various experiments. Gärtner ascribes this difference to the circumstance that “the specific [_typische_] force by which a species, during reproduction, effects the change and transformation of the maternal type varies considerably in different plants, and that, consequently, the periods within which the one species is changed into the other must also vary, as also the number of generations, so that the transformation in some species is perfected in more, and in others in fewer generations.” Further, the same observer remarks “that in these transformation experiments a good deal depends upon which type and which individual be chosen for further transformation.”

If it may be assumed that in these experiments the constitution of the forms resulted in a similar way to that of _Pisum_, the entire process of transformation would find a fairly simple explanation. The hybrid forms as many kinds of egg cells as there are constant combinations possible of the characters conjoined therein, and one of these is always of the same kind as the fertilising pollen cells. Consequently there always exists the possibility with all such experiments that even from the second fertilisation there may result a constant form identical with that of the pollen parent. Whether this really be obtained depends in each separate case upon the number of the experimental plants, as well as upon the number of differentiating characters which are united by the fertilisation. Let us, for instance, assume that the plants selected for experiment differed in three characters, and the species _ABC_ is to be transformed into the other species _abc_ by repeated fertilisation with the pollen of the latter; the hybrids resulting from the first cross form eight different kinds of egg cells, viz.:

_ABC_, _ABc_, _AbC_, _aBC_, _Abc_, _aBc_, _abC_, _abc_.

These in the second year of experiment are united again with the pollen cells _abc_, and we obtain the series

_AaBbCc_ + _AaBbc_ + _AabCc_ + _aBbCc_ + _Aabc_ + _aBbc_ + _abCc_ + _abc_.

Since the form _abc_ occurs once in the series of eight components, it is consequently little likely that it would be missing among the experimental plants, even were these raised in a smaller number, and the transformation would be perfected already by a second fertilisation. If by chance it did not appear, then the fertilisation must be repeated with one of those forms nearest akin, _Aabc_, _aBbc_, _abCc_. It is perceived that such an experiment must extend the farther _the smaller the number of experimental plants and the larger the number of differentiating characters_ in the two original species; and that, furthermore, in the same species there can easily occur a delay of one or even of two generations such as Gärtner observed. The transformation of widely divergent species could generally only be completed in five or six years of experiment, since the number of different egg cells which are formed in the hybrid increases in square ratio with the number of differentiating characters.