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.