This simple law for the constitution of the second generation of
varietal hybrids with a single differentiating mark in their parents is
called the law of Mendel. Mendel published it in 1865, but his paper
remained nearly unknown to scientific hybridists. It is only of late
years that it has assumed a high place in scientific literature, and
attained the first rank as an investigation on fundamental questions of
heredity. [294] Read in the light of modern ideas on unit characters it
is now one of the most important works on heredity and has already
widespread and abiding influence on the philosophy of hybridism in
general.
But from its very nature and from the choice of the material made by
Mendel, it is restricted to balanced or varietal crosses. It assumes
pairs of characters and calls the active unit of the pair dominant, and
the latent recessive, without further investigations of the question of
latency. It was worked out by Mendel for a large group of varieties of
peas, but it holds good, with only apparent exceptions, for a wide range
of cases of crosses of varietal characters. Recently many instances have
been tested, and even in many cases third and later generations have
been counted, and whenever the evidence was complete enough to be
trusted, Mendel's prophecy has been found to be right.
According to this law of Mendel's the pairs of antagonistic characters
in the hybrid split up in their progeny, some individuals reverting to
the pure parental types, some crossing with each other anew, and so
giving rise to a new generation of hybrids. Mendel has given a very
suggestive and simple explanation of his formula. Putting this in the
terminology of to-day, and limiting it to the occurrence of only [295]
one differential unit in the parents, we may give it in the following
manner. In fertilization, the characters of both parents are not
uniformly mixed, but remain separated though most intimately combined in
the hybrid throughout life. They are so combined as to work together
nearly always, and to have nearly equal influence on all the processes
of the whole individual evolution. But when the time arrives to produce
progeny, or rather to produce the sexual cells through the combination
of which the offspring arises, the two parental characters leave each
other, and enter separately into the sexual cells. From this it may be
seen that one-half of the pollen-cells will have the quality of one
parent, and the other the quality of the other. And the same holds good
for [296] the egg-cells. Obviously the qualities lie latent in the
pollen and in the egg, but ready to be evolved after fertilization has
taken place.
Granting these premises, we may now ask as to the results of the
fertilization of hybrids, when this is brought about by their own
pollen. We assume that numerous pollen grains fertilize numerous egg
cells. This assumption at once allows of applying the law of
probability, and to infer that of each kind of pollen grains one-half
will reach egg-cells with the same quality [297] and the other half
ovules with the opposite character.
Calling P pollen and O ovules, and representing the active mark by P and
O, the latent qualities by P' and O', they would combine as follows:
P + 0 giving uniform pairs with the active mark,
P + 0' giving unequal pairs,
P' + 0 giving unequal pairs,
P' + 0' giving uniform pairs with the latent mark.
In this combination the four groups are obviously of the same size, each
containing one-fourth of the offspring. Manifestly they correspond
exactly to the direct results of the experiments, P + O representing the
individuals which reverted to the specific mark, P' + O' those who
reassumed the varietal quality and P + O' and P + O' those who
hybridized [298] for the second time. These considerations lead us to
the following form of Mendel's,
P + O = 1/4 Active or 1A,
P + O'
> = 1/2 Hybrid or 2 H,
P' + O
P' + O' = 1/4 Latent or 1 L,
Which is evidently the same as Mendel's empirical law given above.
To give the proof of these assumptions Mendel has devised a very simple
crossing experiment, [299] which he has effected with his varieties of
peas. I have repeated it with the sugar-corn, which gives far better
material for demonstration. It starts from the inference that if
dissimilarity among the pollen grains is excluded, the diversity of the
ovules must at once became manifest and vice versa. In other terms, if a
hybrid of the first generation is not allowed to fertilize itself, but
is pollinated by one of its parents, the result will be in accordance
with the Mendelian formula.
In order to see an effect on the spikes produced in this way, it is of
course necessary to fertilize them with the pollen of the variety, and
not with that of the specific type. The latter would give partly pure
starchy grains and partly hybrid kernels, but these would assume the
same type. But if we pollinate the hybrid with pollen of a pure
sugar-corn, we may predict the result as follows.
If the spike of the hybrid contains dormant paternal marks in one-half
of its flowers and in the other half maternal latent qualities, the
sugar-corn pollen will combine with one-half of the ovules to give
hybrids, and with the other half so as to give pure sugar-grains. Hence
we see that it will be possible to count out directly the two groups of
ovules on inspecting the ripe and dry spikes. Experience teaches us
[298] that both are present, and in nearly equal numbers; one-half of
the grains remaining smooth, and the other half becoming wrinkled.
The corresponding experiment could be made with plants of a pure
sugar-race by pollination with hybrid pollen. The spikes would show
exactly the same mixture as in the above case, but now this may be
considered as conclusive proof that half the pollen-grains represent the
quality of one parent and the other half the quality of the other.
Another corollary of Mendel's law is the following. In each generation
two groups return to purity, and one-half remains hybrid. These last
will repeat the same phenomenon of splitting in their progeny, and it is
easily seen that the same rule will hold good for all succeeding
generations. According to Mendel's principle, in each year there is a
new hybridization, differing in no respect from the first and original
one. If the hybrids only are propagated, each year will show one-fourth
of the offspring returning to the specific character, one-fourth
assuming the type of the variety and one-half remaining hybrid. I have
tested this with a hybrid between the ordinary nightshade with black
berries, and its variety, _Solanum nigrum chlorocarpum_, with pale
yellow fruits. Eight generations of the hybrids were cultivated, [299]
disregarding always the reverting offspring. At the end I counted the
progeny of the sixth and seventh generations and found figures for their
three groups of descendants, which exactly correspond to Mendel's
formula.
Until now we have limited ourselves to the consideration of single
differentiating units. This discussion gives a clear insight into the
fundamental phenomena of hybrid fertilization. It at once shows the
correctness of the assumption of unit-characters, and of their pairing
in the sexual combinations.
But Mendel's law is not at all restricted to these simple cases. Quite
on the contrary, it explains the most intricate questions of
hybridization, providing they do not transgress the limits of
symmetrical unions. But in this realm nearly all results may be
calculated beforehand, on the ground of the principle of probability.
Only one more assumption need be discussed. The several pairs of
antagonistic characters must be independent from, and uninfluenced by,
one another. This premise seems to hold good in the vast majority of
cases, though rare exceptions seem to be not entirely wanting. Hence the
necessity of taking all predictions from Mendel's law only as
probabilities, which will prove true in most, but not necessarily in all
cases. [300] But here we will limit ourselves to normal cases.
The first example to be considered is obviously the assumption that the
parents of a cross differ from each other in respect to two characters.
A good illustrative example is afforded by the thorn-apple. I have
crossed the blue flowered thorny form, usually known as _Datura Tatula_,
with the white thornless type, designated as _D. Stramonium inermis_.
Thorns and blue pigment are obviously active qualities, as they are
dominant in the hybrids. In the second generation both pairs of
characters are resolved into their constituents and paired anew
according to Mendel's law. After isolating my hybrids during the period
of flowering, I counted among their progeny:
128 individuals with blue flowers and thorns
47 individuals with blue flowers and without thorns
54 individuals with white flowers and thorns
21 individuals with white flowers and without thorns
----
250
The significance of these numbers may easily be seen, when we calculate
what was to be expected on the assumption that both characters follow
Mendel's law, and that both are independent from each other. Then we
would have three-fourths blue offspring and one-fourth individuals with
white flowers. Each of these [301] two groups would consist of
thorn-bearing and thornless plants, in the same numerical relation.
Thus, we come to the four groups observed in our experiment, and are
able to calculate their relative size in the following way:
Proportion
Blue with thorns 3/4 X 3/4 = 9/16 = 56.25% 9
Blue, unarmed 3/4 X 1/4 = 3/16 = 18.75% 3
White with thorns 1/4 X 3/4 = 3/16 = 18.75% 3
White, unarmed 1/4 X 1/4 = 1/16 = 6.25% 1
In order to compare this inference from Mendel's law and the assumption
of independency, with the results of our experiments, we must calculate
the figures of the latter in percentages. In this way we find:
Found Calculated
Blue with thorns 128=51% 56.25%
Blue unarmed 47=19% 18.75%
White with thorns 54=22% 18.75%
White unarmed 21= 8% 6.25%
The agreement of the experimental and the theoretical figures is as
close as might be expected.
This experiment is to be considered only as an illustrative example of a
rule of wide application. The rule obviously will hold good in all such
cases as comply with the two conditions already premised, viz.: that
each character agrees with Mendel's law, and that both are wholly
independent of each other. It is clear that our figures show the
numerical composition [302] of the hybrid offspring for any single
instance, irrespective of the morphological nature of the qualities
involved.
Mendel has proved the correctness of these deductions by his experiments
with peas, and by combining their color (yellow or green) with the
chemical composition (starch or sugar) and other pairs of characters. I
will now give two further illustrations afforded by crosses of the
ordinary campion. I used the red-flowered or day-campion, which is a
perennial herb, and a smooth variety of the white evening-campion, which
flowers as a rule in the first summer. The combination of flower-color
and pubescence gave the following composition for the second hybrid
generation:
Number % Calculation
Hairy and red 70 44 56.25%
Hairy and white 23 14 18.75%
Smooth and red 46 23 18.75%
Smooth and white 19 12 6.25%
For the combination of pubescence and the capacity of flowering in the
first year I found:
Number % Calculated
Hairy, flowering 286 52 56.25%
Hairy, without stem 128 23 18.75%
Smooth, flowering 96 17 18.75%
Smooth, without stem 42 8 6.25%
Many other cases have been tested by different writers and the general
result is the [303] applicability of Mendel's formula to all cases
complying with the given conditions.
Intentionally I have chosen for the last example two pairs of
antagonisms, relating to the same pair of plants, and which may be
tested in one experiment and combined in one calculation.
For the latter we need only assume the same conditions as mentioned
before, but now for three different qualities. It is easily seen that
the third quality would split each of our four groups into two smaller
ones in the proportion of 3/4 : 1/4.
We would then get eight groups of the following composition:
9/16 X 3/4 = 27/64 or 42.2%
9/16 X 1/4 = 9/64 " 14.1%
3/16 X 3/4 = 9/64 " 14.1%
3/16 X 1/4 = 3/64 " 4.7%
3/16 X 3/4 = 9/64 " 14.1%
3/16 X 1/4 = 3/64 " 4.7%
1/16 X 3/4 = 3/64 " 4.7%
1/16 X 1/4 = 1/64 " 1.6%
The characters chosen for our experiment include the absence of stem and
flowers in the first year, and therefore would require a second year to
determine the flower-color on the perennial specimens. Instead of doing
so I have taken another character, shown by the teeth of the capsules
when opening. These curve outwards [304] in the red campion, but lack
this capacity in the evening-campion, diverging only until an upright
position is reached. The combination of hairs, colors and teeth gives
eight groups, and the counting of their respective numbers of
individuals gave the following:
Teeth
Hairs Flowers of capsules Number % Calculated
Hairy red curved 91 47 42.2%
Hairy red straight 15 7.5 14.1%
Hairy white curved 23 12 14.1%
Hairy white straight 17 8.5 4.7%
Smooth red curved 23 12 14.1%
Smooth red straight 9 4.5 4.7%
Smooth white curved 5 2.5 4.7%
Smooth white straight 12 6 1.6%
The agreement is as comprehensive as might be expected from an
experiment with about 200 plants, and there can be no doubt that a
repetition on a larger scale would give still closer agreement.
In the same way we might proceed to crosses with four or more
differentiating characters. But each new character will double the
number of the groups. Four characters will combine into 16 groups, five
into 32, six into 64, seven into 128, etc. Hence it is easily seen that
the size of the experiments must be made larger and larger in the same
ratio, if we intend to expect numbers equally trustworthy. For [305]
seven differentiating marks 16,384 individuals are required for a
complete series. And in this set the group with the seven attributes all
in a latent condition would contain only a single individual.
Unfortunately the practical value of these calculations is not very
great. They indicate the size of the cultures required to get all the
possible combinations, and show that in ordinary cases many thousands of
individuals have to be cultivated, in order to exhaust the whole range
of possibilities. They further show that among all these thousands, only
very few are constant in all their characters; in fact, it may easily be
seen that with seven differentiating points among the 16,384 named
above, only one individual will have all the seven qualities in pure
active, and only one will have them all in a purely dormant condition.
Then there will be some with some attributes active and others latent,
but their numbers will also be very small. All others will split up in
the succeeding generation in regard to one or more of their apparently
active marks. And since only in very rare cases the stable hybrids can
be distinguished by external characters from the unstable ones, the
stability of each individual bearing a desired combination of characters
would have to be established by experiment [306] after pure
fertilization. Mendel's law teaches us to predict the difficulties, but
hardly shows any way to avoid them. It lays great stress on the old
prescript of isolation and pure fertilization, but it will have to be
worked out and applied to a large number of practical cases before it
will gain a preeminent influence in horticultural practice.
Or, as Bailey states it, we are only beginning to find a pathway through
the bewildering maze of hybridization.
This pathway is to be laid out with regard to the following
considerations. We are not to cross species or varieties, or even
accidental plants. We must cross unit-characters, and consider the
plants only as the bearers of these units. We may assume that these
units are represented in the hereditary substance of the cell-nucleus by
definite bodies of too small a size to be seen, but constituting
together the chromosomes. We may call these innermost representatives of
the unit-characters pangenes, in accordance with Darwin's hypothesis of
pangenesis, or give them any other name, or we may even wholly abstain
from such theoretical discussion, and limit ourselves to the conception
of the visible character-units. These units then may be present, or
lacking and in the first case active, or latent.
[307] True elementary species differ from each other in a number of
unit-characters, which do not contrast. They have arisen by progressive
mutation. One species has one kind of unit, another species has another
kind. On combining these, there can be no interchange. Mendelism assumes
such an interchange between units of the same character, but in a
different condition. Activity and latency are such conditions, and
therefore Mendel's law obviously applies to them. They require pairs of
antagonistic qualities, and have no connection whatever with those
qualities, which do not find an opponent in the other parent. Now, only
pure varieties afford such pure conditions. When undergoing further
modifications, some of them may be in the progressive line and others in
the retrogressive. Progressive modifications give new units, which are
not in contrast with any other, retrograde changes turn active units
into the latent condition and so give rise to pairs. Ordinary species
generally originate in this way, and hence differ from each other partly
in specific, partly in varietal characters. As to the first, they give
in their hybrids stable peculiarities, while as to the latter, they
split up according to Mendel's law.
Unpaired or unbalanced characters lie side by side with paired or
balanced qualities, and they [308] do so in nearly all the crosses made
for practical purposes, and in very many scientific experiments. Even
Mendel's peas were not pure in this respect, much less do the campions
noted above differ only in Mendelian characters.
Comparative and systematic studies must be made to ascertain the true
nature of every unit in every single plant, and crossing experiments
must be based on these distinctions in order to decide what laws are
applicable in any case.
[309]
D. EVER-SPORTING VARIETIES