Pedagogical Anthropology by Maria Montessori (new books to read .TXT) 📖
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They have also been verified in certain animals, such as mice, rats, rabbits, caveys, poultry, snails, silk-worms, etc. One of the most typical experiments was that of Cuénot, who, by crossing ordinary mice with jumping mice, obtained as a result a first generation composed wholly of normal mice; the characteristic of jumping was thus shown to be recessive.
Notwithstanding that the first generation is apparently in every way similar to the parent with the dominant character, there is in reality a difference.
Because, if we cross these hybrids together, we meet, in the second generation, with the following phenomenon: to every three individuals possessing the dominant character, one is born having the recessive character. To go back to Mendel's first example, that of the peas with red flowers (dominant) and with white flowers (recessive), we find, by crossing together the hybrids of the first generation, that for every three plants with red flowers, there is one plant with white flowers.
And similarly, the crossing of hybrid nettles with indented leaves will result in a second generation composed of three plants with indented leaves to every one with smooth-edged leaves (see Fig. 5).
Fig. 5.
That is, the characteristics which belonged to the first two parents all survive, even though in a latent form, in the descendants; and they continue to differentiate themselves in well established proportions. In one offspring out of four, the characteristics of the grandfather, which have remained dormant in the father, once more reappear. This intermittent heredity of characteristics, that are passed from grandfather to grandson, overleaping the father, is one of the best-known laws of pathological heredity in man; and it is called atavistic heredity, to distinguish it from direct heredity, which denotes the transmission from parent to offspring. But no explanation had ever been found for this sort of phenomenon. Undoubtedly, it must be connected with the phenomena of Mendelism.
Accordingly, in the second generation Mendel's second law has been established, the law of disjunction, which is stated as follows:
Mendel's Second Law: "In the second generation obtained by reciprocal fertilisation of the first hybrids, three quarters of the offspring will exhibit the dominant character, and one quarter the recessive."
Mendel's Hypothesis, Designed to Explain the Phenomena of Heredity.—Mendel's great service is to have conceived a hypothesis that seems to have disclosed the key adapted to unlock all the secrets of heredity.
While the body of an individual is the resultant of forces so mutually exclusive that the appearance of one characteristic means the disappearance of its antagonist; in the development of the sexual cells the two antagonistic characters are distributed in equal proportion. That is to say, one-half of the male cells contain the dominant character, and one-half the recessive; and the same holds true for the female cells. The characters of the two parents, in other words, never merge in the reproductive cells, but are distributed in equal measure, independently of the question whether they are dominant or recessive. Thus for example: in the case already cited of the first hybrid generation of the peas with red flowers, in every one of the plants, without distinction, half the pollen has potentially the red character and half has the white; and in the same way the female cells have, half of them a red potentiality and half of them a white. Such hybrids of the first generation, therefore, although apparently similar to the parent with red flowers, differ in their germinative powers, which are not made apparent in the individual. And the same may be said of hybrid nettles with indented leaves, etc.
Granting Mendel's hypothesis, we have on the one hand pollen and on the other seed ready to come together in every manner included within the range of possible combinations; the individual is, in its characteristics, nothing else than the product of a combination which must necessarily manifest itself in accordance with the well-known mathematical laws of probability.
For instance, let us proceed to diagram the possible disposition of the sexual cells of the hybrids of peas, all of them having red flowers. In terms of percentage, they will give, out of every hundred, fifty red and fifty white.
P = pollen; O = ova; R = red, dominant; w = white, recessive:
The possible number of combinations between the pollen grains and the ova are four; namely, RR, Rw, wR, ww. But where a dominant characteristic encounters a recessive (Rw, wR), the recessive disappears, to make way in the individual for the dominant characteristic alone. The definitive result is three individuals of dominant character, to one of recessive character.
Fig. 6.
Nevertheless, the hybrids of dominant character are not all equal among themselves. Those belonging to the combination RR, indeed, are permanent in character and in all respects alike, and they reproduce the original red-flower progenitor. The other red-flower hybrids, belonging to the groups Rw and wR are, on the contrary, similar to the hybrids of the first generation and contain reproductive cells differentiated in character; such hybrids, if reciprocally fertilised, will again give three dominant offspring to every one recessive; that is, they will obey the law of disjunction. The hybrids belonging to the fourth group, on the contrary, are constant, like those of the first group, and are permanently of recessive character; and they will reproduce the original progenitor with white flowers.
The same results may be attained with nettles with smooth and indented leaves, and with all other types of plant and animal life that obey the laws of Mendelism.
The figure given actually represents the third generation of nettles; from a combination corresponding to RR, there result only indented leaves, and from another combination corresponding to our ww there result only smooth-edged leaves, and from the two mixed groups there come three offspring with indented leaves to every one with smooth leaves.
It is possible to represent, by means of a general diagram, the mathematical succession of characteristics in hybrids, after the following manner; denoting the dominant character by D, and the recessive by r.
First crossing of individuals with antagonistic characters.
First generation of hybrids, all alike, and similar to the progenitor D (dominant).
Second generation: for each recessive there are three dominant: but of these only one is permanent.
Third generation: disjunction of the hybrid groups takes place and new permanent groups are formed.
Fig. 7.
In each successive generation, provided the fertilisation takes place only between uniform individuals, as indicated in the diagram, and as may be effected by actual experiment with plants, groups identical with the original progenitors will continue to be formed, through successive disjunction of the hybrids; the sexual phenomenon operating in obedience to the laws of probability.
An effective experiment, that anyone may repeat for himself, is the one originated by Darbishire. He took two boxes, typifying respectively the male and female organ, and placed in them black and white disks of equal size, so distributed that each box contained fifty disks of each colour. After mixing these disks very carefully, he proceeded to take at random one disk at a time alternately from each box; and he piled up each pair of disks in such a manner that the black ones should be on top and the white underneath. The result was that for every three black disks on top of the piles there was one white disk; but of the black groups one consisted of two black disks, while in the other two the lower disk was white. This is simply one of the many games dependent on the laws of probability.
Now, supposing that instead of one, there are two characteristics that are in antagonism; in that case, we have the occurrence of double hybridism (dihybridism).
Let us take the strains of peas already considered, but let us choose for observation the character of their seed. One of the plants has round seed and yellow cotyledons; and the other angular seed and green cotyledons. These two characteristics, therefore, are both inherent in the seed; condition of surface (rough, smooth), and colour (green, and yellow).
After fertilisation, Mendel's first law, that of the prevalence of the dominant character, will operate, and all the plants of the first generation will have round seed and yellow cotyledons. Hence these are the dominant characteristics, which we will represent by capital letters: R (round), Y (yellow), to distinguish them from the recessive characteristics, which we will designate with small letters: a (angular), and g (green).
According to Mendel's hypothesis, all these hybrids with round seed and yellow cotyledons, contain sexual cells of opposite potentialities, numerically equal and corresponding to the antagonistic characters of the parent plants. That is, they must have in their pollen grains and their ovarian cells all the possible combinations of their different potentialities.
They should produce in equal quantities:
pollen grains (P) with round seed and yellow cotyledons: R Y " " green " R g angular " yellow " a Y " " green " a g ovarian cells (O) with round " yellow " R Y " " green " R g angular " yellow " a Y " " green " a gThe total number of combinations that may result is sixteen; that is, each one of the four combinations of pollen may unite with any one of the ovarian cells; thus constituting four groups of four. And these groups represent the combinations (of pollen and ova) capable of producing individuals:
R Y - R Y = R Y a Y - R Y = R Y R Y - R g = R Y a Y - R g = R Y R Y - a Y = R Y a Y - a Y = a Y R Y - a g = R Y a Y - a g = a Y R g - R Y = R Y a g - R Y = R Y R g - R g = R g a g - R g = R g R g - a Y = R Y a g - a Y = a Y R g - a g = R g a g - a g = a gFig. 8.
Every time that a dominant characteristic encounters a recessive one (R with a or Y with g), it overpowers and hides it: consequently the results of the different combinations are quite definitely limited as determining forms of different individuals. In fact, the results of the sixteen combinations are as follows:
R Y R Y R Y R Y R Y a Y R Y a Y R Y R Y R g R g R Y a Y R g a gThat is to say, the only forms which occur are the following:
R Y, R g
a Y, a g
whose relative probability of occurrence is:
R Y 9 times in 16 = 56.25% R g 3 times in 16 = 18.75% a Y 3 times in 16 = 18.75% a g 1 time in 16 = 6.25%Now, as a result of actual experiment, the forms obtained show the following relative percentage:
Results of experiments with plants according to the combinations and laws of probability R Y 56.5% 56.25% R g 19.75% 18.75% a Y 18.2% 18.75% a g 5.8% 6.25%The correspondence between these figures is close enough to warrant the acceptance of Mendel's hypothesis as the true interpretation of the phenomena that are shown to take place within the sexual cells; the germinal cells of the hybrid contain potentialities belonging to one or the other only of the parents, and not to both; one-half of the cells contain one of these potentialities, and the other half the other potentiality.
But in the phenomena of hybridism, we have seen the results of another fact which determines Mendel's third law; the Law of the Independence of Characteristics.
That is,
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