Mendel's Principles of Heredity: A Defence · William Bateson
Those forms which in the first generation maintain the recessive character do not further vary in the second generation as regards this character; they remain constant in their offspring.
It is otherwise with those which possess the dominant character in the first generation [bred from the hybrids]. Of these two-thirds yield offspring which display the dominant and recessive characters in the proportion of 3 to 1, and thereby show exactly the same ratio as the hybrid forms, while only one-third remains with the dominant character constant.
The separate experiments yielded the following results:--
Expt. 1.--Among 565 plants which were raised from round seeds of the first generation, 193 yielded round seeds only, and remained therefore constant in this character; 372, however, gave both round and angular seeds, in the proportion of 3 to 1. The number of the hybrids, therefore, as compared with the constants is 1·93 to 1.
Expt. 2.--Of 519 plants which were raised from seeds whose albumen was of yellow colour in the first generation, 166 yielded exclusively yellow, while 353 yielded yellow and green seeds in the proportion of 3 to 1. There resulted, therefore, a division into hybrid and constant forms in the proportion of 2·13 to 1.
For each separate trial in the following experiments 100 plants were selected which displayed the dominant character in the first generation, and in order to ascertain the significance of this, ten seeds of each were cultivated.
Expt. 3.--The offspring of 36 plants yielded exclusively grey-brown seed-coats, while of the offspring of 64 plants some had grey-brown and some had white.
Expt. 4.--The offspring of 29 plants had only simply inflated pods; of the offspring of 71, on the other hand, some had inflated and some constricted.
Expt. 5.--The offspring of 40 plants had only green pods; of the offspring of 60 plants some had green, some yellow ones.
Expt. 6.--The offspring of 33 plants had only axial flowers; of the offspring of 67, on the other hand, some had axial and some terminal flowers.
Expt. 7.--The offspring of 28 plants inherited the long axis, and those of 72 plants some the long and some the short axis.
In each of these experiments a certain number of the plants came constant with the dominant character. For the determination of the proportion in which the separation of the forms with the constantly persistent character results, the two first experiments are of especial importance, since in these a larger number of plants can be compared. The ratios 1·93 to 1 and 2·13 to 1 gave together almost exactly the average ratio of 2 to 1. The sixth experiment has a quite concordant result; in the others the ratio varies more or less, as was only to be expected in view of the smaller number of 100 trial plants. Experiment 5, which shows the greatest departure, was repeated, and then in lieu of the ratio of 60 and 40 that of 65 and 35 resulted. The average ratio of 2 to 1 appears, therefore, as fixed with certainty. It is therefore demonstrated that, of those forms which possess the dominant character in the first generation, in two-thirds the hybrid character is embodied, while one-third remains constant with the dominant character.
The ratio of 3 to 1, in accordance with which the distribution of the dominant and recessive characters results in the first generation, resolves itself therefore in all experiments into the ratio of 2 : 1 : 1 if the dominant character be differentiated according to its significance as a hybrid character or a parental one. Since the members of the first generation spring directly from the seed of the hybrids, it is now clear that the hybrids form seeds having one or other of the two differentiating characters, and of these one-half develop again the hybrid form, while the other half yield plants which remain constant and receive the dominant or recessive characters [respectively] in equal numbers.
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 + 2Aa + 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.
In the experiments above described plants were used which differed only in one essential character. 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.
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 + 2ABb + 2aBb + 2AaB + 2Aab + 4AaBb.
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 + 2Aa + a B + 2Bb + 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. 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.
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 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. 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.
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.
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. 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.
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 + 2Aa + 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 + 2Aa + 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. 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.
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 + 2ABb + 2aBb + 2AaB + 2Aab + 4AaBb. 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 + 2ABb + 2aBb + 2AaB + 2Aab + 4AaBb.
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.
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End of part 5 of 13
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