Generations of cross of tall and dwarf peas.
If we denote a dwarf plant as D, a true breeding tall plant as T, and a tall which gives both talls and dwarfs in the ratio 3 : 1 as T(D), the result of these experiments may be briefly summarised in the foregoing scheme.[2]
Mendel experimented with other pairs of contrasted characters and found that in every instance they followed the same scheme of inheritance. Thus coloured flowers were dominant to white, in the ripe seeds yellow was dominant to green, and round shape was dominant to wrinkled, and so on. In every case where the inheritance of an alternative pair of characters was concerned the effect of the cross in successive generations was to produce three and only three different sorts of individuals, viz. dominants which bred true, dominants which gave both dominant and recessive offspring in the ratio 3 : 1, and recessives which always bred true. Having determined a general scheme of inheritance which experiment showed to hold good for each of the seven pairs of alternative characters with which he worked, Mendel set himself to providing a theoretical interpretation of this scheme which, as he clearly realised, must be in terms of germ cells. Heconceived of the gametes as bearers of something capable of giving rise to the characters of the plant, but he regarded any individual gamete as being able to carry one and one only of any alternative pair of characters. A given gamete could carry tallnessordwarfness, but not both. The two were mutually exclusive so far as the gamete was concerned. It must be pure for one or the other of such a pair, and this conception of the purity of the gametes is the most essential part of Mendel's theory.
Fig. 1. Scheme of inheritance for cross of tall and dwarf peas.Fig. 1.Scheme of inheritance in the cross of tall with dwarf pea. Gametes represented by small and zygotes by larger circles.
Scheme of inheritance in the cross of tall with dwarf pea. Gametes represented by small and zygotes by larger circles.
We may now proceed with the help of the accompanying scheme (Fig. 1) to deduce the results that should flow from Mendel's conception of the nature of the gametes, and to see how far they are in accordance with the facts. Since the original tall plant belonged to a strain which bred true, all the gametes produced by it must bear the tall character. Similarly all the gametes of the original dwarf plant must bear the dwarf character. A cross between these two means the union ofa gamete containing tallness with one bearing dwarfness. Owing to the completely dominant nature of the tall character, such a plant is in appearance indistinguishable from the pure tall, but it differs markedly from it in the nature of the gametes to which it gives rise. When the formation of the gametes occurs, the elements representing dwarfness and tallnesssegregatefrom one another, so that half of the gametes produced contain the one, and half contain the other of these two elements. For on hypothesis every gamete must be pure for one or other of these two characters. And this is true for the ovules as well as for the pollen grains. Such hybrid F1plants, therefore, must produce a series of ovules consisting of those bearing tallness and those bearing dwarfness, and must produce them in equal numbers. And similarly for the pollen grains. We may now calculate what should happen when such a series of pollen grains meets such a series of ovules,i.e.the nature of the generation that should be produced when the hybrid is allowed to fertilise itself. Let us suppose that there are 4xovules so that 2xare "tall" and 2xare "dwarf." These are brought in contact with a mass of pollen grains of which half are "tall" and half are "dwarf." It is obvious that a "tall" ovule has an equal chance of being fertilised by a "tall" or a "dwarf" pollen grain. Hence of our 2x"tall" ovules,xwill be fertilised by "tall" pollen grains andxwill be fertilised by "dwarf" pollen grains. The former must give rise to tallplants, and since the dwarf character has been entirely eliminated from them they must in the future breed true. The latter must also give rise to tall plants, but since they carry also the recessive dwarf character they must when bred from produce both tails and dwarfs. Each of the 2xdwarf ovules, again, has an equal chance of being fertilised by a "tall" or by a "dwarf" pollen grain. Hencexwill give rise to tall plants carrying the recessive dwarf character, whilexwill produce plants from which the tall character has been eliminated,i.e.to pure recessive dwarfs. Consequently from the 4xovules of the self-fertilised hybrid we ought to obtain 3xtall andxdwarf plants. And of the 3xtallsxshould breed true to tallness, while the remaining 2x, having been formed like the original hybrid by the union of a "tall" and a "dwarf" gamete, ought to behave like it when bred from and give talls and dwarfs in the ratio 3 : 1. Now this is precisely the result actually obtained by experiment (cf. p.17), and the close accord of the experimental results with those deduced on the assumption of the purity of the gametes as enunciated by Mendel affords the strongest of arguments for regarding the nature of the gametes and their relation to the characters of the zygotes in the way that he has done.
It is possible to put the theory to a further test. The explanation of the 3 : 1 ratio of dominants and recessives in the F2generation is regarded as due to the F1individuals producing equal numbers of gametes bearing thedominant and recessive elements respectively. If now the F1plant be crossed with the pure recessive, we are bringing together a series of gametes consisting of equal numbers of dominants and recessives with a series consisting solely of recessives. We ought from such a cross to obtain equal numbers of dominant and recessive individuals, and further, the dominants so produced ought all to give both dominants and recessives in the ratio 3 : 1 when they themselves are bred from. Both of these expectations were amply confirmed by experiment, and crossing with the recessive is now a recognised way of testing whether a plant or animal bearing a dominant character is a pure dominant, or an impure dominant which is carrying the recessive character. In the former case the offspring will be all of the dominant form, while in the latter they will consist on the average of equal numbers of dominants and recessives.
So far we have been concerned with the results obtained when two individuals differing in a single pair of characters are crossed together and with the interpretation of those results. But Mendel also used plants which differed in more than a single pair of differentiating characters. In such cases he found that each pair of characters followed the same definite rule, but that the inheritance of each pair was absolutely independent of the other. Thus, for example, when a tall plant bearing coloured flowers was crossed with a dwarf plantbearing white flowers the resulting hybrid was a tall plant with coloured flowers. For coloured flowers are dominant to white, and tallness is dominant to dwarfness. In the succeeding generation there are plants with coloured flowers and plants with white flowers in the proportion of 3 : 1, and at the same time tall plants and dwarf plants in the same proportion. Hence the chances that a tall plant will have coloured flowers are three times as great as its chance of having white flowers. And this is also true for the dwarf plants. As the result of this cross, therefore, we should expect an F2generation consisting of four classes, viz. coloured talls, white talls, coloured dwarfs, and white dwarfs, and we should further expect these four forms to appear in the ratio of 9 coloured talls, 3 white talls, 3 coloured dwarfs, and 1 white dwarf. For this is the only ratio which satisfies the conditions that the talls should be to the dwarfs as 3 : 1, and at the same time the coloured should be to the whites as 3 : 1. And these are the proportions that Mendel found to obtain actually in his experiments. Put in a more general form, it may be stated that when two individuals are crossed which differ in two pairs of differentiating characters the hybrids (F1) are all of the same form, exhibiting the dominant character of each of the two pairs, while the F2generation produced by such hybrids consists on the average of 9 showing both dominants, 3 showing one dominant and one recessive,3 showing the other dominant and the other recessive, and 1 showing both recessive characters. And, as Mendel pointed out, the principle may be extended indefinitely. If, for example, the parents differ in three pair of charactersA,B, andC, respectively dominant toa,b, andc, the F1individuals will be all of the formABC, while the F2generation will consists of 27ABC, 9ABc, 9AbC, 9aBC, 3Abc, 3aBc, 3abC, and 1abc. When individuals differing in a number of alternative characters are crossed together, the hybrid generation, provided that the original parents were of pure strains, consists of plants of the same form; but when these are bred from a redistribution of the various characters occurs. That redistribution follows the same definite rule for each character, and if the constitution of the original parents be known, the nature of the F2generation,i.e.the number of possible forms and the proportions in which they occur, can be readily calculated. Moreover, as Mendel showed, we can calculate also the chances of any given form breeding true. To this point, however, we shall return later.
Of Mendel's experiments with beans it is sufficient to say here that they corroborated his more ample work with peas. He is also known to have made experiments with many other plants, and a few of his results are incidentally given in his series of letters to Nägeli the botanist. To the breeding and crossing of bees he also devoted muchtime and attention, but unhappily the record of these experiments appears to have been lost. The only other published work that we possess dealing with heredity is a brief paper on some crossing experiments with the hawkweeds (Hieracium), a genus that he chose for working with because of the enormous number of forms under which it naturally exists. By crossing together the more distinct varieties, he evidently hoped to produce some of these numerous wild forms, and so throw light upon their origin and nature. In this hope he was disappointed. Owing in part to the great technical difficulties attending the cross fertilisation of these flowers he succeeded in obtaining very few hybrids. Moreover, the behaviour of those which he did obtain was quite contrary to what he had found in the peas. Instead of giving a variety of forms in the F2generation, they bred true and continued to do so as long as they were kept under observation. More recent research has shown that this is due to a peculiar form of parthenogenesis (cf. p.135), and not to any failure of the characters to separate clearly from one another in the gametes. Mendel, however, could not have known of this, and his inability to discover inHieraciumany indication of the rule which he had found to hold good for both peas and beans must have been a source of considerable disappointment. Whether for this reason, or owing to the utter neglect of his work by the scientific world, Mendel gave up his experimentalresearches during the latter part of his life. His closing years were shadowed with ill-health and embittered by a controversy with the Government on a question of the rights of his monastery. He died of Bright's disease in 1884.
Note.—Shortly after the discovery of Mendel's paper a need was felt for terms of a general nature to express the constitution of individuals in respect of inherited characters, and Bateson accordingly proposed the words homozygote and heterozygote. An individual is said to be homozygous for a given character when it has been formed by two gametes each bearing the character, and all the gametes of a homozygote bear the character in respect of which it is homozygous. When, however, the zygote is formed by two gametes of which one bears the given character while the other does not, it is said to be heterozygous for the character in question, and only half the gametes produced by such a heterozygote bear the character. An individual may be homozygous for one or more characters, and at the same time may be heterozygous for others.
Note.—Shortly after the discovery of Mendel's paper a need was felt for terms of a general nature to express the constitution of individuals in respect of inherited characters, and Bateson accordingly proposed the words homozygote and heterozygote. An individual is said to be homozygous for a given character when it has been formed by two gametes each bearing the character, and all the gametes of a homozygote bear the character in respect of which it is homozygous. When, however, the zygote is formed by two gametes of which one bears the given character while the other does not, it is said to be heterozygous for the character in question, and only half the gametes produced by such a heterozygote bear the character. An individual may be homozygous for one or more characters, and at the same time may be heterozygous for others.
THE PRESENCE AND ABSENCE THEORY
It was fortunate for the development of biological science that the rediscovery of Mendel's work found a small group of biologists deeply interested in the problems of heredity, and themselves engaged in experimental breeding. To these men the extraordinary significance of the discovery was at once apparent. From their experiments, undertaken in ignorance of Mendel's paper, de Vries, Correns, and Tschermak were able to confirm his results in peas and other plants, while Bateson was the first to demonstrate their application to animals. Thenceforward the record has been one of steady progress, and the result of ten years' work has been to establish more and more firmly the fundamental nature of Mendel's discovery. The scheme of inheritance, which he was the first to enunciate, has been found to hold good for such diverse things as height, hairiness, and flower colour and flower form in plants, the shape of pollen grains, and the structure of fruits; while among animals the coat colour of mammals, the form of the feathers and of the comb in poultry, the waltzing habit of Japanese mice, and eyecolour in man are but a few examples of the diversity of characters which all follow the same law of transmission. And as time went on many cases which at first seemed to fall without the scheme have been gradually brought into line in the light of fuller knowledge. Some of these will be dealt with in the succeeding chapters of this book. Meanwhile we may concern ourselves with the single modification of Mendel's original views which has arisen out of more ample knowledge.
Fig. 2. Feathers of an ordinary and a silky fowl.Fig. 2.A wing feather and a contour feather of an ordinary and a silky fowl. The peculiar ragged appearance of the silky feathers is due to the absence of the little hooks or barbules which hold the barbs together. The silky condition is recessive.
A wing feather and a contour feather of an ordinary and a silky fowl. The peculiar ragged appearance of the silky feathers is due to the absence of the little hooks or barbules which hold the barbs together. The silky condition is recessive.
As we have already seen, Mendel considered that in the gamete there was either a definite somethingcorresponding to the dominant character or a definite something corresponding to the recessive character, and that these somethings whatever they were could not coexist in any single gamete. For these somethings we shall in future use the termfactor. The factor, then, is what corresponds in the gamete to theunit-characterthat appears in some shape or other in the development of the zygote. Tallness in the pea is a unit-character, and the gametes in which it is represented are said to contain the factor for tallness. Beyond their existence in the gamete and their mode of transmission we make no suggestion as to the nature of these factors.
Fig. 3. Two double and an ordinary single primula flower.Fig. 3.Two double and an ordinary single primula flower. This form of double is recessive to the single.
Two double and an ordinary single primula flower. This form of double is recessive to the single.
Fig. 4. Fowls' combs.Fig. 4.Fowls' combs. A, pea; B, rose; C, single; D, walnut.
Fowls' combs. A, pea; B, rose; C, single; D, walnut.
On Mendel's view there was a factor corresponding to the dominant character and another factor corresponding to the recessive character of each alternative pair of unit-characters, and the characters were alternative because no gamete could carry more than one of the two factors belonging to the alternative pair. On the other hand, Mendel supposed that it always carried either one or the other of such a pair. As experimental work proceeded,it soon became clear that there were cases which could not be expressed in terms of this conception. The nature of the difficulty and the way in which it was met will perhaps be best understood by considering a set of experiments in which it occurred. Many of the different breeds of poultry are characterised by a particular form of comb, and in certain cases the inheritance of these has been carefully worked out. It was shown that the rose comb (Fig. 4, B) with its flattened papillated upper surface and backwardly projecting pike was dominant in the ordinary way to the deeply serrated high single comb (Fig. 4, C) which is characteristic of the Mediterranean races. Experiment also showed that the pea comb (Fig. 4, A), a form with a low central and two well-developed lateral ridges, such as is found in Indian game, behaves as a simple dominant to the single comb. The interesting question arose as to what would happen when the rose and the pea, two forms each dominant to the same third form, were mated together. It seemed reasonable to suppose that things which were alternative to the same thing would be alternative to one another—that either rose or pea would dominate in the hybrids, and that the F2generation would consist of dominants and recessives in the ratio 3 : 1. The result of the experiment was, however, very different. The cross rose × pea led to the production of a comb quite unlike either of them. This, the so-called walnut comb (Fig. 4, D),from its resemblance to the half of a walnut, is a type of comb which is normally characteristic of the Malay fowl. Moreover, when these F1birds were bred together, a further unlooked-for result was obtained. As was expected, there appeared in the F2generation the three forms walnut, rose, and pea. But there also appeared a definite proportion of single-combed birds, and among many hundreds of chickens bred in this way the proportions in which the four forms walnut, rose, pea, and single appeared was 9 : 3 : 3 : 1.Generations of Rose × Pea cross.Now this, as Mendel showed, is the ratio found in an F2generation when the original parents differ in two pairs of alternative characters, and from the proportions in which the different forms of comb occur we must infer that the walnut contains both dominants, the rose and the pea one dominant each, while the single is pure for both recessive characters. This accorded with subsequent breeding experiments, for the singles bred perfectly true as soon as they had once made their appearance. So far the case is clear. The difficulty comes when we attempt to define these two pairs of characters. How are we to express the fact that while single behaves as a simple recessive to either pure rose, or to pure pea, it can yet appear in F2from a crossbetween these two pure forms, though neither of them should, on Mendel's view, contain the single? An explanation which covers the facts in a simple way is that which has been termed the "Presence and Absence" theory. On this theory the dominant character of an alternative pair owes its dominance to the presence of a factor which is absent in the recessive. The tall pea is tall owing to the presence in it of the factor for tallness, but in the absence of this factor the pea remains a dwarf. All peas are dwarf, but the tall is a dwarf plus a factor which turns it into a tall. Instead of the characters of an alternative pair being due to two separate factors, we now regard them as the expression of the only two possible states of a single factor, viz. its presence or its absence. The conception will probably become clearer if we follow its application in detail to the case of the fowl's combs. In this case we are concerned with the transmission of the two factors, rose (R) and pea (P), the presence of each of which is alternative to its absence. The rose-combed bird contains the factor for rose but not that for pea, and the pea-combed bird contains the factor for pea but not that for rose. When both factors are present in a bird, as in the hybrid made by crossing rose with pea, the result is a walnut. For convenience of argument we may denote the presence of a given factor by a capital letter and its absence by the corresponding small letter. The use of the small letter is merely a symbolic way of intimatingthat a particular factor is absent in a gamete or zygote. Represented thus the zygotic constitution of a pure rose-combed bird isRRpp; for it has been formed by the union of two gametes both of which containedRbut notP. Similarly we may denote the pure pea-combed bird asrrPP. On crossing the rose with the pea union occurs between a gameteRpand a gameterP, resulting in the formation of a heterozygote of the constitutionRrPp. The use of the small letters here informs us that such a zygote contains only a single dose of each of the factorsRandP, although, of course, it is possible for a zygote, if made in a suitable way, to have a double dose of any factor. Now when such a bird comes to form gametes a separation takes place between the part of the zygotic cell containingRand the part which does not contain it (r). Half of its gametes, therefore, will containRand the other half will be without it (r). Similarly half of its gametes will containPand the other half will be without it (p). It is obvious that the chances ofRbeing distributed to a gamete with or withoutPare equal. Hence the gametes containingRwill be of two sorts,RPandRp, and these will be produced in equal numbers. Similarly the gametes withoutRwill also be of two sorts,rPandrp, and these, again, will be produced in equal numbers. Each of the hybrid walnut-combed birds, therefore, gives rise to a series consisting of equal numbers of gametes of the four different typesRP,Rp,rP, andrp; and the breedingtogether of such F1birds means the bringing together of two such series of gametes. When this happens an ovum of any one of the four types has an equal chance of being fertilised by a spermatozoon of any one of the four types. A convenient and simple method of demonstrating what happens under such circumstances is the method sometimes termed the "chessboard" method. For two series each consisting of four different types of gamete we require a square divided up into 16 parts. The four terms of the gametic series are first written horizontally across the four sets of four squares, so that the series is repeated four times. It is then written vertically four times, care being taken to keep to the same order. In this simple mechanical way all the possible combinations are represented and in their proper proportions.Fig. 5. Combs in F2.Fig.5.Diagram to illustrate the nature of the F2generation from the cross of rose comb × pea comb.Fig. 5 shows the result of applying this method to our seriesRP,Rp,rP,rp, and the 16 squares represent the different kinds of zygotes formed and the proportions in which they occur. Asthe figure shows, 9 zygotes contain bothRandP, having a double or a single dose of either or both of these factors. Such birds must be all walnut combed. Three out of the 16 zygotes containRbut notP, and these must be rose-combed birds. Three, again, containPbut notRand must be pea-combed birds. Finally one out of the 16 contains neitherRnorP. It cannot be rose—it cannot be pea. It must, therefore, be something else. As a matter of fact it is single. Why it should be single and not something else follows from what we already know about the behaviour of these various forms of comb. For rose is dominant to single; therefore on the Presence and Absence theory a rose is a single plus a factor which turns the single into a rose. If we could remove the "rose" factor from a rose-combed bird the underlying single would come into view. Similarly a pea comb is a single plus a factor which turns the single into a pea, and a walnut is a single which possesses two additional modifying factors. Singleness, in fact, underlies all these combs, and if we write their zygotic constitution in full we must denote a walnut asRRPPSS, a rose asRRppSS, a pea asrrPPSS, and a single asrrppSS. The crossing of rose with pea results in a reshuffling of the factors concerned, and in accordance with the principle of segregation some zygotes are formed in which neither of the modifying factorsRandPare present, and the single character can then become manifest.
The Presence and Absence theory is to-day generally accepted by students of these matters. Not only does it afford a simple explanation of the remarkable fact that in all cases of Mendelian inheritance we should be able to express our unit-characters in terms of alternative pairs, but, as we shall have occasion to refer to later, it suggests a clue as to the course by which the various domesticated varieties of plants and animals have arisen from their wild prototypes.
Fig. 6. Fowls' combs, rose and Breda.Fig. 6.Fowls' combs. A and B, F1hen from rose × Breda; C, an F1cock from the cross of single × Breda; D, head of Breda cock.
Fowls' combs. A and B, F1hen from rose × Breda; C, an F1cock from the cross of single × Breda; D, head of Breda cock.
Before leaving this topic we may draw attention to some experiments which offer a pretty confirmation of the view that the rose comb is a single to which a modifying factor for roseness has been added. It was argued that if we could find a type of comb in which the factor for singleness was absent, then on crossing such a comb with a rose we ought, if singleness really underlies rose, to obtain some single combs in F2from such a cross. Such a comb we had the good fortune to find in the Breda fowl, a breed largely used in Holland. This fowl is usually spoken of as combless, for the place of the comb is taken by a covering of short bristlelike feathers (Fig. 6, D). In reality it possesses the vestige of a comb in the form of two minute lateral knobs of comb tissue. Characteristic also of this breed is the high development of the horny nostrils, a feature probably correlated with the almost complete absence of comb. The first step in the experiment was to prove the absence of the factor for singleness in the Breda.On crossing Breda with single the F1birds exhibit a large comb of the form of a double single comb in which the two portions are united anteriorly, but diverge from one another towards the back of the head (Fig. 6, C). The Breda contains an element of duplicity which is dominant to the simplicity of the ordinary single comb. But it cannot contain the factor for the single comb, because as soon as that is put into it by crossing with a single the combBreda and rose.assumes a large size, and is totally distinct in appearance from its almost complete absence in the pure Breda. Now when the Breda is crossed with the rose duplicity is dominant to simplicity, and rose is dominant to lack of comb, and the F1generation consists of birds possessing duplex rose combs (Fig. 6, A and B). On breeding such birds together we obtain a generation consisting of Bredas, duplex roses, roses, duplex singles, and singles. From our previous experiment we know that the singles could not have come from the Breda, since a Breda comb to which the factor for single has been added no longer remains a Breda. Therefore it must have come from the rose, thus confirming our view that the rose is in reality a single comb which contains in addition a dominant modifying factor (R) whose presence turns it into a rose. We shall take it, therefore, that there is good experimental evidence for the Presence and Absence theory, and we shall express in terms of it the various cases which come up for discussion in succeeding chapters.
INTERACTION OF FACTORS
We have now reached a point at which it is possible to formulate a definite conception of the living organism. A plant or animal is a living entity whose properties may in large measure be expressed in terms of unit-characters, and it is the possession of a greater or lesser number of such unit-characters renders it possible for us to draw sharp distinctions between one individual and another. These unit-characters are represented by definite factors in the gamete which in the process of heredity behave as indivisible entities, and are distributed according to a definite scheme. The factor for this or that unit-character is either present in the gamete or it is not present. It must be there in its entirety or completely absent. Such at any rate is the view to which recent experiment has led us. But as to the nature of these factors, the conditions under which they exist in the gamete, and the manner in which they produce their specific effects in the zygote, we are at present almost completely in the dark.
The case of the fowls' combs opens up the important question of the extent to which the various factors caninfluence one another in the zygote. The rose and the pea factors are separate entities, and each when present alone produces a perfectly distinct and characteristic effect upon the single comb, turning it into a rose or a pea as the case may be. But when both are present in the same zygote their combined effect is to produce the walnut comb, a comb which is quite distinct from either and in no sense intermediate between them. The question of the influence of factors upon one another did not present itself to Mendel because he worked with characters which affected different parts of the plant. It was unlikely that the factor which led to the production of colour in the flower would affect the shape of the pod, or that the height of the plant would be influenced by the presence or absence of the factor that determined the shape of the ripe seed. But when several factors can modify the same structure it is reasonable to suppose that they will influence one another in the effects which their simultaneous presence has upon the zygote. By themselves the pea and the rose factors each produce a definite modification of the single comb, but when both are present in the zygote, whether as a single or double dose, the modification that results is quite different to that produced by either when present alone. Thus we are led to the conception of characters which depend for their manifestation on more than one factor in the zygote, and in the present chapter we may consider a few of thephenomena which result from such interaction between separate and distinct factors.
Generation of cross of red and white sweet peas.
One of the most interesting and instructive cases in which the interaction between separate factors has been demonstrated is a case in the sweet pea. All white sweet peas breed true to whiteness. And generally speaking the result of crossing different whites is to produce nothing but whites, whether in F1or in succeeding generations. But there are certain strains of white sweet peas which when crossed together produce only coloured flowers. The colour may be different in different cases, though for our present purpose we may take a case in which the colour is red. When such reds are allowed to self-fertilise themselves in the normal way and the seeds sown, the resulting F2generation consists of reds and whites, the former being rather more numerous than the latter in the proportion of 9 : 7. The raising of a further generation from the seeds of these F2plants shows that the whites always breed true to whiteness, but that different reds may behave differently. Some breed true, others give reds and whites in the ratio 3 : 1, while others, again, give reds and whites in the ratio 9 : 7. As in the case of the fowls' combs, this case may be interpreted in terms of the presence and absence of two factors.Factors in red and white sweet peas.Red in the sweet pea results from the interaction of two factors, and unless these are both present the red colour cannot appear. Each of the white parents carried one of the two factors whose interaction is necessary for the production of the red colour, and as a cross between them brings these two complementary factors together the F1plants must all be red. As this case is of considerable importance for the proper understanding of much that is to follow, and as it has been completely worked out, we shall consider it in some detail. Denoting these two colour factors byAandBrespectively we may proceed to follow out the consequences of this cross. Since all the F1plants were red the constitution of the parental whites must have beenAAbbandaaBBrespectively, and their gametes consequentlyAbandaB. The constitution of the F1plants must, therefore, beAaBb. Such a plant being heterozygous for two factors produces a series of gametes of the four kindsAB,Ab,aB,ab, and produces them in equal numbers (cf. p.36). To obtain the various types of zygotes which are produced when suchFig. 7. Scheme of inheritance for red and white sweet peas.Fig. 7.Diagram to illustrate the nature of the F2generation from the two white sweet peas which give a coloured F1.a series of pollen grains meets a similar series of ovules we may make use of the same "chessboard" system which we have already adopted in the case of the fowls' combs. An examination of this figure (Fig. 7) shows that 9 out of the 16 squares contain bothAandB, while 7 contain eitherAorBalone, or neither. In other words, on this view of the nature of the two white sweet peas we should in the F2generation look for the appearance of coloured and white flowers in the ratio 9 : 7. And this, as we have already seen, is what was actually found by experiment. Further examination of the figure shows that the coloured plants are not all of the same constitution, but are of four kinds with respect to their zygotic constitution, viz.AABB,AABb,AaBB, andAaBb. SinceAABBis homozygous for bothAandB, all the gametes which it produces must contain both of these factors, and such a plant must therefore breed true to the red colour. A plant of theconstitutionAABbis homozygous for the factorA, but heterozygous forB. All of its gametes will containA, but only one-half of them will containB,i.e.it produces equal numbers of gametesABandAb. Two such series of gametes coming together must give a generation consisting ofxAABB, 2xAABb, andxAAbb, that is, reds and whites in the ratio 3 : 1. Lastly the red zygotes of the constitutionAaBbhave the same constitution as the original red made from the two whites, and must therefore when bred from give reds and whites in the ratio 9 : 7. The existence of all these three sorts of reds was demonstrated by experiment, and the proportions in which they were met with tallied with the theoretical explanation.
The theory was further tested by an examination into the properties of the various F2whites which come from a coloured plant that has itself been produced by the mating of two whites. As Fig. 7 shows, these are, in respect of their constitution, of five different kinds, viz.AAbb,Aabb,aaBB,aaBb, andaabb. Since none of them produce anything but whites on self-fertilisation it was found necessary to test their properties in another way, and the method adopted was that of crossing them together. It is obvious that when this is done we should expect different results in different cases. Thus the cross between two whites of the constitutionAAbbandaaBBshould give nothing but coloured plants; for these two whites are ofthe same constitution as the original two whites from which the experiment started. On the other hand, the cross between a white of the constitutionaabband any other white can never give anything but whites. For no white contains bothAandB, or it would not be white, and a plant of the constitutionaabbcannot supply the complementary factor necessary for the production of colour. Again, two whites of the constitutionAabbandaaBbwhen crossed should give both coloured and white flowers, the latter being three times as numerous as the former. Without going into further detail it may be stated that the results of a long series of crosses between the various F2whites accorded closely with the theoretical explanation.
From the evidence afforded by this exhaustive set of experiments it is impossible to resist the deduction that the appearance of colour in the sweet pea depends upon the interaction of two factors which are independently transmitted according to the ordinary scheme of Mendelian inheritance. What these factors are is still an open question. Recent evidence of a chemical nature indicates that colour in a flower is due to the interaction of two definitive substances: (1) a colourless "chromogen," or colour basis; and (2) a ferment which behaves as an activator of the chromogen, and by inducing some process of oxidation, leads to the formation of a coloured substance. But whether these two bodies exist as suchin the gametes or whether in some other form we have as yet no means of deciding.
Since the elucidation of the nature of colour in the sweet pea phenomena of a similar kind have been witnessed in other plants, notably in stocks, snapdragons, and orchids. Nor is this class of phenomena confined to plants. In the course of a series of experiments upon the plumage colour of poultry, indications were obtained that different white breeds did not always owe their whiteness to the same cause. Crosses were accordingly made between the white Silky fowl and a pure white strain derived from the white Dorking. Each of these had been previously shown to behave as a simple recessive to colour. When the two were crossed only fully coloured birds resulted. From analogy with the case of the sweet pea it was anticipated that such F1coloured birds when bred together would produce an F2generation consisting of coloured and white birds in the ratio 9 : 7, and when the experiment was made this was actually shown to be the case. With the growth of knowledge it is probable that further striking parallels of this nature between the plant and animal worlds will be met with.
Before quitting the subject of these experiments attention may be drawn to the fact that the 9 : 7 ratio is in reality a 9 : 3 : 3 : 1 ratio in which the last three terms are indistinguishable owing to the special circumstances that neither factor can produce a visible effect withoutthe co-operation of the other. And we may further emphasise the fact that although the two factors thus interact upon one another they are nevertheless transmitted quite independently and in accordance with the ordinary Mendelian scheme.
Coat colours of mice.
One of the earliest sets of experiments demonstrating the interaction of separate factors was that made by the French zoologist Cuénot on the coat colours of mice. It was shown that in certain cases agouti, which is the colour of the ordinary wild grey mouse, behaves as a dominant to the albino variety,i.e.the F2generation from such a cross consists of agoutis and albinos in the ratio 3 : 1. But in other cases the cross between albino and agouti gave a different result. In the F1generation appeared only agoutis as before, but the F2generation consisted of three distinct types, viz. agoutis, albinos,and blacks. Whence the sudden appearance of the new type? The answer is a simple one. The albino parent was really a black. But it lacked the factor without which the colour is unable to develop, and consequently it remained an albino. If we denote this factor byC, then the constitution of an albino must becc, while that of a coloured animal may beCCorCc, according as to whether it breeds true to colour or canthrow albinos. Agouti was previously known to be a simple dominant to black,i.e.an agouti is a black rabbit plus an additional greying factor which modifies the black into agouti. This factor we will denote byG, and we will useBfor the black factor. Our original agouti and albino parents we may therefore regard as in constitutionGGCCBBandggccBBrespectively. Both of the parents are homozygous for black. The gametes produced by the two parents areGCB, andgcB, and the constitution of the F1animals must beGgCcBB. Being heterozygous for two factors they will produce four kinds of gametes in equal numbers, viz.GCB,GcB,gCB, andgcB. The results of the mating of two such similar series of gametes when the F1animals are bred together we may determine by the usual "chessboard" method (Fig. 8). Out of the 16 squares 9 contain bothCandGin addition toB. Such animals must be agoutis. Three squares containCbut notG. Such animals must be coloured, but as they do not contain the modifying agouti factor their colour will be black. The remaining four squares do not containC, and in the absence of this colour-developing factor they must all be albinos. Theory demands that the three classes agouti, black, and albino should appear in F2in the ratio 9 : 3 : 4; experiment has shown that these are the only classes that appear, and that the proportions in which they are produced accord closely with the theoretical expectation. Put briefly, then, the explanationFig. 8. Scheme of inheritance for agouti and black mice.Fig. 8.Diagram to illustrate the nature of the F2generation which may arise from the mating of agouti with albino in mice or rabbits.of this case is that all the animals are black, and that we are dealing with the presence and absence of two factors, a colour developer (C), and a colour modifier (G), both acting, as it were, upon a substratum of black. The F2generation really consists of the four classes agoutis, blacks, albino agoutis, and albino blacks in the ratio 9 : 3 : 3 : 1. But since in the absence of the colour developerCthe colour modifierGcan produce no visible result, the last two classes of the ratio are indistinguishable, and our F2generation comes to consist of three classes in the ratio 9 : 3 : 4, instead of four classes in the ratio 9 : 3 : 3 : 1. This explanation was further tested by experiments with the albinos. In an F2family of this nature there ought to be three kinds, viz. albinos homozygous forG(GGccBB), albinos heterozygous forG(GgccBB), and albinos withoutG(ggccBB). These albinos are, as it were, like photographic plates exposed but undeveloped.Their potentialities may be quite different, although they all look alike, but this can only be tested by treating them with a colour developer. In the case of the mice and rabbits the potentiality for which we wish to test is the presence or absence of the factorG, and in order to develop the colour we must introduce the factorC. Our developer, therefore, must containCbut notG. In other words, it must be a homozygous black mouse or rabbit,ggCCBB. Since such an animal is pure forCit must, when mated with any of the albinos, produce only coloured offspring. And since it does not containGthe appearance of agoutis among its offspring must be attributed to the presence ofGin the albino. Tested in this way the F2albinos were proved, as was expected, to be of three kinds: (1) those which gave only agouti,i.e.which were homozygous forG; (2) those which gave agoutis and blacks in approximately equal numbers,i.e.which were heterozygous forG; and (3) those which gave only blacks, and therefore did not containG.
Though albinos, whether mice, rabbits, rats, or other animals, breed true to albinism, and though albinism behaves as a simple recessive to colour, yet albinos may be of many different sorts. There are in fact just as many kinds of albinos as there are coloured forms—neither more nor less. And all these different kinds of albinos may breed together, transmitting the various colour factors according to the Mendelian scheme of inheritance,and yet the visible result will be nothing but albinos. Under the mask of albinism is all the while occurring that segregation of the different colour factors which would result in all the varieties of coloured forms, if only the essential factor for colour development were present. But put in the developer by crossing with a pure coloured form and their variety of constitution can then at last become manifest.
So far we have dealt with cases in which the production of a character is dependent upon the interaction of two factors. But it may be that some characters require the simultaneous presence of a greater number of factors for their manifestation, and the experiments of Miss Saunders have shown that there is a character in stocks which is unable to appear except through the interaction of three distinct factors. Coloured stocks may be either hoary, with the leaves and stem covered by small hairs, or they may lack the hairy covering, in which case they are termed glabrous. Hoariness is dominant to glabrousness; that is to say, there is a definite factor which can turn the glabrous into a hoary plant when it is present. But in families where coloured and white stocks occur the white are always glabrous, while the coloured plants may or may not be hoary. Now colour in the stock as in the sweet pea has been proved to be dependent upon the interaction of two separate factors. Hence hoariness depends upon three separate factors, and a stock cannot be hoary unlessit contains the hoary factor in addition to the two colour factors. It requires the presence of all these three factors to produce the hoary character, though how this comes about we have not at present the least idea.