nized as being clearly the same in both cases, and there is no dif- ference in the numerical proportions in which the parental combina- tions respectively reappear. It should be observed that the factors thus linked have plainly no connexion with each other as regards the effects which they produce in the zygote, but may concern the most dissimilar characters. For instance, in the example first observed the linkage was that between the factor which makes the flower of the sweet pea blue or purple (as distinguished from red) and that which makes the pollen grains long (as distinguished from round). According as the proportion of cross-overs is small or large the linkage is more or less complete. If both parental and cross-over terms are equally common there is no linkage. The most satisfac- tory test of the linkage-ratio is obviously provided by breeding the double heterozygote (Aa-Bb) with the double recessive (aabb), and this mating should be carried out reciprocally since it is known that in plants (e.g., Primula sinensis) the male and female sides of the same plant may show different degrees of linkage (R. P. Gregory), and that in animals (e.g., Drosophila and the silkworm) crossing-over may be entirely absent in one sex though occurring in the other.
Allelomorphism: Multiple Allelomorphs. Apart from linkage, seg- regation is always a separation of units affecting the same charac- ter, and from a very large range of observations it is possible to repre- sent the distinction between the allelomorphic pair as one in which a positive element separates from a negative.' In other words, allelo- morphism may commonly be conceived as a difference which con- sists in the presence of something on the one side and its absence on the other. This conception is applicable whenever there is definitely pronounced dominance. It is natural that the characteristic which possesses dominance should be looked upon as due to the positive or present element, the recessive being the consequence of its absence. Nevertheless there is as yet no strict proof that this representation is physiologically correct. For since we know that many factors may operate by inhibition it is always possible to invert the conventional representation and, by putting negative for positive, to make a fac- torial scheme which equally agrees with the observed results. Con- ventionally, for instance, the tall pea is represented as either TT (homozygous) or Tt (heterozygous), the dwarf being It, from which the positive element T tallness is absent. But we cannot positively declare that the dwarfs may not be TT homozygous in the presence of an inhibitor T, whereas the tall plants might be either Tt heterozy- gous or tt homozygous in respect of the absence of this inhibitor. The significance of this alternative mode of representation will be appar- ent when the application of factorial systems to evolutionary theory is attempted (see MENDBLISll). But when the heterozygote is inter- mediate between the two homozygous forms the " presence-and- absence" method of representation cannot be applied with any con- fidence. From the existence of such cases and from certain other considerations it has been urged, especially by American geneticists, that the method of representation by presence-and-absence is in- correct, and that a negative allelomorph should be treated as a real entity. There is no valid means of deciding this question as yet. The probability is perhaps that the absence should always be regarded as relative only. As a mode of symbolic expression the representa- tion of the two allelomorphs as differing quantitatively is often convenient, though certainly not universally applicable.
Allelomorphism is, as the term implies, a relation between two alternatives, and in any one zygote there can be no more than two. Nevertheless there are instances in which the same unit-factor enters into heterozygous combination with various alternatives in different zygotes, and each of these may thus be in allelomorphic relation with it. Alternatives composing such a group of possibilities have been termed by Morgan multiple allelomorphs, and this expression is com- monly adopted. Its use, however, makes the application of the term " multiple ' to " factors " in a totally different sense a probable source of confusion, and for this reason the word cumulative or some equiva- lent is there to be preferred, as suggested above. The distinctions which together make up a set of multiple allelomorphs may com- monly be recognized as a series of quantitative differences, the charac- ter affected being throughout the series the same. One of the most familiar illustrations is provided by the degree of albinism in rabbits. The fully albino form is white with pink eyes, but there is a variety called Himalayan, which, though born white with pink eyes, acquires some chocolate pigment in certain parts. Himalayan is dominant to albino but recessive to the ordinary coloured types. If a coloured type is bred with Himalayan the heterozygotes so raised cannot, when interbred, throw albinos, nor can heterozygotes raised from coloured X albino throw Himalayans, even though the albino used as their parent had itself been extracted from Himalayans. The degree of albinism put in by the parents comes out in F 2 and in the same degree. Hence it is not possible from similar parents to breed all three kinds, but, on the other hand, each family can contain at most two of them.
This phenomenon can be interpreted in either of two ways. The Himalayan pattern may be regarded simply as a quantitative dimi- nution or fraction of the sum total of colour needed to make the self- coloured type. The real albino is thus produced by the absence of the whole unit needed for colour, and the Himalayan by the absence of part of this total. It is then obvious that the heterozy- gote, coloured X albino, could never produce a Himalayan unless the colour-complex broke up again de novo. But on the analogy of the
behaviour of other colour patterns the self and the Himalayan might be conceived as each consisting of two units: one for colour and one a factor determining its pattern, intensity or distribution. If there were a very close linkage between each "pattern" factor and colour the observed facts could then be represented; but by continued breeding the supporters of this view would expect the missing cross- over eventually to appear as either a Himalayan associated with recessive albinos or an albino associated with recessive Himalayan. On the ground of simplicity the former view seems preferable. The significance of these two alternatives will presently appear.
More complex illustrations of these possibilities have been de- scribed by Nabours in certain grasshoppers (Paratettix). The species studied presents a long series of 'colour forms, and experimental breeding showed that with certain exceptions all the pure forms be- haved as if allelomorphic to each other. In other words, whichever two pure forms A and B were crossed together, the FI generation was .<4Bgivingin.F2afamilyapproximatingto 1^4/1 :2AB:iBB. Thewhole series of colours is thus often described as a vast set of multiple allelomorphs. Nevertheless there are curious features in that case which raise a doubt whether this account is really correct. Many of the distinctions are plainly quantitative degrees in development of some one type of coloration which are, as might be expected, alle- lomorphic to each other (cf. the Himalayan rabbit) ; but among the elements comprising the total coloration of these grasshoppers there are several in which both the pigments and the positions they occupy are so distinct that the characters cannot easily be represented as de- termined by factors allelomorphic to each other. Only by a very loose application of the term colour can the distinctions be said to apply -to the same character. Hence, in this hitherto generally accepted illustration it seems probable that, in so far as the distinc- tions are actually quantitative differences in one respect, true allelo- morphism may be recognized, but that the appearance of an alle- lomorphism between factors of differing scope is more probably spurious, and referable to close linkage (cf. Haldane). No decision on this question can yet be made with any confidence.
Allelomorphic Complexes. Among recent extensions of geneti- cal theory none is more remarkable than the discovery that large and apparently miscellaneous groups of characters are sometimes governed by elements capable of segregating collective- ly as a single complex. Nevertheless, in the case of sex,we have long been familiar with one example. Since the distinction between the two sexes in many animals is known to behave in segregation as if it depended on a single Mendelian factor, we have to recog- nize that a number of distinctions of all kinds, structural and functional, may be treated in segregation as factorially single. In the special case of se^c we know further that particular genetic elements may be detached from the complex (e.g. the elements governing spur and broodiness in fowls, the beard in man, etc.), though the possible limits of such disintegration are unknown.
Renner's experiments have shown that the inheritance of the protean variations of several Oenotheras is largely effected by the transmission of similar complexes. Each of these large composite factors or groups of factors (in so far as they prove to be divisible) may govern many characters of form, colour, habit, etc., and the whole group is transmitted as a single heritable entity. Similar dis- coveries will probably be made in regard to other forms. The details are beyond the scope of this article, but it may be remarked that these complexes in Oenothera supply one of the most striking illus- trations of the phenomenon which may be called unilaterality (see " Somatic Segregation," infra) or the relegation of a factor or factors exclusively to one sex-side of a plant. For instance, whereas Oeno- thera Lamarckiana, the species which provided de Vries with his most celebrated but unsound evidence of mutation, can be proved to be a permanently heterozygous form having two complexes equally distributed in segregation to both the male and the female gametes, the species biennis and many more, though similarly hetero- zygotes of two complexes, in segregation pass the whole of the one complex into the male gametes and the whole of the other into the female gametes. The question whether the apparently simple fac- tors which commonly behave as Mendelian units are capable of fur- ther resolution is of much theoretical importance in its bearing on the problem of the nature of variation. Such a complex factor as that which determines sex may evidently break up into simpler com- ponents, but for various reasons some geneticists incline to the belief that factors in general are permanent and irresoluble. Whenever a series in Ft, derived from two clearly distinct and true-breeding types, consists of a number of intergrading forms it is possible to interpret this result as due to the operation of a multitude of originally dis- tinct factors, or to the fractionation of some one or more of them. Not very rarely in such series an extreme parental type fails to re- appear at all (e.g. the many-feathered tail of the fantail pigeon [Staples-Brown], or the long glumes of Polish wheat) from crosses with ordinary types. It is difficult to interpret the absence of the extremes simply as an indication of their statistical infrequency. The recent production of an innumerable series of colour-forms, as in the sweet pea, is almost certainly due to the fractionation of the
