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exact meaning. For example, reversion or " throwing-back " to an ancestral form, previously regarded as a mere caprice of nature, can at once be perceived to be due to one of two definite causes which operate with regularity. The reversion is either (a) the reappearance of a recessive characteristic, or (b) it is the consequence of the reunion of complementary factors which, though both present together in the ancestor, had been separated by variation and transmitted in distinct strains. For example, when a red-haired child is born to dark -haired parents the fact proves that the two parents are heterozygous in respect of the recessive red, which reappears when two germ-cells carrying it unite in fertilization. Moreover, if the statistics of a considerable number of such families of children were collected and added to- gether it would be found that the proportion of red-haired was approximately a quarter of the whole. The mere fact that one or both of the parents traces descent from a red-haired ancestor is not the cause of the reversion for if either of the parents were homozygous in dark hair the red would not have reappeared.

The reversion to an actual or supposed ancestral form conse- quent on the meeting of complementary factors is less common in the ordinary practice of breeders, but is frequently seen in experimental crossing. When two white orchids crossed to- gether give a coloured flower in FI, or when a rose-combed fowl bred with a pea-combed bird gives chickens with the walnut comb of the Malay fowl, the production of the unexpected colour or structure is due to complementary action of two in- dependent factors. But the old interpretation of the phenomenon as a consequence of such an ancestor having occurred in the pedigree is illogical and misleading. In the case of the walnut comb, for instance, it is quite possible that either or both of the parent breeds never had a Malay ancestor. The production of a new form by the meeting of complements should be regarded, like the properties of a chemical compound, simply as the em- pirical consequence of a certain combination of units, without reference to the previous history of those units.

Purity of Type. Of greater importance, both theoretical and practical, is the fact that it is now possible to assign a precise meaning to this expression. To the pre-Mendelian evolutionist purity was always a matter of degree, which might be gradually and, as it were, asymptotically approached in successive genera- tions of selection, but never actually attained. The practical breeder also has always regarded purity as a property necessarily dependent on a long course of selection. Purity is now seen to be the condition of the animal or plant which is formed by the union of gametes bearing identical units. In respect of any aHelo- morphic pair purity may thus be conferred, though in respect of other pairs of units the same organism may be impure, i.e. heterozygous, or, in ordinary parlance, cross-bred. This is the central fact of Mendelism, and on it Genetics is based.

The question of purity must therefore be considered separately for each pair of units. A thoroughbred horse, for example, may be pure in a number of characteristics which go to the making of the breed, but it may be impure in, say, colour. A chestnut horse, however, of whatever parentage, is pure-bred in colour, since that colour is the lowest of the series of horse colours, and chestnuts bred together give chestnuts only. By selection the likelihood of producing purity is increased, but, as will subsequent- ly appear, no amount of selection can ensure purity. On the other hand, purity in respect of any character may be attained at once in any mating by which gametes of similar factorial com- position happen to be brought together in fertilization. From this proposition the corollary follows that the combination of two strains pure in any given respect will give a family uniform as regards the character considered, and the uniformity of such cross-bred families, especially when one of the parents contains few dominant factors, is in practice one of the simplest and most convincing tests of purity.

Genetic Analysis. By the institution of a series of crosses with varieties and study of the composition of the succeeding genera- tions an analysis of the factorial constitution of a given type can be made. The numerical proportions or ratios in which the several combinations of characters are represented, the number of

these terms in the series, and their respective genetical powers of transmission furnish the data from which the nature and number of the factors comprising the parental type may be determined. In the earlier article on Mendelism (see 18.115) some of the simpler ratios and their significance are explained, but examples of a much higher order of complexity are often encountered. The unravelling of these complications has led to some important discoveries. The many ways in which it may come to pass that two or more terms in a series of factorial com- binations may be indistinguishable from each other cannot be enumerated here, but a knowledge of some of the more significant causes of disturbance of what may be called the normal ratios (9:3:3:1; 9:3:4; 27:9:9:9:3:3:3:1, etc.) is essential to a proper comprehension of Genetics.

Cumulative Factors. From certain crosses (especially of cereals) into which only one pair of differences had apparently been intro- duced it was observed (Nilsson-Ehle; East) that the recessives re- appearing in F 2 were only I :i5 instead of the usual I 3. Investiga- tion proved that from the dominant side two factors with identical functions, though belonging to distinct pairs, had been introduced. Consequently, among the dominants in FI were some containing both these factors and others having one only. Various results suggest that this multiplication, or better, accumulation, of similar factors is a phenomenon of common occurrence, and that the process may be extended in special cases.

Inhibiting and Lethal Factors. Many factors act by producing a negative result, inhibiting the development of some character, the determining elements of which are present though their action is not perceptible or largely diminished. Of these the most easily demon- strable operate by inhibiting the formation of colour. The white pigment of the coats of animals and the feathers of birds, or of flowers, for example, is commonly due to the absence of the elements necessary for the formation of colour, but both in animals and in plants varieties have been found which are white, or nearly so, not through absence of pigment, but through the presence of factors which, in some way not yet defined, inhibit the production of the coloured pigments. From some matings a mixture of white individ- uals may be obtained, which to the eye look alike, or nearly so, though they represent various factorial terms and are genetically dissimilar. The process of inhibition may be carried much further, and there are well-established instances in which the animal or the plant cannot live if it is homozygous (containing two "doses," in popular terms) for a given factor. The classical instance of such lethal factors, as Morgan has called them, was met with in the breed- ing of yellow mice (Cuenot; F. M. Durham). Mice with yellow coats, bred together, give a majority of yellows, but always throw a proportion of some other colour for example, chocolate or black. Since in mice yellow is a dominant, it is clearly caused by a factor which the gametes can carry. But the union of two gametes, both carrying this factor, does not give rise to a viable animal. It was sug- gested that two such gametes could not unite in fertilization, but later work has practically proved that these fertilizations occur and that the resulting embryo perishes at an early stage (Ibsen). The physiological action of the yellow factor in causing death is not known. In plants the " golden "-leaved varieties are comparable. They cannot breed true, but throw 2 yellow: I green. The purely yellow term is missing, and is clearly not viable (Baur). The sug- gestion has been made that the yellow factor acts not merely nega- tively by diluting the amount of chlorophyll, but by inhibiting its formation, probably producing a body with this specific power. This is the more likely since golden varieties in dull weather turn almost a full green, whereas in sunlight they bleach to a full yellow, the fact indicating that the production of the inhibiting body is promoted by sunlight. Two doses of this factor kill the plant alto- gether, probably during embryonic life.

Linkage. At an early stage in these inquiries it was observed that factorial units belonging to separate allelomorphic pairs are not always distributed independently among the gametes of a heterozy- gote, but that some combinations occur regularly with a greater frequency than others. The next step was the discovery that this linkage depends on the association of the linked factors in the parent from which the heterozygote was formed. For example, if a form AB is crossed with ab the normal expectation is that the double heterozy- gote AaBb will form gametes AB, Ab, aB, ab in equal numbers; but if there is linkage between A and B, then the parental combina- tions AB and ab will be more frequently represented in the gametic series than the other, or "cross-over" combinations, Ab and aB. But if the original cross were in the form Ab x aB, then the most fre- quent gametes will be Ab and aB, the cross-overs, AB and ab being the rarer. This observation forms the starting-point from which modern genetical theory has been very largely developed. The terminology followed above is that introduced by T. H. Morgan, to whom progress has been especially due. It is sometimes convenient to distinguish the case in which the two dominants (AB x ab) are introduced together by the parent as coupling, and the converse (Ab x aB) as repulsion, but the physiological process is now recog-