PROCEEDINGS OF THE
WASHINGTON ACADEMY OF SCIENCES
VOL. IX, PP. 189-240. JULY 31, 1907.
MENDELISM AND OTHER METHODS OF DESCENT.1
By O. F. COOK
|The nature of experiments in descent||191|
|Parent organisms produce parent gametes||192|
|Parent gametes produce conjugate organisms||192|
|Conjugate and exjugate reproduction||193|
|Conjugates produce perjugates||195|
|Summary of the five elements of descent||197|
|Mendelism as a method of descent||198|
|Primary methods of descent||198|
|Synopsis of methods of descent||199|
|Diagram of methods of descent||216|
|Position of Mendelism as a method of descent||218|
|Mendelian "principles" not demonstrated||218|
|Mendelian inheritance of mutations||220|
|Problems of expression and transmission||224|
|Relation of Mendelism to normal diversity of descent||230|
|Evolutionary implications of Mendelism||232|
|1An outline of this paper was presented in a discussion of Professor Davenport's lecture on "Heredity and Mendel's Law," before a meeting of the Washington Academy of Sciences, on February 26, 1907. Considerable amplification has been found desirable in order to carry out more fully the plan of a definite comparison of Mendelism with other methods of descent.|
Phenomena of this kind have received a large amount of special study in recent years, because it has been claimed that they prove new principles of heredity and open new routes to the solution of the larger problems of organic development. Such claims of great and special significance for Mendelism are due largely to the fact that these experiments brought for the first time a fairly definite mathematical factor into the problem of descent. In Mendelian crosses or hybrids there is a definite and uniform proportion between the expression of characters in what are called the first and second generations. It has not unnaturally been supposed that this regularity of proportion must obey an internal law or principle of descent governing the relations and combinations of characters. Definite mathematical relations must represent, it has been argued, definite entities inside the germ-cells. Here, at last, appeared to be a triumphant justification for the mechanical speculations of Darwin, Nägeli, and Weismann, to the effect that characters are transmitted from generation to generation by means of minute determinant particles or character-units of the germ-cells. It was found possible to explain the mathematical relations of typical cases of Mendelism by supposing that the presence or absence of certain particles in the germ-cells determined the presence or absence of the character in the adult organism.
In a Mendelian cross the parents differ in at least one pair of definitely contrasted characters. All the individuals of the so-called first generation show the character of one of the parents, which is called the dominant. In the following generations  three quarters of the individuals have this character of the dominant parent, and one quarter the other character (recessive), which did not appear at all in the first generation. It is this definite difference of proportions in the two generations which Professor Davenport has accepted as the basis of the Mendelian principles of heredity, and as a demonstration of the theory of evolution by mutation.
"We find that when two varieties that differ in some characteristic are crossed it frequently happens that one only of the two forms will reappear in the offspring (viz., the dominant characteristic, of Mendel), and it will be little modified by the presence, in that offspring, of the germ of the opposite characteristic. This is in accordance with the theory that most characteristics are, or may be resolved into, elementary units. Similarly, when a variety that has some new feature not possessed by the ancestor is crossed with that ancestor the offspring usually have the character fully developed (dominant). If these offspring are crossed together the character is absent in a small proportion only, on the average one-quarter, of their offspring . . . ."
|1Davenport, C. B., 1906. Report on Experimental Biology, Yearbook No. 5, Carnegie Institution of Washington, D. C., p. 94.|
"The fact that in crossing varieties their dissimilar characters do not blend is important, since it supports the theory that such characters first appear as they now are, fully formed. It indicates that since evolution has advanced by the addition of new characteristics it has advanced by steps or jumps. A new species has not gradually arisen from an old one, but suddenly, by mutation."1
THE NATURE OF EXPERIMENTS IN DESCENT.
But if the facts of Mendelism are examined somewhat more closely and in the light of modern knowledge of the peculiar nature of the reproductive processes of the higher plants and animals, it will be found that the definite mathematical relations which appear in a Mendelian experiment arise from the methods of reproduction rather than from the methods of inheritance. Other interpretations are possible, which render entirely unnecessary  the more general inferences which have been drawn from Mendelism, such as the existence of character unit particles and the purity of germ-cells.
Instead of being a simple process of making two successive combinations or crosses, of like nature, but with constantly different results, the reproductive processes involved in a Mendelian experiment are highly complex, and very different from what is commonly supposed. Before the bearings of Mendelism on the general problems of descent and evolution can be appreciated, it is necessary that the components of the phenomenon be clearly distinguished.
PARENT ORGANISMS PRODUCE PARENT GAMETES.
It is customary to say in describing Mendelian experiments that a cross was made of two individual plants or animals representing certain contrasts of characters. But this simple statement may carry us at once on to false ground, unless we follow closely the details of the process. What we refer to as crossing the plants or animals is merely bringing together the gametes or sex-cells which these particular organisms have produced. The organisms themselves are not involved in the experiment, except to the extent that they have furnished the sex-cells and provided nourishment for the embryos to which the sex-cells give rise. It is the sex-cells or gametes with which the experiment in crossing really begins. They are the true parents of the cross, rather than the organisms selected as parents. Gametes do not belong to the same generation or conjugation period as the parent organisms, but represent a new generation which is already begun before the intention to make a Mendelian or other cross can become effective.
PARENT GAMETES PRODUCE CONJUGATE ORGANISMS.
The union of the gamete parents opens the way to the development of a new organism, which it is customary to consider as the first generation of the desired cross. But again we may ask, what are the detailed facts of the case?
The prevalent view has been that the production of a new organic individual is the result of a conjugation, a complete  fusion of the parent sex-cells or gametes, but this is only partially true among the higher plants and animals. Among the lower groups of sexual organisms no distinction is to be made between conjugation and fertilization, but among the higher types fertilization (the union of sex-cells which initiates the development of a new plant or animal), no longer represents the whole process of conjugation, but only the first part of it. The outer protoplasms of the sex-cells have fused, and also their nuclei, but the conjugation is not yet complete, for the fertilized egg-cell still retains a double equipment of chromatin, derived from the two parents. And since this chromatic material represents the most highly specialized and active form of protoplasmic substance, it is proper to hold that the fertilized egg-cell and all its subdivisions are double cells as long as they contain this double equipment of chromatin.
The gametes can be thought of as persisting through the whole life-history of the individual organism, and do not become finally and completely united until the chromatin has fused in mitapsis, preceding the formation of sex-cells for the next generation. All the cells formed between fertilization and mitapsis are double in the above sense, that they contain two complete sets of chromatin elements, derived from those of the parent gametes. Organisms built up of cells formed while conjugation continues, that is, between fertilization and metapsis, may be called conjugate organisms. After the chromatin has fused in mitapsis new gametes are formed with single equipments of chromatin, capable of undertaking new conjugations. Then the number of chromosomes is again doubled, and the vegetative subdivisions of the conjugating cells are resumed.
CONJUGATE AND EXJUGATE REPRODUCTION.
|1The third and final stage of the process of conjugation has been named mitapsis from the Greek words meaning thread-fusion, because the chromatin granules, supposed to represent the two original parents, are, at least in some striking cases, stretched out in long threads. This permits them to fuse in pairs and thus to achieve a much more thorough and complete union than by any less definite method of combination.|
There is thus a fundamental difference between the reproductive processes of the lower types and the higher. The cells which compose the bodies of the higher organisms are of this double or persistently conjugate character. Reproduction is still a process of cell-divisions, since it is only by cell-divisions that the cellular bodies of plants and animals can be built up. But in the higher types conjugation is not finished before these  reproductive subdivisions occur. It is not until the sex-cells for the next generation are to be formed that conjugation is resumed and brought to a conclusion by mitapsis.1
Among the lower groups new organisms are built up at this stage, after conjugation has been completed by mitapsis, and before a new conjugation begins, as in the mosses, liverworts, and lower algae and fungi. But the higher plants and animals do not attempt to build up structures of these simple cells which are the products of completed conjugations. Instead of forming cellular structures in the intervals between conjugations, the process of reproduction in the higher types hastens from one conjugation to another, as though the superiority of the double cells for structure building were clearly recognized.
The ferns may be cited as an example of a group in which two different structures are built. A little liverwort-like prothallus is formed after conjugation, and a large leafy structure, or frond, during conjugation. Flowering plants, however, have closely approximated the reproductive methods of the higher animals. They do not waste time in structure-building celldivisions after or between conjugations, but pass promptly from one conjugation to another.
Applying these facts to our experiment in Mendelism, we find that the process of reproduction, as conducted by the higher plants and animals, does not permit of a complete conjugation before the building up of the new organisms which we have been describing as the first generation of the cross we intended to make. Another discrepancy between words and facts has to be admitted. Just as we found ourselves unable to cross the original parents, and were obliged to content ourselves with the intention of combining gametes produced by those parents, so we have now encountered a new limitation, inherent in the methods of reproduction followed by the higher plants and animals. We are unable to bring about an immediately complete union of  the gamete parents, but must wait for them to build up a new organism, which is not a true cross or product of conjugation, but a reproductive by-product, so to speak, which has been intercalated into the experiment which we originally intended to perform. The further progress of our desired conjugation is meanwhile suspended, and remains in abeyance until preparations are made for the production of the next generation of sex-cells. The results we were seeking, as a means of testing the inheritance relations of the characters of the original parental organisms, have not yet been attained.
CONJUGATE ORGANISMS PRODUCE PERJUGATE GAMETES.
The organisms built up by the parent gametes while in the conjugate condition may be called conjugate organisms, or conjugates. The next generation may be termed the perjugate generation to indicate that it has passed through conjugation. The gametes which produce this generation are perjugate gametes, and are the first result of the completed conjugation of the original gamete parents. The organisms which these gametes build up afford our first visible evidence of the relations which the parental characters have assumed as a result of conjugation.
What we have been calling the first generation of offspring of such a cross is thus found not to be a true result of the cross, but a structure built of double or conjugate cells which represent vegetative subdivisions of the gamete parents before their conjugation has been completed. What we have been calling the second generation of the cross is really the first generation of the organisms which represent the results of a true union or completed conjugation of the original gamete parents.
With reference to the next preceding generation each sexually reproduced higher plant or animal is a conjugate, that is, it is built up by conjugating gametes derived from the preceding generation. With reference to the second preceding generation each individual is to be reckoned as a perjugate, that is, it represents the result of the completed conjugation of the gametes derived from the second preceding generation. The relation of an organism to the grandparent generation is distinct and different from its relation to the parent generation. It is produced  before the conclusion of the conjugation of the gametes derived from the parent generation, but is the product of the completed conjugation of the gametes derived from the grandparental generation.
Though we may for some purposes make a contrast between the two generations, describing one as conjugate and the other as perjugate, this should not cause us to forget that all organisms of the higher groups are conjugate organisms. This is in fundamental contrast with the exjugate organisms of the lower groups, which are built up, not during conjugation, but in the intervals after, or between, conjugations.
This system of reproduction of the higher plants and animals, which enables them to build up new organisms while conjugation continues, and before it is completed, is responsible for the ability of the higher groups to form sterile hybrids, that is, hybrids between groups which are so diverse that their gametes are unable to effect a complete conjugation, so that no perjugate generation is produced. Such conjugate hybrids are an impossibility, of course, among the lower groups where conjugation has to be completed before cell-divisions begin.
|1Castle, W. E., and Allen, Glover M., 1903. Mendel's Law and the Heredity of Albinism. Mark Anniversary Volume, pp. 383. Henry Holt and Co., N. Y.|
Thus Mendelism is not the only phenomenon which results from the fact that higher organisms are built up before the conjugation of the parent gametes is completed. Conjugate hybrids prove that the conjugate relation is different and less exacting than the perjugate relation, and may thus help to reconcile us to the fact that differences between the two generations are inherent in the method of reproduction and not necessarily indicative of general principles of inheritance. Indeed, it is claimed by some Mendelians, such as Castle and Allen, that dominance, the relation sustained by the gametes in the conjugate generation, has nothing to do with what they consider Mendelism proper, the "principle of gametic purity." 1
"The principle illustrated by these examples is, as pointed out by Bateson, the most fundamental and farreaching of the Mendelian ideas. It is known as the "law of segregation," or "splitting" of the parental characters at gamete-formation, or as the "principle of gametic purity." Dominance is purely a secondary matter; it may or may not occur along with segregation, though the latter can be more easily demonstrated in cases where it is associated with the former. The principle of gametic purity rests upon the assumption that gamete formation is the reverse of fertilization. In fertilization gametes A and B unite to form a zygote AB; when this zygote in turn forms gametes, they will be again A and B. From a knowledge of the somatic form alone of pure A's and B's, one can make no trustworthy prediction as to the form of AB . . . . But, no matter what the somatic form of AB is, we may with confidence predict that its gametes will be essentially pure A's and B's, and in equal proportions. This is the Mendelian expectation in all cases of alternative inheritance. Whether it applies to other cases also, and, if so, to what extent, is not yet known."
SUMMARY OF THE FIVE ELEMENTS OF DESCENT.
Every test of the behavior of different parental characteristics in crosses or hybrids involves these five cases or elements, which may be summarized briefly as follows:
Even the simplest experiment in Mendelism involves consideration of at least these five distinct periods of existence. The adult organisms of three generations are included, and the gametes or sex-cells of two generations. One generation is required for the conjugation of the gametes of the original parents to be accomplished, and another generation for the results of the combination to be brought to expression in adult form. The third generation differs profoundly from the previous generation in its relation to the original parents of the cross, and not merely in the proportional representation of the parental characters, as shown in experiments in Mendelism.
MENDELISM AS A METHOD OF DESCENT.
By means of these five categories, it is possible to describe Mendelism, as well as other methods of descent, in a more direct and definite manner. Thus Mendelism may be defined as a method of descent which yields conjugates all like one parent, and perjugates like both parents in the proportion of three to one. But to clearly understand the status of Mendelism as a method of descent it is necessary to compare it with other methods, described in corresponding terms. To make formal definitions and laws of Mendelism in the absence of any formulation of other methods of descent, is to only apply another way of claiming unique significance for this one group of phenomena, to the exclusion of others equally worthy of our attention. When the matter is thus brought to a definite issue it becomes evident that there are numerous methods of descent instead of one or two. Indeed, so many methods are now known that a general classification or arrangement of them becomes almost necessary.
Such a classification of methods of descent seems likely to afford a better means of comparison than by attempting to formulate a series of new principles to correspond to the more abstract presentations of Mendelism which have been made. Our so-called natural laws and principles represent, after all, only sequences, processes or groups of phenomena. To call anything a law or a principle is to bespeak for it a somewhat superstitious reverence inconsistent with the thoroughly concrete methods of treatment which afford the only assurance of permanent scientific results. Principles and laws are abstractions, but processes are sequences of relations between tangible things. Mendelism is one of these processes or methods of descent, but it is not the only method, nor the most frequent or important method. Nor does it differ in any very serious or important respect from other methods of descent with which we are all familiar.
PRIMARY METHODS OF DESCENT.
The tendency of the past has been to seize upon one or another of the methods of descent as typical, and then to try to prove that it includes or represents all the others. One way  of avoiding this confusion of unlike conditions is to keep in mind the fact that different kinds of crosses may differ, not only in the particular differences or amounts of difference which the parent organisms show, but also in the fact that the parents may belong to different kinds of groups.
Thus if there is indiscriminate individual diversity, among the members of the parent group (as in a natural, freely interbreeding species) this diversity will not disappear at once, even though care be taken to bring together as parents two individuals which seem to be closely alike. But by selection a uniform type may be bred in which the traditional ideal of heredity, that like produces like, may appear to be fully exemplified. And yet if the narrow breeding be carried on with persistence, mutative reactions toward greater diversity will appear, and these sudden deviations from an established heredity are even more different than were the normally diverse individuals of the original species.
Mendelism belongs to another series of methods of descent, in which the parents are diverse in a more definite manner, that is, by discriminate or regularly established differences, like those existing between the sexes of a species or between selected varieties. Finally, there is the still more fundamental diversity between species which have been separated long enough for definitely divergent characters to be developed.
|SYNOPSIS OF METHODS OF DESCENT.|
|Descent with unrestricted, indiscriminate diversity (heterism).|
|Genetic variation in unrestricted descent (neism).|
|Descent with restricted diversity (heredity).|
|Discontinuous variation in restricted descent (mutation).|
|Reappearance of ancestral characters (atavism).|
|Descent with discriminate intraspecific diversity (ropism).|
|Descent with integradation of differences (scalar).|
|Descent with preservation of differences (polar).|
|Polar inheritance in dimorphic species.|
|Diversity in social organisms (politism).|
|Polar inheritance in crosses of narrow-bred varieties.|
|Complete dominance (mendelism).|
|Descent with averaging of differences (intermediate).|
|Descent with specific diversity (hybridism).|
|Sterile or mule hybrids (conjugate hybridism).|
|Fertile hybrids between species (perjugate hybridism).|
Unrestricted Descent with Normal Diversity (Heterism).— Heterism is a method of descent in which the parent organisms are members of an individually diverse, freely interbreeding group, and the offspring reproduce the group diversity, instead of being restricted to the expression of characters of the parent individuals. Heterism is the most general condition or method of descent, that found in widely distributed, broad-bred species in nature.
|1Cook, O. F., 1906. The Vital Fabric of Descent. Proc. Washington Academy of Sciences, 7: 301. Aspects of Kinetic Evolution. Proc. Washington Academy of Sciences, 8: 197-403.|
Reasons have been given in other places for believing that organic evolution is a function of normal, specific networks of descent — a process of change in a broad fabric of interbreeding lines of descent.1
Inheritance, like descent, is a group phenomenon. Uniformity of inheritance is proportional to the uniformity of the group to which the parent organisms belong. In broad-bred groups parent organisms are usually unlike. The offspring are also unlike, and they do not merely reproduce the differences of the parents, but share the indiscriminate individual diversity of the group. Even the simultaneous offspring of the  same parents are often definitely unlike, thus showing that these differences arise from the method of descent, and do not depend merely upon the influences of external conditions.
Genetic Variation with Unrestricted Descent (Neism).— Neism is a form of descent in which the parent organisms have the usual individual diversity of the group to which they belong, while the conjugates and perjugates are more diverse than usual, and differ from the remaining members of the group in the manifestation of a new character.
Uniformity of Restricted Descent (Heredity).— Heredity is a method of descent in which the indiscriminate individual diversity of heterism has been eliminated by narrow breeding or selective restriction of descent. In this way relatively great uniformity may be brought about and maintained for a long series of generations.
To treat heredity as but one among many forms or methods of descent may appear unusual, or even unwarranted. This is because heredity — the production of like by like — has been considered the typical method of descent under theories which hold that differences among the members of a species are not normal phenomena of descent, but due to external conditions. The popularity of this doctrine of normal uniformity in descent has been so great that descent and heredity have often been used as completely synonymous terms, just as it is now proposed by some to extend the inferences drawn from Mendelian inheritance over the whole field of evolution. Under the present interpretation of the facts other methods of descent are recognized as more general and more normal than the production of like by like. Descent is a wider term than heredity, since it includes all the methods of propagation by which organic series are maintained.
Heredity, in the more definite sense, is a fact, but only under conditions of restricted descent. It is only among our narrow-bred domesticated varieties of plants and animals, or among similarly limited groups in nature, that like produces like in any manner which approximates uniformity, so that the descendants may appear "perfectly true to the physical characters of their progenitors." And even this artificial uniformity of restricted  descent is not permanent, but gives way in time to the diversity of mutative degeneration.
Abrupt Variation in Restricted Descent (Mutation).— Mutation is a method of descent in which the parent organisms are alike, but abrupt differences appear among the offspring, usually as the result of variations of the parent gametes.
The parent organisms are not only alike with respect to some particular character, but belong to the same series of like individuals, in which like has produced like for numerous generations.
If the new character is dominant it becomes apparent among the conjugates, but if recessive it can not attain expression unless two recessive gametes can be brought together, which is not possible until the perjugate generation. Mutations differ from genetic variations in the conditions of uniformity and restricted descent in which they appear, and usually also in the greater amplitude of the differences acquired by mutation.
Mutative variations are usually preserved by polar inheritance, and the new character may be either dominant or recessive, quite as in Mendelian crosses of mutative varieties. The condition of restricted descent in which mutations appear is also the condition in which polarity of inheritance is most pronounced, as though an effort were being made to restore the normal diversity of the group, by preserving all of the mutative differences.
Atavism.— Atavism is a method of descent in which the offspring diverge from the parents and their immediate relatives in the expression of a character in some more remote ancestor. Thus many mutative variations of narrow-bred domesticated varieties are in the direction of characters of the wild type of the species. Atavism is related to reversion, but a distinction may be made by calling those cases reversion in which the return to the ancestral character has been occasioned by the interbreeding of members of two or more narrow-bred varieties.
Descent with Discriminate Diversity.— Discriminate inheritance includes those forms of descent in which the parent organisms represent narrow-bred groups, so that their differences are not merely individual or indiscriminate. The different methods of descent in discriminate inheritance can be conveniently  illustrated by thinking of the characters of the two parents as the ends of a graduated series or scale like that of a thermometer. With reference to such a scale three forms of discriminate descent may be distinguished.
In the first form the offspring present a complete series of gradations between the parental extremes. This may be called scalar or intergraded inheritance. It resembles most nearly the indiscriminate diversity of descent of natural species.
In the second form of discriminate descent the progeny, and especially the perjugate gametes, are adjusted to favor the complete preservation of the divergent parental characters, or poles of the series, but do not produce the connecting series between.
In the third form of discriminate descent the divergent characters are not preserved by separate expressions, but are combined into an intermediate average.
Inheritance of Intergradations (Scalar).— Scalar or intergraded inheritance is a method of descent in which the offspring show a complete series of gradations between the divergent characters of the parents. The result of such crosses is to release again the normal tendency to diversity, so that the pendulum of variations swings over the entire series of gradations between the parental poles of the scale of inheritance.
With reference to their expression in any single individual the two parental characters may be said to be combined or blended, but the existence of a complete series of gradations is the characteristic which distinguishes this method of descent from the combinations which result in a uniform or intermediate  average, and those in which the parental diversities are preserved by alternative expression. Nor is it to be supposed that there are not conditions intermediate between scalar, polar and intermediate inheritance. In some characters there may be a tendency to prefer the extremes of the series, and in others the mean, or some other maximum point. Such relations have been investigated at length by Galton and other statistical biologists.
Scalar inheritance is in some respects intermediate between indiscriminate inheritance and polar inheritance. The parental diversities become established as the poles of the series, but the polarity is not so definite as when the parental differences are fully preserved.
G. C., 1906. Quotations in Obituary
Notice, Kew Bulletin, No. 9, 1906, 384.
Scalar inheritance is commonly manifested in crosses between selected varieties of domesticated plants and animals. It was formerly taken for granted that similar series of intergradations were often produced in nature by the hybridizing of species, but the evidence has failed to convince the late G. C. Churchill, an English botanist who appears to have given this particular point very extensive and discriminating study.1
The fact seemed to be established that in the great majority of cases, at least, the hybrids between adjacent species of gentians and other alpine plants were limited to one or two definitely intermediate forms, without series of connecting links or intergradations (Uebergangsformen). The ability to form intermediate sterile hybrids would not really intermingle the species or interfere with their continued differentiation. Less differentiated species with separate geographical ranges might form intergraded crosses like selected varieties of the same species, but it is not to be supposed that species which freely interbreed and intergrade, could become differentiated while occupying the same geographical distribution. Whenever two related, but definitely distinguishable species occupy the same area we may expect to find that they have some other form of segregation, such as differences of time of flowering, or inability of the germcells to effect normal conjugations.
Descent with Preservation of Differences by Polar Inheritance.— Polar inheritance is a general type of descent which includes  all cases in which the parent organisms differ by two or more characters which are preserved in the offspring. All species in which definite diversities are maintained like those of sexes, castes, dimorphism, polymorphism, etc., are examples of polar inheritance, as are also the crosses of different varieties when the parental diversities are repeated in later generations. The general opinion has been that when two unlike individuals are bred together their differences tend to average away or come to an intermediate point in the offspring, but this is not true when descent follows the methods of polar inheritance.
The diverse characters of the parent organisms continue to be represented in the perjugate gametes and the perjugate offspring, instead of being lost by intermediate or graded inheritance or other more miscellaneous variations. In several forms of polar inheritance equal numbers of the perjugate gametes represent the divergent parental characters, but there is great diversity in the relations assumed by the parent gametes, as shown by diversity of behavior in the conjugate generation.
Polar Inheritance in Dimorphic and Polymorphic Species.— Two conditions of polar inheritance may be distinguished, those in which the polarity is already established under conditions of free interbreeding and those in which relations of polarity are manifested when representatives of different varieties and species are bred together. In the one case the polarity is altogether natural, in the other somewhat artificial or experimental. That there is any essential difference in the nature of the polarity phenomena of the two series of cases, is scarcely to be claimed, but it is very desirable to distinguish them in attempting to estimate correctly the general significance of the polarity phenomena.
Polar Inheritance of Sexual Differences (Sexual Dimorphism).— The most familiar phenomenon of polar inheritance is that of sex. The parents are diverse, often by a large series of definitely contrasted characters, and the offspring, both conjugates and perjugates, preserve all these contrasts. Sex-inheritance differs from Mendelism mostly in being a much more specialized form of the same phenomenon of polarity in the expression of divergent characters.
Semisexual Dimorphism.— Semisexual dimorphism is a  method of descent in which the members of the same species of two definite kinds or castes, so formed as to require or to facilitate cross-fertilization, though without the separation of the sexes in different individuals. The differences found in semisexual species correspond in all respects, to the secondary sexual characters of completely sexual species, except that they do not accompany sex-differentiation. Examples of semisexual dimorphism are numerous among plants, as in the species of Primula, Houstonia, etc. In some species of Oxalis and Lythrum there is even a trimorphism involving three kinds of stamens, pistils and pollen-grains.
|1Examples of Semisexual, Subsexual, and Supersexual differentiations are given in Cook, in Aspects of Kinetic Evolution. Proc. Wash. Acad. Sci., 8: 320-376.|
Subsexual Dimorphism and Polymorphism.— Subsexual dimorphism is a method of descent in which the members of the same species are of two or more different kinds, castes or "elementary species ", but without regard to sexuality or to provisions for cross-fertilization. The phenomenon may prove to be completely analogous with Mendelism and other related forms of polarity of character-expression in crosses between narrow-bred varieties. It is, in short, polar inheritance under natural conditions of free interbreeding, not complicated by the more highly specialized polarity of sex-differentiation.1
A recently recorded addition to this series of phenomena is that of a color-diversity in Verbena stricta, discovered in Kansas by Professor Schaffner.
"The peculiar form which I discovered was very different from the type and its variants. The color of the corolla was a pinkish-white [instead of deep purplish blue] and the individuals, numbering several thousands, were found to be remarkable for the uniformity of this character. There were no transition forms whatever. The mutant had a much smaller color variability than the parent species, and no other peculiarity than the color of the corolla was discovered.
"The mutants covered about a square mile of territory. In some directions, however, they have advanced for nearly a mile beyond what seems to have been the center of distribution. . . . The mutant was found indifferently on nearly all kinds of soil  and habitat which the section afforded. In some places the normal type was more abundant, in others the mutant, while in still other spots both were present in about equal numbers, growing together closely intermingled.
J. H., 1906. A Successful Mutant of
Verbena without External Isolation. Ohio Naturalist, 7:31.
"This mutant is not of hybrid origin. Hybrids between certain species of Verbena are common but are easily recognized from morphological characters. No hybrids were found in the locality. A careful search was made in all directions. . . ."1
A new character is obviously analogous to a mutation, though it does not behave as mutations are supposed to do. At present it seems to have brought about a condition of dimorphism in the parent species, instead of requiring to be isolated in order to be preserved, though the possibility of segregation by some form of reproductive incompatibility is not absolutely excluded.
Supersexual Dimorphism.— Similarly definite diversities of color are also known among sexually higher differentiated animals, and may be reckoned as constituting still another method of descent, supersexual dimorphism. The present interest of this phenomenon lies in the fact that it proves that polarities of expression may be maintained even in sexually differentiated species and under conditions of free interbreeding. The diversities of eye-color in the European races constitute a mild form of such a dimorphism or alternative inheritance phenomenon, as shown by the studies of Galton.
Diversity in Social Organisms (Politism).-- Politism is a method of descent in which a part of the offspring regularly show characters different from any of their parents or ancestors, accompanied by a deficient development of the sexual organs and powers of reproduction, as in the highly socialized groups of insects, such as the ants and the termites. Politism differs from other kinds of dimorphism in that the offspring represent from one to four specialized sterile castes, in addition to the reproduction of the unspecialized sexual types.
Character-transmission is here completely divorced from character-expression, for the sexual insects never express the characters transmitted to the sterile castes, nor do the sterile castes propagate their own characters or those of their parents. That  the characters which a particular individual shall express as an adult may be determined by external conditions constitutes additional evidence that the expression of characters does not depend upon the same factors as the transmission of characters. Cases of politism occur also among plants. The vegetative internodes, which correspond to the neuter individuals of the insect colonies, may become unlike. Some of the branches are then unable to replace the main stem, though in most plants all the branches and internodes are potentially equal.
Polar Inheritance in Crosses of Narrow-Bred Varieties.— The general result of this class of experiments has been to prove that narrow-bred varieties may assume the same or very similar relations of polar inheritance as those regularly manifested by the sexes and castes of dimorphic species. Indeed, the narrow breeding which has restricted the descent of the parental groups appears to intensify the polarity phenomena in such a way that very definite mathematical relations are sometimes assumed.
Equipolar Inheritance.— Equipolar inheritance is a method of descent in which the diverse characters of the parents are expressed in equal numbers of the conjugates and perjugates, just as in sex-inheritance. This shows that the diversities are also represented in equal numbers of the gamete parents and the gamete offspring, but they are not united with the sexual characters. There are many secondary sexual characters which are to be distinguished from equipolar characters only by this relation to sex-differentiation.
Instances of equipolar descent like that of Professor Davenport's cross between the four-toed and five-toed chickens are of special interest as connecting links between sex-inheritance and other forms of polarized descent. Thus if Professor Davenport were to mate five-toed cocks with four-toed hens for a series of generations we may expect that the five-toed character would become definitely attached to the other polarities of sex-inheritance, just as the enlarged spur is now a part of the regular, normal equipment of the male birds.
Some of the mutations of the coffee tree are purely pistillate and some purely staminate. If a dimorphic type of coffee were desirable it would probably not be difficult of development by breeding from such a pair. 
That polarity of inheritance also exists in nature apart from sex-inheritance is shown in numerous instances of dimorphism and dichromatism. Some animals have dichromatism superposed upon sex, and many plants are dimorphic in which the sexes are not separated.
Partial Dominance.— Partial dominance is a form of polar inheritance in which the diverse characters of the parents are brought to expression in unequal numbers of the conjugates and perjugates. The relation between the parent gametes is not uniform, one of the divergent characters gaining expression as a dominant in one conjugate individual, but remaining abeyant in another. Nevertheless, the gametes formed by these unlike conjugates may follow the law of polar inheritance. Equal numbers of gametes would then represent the expression of the divergent parental characters, though the partial dominance of the conjugate relation would again affect the proportion in which the characters would be expressed among the perjugate organisms.
|1Gates, R. R., 1907. Preliminary Note on Pollen Development in OEnothera lata De Vries and its Hybrids.Science, N. S., 25: 259, and Bot. Gaz. 44 : 1-21.|
A good example of partial dominance is to be found in crosses between OEnothera lata, one of De Vries's mutations, and the parent type O. lamarckiana. About 15, percent show characters of O. lata, that is O. lata is dominant to the extent of 15 percent, O. lamarckiana to the extent of 85 percent. As this mutation does not itself produce any pollen, its characters must be considered as receiving expression only in this condition of partial dominance. The instance is interesting because of the further fact that the lata mutation has very recently been found to have only 14 chromosomes in the somatic cells, while the lamarckiana form of the cross has at least 20.1 This shows that dominance, at least, does not depend upon the number of chromosomes.
There is no assurance, of course, that a character once recessive is always recessive, or that the proportions of expression may not change. Even in Mendelian experiments different crossings of the same stocks often show different results, as in the case of the tailless fowls and other deviations from the Mendelian expectations described by Professor Davenport.  None of the 200 offspring of one of the tailless birds was tailless, but in the progeny of a son of the same bird the tailless character gained expression in the regular Mendelian proportions.
Complete Dominance (Mendelism).— Complete dominance, or Mendelism, is a form of polar inheritance in which only one of the divergent parental characters (dominant) is expressed in the conjugates, but the perjugates are like both parents in a proportion of three to one. The parent organisms and gamete parents are diverse with respect to the expression of one or more definitely contrasted characters. The conjugates show the divergent character of only one of the parents, which is called the dominant. The perjugates are again diverse like the parent organisms, but the expression of the divergent characters of the organic parents is unequal, three-quarters having the dominant character expressed in the conjugates, and one-quarter the character which was recessive or abeyant in the conjugates. Subsequent generations will continue to reproduce the latter, three dominants to one recessive. Thus Mendelism might be reckoned as a weaker form of sex-inheritance in which the phenomenon of dominance interfered with a strict equality of expression-polarities in the conjugate phases.
The inferences which have been based on the differences of proportion in the expression of the parental characters of the so-called first and second generations of a Mendelian cross fall to the ground as soon as we consider in sufficient detail the reproductive processes by which they are produced. The two generations have an entirely different relation to the original organisms or to the gamete parents, but at the same time the relation of the characters to each other is not different in the generations, in spite of the difference of proportions. In the conjugate generation all the organisms arise from combinations of unlike gametes, while in the perjugate generation only half of them represent such combinations. But all of these show the phenomenon of dominance, quite as in the first generation. The behavior of first generations proves to us that characters may be expressed by polarity, or as reciprocals, instead of as averages or resultants. If we admit the same possibility for  the expression tendencies of gametes the mathematical relations of Mendelism can all be understood without the necessity of predicating character-units or pure germ cells.
Dominance, as a manifestation of expression-polarity, is not a merely secondary matter in Mendelism, but affords a key to the whole phenomenon, since it renders unnecessary the false assumption that gamete formation is the reverse of fertilization.
Interpolar Inheritance.— In interpolar inheritance one of the divergent characters is not dominant over the other, but the two characters receive intermediate expression in all of the conjugates and in one half of the perjugates.
This shows that the gametes formed by the intermediate conjugates represent the divergent parental characters in equal numbers, as in Mendelism, but the lack of dominance leads to intermediate expression of characters in the conjugate generation, and in one half of the perjugates and other succeeding generations, since half of the gametes may be expected to mate with others having the same polarity, and half with those having a different polarity.
Mosaic Inheritance.— Mosaic inheritance differs from interpolar inheritance in that the divergent characters are not completely averaged or blended, but pieced together, as it were, after the manner of a mosaic. Thus in crosses between black and white poultry, interpolar inheritance brings a conjugate generation of an intermediate gray or blue color, while mosaic inheritance yields larger or smaller spots of black and white.
Mosaic inheritance might also be compared with scalar inheritance.
Extrapolar Inheritance.— Extrapolar inheritance is a form of descent in which conjugate organisms present characters diverse from those of the parents, instead of being like either parent or intermediate between them. Such divergent conjugates are called heterozygotes in the specialized vocabulary of Mendelism. The fact that such characters depend for their expression, not on the polarity possessed by the gametes before conjugation, but upon the relations assumed during conjugation, enables us to understand the general opinion of Mendelists that heterozygote characters cannot be "fixed" by selection. Simple  selection might have, it is true, no tendency to render such a conjugate character transmissible, but the chance that gametes might be found which tended to the same expression as the conjugates might warrant such an effort if the heterozygote character was sufficiently valuable.
Whether any heterozygote characters represent really new variations seems not to have been definitely ascertained. In case they should all prove to be in the nature of reversions this method of descent will coincide with the next.
Conjugate Reversion.— Conjugate reversion is a form of descent in which the conjugates become different from both of the parent organisms by returning to the expression of an ancestral character of one or both of the parents. Thus Darbishire reports that numerous crosses of two varieties of pink-eyed mice yielded only black-eyed offspring in the first or conjugate generation.
Perjugate Reversion.— Perjugate reversion is a method of descent in which the conjugates do not depart from the characters of the parents, but the perjugates become abruptly different by returning to the expression of an ancestral character. Perjugate reversion differs from conjugate reversion in that the ancestral character reappears in the perjugate generation, instead of in the conjugate generation.
|1"Where the smooth-seeded Klondike upland was used in crossing with Sea Island the second generation hybrids exhibited a very peculiar case of reversion. The Klondyke, while originally a fuzzy-seeded type, had been carefully selected for a number of generations before the crossing was done, until it produced regularly and normally a smooth black seed. When crossed with Sea Island the first generation hybrids all had smooth black seeds. In the second generation, however, quite a number of the progeny had fuzzy seed, showing that the fuzzy seed potent still existed in the Klondike though dormant. This would seem to be an important point, as indicating the non-purity of the germ-cell." Webber, H. J., 1905. Cotton Breeding. Proc. Amer. Breeders' Association, 1: 40.|
Perjugate reversion may be illustrated by an experiment reported by Dr. Herbert J. Webber. The crossing of Sea Island cotton with a smooth-seeded Upland variety resulted in a conjugate generation which was smooth-seeded like the parents, but in the second or perjugate generation woolly seeds reappeared, and for several generations afterward.1
Both kinds of reversion may be considered as due to a restoration  of polarity of expression to an ancestral character which has remained latent for numerous generations. In conjugate reversion the change of polarity comes about through the bringing of the gametes together in fertilization. In perjugate reversion the change of polarity probably occurs at initapsis, when the new gametes are formed. Perjugate reversion may also be described as mitaptic reversion or as gamete reversion, when it is desired to emphasize these contrasts. But from the standpoint of analogy with Mendelism perjugate reversion seems the better term, since it indicates more definitely the fact that the reappearance of the previously latent ancestral character does not become evident in the conjugate generation, but in the perjugate.
|1Simpson, Q. I. and J. P., 1907. Reversion Induced by Cross-Breeding. Science, N. 5., 25: 427.|
A curiously complex instance of reversion in later perjugate generations has been reported recently in pigs. Two threequarters Berkskire and Poland China sows, when bred to a similarly crossed male produced litters of pigs each of which showed, while young, seven longitudinal stripes like wild pigs. The parents had retained the black color and white points of the parent breeds. The mating of a pair of the pigs which had been striped when young yielded a diverse litter, some with the ancestral stripes, some with solid sandy black, the usual coloration of the Berkshire breed of sixty years ago, and some with black and white spots like the Poland Chinas of thirty years ago.1
Prepotent Polarity.— This is a form of polarized descent in which the divergent character of one parent is expressed in more than three-quarters of the perjugates, showing that more than half of the prejugate gametes tend to express the character of the one parent.
|1De Vries, H., 1907. Evolution and Mutation. The Monist, 17: 19.|
An instance which may be interpreted as polar prepotency is described by Professor De Vries. All the seeds of a plant which had shown only a few ligulate disk-flowers produced plants with completely double flowers. The expression of the double variation may have been restricted in the first generation by the non-mutated gamete, but the new character appears  to have been prepotent in all the gametes of the next generation.1
"The double variety of the corn-marigold (Chrysanthemum segetum) arose in my garden in a culture in which I was increasing the number of ray-florets by continuous selection. During four years I had succeeded in increasing this number to about sixty on each head, starting from the cultivated variety with an average of twenty-one. All the ray-florets, however, belonged to the outer rows of the heads, as in the original variety. At once a plant arose which produced some-few ligulate florets in the midst of the disc. This indicated the production of a double race. When the seeds of this mutating individual were sown the next year, they yielded a uniformly double group; and from this time the new variety remained constant."
Descent with Combination or Averaging of Differences (Intermediate).— Intermediate discriminate inheritance is a form of descent in which the differences of the parents are reduced in the offspring to an intermediate blend or average.
The difference between interpolar inheritance and intermediate inheritance is that in the former the intermediate expression of the diverse parental characters is general only in the first or conjugate generation, since the perjugate gametes tend to express the parental characters, as well as the intermediate. But in true intermediate inheritance the gametes also tend to intermediate expression, so that the perjugate generation may be as definitely intermediate as the conjugate. In the language of Mendelism, dominance is lacking, and the germ-cells are not "pure." Both interpolar inheritance and mosaic inheritance will be found, no doubt, to shade off by imperceptible gradations into intermediate or completely blended inheritance. Some of the gradations were well shown in Professor Davenport's poultry-hybrids.
Descent with Specific Diversity (Hybridism).— No absolute distinction can be made between crosses of groups which have become isolated by natural causes and those which have become isolated by man; but there is usually this very important difference that conscious human selection narrows the network of descent much more suddenly arid definitely than unconscious agencies of the environment. Unconscious selection rejects only the end of the procession, but conscious selection saves only the head, or some other equally restricted section. Species usually do not differ from each other in the same definite ways that narrow-bred  mutative varieties differ, and interspecific hybrids usually do not show the same definite polarities of character-expression.
Sterile or Mule Hybrids (Conjugate Hybridism).— Conjugate hybridism is a form of descent in which the parent gametes are not able to accomplish a complete conjugation, though they are able to unite in fertilization and build up a conjugate organism. Normal perjugate gametes are not formed, nor any perjugate organisms.
Conjugate hybridism may be illustrated by the mule and other sterile crosses between the members of distinct species, but mutative variations may also be sterile like conjugate hybrids. Usually these sterile conjugate hybrids are definitely and uniformly intermediate between the two parents, as though there were definite tensions which had yielded a uniform resultant. Thus there seems to be rather less diversity among mules than among horses.
Fertile Hybrids between Species (Perjugate Hybridism).— Perjugate hybridism is a form of descent in which gametes representing different species are able to perform a complete conjugation, so that a perjugate generation is produced.
There are many stages and gradations between conjugate and perjugate hybridism, and of perjugate hybridism many different degrees might be distinguished. Between some species perjugate hybrids are to be obtained only rarely and are then weak, short-lived or sterile. Where the parental incompatibility is somewhat less, the perjugate generation, though more readily produced, shows a wide range of diversity like that of mutations of narrow-bred varieties. The following generations of such mutative hybrids may also be very unstable, but in plants capable of vegetative propagation these mutative hybrids are often valuable. Other species hybridize with greater freedom, and show less abnormal diversity. Finally, some hybrids between species appear to be nearly as normal and stable as crosses between related varieties of the same species.
|Heterism||Indiscriminately diverse||Diverse||Diverse like
|Diverse||Diverse like parent group|
|Genetic variation (neism)||Indiscriminately diverse||Diverse||More diverse than parent group||Diverse||More diverse than parent group|
|Heredity||Alike, narrow bred||Alike||Alike||Alike||Alike|
|Mutation||Alike, narrow bred||Diverse||Diverse||Diverse||Diverse with polar inheritance|
|Atavism||Alike||Alike or Diverse||Diverse, some like remote ancestor||Alike or Diverse||Alike or diverse|
|Scalar inheritance||Diverse groups||Diverse||Intermediate intergraded||Diverse||Diverse, showing all gradations between parents|
|Sexual dimorphism||Diverse sexes||Diverse||Diverse sexes||Diverse||Diverse sexes|
|Semisexual dimorphism||Diverse semisexes||Diverse||Diverse semisexes||Diverse||Diverse semisexes|
|Subsexual dimorphism||Diverse without reference to sex||Diverse||Diverse subsexes||Diverse||Diverse subsexes|
|Supersexual dimorphism||Alike or diverse||Diverse||Diverse supersexes||Diverse||Diverse supersexes|
|Politism||Alike, unspecialized||?||Unlike, fertile and sterile||?||Unlike, fertile and sterile|
|Equipolar inheritance||Diverse groups||Diverse||Like both parents in equal numbers||Diverse in equal numbers||One-half like one parent, one-half like other parent|
|Partial dominance||Diverse groups||Diverse||Like both parents in unequal numbers||Diverse in equal numbers||Like both parents in equal numbers|
|Complete dominance (Mendelism)||Diverse groups||Diverse||Like one parent (dominant)||Diverse in equal numbers||Three-fourths like dominant parent, one-fourth like recessive parent|
|Interpolar||Diverse groups||Diverse||Intermediate, blended||Diverse in equal numbers||One-fourth like one parent, one-half intermediate, one-fourth like other parent|
|Mosaic||Diverse groups||Diverse||Intermediate, mosaic||Diverse in equal numbers||One-fourth like one parent, one-half mosaic, one-fourth like other parent|
|Extrapolar||Diverse groups||Diverse||Different from both parents (heterozygotes)||Diverse in equal numbers||One-fourth like one parent, one-fourth like ofhter, one-half different from either|
|Conjugate reversion||Alike, but of different origin||Alike||Different from parents, like remote ancestor||Alike or diverse||Diverse, some like parents, some like conjugates|
|Perjugate reversion||Alike, but of different origin||Alike||Like parents||Unlike parents||Like remote ancestors|
|Polar prepotency||Diverse||Diverse||Usually like one parent||More than half like dominant||More than three-fourths like dominant|
|Conjugate hybridism||Diverse species||Diverse||Intermediate, sterile||No perjugate gametes||No perjugate organisms|
|Perjugate hybridism||Diverse species||Diverse||Intermediate or diverse, fertile||Alike or diverse||Intermediate or diverse like mutations|