Genetic Analysis

Genetic Analysis, a system of experiments, observations, and calculations having as its purpose the decomposition of organism properties into separate hereditary elements, 'individual traits,' and the study of the properties corresponding to these traits in genes. Genetic analysis began to be developed after the rediscovery of Mendelism (see). The first, more instructive examples of genetic analysis were given by researchers on the coloration of rodents (rabbits, mice) and the coloration of snapdragons (E. Baur). It turned out, for example, that the ordinary concept of 'gray coloration of mice' decomposes into a series of separate traits, such as: 'presence of coloration in general,' 'presence of yellow pigment,' 'presence of pigment capable of blackening,' 'presence of intensification of coloration to black' (which, in turn, is decomposed into several separate traits), 'presence of yellow rings on each hair.' Each of these separate traits corresponds to its own gene; therefore, 'gray coloration' results only from the simultaneous presence of all these genes. The coloration of 'snapdragons' is decomposed into an even greater number of elements. The basic method of genetic analysis is crossing the organism being studied with others that differ from it in some respect, with the first generation (F1), the second generation (F₂), and, if needed, F₃, F₄, etc., as well as particularly often 'backcrossing,' or 'reverse' crossing of F₁ with the parents, being examined. If the difference between the crossed individuals was hereditary, then the F₂ generation, according to the laws of Mendelism (see), breaks down in its traits into several groups in certain numerical relationships, the careful study of which allows one to analyze the difference between the parents, i.e., to determine by how many genes they differed from each other and what the properties of these genes are. If, for example, the F₂ offspring breaks down into two categories (children with brown and blue eyes) in a 3:1 ratio, then obviously we are dealing with monohybrid crossing, i.e., one dominant and one recessive gene were involved in the crossing, with the dominance of brown coloration over blue being complete, and the AA and Aa forms being indistinguishable from each other. If, as a result of crossing, three phenotypes (see) are obtained, for example, black, blue, and white chickens in a 1:2:1 ratio, then again we are dealing with a monohybrid formula, but with incomplete dominance; the dominant black color with the recessive white gives blue chickens. If more complex pictures appear in the first generations (see below), then by continuing the study of further generations, an attempt is made to achieve the described monohybrid pictures, when the establishment of a given gene can be considered completed. If four phenotypes arise in F₂, for example, in Mendel's experiments with plants having round yellow, angular yellow, round green, and angular green seeds, and in a 9:3:3:1 ratio, then we are dealing with a dihybrid formula, i.e., two dominant and two recessive genes were involved in the crossing (let us call them A, B, a, and b), with the most numerous class (9) having A and B, the least numerous (1) having a and b, and each of the '3' having either Ab or aB. Depending on which of these four phenotypes the parent resembles, we decide whether it had AB, Ab, or aB. The dihybrid formula provides the richest material for various conclusions, as it often changes characteristically in response to various properties of genes. These modifications can be of four kinds: 1) random ones, which must be kept in mind, about which we will not speak now; 2) those depending on the influence of genes on the viability of the organism; 3) those depending on 'interaction of traits' and 4) those depending on 'interaction of genes,' i.e., on their linkage or repulsion. Distortions based on different viability can arise if, for example, individuals lacking genes A and B die early (achlorophyllous plants, etc.) in a higher percentage than other phenotypes, or, conversely, survive more easily than others. To clarify this source of distortion, either special formulas are used or control experiments are conducted to determine the difference in viability of different phenotypes, and appropriate coefficients are introduced. This rather painstaking stage of genetic analysis is necessary in order to be able to prove the presence or absence of the 3rd, and especially the 4th, source of distortions. In the presence of 'interaction of traits,' the dihybrid formula 9:3:3:1 changes in various ways. For example, when crossing white mice (albinos) with black mice, in the second generation we get 9 agouti, 3 black, and 4 white. The ratio 9:3:4 indicates the presence of cryptomerism (see), i.e., the non-manifestation of one trait in the absence of another. The phenotypes Ab and ab become indistinguishable. In our example, agouti coloration is determined by the presence of two genes—the color gene A (in the absence of which mice are albinos) and the gene G causing agouti coloration. Individuals aG and ab are white. The ratio 12:3:1 indicates that 9AB+3Ab are indistinguishable from each other, i.e., in the presence of gene A, gene B no longer manifests itself (see Epistasis). For example, when crossing white chickens having a dominant gene for white coloration with colored ones, in the second generation the categories AB and Ab are white. When genes A and B manifest themselves identically, we get a ratio of 9:6:1 (see Polymericity). For example, the size and weight of chickens are caused by several equivalent factors, due to which individuals Ab and aB have the same phenotype. The ratio 9:7 is obtained when the categories 9AB+3Ab+3aB+ab are indistinguishable, which happens when the trait characteristic of the AB category appears only with the simultaneous presence of genes A and B (paired genes). For example, Bateson, when crossing white chickens, obtained in the offspring 9 colored and 7 white chickens. The only explanation for this is that both dominant genes A and B are necessary to obtain colored individuals. There are also other ratios in F₂, for example, 13:3 or 9:6:1. When incompletely dominant genes participate in the crossing, the number of possible ratios in F₂ significantly increases. The entire art of the genetic analyst consists in whether he can understand with which particular ratio he is dealing, which is often very difficult due to the simultaneous participation of distortions based on viability, randomness, and interaction of genes. This task is significantly facilitated in many cases by studying not F₂, but F_h, i.e., offspring obtained from backcrossing F₁ hybrids with one of the parents or with a foreign organism similar in genotype. In such a crossing, instead of 9:3:3:1, a 1:1:1:1 ratio arises, i.e., four categories of offspring in equal quantities. The degree of dominance no longer plays a role here, does not increase the number of categories. In this crossing, epistasis is recognized by the ratio 2:1:1, cryptomerism by the ratio 1:1:2, polymericity by the ratio 3:1, corresponding to the 15:1 ratio in F₂, or by the ratio 1:2:1, corresponding to 9:6:1 in F₂. The ratio 3:1 is also obtained instead of the 13:3 ratio of F₂, and the ratio 1:3 instead of 9:7. For greater accuracy of conclusions, usually both F₃ and F_h are obtained simultaneously, and even both possible F_b. When three or more genes participate in the crossing, the ratios become already so diverse and complex (in the simplest case in F₂ 27:9:9:9:3:3:3:1) that one has to obtain additional, simpler crossings. The ratio of dihybrid crossing 9:3:3:1 also changes depending on the presence of so-called linkage of genes with each other or their repulsion. Indeed, if the genes are in the same chromosome, then gametes containing or not containing both of these genes simultaneously are formed more than gametes containing one of these genes, i.e., the categories AB and ab are more numerous than aB and Ab. In the case of complete linkage of the latter categories, they may not be obtained at all, and we get a ratio of 12:0:0:4 or 3:1, i.e., indistinguishable from monohybrid. In the case where both dominant genes were received from different parents, i.e., are in different chromosomes of the same pair, gametes simultaneously carrying A and B and a and b are formed less frequently than Ab and aB, and in the case of complete repulsion the ratio changes to 8:4:4:0, indistinguishable from monohybrid 2:1:1. Based on the degree of approach to these extreme ratios ('complete linkage' and 'complete repulsion'), conclusions are drawn about the strength of linkage or repulsion, i.e., about the proximity of gene location in the same chromosome (linkage) or in homologous chromosomes, i.e., in chromosomes belonging to the same pair (see Morganism). This task is much easier to solve by studying not F₂, but F_h. In this crossing, in the presence of linkage, the ratio 1:1:1:1 through the ratio 1:n:n:1, where n<1, changes to 1:0:0:1, and with repulsion—through n:1:1:n changes to 0:1:1:0. The value d=100(n-1)/n gives directly the distance between genes in accepted units of distance—'morgans.'

Genetic analysis can be either comparatively simple or very difficult, depending on how clearly the traits being studied are expressed and how little they are altered by various external causes. If it is difficult to determine exactly how many different categories of offspring have arisen in F₂ or into which category a particular individual should be placed (e.g., when there are gradual transitions from one category to another: various nuances of shades, various transitional sizes of the trait, etc.), then genetic analysis becomes very difficult. This is especially the case when studying "quantitative traits" expressed in numbers, for example, size, height, weight, physiological properties, such as milk yield, immunity, etc. In these cases, a clear division into categories is rarely observed, and the usual method of genetic analysis is inapplicable. However, due to the importance of analyzing these often economically or medically important traits, several methods have been proposed for this purpose. The idea of the first method is to determine the portion of F₂ or F₆ that will, upon further breeding, repeat the properties of the parental forms, or F_x, since depending on the number of genes involved, this portion should be different, and the smaller the more genes there are. If out of the F₂ generation 25% will behave like one parent, 25% like the other parent, and 50% like F₁ individuals, then consequently F₂ consisted of three genotypes in the ratio 1:2:1, and therefore the crossing was monohybrid. Other methods of analysis are also possible—using the F₃ generation instead of F₂, and so on. With this method, East gave a good analysis of tobacco growth. Another method is based on the fact that the variability of the F₂ generation depends on both phenotypic and genotypic variability, whereas the F₁ generation in crosses of pure lines is genotypically identical and varies only phenotypically. By calculating the values characterizing variability ("quadratic deviation"; see Variational Statistics), one can calculate that portion of F₂ variability that depends on segregation and draw some conclusions about the number of genes. This method, however, requires further mathematical development of the theory for more complex cases. In addition to calculations, some conclusions can be drawn from the shape of the distribution curves of the trait value in different generations. For example, if the distribution curve of the F₁ generation is symmetrical, and in the F₂ generation it becomes asymmetrical, this indicates the involvement of fully dominant genes in the segregation, etc. The third method of analyzing quantitative traits, as well as generally poorly expressed traits, utilizes the phenomena of linkage and repulsion. In the cross, some clearly Mendelian "marker" genes are introduced, with the help of which the F₂ or F₃ generation is divided into clear categories, and then the value of the trait being studied is compared in these categories. If the chosen "marker gene" is located in the same chromosome as one or more genes affecting the trait being studied, then due to the phenomena of linkage or repulsion, the value of the trait will be different in different categories. By introducing a larger or smaller number of marker genes, it is possible to solve the most complex problems, brilliant examples of which have been given by a number of researchers in Drosophila. With this same method, all further, most profound problems about the location of genes in chromosomes are solved and the properties of chromosomes are analyzed (see Crossing over of chromosomes). Genetic analysis of populations. In addition to special crosses, which are the main method of genetic analysis, it is possible to use free crosses occurring without the experimenter's intervention in populations (see), in herds, in human society. In free populations, each gene is distributed according to the Hardy-Weinberg formula, forming three genotypes in a certain proportion: p²AA + 2pqAa + q²aa, where p and q are the probabilities of finding gametes carrying gene A and corresponding gene a. On the basis of this formula, various predictions can be made about the offspring of different phenotypes found in populations, and based on how well these predictions are confirmed, their correctness is concluded. For example, if in a population there are 2% red-haired and 98% non-red-haired individuals, then the simplest hypothesis will be that this difference depends on one gene. If red color is dominant over non-red, then red-haired individuals will consist of p²AA + 2pqAa, and non-red-haired individuals will be q²aa; with recessiveness of red hair it will be the opposite. From this, for both hypotheses, the value of p and q (p+q=1) can be calculated and predictions can be made about the offspring from marriages between red-haired individuals, between red-haired and non-red-haired individuals, etc. If the numerical relationships do not match any prediction, one will have to assume that there are two genes A and B, each of which is distributed according to the Hardy-Weinberg formula, and so on. With this method, it is possible to determine, for example, whether the gene being studied is located in the sex chromosome or not. In humans, for example, in the first case the trait will be distributed differently in both sexes, since the recessive phenotype among women will occur with a probability of q², and among men with a probability of q, i.e., q times more often. There is no systematic presentation of the entire theory and practice of genetic analysis. Individual questions of genetic analysis are covered in special journal articles.